Add Batch 366c3dbc-89d0-45fa-b8c0-60431f29c72e data

.gitattributes

@@ -7170,3 +7170,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
 2024/Communication[[:space:]]Efficient[[:space:]]Distributed[[:space:]]Training[[:space:]]with[[:space:]]Distributed[[:space:]]Lion/0525131e-f721-457b-a934-7b076b69ff55_origin.pdf filter=lfs diff=lfs merge=lfs -text
 2024/Communication-Efficient[[:space:]]Federated[[:space:]]Group[[:space:]]Distributionally[[:space:]]Robust[[:space:]]Optimization/0633115a-5a3a-480c-b721-10f3cd29d97b_origin.pdf filter=lfs diff=lfs merge=lfs -text
 2024/Community[[:space:]]Detection[[:space:]]Guarantees[[:space:]]using[[:space:]]Embeddings[[:space:]]Learned[[:space:]]by[[:space:]]Node2Vec/da722078-c348-47aa-865b-117fed108c91_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compact[[:space:]]Language[[:space:]]Models[[:space:]]via[[:space:]]Pruning[[:space:]]and[[:space:]]Knowledge[[:space:]]Distillation/f80b8966-d2c6-4f2f-8745-be764bb15dcb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compact[[:space:]]Proofs[[:space:]]of[[:space:]]Model[[:space:]]Performance[[:space:]]via[[:space:]]Mechanistic[[:space:]]Interpretability/e74db359-ab39-478b-9754-ba6feb4e17de_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Complete[[:space:]]Graphical[[:space:]]Criterion[[:space:]]for[[:space:]]Sequential[[:space:]]Covariate[[:space:]]Adjustment[[:space:]]in[[:space:]]Causal[[:space:]]Inference/9a3cdc8e-5eba-41f3-8826-86b07d0b76d4_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compositional[[:space:]]3D-aware[[:space:]]Video[[:space:]]Generation[[:space:]]with[[:space:]]LLM[[:space:]]Director/dd7ce9ce-8f01-4b4e-9ddc-554ba692ea02_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compositional[[:space:]]Automata[[:space:]]Embeddings[[:space:]]for[[:space:]]Goal-Conditioned[[:space:]]Reinforcement[[:space:]]Learning/efed71db-e1cf-4991-9669-febad5d9f10a_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compositional[[:space:]]Generalization[[:space:]]Across[[:space:]]Distributional[[:space:]]Shifts[[:space:]]with[[:space:]]Sparse[[:space:]]Tree[[:space:]]Operations/9c3a27e6-c5e2-4c70-8fb6-7852c705e3bd_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compositional[[:space:]]PAC-Bayes_[[:space:]]Generalization[[:space:]]of[[:space:]]GNNs[[:space:]]with[[:space:]]persistence[[:space:]]and[[:space:]]beyond/51957fc1-737c-40b8-b340-f596e9d5faca_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Compressing[[:space:]]Large[[:space:]]Language[[:space:]]Models[[:space:]]using[[:space:]]Low[[:space:]]Rank[[:space:]]and[[:space:]]Low[[:space:]]Precision[[:space:]]Decomposition/fd06d0d7-0c15-4a35-8837-b611ad3cf9d3_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Computation-Aware[[:space:]]Gaussian[[:space:]]Processes_[[:space:]]Model[[:space:]]Selection[[:space:]]And[[:space:]]Linear-Time[[:space:]]Inference/783307ee-5f1a-40b1-963d-4ceca8d5699c_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Computational[[:space:]]Aspects[[:space:]]of[[:space:]]Bayesian[[:space:]]Persuasion[[:space:]]under[[:space:]]Approximate[[:space:]]Best[[:space:]]Response/4caa60c7-1994-45dd-8e00-7ac55faadabf_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Computerized[[:space:]]Adaptive[[:space:]]Testing[[:space:]]via[[:space:]]Collaborative[[:space:]]Ranking/86d61102-9f35-41b6-bfe4-b0c03a19ea9d_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Computing[[:space:]]the[[:space:]]Bias[[:space:]]of[[:space:]]Constant-step[[:space:]]Stochastic[[:space:]]Approximation[[:space:]]with[[:space:]]Markovian[[:space:]]Noise/ffb537a0-2615-416f-b26e-e9c43a12050c_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Con4m_[[:space:]]Context-aware[[:space:]]Consistency[[:space:]]Learning[[:space:]]Framework[[:space:]]for[[:space:]]Segmented[[:space:]]Time[[:space:]]Series[[:space:]]Classification/19beba60-e39f-4f0f-a6a5-4c69649c87b3_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ConMe_[[:space:]]Rethinking[[:space:]]Evaluation[[:space:]]of[[:space:]]Compositional[[:space:]]Reasoning[[:space:]]for[[:space:]]Modern[[:space:]]VLMs/2f2a06f6-f421-40f6-9f8a-68235c8c8bb6_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ConStat_[[:space:]]Performance-Based[[:space:]]Contamination[[:space:]]Detection[[:space:]]in[[:space:]]Large[[:space:]]Language[[:space:]]Models/5e46c870-066e-4828-b237-5009bd9eedbc_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Concentrate[[:space:]]Attention_[[:space:]]Towards[[:space:]]Domain-Generalizable[[:space:]]Prompt[[:space:]]Optimization[[:space:]]for[[:space:]]Language[[:space:]]Models/7f5f0145-3de6-4570-916f-f359a1120e21_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ConceptFactory_[[:space:]]Facilitate[[:space:]]3D[[:space:]]Object[[:space:]]Knowledge[[:space:]]Annotation[[:space:]]with[[:space:]]Object[[:space:]]Conceptualization/81a3a248-cb4b-4f96-b619-f2c1200dfdd9_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ConceptMix_[[:space:]]A[[:space:]]Compositional[[:space:]]Image[[:space:]]Generation[[:space:]]Benchmark[[:space:]]with[[:space:]]Controllable[[:space:]]Difficulty/0cd05233-103b-47d5-92f3-65ab3f239805_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/CondTSF_[[:space:]]One-line[[:space:]]Plugin[[:space:]]of[[:space:]]Dataset[[:space:]]Condensation[[:space:]]for[[:space:]]Time[[:space:]]Series[[:space:]]Forecasting/92df3997-d109-4323-82e5-278b53226b24_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditional[[:space:]]Controllable[[:space:]]Image[[:space:]]Fusion/535bb689-8e39-4f56-ae39-7133b6cbf54f_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditional[[:space:]]Density[[:space:]]Estimation[[:space:]]with[[:space:]]Histogram[[:space:]]Trees/90faaa38-56f5-4f53-acd3-d0e78012d0c2_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditional[[:space:]]Generative[[:space:]]Models[[:space:]]are[[:space:]]Sufficient[[:space:]]to[[:space:]]Sample[[:space:]]from[[:space:]]Any[[:space:]]Causal[[:space:]]Effect[[:space:]]Estimand/862e405e-35a4-4f64-9e0c-6fbe3164e631_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditional[[:space:]]Outcome[[:space:]]Equivalence_[[:space:]]A[[:space:]]Quantile[[:space:]]Alternative[[:space:]]to[[:space:]]CATE/ed26e5c4-4bab-449d-a8f2-c00fb897be1d_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditional[[:space:]]Synthesis[[:space:]]of[[:space:]]3D[[:space:]]Molecules[[:space:]]with[[:space:]]Time[[:space:]]Correction[[:space:]]Sampler/ed1ec1bb-4671-4aaf-8794-988829429cf1_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conditioning[[:space:]]non-linear[[:space:]]and[[:space:]]infinite-dimensional[[:space:]]diffusion[[:space:]]processes/6921b64e-d461-4b9c-90ef-ae792342979e_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Confidence[[:space:]]Calibration[[:space:]]of[[:space:]]Classifiers[[:space:]]with[[:space:]]Many[[:space:]]Classes/c6f8a4a0-e15e-4d79-b820-14c9cd3395d5_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Confidence[[:space:]]Regulation[[:space:]]Neurons[[:space:]]in[[:space:]]Language[[:space:]]Models/c9ae4f6a-f0fa-473a-9429-4b36850c30e5_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Confident[[:space:]]Natural[[:space:]]Policy[[:space:]]Gradient[[:space:]]for[[:space:]]Local[[:space:]]Planning[[:space:]]in[[:space:]]$q__pi$-realizable[[:space:]]Constrained[[:space:]]MDPs/daf9b458-9333-4dad-8eae-1fa3c373bef7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformal[[:space:]]Alignment_[[:space:]]Knowing[[:space:]]When[[:space:]]to[[:space:]]Trust[[:space:]]Foundation[[:space:]]Models[[:space:]]with[[:space:]]Guarantees/250f812c-8643-4cb5-99ca-d966671f74b7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformal[[:space:]]Classification[[:space:]]with[[:space:]]Equalized[[:space:]]Coverage[[:space:]]for[[:space:]]Adaptively[[:space:]]Selected[[:space:]]Groups/6caeb946-c7c4-4545-a5eb-9a616e5b6f8c_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformal[[:space:]]Inverse[[:space:]]Optimization/af94386c-0230-4afb-abfa-9e2b2cefd39c_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformal[[:space:]]Prediction[[:space:]]for[[:space:]]Class-wise[[:space:]]Coverage[[:space:]]via[[:space:]]Augmented[[:space:]]Label[[:space:]]Rank[[:space:]]Calibration/ca15fb5c-3b81-4f1c-a5a1-4923906fc91a_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformalized[[:space:]]Credal[[:space:]]Set[[:space:]]Predictors/867c801a-2983-4d24-92f7-760aeb04f8a8_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformalized[[:space:]]Multiple[[:space:]]Testing[[:space:]]after[[:space:]]Data-dependent[[:space:]]Selection/95d80cf2-4da3-43aa-845b-b85a4a7082ad_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conformalized[[:space:]]Time[[:space:]]Series[[:space:]]with[[:space:]]Semantic[[:space:]]Features/b2f1de90-b346-4bf6-a989-2f68444e91ef_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Confusion-Resistant[[:space:]]Federated[[:space:]]Learning[[:space:]]via[[:space:]]Diffusion-Based[[:space:]]Data[[:space:]]Harmonization[[:space:]]on[[:space:]]Non-IID[[:space:]]Data/0d2c2948-6506-4504-b1f6-0b8d300952a9_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conjugate[[:space:]]Bayesian[[:space:]]Two-step[[:space:]]Change[[:space:]]Point[[:space:]]Detection[[:space:]]for[[:space:]]Hawkes[[:space:]]Process/dc67502a-73a6-4c62-939b-453908512287_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Conjugated[[:space:]]Semantic[[:space:]]Pool[[:space:]]Improves[[:space:]]OOD[[:space:]]Detection[[:space:]]with[[:space:]]Pre-trained[[:space:]]Vision-Language[[:space:]]Models/8b6a923b-4754-45d7-9e91-846777eaf6d9_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Connecting[[:space:]]Joint-Embedding[[:space:]]Predictive[[:space:]]Architecture[[:space:]]with[[:space:]]Contrastive[[:space:]]Self-supervised[[:space:]]Learning/dd5b8ca9-e73d-46fc-8a67-05e2c4610218_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Connecting[[:space:]]the[[:space:]]Dots_[[:space:]]LLMs[[:space:]]can[[:space:]]Infer[[:space:]]and[[:space:]]Verbalize[[:space:]]Latent[[:space:]]Structure[[:space:]]from[[:space:]]Disparate[[:space:]]Training[[:space:]]Data/c9915a40-47a7-4253-bac9-625f1025fd40_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Connectivity[[:space:]]Shapes[[:space:]]Implicit[[:space:]]Regularization[[:space:]]in[[:space:]]Matrix[[:space:]]Factorization[[:space:]]Models[[:space:]]for[[:space:]]Matrix[[:space:]]Completion/20797252-58bf-41b7-9c7e-80faece69c22_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Connectivity-Driven[[:space:]]Pseudo-Labeling[[:space:]]Makes[[:space:]]Stronger[[:space:]]Cross-Domain[[:space:]]Segmenters/1e0f6466-b484-4fc4-9f97-3155777def53_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consensus[[:space:]]Learning[[:space:]]with[[:space:]]Deep[[:space:]]Sets[[:space:]]for[[:space:]]Essential[[:space:]]Matrix[[:space:]]Estimation/0fadae7b-f421-4ef4-99a6-43308f37e24c_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consent[[:space:]]in[[:space:]]Crisis_[[:space:]]The[[:space:]]Rapid[[:space:]]Decline[[:space:]]of[[:space:]]the[[:space:]]AI[[:space:]]Data[[:space:]]Commons/c55c7ea1-e31a-4c64-8f9f-16dcf8e9f6ff_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consistency[[:space:]]Diffusion[[:space:]]Bridge[[:space:]]Models/34658f2f-201d-463c-90d3-18085f46aedf_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consistency[[:space:]]Models[[:space:]]for[[:space:]]Scalable[[:space:]]and[[:space:]]Fast[[:space:]]Simulation-Based[[:space:]]Inference/85a8ecb5-71af-487d-b3b1-a3253e5f261f_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consistency[[:space:]]Purification_[[:space:]]Effective[[:space:]]and[[:space:]]Efficient[[:space:]]Diffusion[[:space:]]Purification[[:space:]]towards[[:space:]]Certified[[:space:]]Robustness/46eb8946-dbd6-40e7-ae87-f265d7efd03b_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Consistency[[:space:]]of[[:space:]]Neural[[:space:]]Causal[[:space:]]Partial[[:space:]]Identification/dbe954c1-ed35-4acf-93b1-3ae7e5db81d3_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constant[[:space:]]Acceleration[[:space:]]Flow/5af3f4d6-5592-4d5b-ba6e-5ade7f7d366b_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Adaptive[[:space:]]Attack_[[:space:]]Effective[[:space:]]Adversarial[[:space:]]Attack[[:space:]]Against[[:space:]]Deep[[:space:]]Neural[[:space:]]Networks[[:space:]]for[[:space:]]Tabular[[:space:]]Data/dcce2806-55b8-4a79-a840-7ceb1a853da0_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Binary[[:space:]]Decision[[:space:]]Making/0223d4fa-6817-462f-a26f-f6a284e1bcf8_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Diffusion[[:space:]]Models[[:space:]]via[[:space:]]Dual[[:space:]]Training/a08b68ed-71b3-4c1e-9ec2-7ba6ad2f3563_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Diffusion[[:space:]]with[[:space:]]Trust[[:space:]]Sampling/6cf0358b-fb34-41cc-846c-3fd360236c2d_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Human-AI[[:space:]]Cooperation_[[:space:]]An[[:space:]]Inclusive[[:space:]]Embodied[[:space:]]Social[[:space:]]Intelligence[[:space:]]Challenge/0a6e8fe0-2311-44dc-b572-444f0245c627_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Latent[[:space:]]Action[[:space:]]Policies[[:space:]]for[[:space:]]Model-Based[[:space:]]Offline[[:space:]]Reinforcement[[:space:]]Learning/e778c97c-40a3-4e47-9b81-6d02a7c765e0_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Sampling[[:space:]]with[[:space:]]Primal-Dual[[:space:]]Langevin[[:space:]]Monte[[:space:]]Carlo/ba741688-be89-4f69-b9de-e3c4d5aaedf4_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constrained[[:space:]]Synthesis[[:space:]]with[[:space:]]Projected[[:space:]]Diffusion[[:space:]]Models/b8ef3a78-01a0-40f5-9444-cd65250d23f9_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Constructing[[:space:]]Semantics-Aware[[:space:]]Adversarial[[:space:]]Examples[[:space:]]with[[:space:]]a[[:space:]]Probabilistic[[:space:]]Perspective/62157804-1aa6-48b7-bbaa-8d25572278dd_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Construction[[:space:]]and[[:space:]]Application[[:space:]]of[[:space:]]Materials[[:space:]]Knowledge[[:space:]]Graph[[:space:]]in[[:space:]]Multidisciplinary[[:space:]]Materials[[:space:]]Science[[:space:]]via[[:space:]]Large[[:space:]]Language[[:space:]]Model/afd26e7a-43a8-403f-96f6-7e725c02b04a_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ContactField_[[:space:]]Implicit[[:space:]]Field[[:space:]]Representation[[:space:]]for[[:space:]]Multi-Person[[:space:]]Interaction[[:space:]]Geometry/9b3f69c7-198b-4569-8184-4118534c269f_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Context[[:space:]]and[[:space:]]Geometry[[:space:]]Aware[[:space:]]Voxel[[:space:]]Transformer[[:space:]]for[[:space:]]Semantic[[:space:]]Scene[[:space:]]Completion/485fb7a7-c610-4511-aae8-ee77a5559b95_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/Context-Aware[[:space:]]Testing_[[:space:]]A[[:space:]]New[[:space:]]Paradigm[[:space:]]for[[:space:]]Model[[:space:]]Testing[[:space:]]with[[:space:]]Large[[:space:]]Language[[:space:]]Models/db1f9f39-0406-421d-befa-50e89313d2cc_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ContextCite_[[:space:]]Attributing[[:space:]]Model[[:space:]]Generation[[:space:]]to[[:space:]]Context/fcf31f94-a0ae-4345-ad10-d097d886c001_origin.pdf filter=lfs diff=lfs merge=lfs -text
+2024/ContextGS[[:space:]]_[[:space:]]Compact[[:space:]]3D[[:space:]]Gaussian[[:space:]]Splatting[[:space:]]with[[:space:]]Anchor[[:space:]]Level[[:space:]]Context[[:space:]]Model/c6714df0-edbd-41d7-a734-e38617adcf3d_origin.pdf filter=lfs diff=lfs merge=lfs -text

2024/Compact Language Models via Pruning and Knowledge Distillation/f80b8966-d2c6-4f2f-8745-be764bb15dcb_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b4e7a96f0885f861b0edd87011ceeaa78992057139c49e8b3564569f19c0237e
+size 1506411

2024/Compact Language Models via Pruning and Knowledge Distillation/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dbb24f02e7f2e3a585128a027211163a5fdd8812c45421b1eee06c7d7ba5738a
+size 820502

2024/Compact Proofs of Model Performance via Mechanistic Interpretability/e74db359-ab39-478b-9754-ba6feb4e17de_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3979e11487cf3685bfe2ea22ea4a5401685f83a6afd9b5b3a9c53dfa3b30c430
+size 6970155

2024/Compact Proofs of Model Performance via Mechanistic Interpretability/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b0019af868d6834f0ce2d712ae507b1809eb583dc4bac7519c0f55420489a30b
+size 2682386

2024/Complete Graphical Criterion for Sequential Covariate Adjustment in Causal Inference/9a3cdc8e-5eba-41f3-8826-86b07d0b76d4_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ec18e89774cb0fbb089c5798f448a53deab92e84258dc35515d1fcbe670860a2
+size 556563

2024/Complete Graphical Criterion for Sequential Covariate Adjustment in Causal Inference/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ad214e3ed7c901c78d84db474ca492e2d4692ad1cb271c9261c47861e25baa5e
+size 535003

2024/Compositional 3D-aware Video Generation with LLM Director/dd7ce9ce-8f01-4b4e-9ddc-554ba692ea02_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50ecb151e585eebcf276b0d982a77896b9276986c15af5de83a9188c430e0c23
+size 4763965

2024/Compositional 3D-aware Video Generation with LLM Director/full.md

@@ -0,0 +1,918 @@
+# Compositional 3D-aware Video Generation with LLM Director
+
+Hanxin Zhu $^{1*}$ ; Tianyu He $^{2}$ , Anni Tang $^{3}$ , Junliang Guo $^{2}$ , Zhibo Chen $^{1}$ , Jiang Bian $^{2}$
+
+<sup>1</sup>University of Science and Technology of China
+
+2Microsoft Research Asia
+
+$^{3}$ Shanghai Jiao Tong University
+
+hanxinzhu@mail.ustc.edu.cn, tianyuhe@microsoft.com, memory97@sjtu.edu.cn,
+
+junliangguo@microsoft.com, chenzhibo@ustc.edu.cn, jiang.bian@microsoft.com
+
+# Abstract
+
+Significant progress has been made in text-to-video generation through the use of powerful generative models and large-scale internet data. However, substantial challenges remain in precisely controlling individual concepts within the generated video, such as the motion and appearance of specific characters and the movement of viewpoints. In this work, we propose a novel paradigm that generates each concept in 3D representation separately and then composes them with priors from Large Language Models (LLM) and 2D diffusion models. Specifically, given an input textual prompt, our scheme consists of three stages: 1) We leverage LLM as the director to first decompose the complex query into several sub-prompts that indicate individual concepts within the video (e.g., scene, objects, motions), then we let LLM to invoke pre-trained expert models to obtain corresponding 3D representations of concepts. 2) To compose these representations, we prompt multi-modal LLM to produce coarse guidance on the scales and coordinates of trajectories for the objects. 3) To make the generated frames adhere to natural image distribution, we further leverage 2D diffusion priors and use Score Distillation Sampling to refine the composition. Extensive experiments demonstrate that our method can generate high-fidelity videos from text with diverse motion and flexible control over each concept. Project page: https://aka.ms/c3v.
+
+# 1 Introduction
+
+Benefitting from large-scale data and the advancement of the generative models [1, 2], we have witnessed plenty of astonishing results across a wide array of tasks. For example, Large Language Models (LLM) pre-trained on web-scale datasets are revolutionizing machine learning with strong capability of zero-shot learning [3] and planning [4, 5], while diffusion models [6] empower text-to-image generation with a rapid surge in both quality and diversity [7-9].
+
+To harness the power of text-to-image models in text-to-video generation, modern solutions directly view video as multiple images. In this way, tremendous efforts have been dedicated to extending text-to-image models with temporal interaction to ensure consistency between frames [10-17]. However, generating visual content conditioned on the textual prompt alone struggles to express multiple concepts with precise spatial layout control [18-20]. To tackle this issue, LVD [21] and VideoDirectorGPT [22] propose to first generate spatiotemporal bounding boxes of each object based on the textual prompt with LLM, and then condition the video generation on the obtained layouts. Although rough layout control can be realized, they still have inherent limitations for detailed concept control, e.g., the motion and appearance of specific characters, and the movement of viewpoints.
+
+In nature, our understanding of the world is compositional [23, 24, 20], and the interaction with the world takes place in a 3D. Motivated by this, in contrast to the prior endeavors that implicitly learn different concepts in 2D space, we are interested in exploring an alternative solution that explicitly composes concepts in 3D space for video generation. To this end, we in particular identify two key technical challenges: 1) Since a textual prompt contains multiple concepts, how to coordinate the generation of various concepts? 2) Given the generated concepts, how to compose them to follow common sense in the real world?
+
+In this work, we introduce text-guided compositional 3D-aware video generation (C3V), a novel paradigm that regards LLM as director and 3D as structural representation for video generation. C3V consists of three main stages: 1) Given a textual prompt, to coordinate the generation of various concepts, we leverage LLM to disassemble the input prompt into sub-prompts, where each sub-prompt describes an individual concept, e.g., the scene, objects, and motion. For each concept, a pre-trained expert model is assigned by LLM to generate its corresponding 3D representation (e.g., 3D Gaussians [25], SMPL parameters [26]) according to the textual description. 2) To provide coarse instruction for composition (i.e., the scale and trajectory of each object in the scene), we further resort to the priors in multi-modal LLM by querying it with the rendered scene image and the textual goals. However, directly instructing multi-modal LLM to return the scale and trajectory of each object leads to unexpected results, as it is challenging for LLM to estimate visual dynamics. Therefore, we follow a step-by-step reasoning philosophy [27] by representing the object with the bounding boxes and dividing the trajectory estimation into sub-tasks, i.e., estimating the starting points, ending points, and trajectories step-by-step. 3) After obtaining the coarse trajectories from the language space, we also propose to refine the scales, rotations, and exact locations with priors from large-scale visual data. Specifically, taking inspiration from DreamFusion [28], which proposes to distill generative priors from pre-trained image diffusion models into 3D objects, we employ Score Distillation Sampling (SDS) [28] to optimize the transformation matrix of each object in 3D space.
+
+Our system has three main advantages: 1) Because each concept is represented by individual 3D representations, it naturally supports flexible control and interaction of each concept. 2) It inherently excels at synthesizing complex and long videos such as drama, etc. 3) The viewpoint is controllable.
+
+Extensive experiments demonstrate that our proposed method can generate 3D-aware videos with diverse motion and high visual quality, even from complex queries that contain multiple concepts and relationships. We also illustrate the flexibility of C3V by editing various concepts of the generated videos. The generated videos are presented on our project page. To the best of our knowledge, we make the first attempt towards text-guided compositional 3D-aware video generation. We hope it can inspire further explorations on the interplay between video and 3D generation.
+
+# 2 Related Works
+
+# 2.1 Video Generation with LLM
+
+Recently, there have been substantial efforts in training text-to-video models on large-scale datasets with autoregressive Transformer [29, 30, 17] or diffusion models [10-13, 16]. A prominent approach for text-to-video generation is to extend a pre-trained text-to-image model by inserting temporal layers into its architecture, and fine-tuning models on video data. However, although effective, it remains challenging to generate objects with specific attributes or positions. To address this challenge, a series of studies proposed to exploit knowledge from LLM [31, 32] to achieve controllable generation [21, 19, 22, 33-35], zero-shot generation [36-39], or long video generation [40]. For example, Free-Bloom [36] and DirecT2V [38] used LLM to transform the input textual prompt into a sequence of sub-prompts that describe each frame. LVD [21] and VideoDirectorGPT [22] employed LLM to generate spatiotemporal bounding boxes to control the object-level dynamics in video generation.
+
+In light of the above success of exploiting LLM to direct video generation in 2D space, we view LLM as a director in 3D, which differs from previous methods not only in terms of technical route but also in benefits: providing free interaction with individual concepts and flexible viewpoint control.
+
+# 2.2 Compositional 3D Generation
+
+Generating 3D assets from textual prompt has garnered significant attention owing to its promising applications in various fields such as AR [41], VR [42], and autonomous driving [43]. However, due to the lack of large-scale 3D data, it is challenging to apply 2D generative models to 3D directly. Therefore, building upon Dream Fields [44], DreamFusion introduced the Score Distillation Sampling (SDS) [28], a technique enhancing 3D generation by distilling 2D diffusion priors from pre-trained text-to-image generative models. Motivated by the success of DreamFusion [28], dedicated efforts have been made to improve SDS [45-47]. Though achieving remarkable results, these methods struggle to generate scenes with multiple distinct elements. To mitigate this issue, several techniques was proposed to guide 3D generation with additional conditions like layout priors, which we refer to as compositional 3D generation [48-50]. However, these works still focus on static compositional 3D generation and lack visual dynamic modeling.
+
+Recently, two concurrent works Comp4D [51] and TC4D [52] also achieved compositional 4D generation (i.e., dynamic 3D generation). However, they only considered composition between objects, and the trajectory of these methods is either formulated by kinematics-based equations or pre-defined by users. Differently, we explore 3D-aware video generation with integrated 3D scenes and compose various concepts with priors from both LLM and 2D diffusion models.
+
+# 3 Preliminaries
+
+# 3.1 3D Gaussian Splitting
+
+3D Gaussian Splitting (3DGS) [25] has been attracting a lot of interest for novel view synthesis, due to its photorealistic visual quality and real-time rendering. 3DGS utilizes a set of anisotropic ellipsoids (i.e., 3D Gaussians) to encode 3D properties, in which each Gaussian is parameterized by position  $\mu \in \mathbb{R}^3$ , covariance  $\pmb{\Sigma} \in \mathbb{R}^{3 \times 3}$  (obtained from scale  $\mathbf{s} \in \mathbb{R}^3$  and rotation  $\mathbf{r} \in \mathbb{R}^3$ ), opacity  $\alpha \in \mathbb{R}$ , and color  $\mathbf{c} \in \mathbb{R}^3$ .
+
+To render a novel view, 3DGS adopts a tile-based rasterization, where 3D Gaussians are projected onto the image plane as 2D Gaussians. The final color  $\mathbf{c}(\mathbf{p})$  of pixel  $\mathbf{p}$  is denoted as:
+
+$$
+\mathbf {c} (\mathbf {p}) = \sum \hat {\mathbf {c}} \hat {\sigma} \prod (1 - \hat {\sigma}), \tag {1}
+$$
+
+where  $\hat{\mathbf{c}}$  and  $\hat{\sigma}$  represent the individual color and opacity values of a series of 2D Gaussians contributing to this pixel. 3DGS are then optimized using L1 loss and SSIM [53] loss in a per-view optimization manner. Thanks to the nature of modeling 3D scenes explicitly, optimized 3D Gaussians can be easily controlled and edited.
+
+# 3.2 Score Distillation Sampling
+
+Different from text-to-image generation which benefits from a large number of text-image pairs available, text-to-3D generation suffers from a severe lack of data. To mitigate this issue, Score Distillation Sampling (SDS) [28] was proposed to distill generative priors from pretrained diffusion-based text-to-image models  $\phi$ . Specifically, for a 3D representation parameterized by  $\theta$ , SDS is served as a way to measure the similarity between the rendered images  $x = g(\theta)$  and the given textual prompts  $y$ , where  $g$  represents the rendering operation. As a result, the gradients used to update  $\theta$  are computed as follows:
+
+$$
+\nabla_ {\theta} \mathcal {L} _ {S D S} (\phi , x = g (\theta)) = \mathbb {E} _ {t, \epsilon} [ w (t) \left(\hat {\epsilon} _ {\phi} \left(x _ {t}; y, t\right) - \epsilon\right) ], \tag {2}
+$$
+
+where  $t$  is the noise level,  $\epsilon$  is the ground-truth noise,  $w(t)$  is a weighting function,  $\hat{\epsilon}_{\phi}$  is the estimated noise given noised images  $x_{t}$  with text embeddings  $y$ . Please refer to DreamFusion [28] for details.
+
+# 4 Method
+
+Overview. To achieve text-guided compositional 3D-aware video generation (C3V), we regard LLM as director and 3D as structural representation. To this end, our method consists of three stages. To begin with, we utilize LLMs to decompose the input textual prompts into three sub-prompts, each
+
+![](images/dd78f8be920d18010b38883eb787f5d3b0a277c594ab0da1e7e6e54386632807.jpg)  
+Figure 1: Illustration of our method. It consists of three stages: 1) The input textual prompt is decomposed into individual concepts by the LLM. Then we generate each concept in the form of 3D with the corresponding pre-trained expert model (left & Sec. 4.1). 2) We leverage knowledge in multi-modal LLM to estimate the 2D trajectory of objects step-by-step (middle & Sec. 4.2). 3) After lifting the estimated 2D trajectory into 3D as initialization, we refine the scales, locations, and rotations of objects within the 3D scene using 2D diffusion priors (right & Sec. 4.3).
+
+of which provides a description for generating a corresponding concept (i.e., scene, object, motion, etc.) respectively (Sec. 4.1). Subsequently, we leverage multi-modal LLM to obtain coarse-grained scales and trajectories for each animatable object (Sec. 4.2). Finally, we employ 2D diffusion priors to refine the objects' location, scale, and rotation for a fine-grained composition (Sec. 4.3).
+
+# 4.1 Task Decomposition with LLM
+
+Task Instructions. Given a textual prompt, we invoke LLM (e.g., GPT-4V [32]) to decompose it into several sub-prompts. Each sub-prompt describes an individual concept such as the scene, object, and motion. Specifically, for an input prompt  $y$ , we query LLM with the instruction like: "Please decompose this prompt into several sub-prompts, each describing the scene, objects in the scene, and the objects' motion.", from which we obtain the corresponding sub-prompts.
+
+3D Representation. After obtaining the sub-prompt for each concept, we aim to generate its corresponding 3D representations using the pre-trained expert models. In this work, we build structural representation on 3DGS [25], which is an explicit form and therefore flexible enough to compose or animate. Concerning concepts like motion, our framework can generalize to arbitrary animatable 3D Gaussian-based objects. For simplicity, we take human motion as an instantiation because it is general for various scenarios. In order to obtain diverse human motions, we take a retrieval-augmented approach [54] to acquire motion in the form of SMPL-X parameters [55] from large motion libraries [56] according to the motion-related sub-prompt.
+
+Instantiation. To illustrate the scheme formally, consider the following example. We have subprompts  $y_{1}, y_{2}$  and  $y_{3}$  that describe scene, object, and motion respectively. Additionally, we have corresponding pre-trained text-guided expert models  $\phi_{1}$ ,  $\phi_{2}$ , and  $\phi_{3}$  that are selected by the LLM. The concept generation can be formulated as follows:
+
+$$
+G _ {1} = \phi_ {1} (y _ {1}), G _ {2} = \phi_ {2} (y _ {2}, M), M = \phi_ {3} (y _ {3}), \tag {3}
+$$
+
+Please give me a trajectory represents that an alien walking on the floor, starting from the cabin's door to the mow near the bottom right corner of this image.
+
+![](images/c634ef07409430f1714ac53e8646ee820f7c671bc726054572cdcabf9909135c.jpg)  
+Figure 2: Illustration of coarse-grained trajectory generation with LLM. Instead of querying multi-modal LLM to estimate dynamic trajectory directly, we generate trajectory in a step-by-step manner: estimating the locations of starting and ending points first, then reasoning the path between them.
+
+where  $G_{1}$  and  $G_{2}$  represent the 3D Gaussians, and  $M$  means the motions used to drive  $G_{2}$ . In the following sections, we will provide details on the composition of the generated concepts.
+
+# 4.2 Coarse-grained Trajectory Generation with LLM
+
+Given the generated concepts, we aim to compose them into a dynamic 3D representation to render videos that align with the input textual prompt. Achieving this requires scales and trajectories of the objects to indicate their sizes and locations within the scene. To this end, we propose to leverage knowledge encoded in multi-modal LLMs (i.e., GPT-4V [32]) to provide priors.
+
+For the scale of the object, we find that directly querying GPT-4V with the input prompt and rendered scene image can yield a reasonable estimation of its resolution  $(H_{2D}$  and  $W_{2D})$ . However, this is not the case for trajectory estimation. As demonstrated in Fig. 2, directly querying GPT-4V for trajectory will lead to a result that deviates conspicuously from common sense. Based on this observation, we conclude two issues: 1) it is too difficult for GPT-4V to generate the trajectory within a single query, as it lacks priors on visual dynamics; 2) since GPT-4V is trained to generate text, it has limitations on imagining visual content.
+
+To mitigate this, we introduce two simple yet effective techniques. 1) Although GPT-4V lacks visual knowledge of the object, we can alleviate this by representing the object as a bounding box with the estimated resolution. 2) We follow a step-by-step reasoning philosophy [27] and propose to let GPT-4V estimate the locations of starting and ending points first, then reason the path between them.
+
+Overall, we can formulate the above process as follows:
+
+$$
+\begin{array}{l} \left\{L _ {p} ^ {i} \right\} _ {i = 1} ^ {N} = \Phi (y _ {p}, I, S, L _ {s}, L _ {e}), \\ S = \Phi (y, I), L _ {s} = \Phi (y _ {s}, I), L _ {e} = \Phi (y _ {e}, I), \\ \end{array}
+$$
+
+where  $\Phi$  represents the multi-modal LLM (i.e., GPT-4V),  $I$  denotes the rendered scene image,  $S$  represents the estimated scale of the object given textual prompt  $y$  and  $I$ ,  $L_{s}$  and  $L_{e}$  represent the locations of starting and ending points respectively,  $\{L_p^i\}_{i = 1}^N$  represent  $N$  locations indicating the path between  $L_{s}$  and  $L_{e}$ . Notably, all locations (i.e.,  $L_{s}$ ,  $L_{e},\{L_{p}^{i}\}_{i = 1}^{N}$ ) are represented by 2D pixel coordinates on  $I$ .
+
+# 4.3 Fine-grained Composition with 2D Diffusion Priors
+
+Lift Trajectory from 2D to 3D. In Sec. 4.2, we obtain the 2D pixel coordinates  $L_{p}^{i} = (p_{x}^{i}, p_{y}^{i})$  of the estimated trajectory. However, 2D trajectory is not enough for composition in 3D space. Therefore, we convert it into corresponding 3D world coordinate  $L_{3D}^{i} = (x^{i}, y^{i}, z^{i})$ . Specifically, we first predict the depth map  $D$  of the rendered scene image with a monocular depth estimator [57].
+
+Then, we use the depth value of the center point of the lower boundary of the bounding box as the trajectory's depth. As a result, we can transform 2D trajectory into 3D:
+
+$$
+(x ^ {i}, y ^ {i}, z ^ {i}, 1) ^ {T} = R ^ {- 1} K ^ {- 1} \left[ \left(p _ {x} ^ {i} + \frac {H _ {2 D}}{2}, p _ {y} ^ {i}, 1\right) ^ {T} \cdot D \left(p _ {x} ^ {i} + \frac {H _ {2 D}}{2}, p _ {y} ^ {i}\right) \right] - \left(\frac {H _ {3 D}}{2}, 0, 0, 0\right) ^ {T}, \tag {5}
+$$
+
+where  $R$  and  $K$  represent camera extrinsic and intrinsic respectively,  $H_{2D}$  and  $W_{2D}$  represent the resolution of the 2D bounding box.  $H_{3D}$  represent the actual height of the 3D bounding box of this object within the scene.
+
+Composition Refinement with 2D Diffusion Priors. With the lifted 3D trajectory, we then integrate the object into the scene. However, the trajectory estimated by LLM is still rough and may not obey natural image distribution. To address this, we propose to further refine the object's scale, location, and rotation by distilling generative priors from pre-trained image diffusion models [7] into 3D space. Specifically, we treat the parameters for these attributes as estimizable variables and use SDS (Eq. 2) to improve the fidelity of rendered images. As a result, scale refinement can be formulated as follows:
+
+$$
+\nabla_ {\hat {S}} \mathcal {L} _ {S D S} ^ {S c a l e} = \mathbb {E} _ {t, \epsilon} [ w (t) (\hat {\epsilon} _ {\phi} (x _ {t} (L _ {3 D} ^ {1}, (S + \sigma (\hat {S}) \cdot \tau_ {s} - \frac {\tau_ {s}}{2}) \cdot G _ {2}); y, t) - \epsilon) ], \tag {6}
+$$
+
+where  $\hat{S}$  represents the estimizable variable,  $S$  represents the scale estimated by GPT-4(V),  $\sigma$  means the Sigmoid function,  $\tau_{s}$  is a threshold,  $G_{2}$  represents the 3D gaussians of the object, and  $x_{t}$  is the noised 2D image given  $L_{3D}^{i}$  and scaled  $G_{2}$ .
+
+After obtaining a more precise scale, we then refine the locations of the estimated 3D trajectory similarly, where the location refinement is denoted as:
+
+$$
+\nabla_ {\hat {L} ^ {i}} \mathcal {L} _ {S D S} ^ {L o c a t i o n} = \mathbb {E} _ {t, \epsilon} [ w (t) (\hat {\epsilon} _ {\phi} (x _ {t} (L _ {3 D} ^ {i} + \sigma (\hat {L} ^ {i}) \cdot \tau_ {L} - \frac {\tau_ {L}}{2}, (S + \sigma (\hat {S}) \cdot \tau_ {s} - \frac {\tau_ {s}}{2}) \cdot G _ {2}); y, t) - \epsilon) ], (7)
+$$
+
+where  $\hat{L}^i$  represents the estimizable variable,  $\tau_L$  is a threshold.
+
+For the rotation of the object at different timesteps, we can directly compute the corresponding rotation matrix, based on the assumption that the object at the current time step should face the location of the object at the next time step. As a result, the rotation matrix  $\hat{R}^i$  at time step  $i$  can be computed using the following equation:
+
+$$
+\hat {R} ^ {i} = \left[ \begin{array}{c c c} t x ^ {2} + c & t x y - z s & t x z + y s \\ t x y + z s & t y ^ {2} + c & t y z - x s \\ t x z - y s & t y z + x s & t z ^ {2} + c \end{array} \right], \tag {8}
+$$
+
+$$
+t = 1 - c, c = \cos (\theta), s = \sin (\theta), \mathbf {u} = (x, y, z) ^ {T}
+$$
+
+where  $\theta$  and  $\mathbf{u}$  represent the rotation angle and axis obtained through the cross product of  $(L_{3D}^{i + 1} + \sigma (L^{\hat{i} +1})\cdot \tau_L - L_{3D}^i -\sigma (\hat{L}^i)\cdot \tau_L)$  and  $(0,0,1)^T$
+
+Inference. After obtaining individual concepts in the form of 3D and the optimized parameters that indicate how to compose various concepts, we can render the 3D representation into 2D video with flexible camera control in real time [25].
+
+# 5 Experiments
+
+In this section, we instantiate C3V with three concepts: scene, humanoid object, and human motion, to generate 3D-aware video from text. We compare our proposed method with state-of-the-art text-to-4D models (4D-FY [58]), compositional 4D generation models (Comp4D [51]) and text-to-video models (VideoCrafter2 [59]). Videos are available on our anonymous project page.
+
+Implementation Details. We use LucidDreamer [60], HumanGaussian [61] and Motion-X [56] to generate 3D scenes, humanoid objects and motions respectively. To realize SDS, we utilize Stable Diffusion [7] as the image diffusion model. All the videos of our proposed method are rendered at a resolution of  $512 \times 512$  in real time. Please refer to the appendix for more details.
+
+![](images/14414c0fa4c861da1a5a13e9032f4447e4ba3900e45a616f7d3ce88c3d48037c.jpg)  
+(a) Text prompt: "In a Magician's magical cabin alone in a serene forest, an alien walking on the floor, starting from the cabin's door to the mow near the bottom right corner of this image".
+
+![](images/482cab37771af17f34312cfd021d8d7722aba59392b0152fcd45198149b1daa8.jpg)  
+(b) Text prompt: "Four characters stood on the stage. In front of the stage, a man and a woman are performing Kung Fu and dancing respectively. On the right side of the stage, a skeleton man is dancing, and behind them, a clown is performing".
+
+Figure 3: Qualitative comparisons with baselines. When prompting complex queries, the baseline methods fail to follow the queries in terms of the number of objects and the corresponding motion. In contrast, our method excels in yielding both diverse motion and high visual quality.
+
+Metrics. Following Comp4D [51], we choose Q-Align [62] as the referee to measure the quality and aesthetics of the video. The Q-Align score is a number ranging from 1 (worst) to 5 (best) where a higher score indicates a better performance. We also report the CLIP score [63] to measure the alignment between the generated videos and the input texts.
+
+# 5.1 Comparison with Competitors
+
+In Fig. 3, we conduct a comparative analysis of our method against 4D-FY [58], Comp4D [51], and VideoCrafter2 [59] with the same textual prompt. It can be observed that all three baselines fail to provide diverse motion from the textual prompt, while our method excels in yielding large motion and high visual quality. For example, our scheme successfully obeys the complex query in terms of
+
+Table 1: Quantative comparisons with competitors. Our method consistently outperforms all baseline methods in terms of both the video quality and the alignment with textual prompts.  
+
+<table><tr><td>Metric</td><td>4D-FY [58]</td><td>Comp4D [51]</td><td>VideoCrafter2 [59]</td><td>Ours</td></tr><tr><td>QAlign-Img-quality ↑ [62]</td><td>1.681</td><td>1.687</td><td>3.839</td><td>4.030</td></tr><tr><td>QAlign-Img-aesthetic↑ [62]</td><td>1.475</td><td>1.258</td><td>3.199</td><td>3.471</td></tr><tr><td>QAlign-vid-quality↑ [62]</td><td>2.154</td><td>2.142</td><td>3.868</td><td>4.112</td></tr><tr><td>QAlign-vid-aesthetic↑ [62]</td><td>1.580</td><td>1.425</td><td>3.159</td><td>3.723</td></tr><tr><td>CLIP Score↑ [63]</td><td>30.47</td><td>27.50</td><td>35.20</td><td>38.36</td></tr></table>
+
+![](images/f3e72c69fd1b5cefb7912e2bd948cb196828b9d83e7e0a2d78312e142e049cee.jpg)  
+(I) Direct trajectory estimation.
+
+![](images/39470127ede02a1cc947117e0a17aaad7de12ee33818601a2251e16e9249136d.jpg)  
+(II) Trajectory estimation with bounding box indicating objects.
+
+![](images/98b80ac44b06043ef7bb8e11fa82d2eca8d5de74fe0da03d19f2dc6dec15aba1.jpg)  
+(III) Trajectory estimation in a step-by-step manner.
+
+![](images/5e4499c47a2b35a24b77e6dce96e7b6967c9e1440a279c51cab0e629ea3cddb6.jpg)  
+(IV) Ours.
+
+![](images/e998b89f8dbc821410569303c125d0111f9c3d8628c0de60959b476ec343feac.jpg)  
+(I) Without SDS refinement.
+
+![](images/4a934796a792724269b567b72913933d8864ea2e7cea756850fa215286551dbb.jpg)  
+(a) Ablation studies on trajectory estimation with multi-modal LLM.  
+(II) With scale refinement  
+(b) Ablation studies on composition with 2D diffusion models.
+
+![](images/e9bf8bfaecfc0fa3b646755b10fe8d50e8ace28adfe8ae5250b8d9f1422c2719.jpg)  
+(III) With trajectory refinement.  
+Figure 4: Ablation studies on framework design. Each ablation is prompted with the same text.
+
+![](images/5cd04e597978af3fc7bcd786133bb984335a9ca177b8f8e4728a856c186e8b42.jpg)  
+(IV) With rotation refinement.
+
+the number of objects and the corresponding motion. In addition, since 4D-FY and Comp4D focus on object-centric generation, they fail to generate videos with natural backgrounds. In Tab. 3, we perform quantitative comparisons by utilizing Q-Align Score [62] and CLIP Score [63] to assess the quality of generated videos. Our method consistently outperforms the baseline models in terms of both the video quality and the alignment with textual prompts. More results are available in the appendix.
+
+# 5.2 Ablation Studies
+
+Ablations on Trajectory Estimation with Multi-modal LLM. As shown in Fig. 4(a)(I), a direct prompt of GPT-4V will lead to obvious unsatisfactory trajectory estimation. When only depending on bounding boxes to indicate the location of objects within the scene (Fig. 4(a)(II)), though a roughly better trajectory can be achieved, it still leads to unreasonable results, such as several floating bounding boxes. Similarly, using only the step-by-step estimation strategy described in Sec. 4.2 typically results in a trajectory that is merely a simple straight line connecting the starting and ending points (Fig. 4(a)(III)). With both of the two techniques, we can achieve the best performance, with a more reasonable and smooth trajectory (Fig. 4(a)(IV)).
+
+Ablations on Composition with 2D Diffusion Models. To figure out whether it is necessary to conduct fine-grained composition with 2D generative priors, we gradually refine the scales, locations, and rotations with SDS and visualize the results in Fig. 4(b). All results are generated with the same textual prompt: "An alien walking on the floor in front of the cabin's door." It shows that when we optimize the attributes with SDS, we can obtain consistently improved performance with a reasonable scale (Fig. 4(b)(II), accurate locations that are aligned with the input prompt (Fig. 4(b)(III), and orientation that accords with common sense (Fig. 4(b)(IV)).
+
+![](images/b7b28db0c6945748449173b1633b887d88abfe0eda0411b2ec0956dc2a1c73df.jpg)  
+Figure 5: Our method offers flexible control of individual concepts. We demonstrate this by editing different concepts: the appearance and motion of the actors, and the scenes.
+
+Table 2: Quantative comparisons of ablation studies on trajectory estimation with multi-modal LLM.  
+
+<table><tr><td>Methods</td><td>Direct Estimation.</td><td>Estimation using bounding box.</td><td>Step-by-step estimation.</td><td>Ours</td></tr><tr><td>QAlign-Img-quality ↑ [62]</td><td>2.056</td><td>2.894</td><td>3.752</td><td>4.030</td></tr><tr><td>QAlign-Img-aesthetic ↑ [62]</td><td>1.568</td><td>2.156</td><td>3.047</td><td>3.471</td></tr><tr><td>QAlign-vid-quality ↑ [62]</td><td>2.178</td><td>3.043</td><td>3.904</td><td>4.112</td></tr><tr><td>QAlign-vid-aesthetic ↑ [62]</td><td>1.680</td><td>2.346</td><td>3.342</td><td>3.723</td></tr><tr><td>CLIP Score ↑ [63]</td><td>25.68</td><td>29.84</td><td>36.73</td><td>38.36</td></tr></table>
+
+# 5.3 Applications on Controllable Generation
+
+Due to our underlying 3D structural representation, our scheme has the natural merits of editing individual concepts. We illustrate this character in Fig. 5 by editing three different concepts: the appearance and motion of the actors, and the scenes. For the appearance and motion of the actor, we can seamlessly replace them in a zero-shot manner according to the textual prompt (Fig.5(a)(b)), while this is still challenging for implicit models [64, 65]. For scene editing, to ensure a smooth composition of objects within the target scene, we re-estimate the trajectory of the objects given the target scene. Kindly refer to appendix for more results.
+
+# 6 Conclusion
+
+In this paper, we present a novel paradigm for 3D-aware video generation by conceptualizing videos as compositions of independent concepts represented in 3D space. To this end, we leverage LLM as director to decompose the input textual prompts into individual concepts and then invoke pre-trained expert models to generate them separately. To compose various concepts, we first prompt multi-modal LLM in a step-by-step manner to provide coarse guidance on the scale and trajectory of objects,
+
+Table 3: Quantative comparisons of ablation studies on composition with 2D diffusion models.  
+
+<table><tr><td>Methods</td><td>Without SDS.</td><td>With scale refinement.</td><td>With trajectory refinement.</td><td>Ours</td></tr><tr><td>QAlign-Img-quality ↑ [62]</td><td>3.045</td><td>3.674</td><td>3.826</td><td>4.030</td></tr><tr><td>QAlign-Img-aesthetic ↑ [62]</td><td>2.752</td><td>3.046</td><td>3.341</td><td>3.471</td></tr><tr><td>QAlign-vid-quality ↑ [62]</td><td>3.129</td><td>3.794</td><td>3.983</td><td>4.112</td></tr><tr><td>QAlign-vid-aesthetic ↑ [62]</td><td>2.704</td><td>3.468</td><td>3.603</td><td>3.723</td></tr><tr><td>CLIP Score ↑ [63]</td><td>31.35</td><td>35.27</td><td>37.04</td><td>38.36</td></tr></table>
+
+then refine the composition with 2D generative priors. We verify our scheme in different scenarios, demonstrating its superiority over the baseline methods.
+
+Limitations and Future Works. Although we demonstrate promising results in 3D-aware video generation, there still are limitations to be improved in the future. First, our framework is instantiated with limited concepts in this work, i.e., scene, humanoid object, and human motion. It is exciting to generalize the framework to more concepts like animals, vehicles, etc. Second, the composition between concepts is conducted with priors from LLM and 2D diffusion priors in our method. However, it is still interesting to introduce physically grounded dynamics into 3D representation [66]. Third, though our method is naturally suitable for maintaining the consistency of actors across different scenes, it still needs further exploration on long video generation with multiple scenes, e.g., a full-length film.
+
+Ethics Statement. C3V is exclusively a research initiative with no current plans for product integration or public access. We are committed to adhering to Microsoft AI principles during the ongoing development of our models. The model is trained on AI-generated content, which has been thoroughly reviewed to ensure that they do not include personally identifiable information or offensive content. Nonetheless, as these generated data are sourced from the Internet, there may still be inherent biases. To address this, we have implemented a rigorous filtering process on the data to minimize the potential for the model to generate inappropriate content.
+
+Acknowledgement. This work was supported in part by NSFC under Grant 62371434, 62021001.
+
+# References
+
+[1] Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.  
+[2] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems (NeurIPS), 33:6840-6851, 2020.  
+[3] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in Neural Information Processing Systems (NeurIPS), 33:1877-1901, 2020.  
+[4] Timo Schick, Jane Dwivedi-Yu, Roberto Dessi, Roberta Raileanu, Maria Lomeli, Eric Hambro, Luke Zettlemoyer, Nicola Cancedda, and Thomas Scialom. Toolformer: Language models can teach themselves to use tools. Advances in Neural Information Processing Systems, 36, 2024.  
+[5] Wenlong Huang, Chen Wang, Ruohan Zhang, Yunzhu Li, Jiajun Wu, and Li Fei-Fei. Voxposer: Composable 3d value maps for robotic manipulation with language models. In Conference on Robot Learning, pages 540–562. PMLR, 2023.  
+[6] Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in Neural Information Processing Systems (NeurIPS), 34:8780-8794, 2021.  
+[7] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10684-10695, 2022.
+
+[8] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125, 2022.  
+[9] Chitwan Sahara, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in Neural Information Processing Systems (NeurIPS), 35:36479-36494, 2022.  
+[10] Jonathan Ho, Tim Salimans, Alexey Gritsenko, William Chan, Mohammad Norouzi, and David J. Fleet. Video diffusion models. arXiv:2204.03458, 2022.  
+[11] Jonathan Ho, William Chan, Chitwan Sahara, Jay Whang, Ruiqi Gao, Alexey Gritsanko, Diederik P Kingma, Ben Poole, Mohammad Norouzi, David J Fleet, et al. Imagen video: High definition video generation with diffusion models. arXiv preprint arXiv:2210.02303, 2022.  
+[12] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 22563-22575, 2023.  
+[13] David Junhao Zhang, Jay Zhangjie Wu, Jia-Wei Liu, Rui Zhao, Lingmin Ran, Yuchao Gu, Difei Gao, and Mike Zheng Shou. Show-1: Marrying pixel and latent diffusion models for text-to-video generation. arXiv preprint arXiv:2309.15818, 2023.  
+[14] Haoxin Chen, Menghan Xia, Yingqing He, Yong Zhang, Xiaodong Cun, Shaoshu Yang, Jinbo Xing, Yaofang Liu, Qifeng Chen, Xintao Wang, et al. Videocrafter1: Open diffusion models for high-quality video generation. arXiv preprint arXiv:2310.19512, 2023.  
+[15] Rohit Girdhar, Mannat Singh, Andrew Brown, Quentin Duval, Samaneh Azadi, Sai Saketh Rambhatla, Akbar Shah, Xi Yin, Devi Parikh, and Ishan Misra. Emu video: Factorizing text-to-video generation by explicit image conditioning. arXiv preprint arXiv:2311.10709, 2023.  
+[16] Agrim Gupta, Lijun Yu, Kihyuk Sohn, Xiuye Gu, Meera Hahn, Li Fei-Fei, Irfan Essa, Lu Jiang, and José Lezama. Photorealistic video generation with diffusion models. arXiv preprint arXiv:2312.06662, 2023.  
+[17] Dan Kondratyuk, Lijun Yu, Xiuye Gu, José Lezama, Jonathan Huang, Rachel Hornung, Hartwig Adam, Hassan Akbari, Yair Alon, Vighnesh Birodkar, et al. Videopoet: A large language model for zero-shot video generation. arXiv preprint arXiv:2312.14125, 2023.  
+[18] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3836-3847, 2023.  
+[19] Weixi Feng, Wanrong Zhu, Tsu-jui Fu, Varun Jampani, Arjun Akula, Xuehai He, Sugato Basu, Xin Eric Wang, and William Yang Wang. Layoutgpt: Compositional visual planning and generation with large language models. Advances in Neural Information Processing Systems, 36, 2024.  
+[20] Nan Liu, Shuang Li, Yilun Du, Antonio Torralba, and Joshua B Tenenbaum. Compositional visual generation with composable diffusion models. In European Conference on Computer Vision, pages 423-439. Springer, 2022.  
+[21] Long Lian, Baifeng Shi, Adam Yala, Trevor Darrell, and Boyi Li. Llm-grounded video diffusion models. In International Conference on Learning Representations, 2024.  
+[22] Han Lin, Abhay Zala, Jaemin Cho, and Mohit Bansal. Videodirectorgpt: Consistent multi-scene video generation via llm-guided planning. arXiv preprint arXiv:2309.15091, 2023.  
+[23] Noam Chomsky. Aspects of the Theory of Syntax. Number 11. MIT press, 2014.  
+[24] Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning through probabilistic program induction. Science, 350(6266):1332-1338, 2015.
+
+[25] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkuhler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics, 42(4):1-14, 2023.  
+[26] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J Black. Smpl: a skinned multi-person linear model. ACM Transactions on Graphics (TOG), 34(6):1-16, 2015.  
+[27] Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. In The Twelfth International Conference on Learning Representations, 2024.  
+[28] Ben Poole, Ajay Jain, Jonathan T Barron, and Ben Mildenhall. Dreamfusion: Text-to-3d using 2d diffusion. In The Eleventh International Conference on Learning Representations, 2023.  
+[29] Ruben Villegas, Mohammad Babaeizadeh, Pieter-Jan Kindermans, Hernan Moraldo, Han Zhang, Mohammad Taghi Saffar, Santiago Castro, Julius Kunze, and Dumitru Erhan. Phenaki: Variable length video generation from open domain textual descriptions. In International Conference on Learning Representations, 2023.  
+[30] Wenyi Hong, Ming Ding, Wendi Zheng, Xinghan Liu, and Jie Tang. Cogvideo: Large-scale pretraining for text-to-video generation via transformers. In International Conference on Learning Representations, 2023.  
+[31] OpenAI. Chatgpt. https://openai.com/chatgpt, 2022.  
+[32] OpenAI. Gpt-4v(ision) system card. https://openai.com/index/gpt-4v-system-card, 2023.  
+[33] Sitong Su, Litao Guo, Lianli Gao, Hengtao Shen, and Jingkuan Song. Motionzero: Exploiting motion priors for zero-shot text-to-video generation. arXiv preprint arXiv:2311.16635, 2023.  
+[34] Yash Jain, Anshul Nasery, Vibhav Vineet, and Harkirat Behl. Peekaboo: Interactive video generation via masked-diffusion. arXiv preprint arXiv:2312.07509, 2023.  
+[35] Sixiao Zheng, Jingyang Huo, Yu Wang, and Yanwei Fu. Intelligent director: An automatic framework for dynamic visual composition using chatgpt. arXiv preprint arXiv:2402.15746, 2024.  
+[36] Hanzhuo Huang, Yufan Feng, Cheng Shi, Lan Xu, Jingyi Yu, and Sibei Yang. Free-bloom: Zero-shot text-to-video generator with llm director and ldm animator. Advances in Neural Information Processing Systems, 36, 2024.  
+[37] Yu Lu, Linchao Zhu, Hehe Fan, and Yi Yang. Flowzero: Zero-shot text-to-video synthesis with llm-driven dynamic scene syntax. arXiv preprint arXiv:2311.15813, 2023.  
+[38] Susung Hong, Junyoung Seo, Heeseong Shin, Sunghwan Hong, and Seungryong Kim. Direct2v: Large language models are frame-level directors for zero-shot text-to-video generation. arXiv preprint arXiv:2305.14330, 2023.  
+[39] Gyeongrok Oh, Jaehwan Jeong, Sieun Kim, Wonmin Byeon, Jinkyu Kim, Sungwoong Kim, Hyeokmin Kwon, and Sangpil Kim. Mtvg: Multi-text video generation with text-to-video models. arXiv preprint arXiv:2312.04086, 2023.  
+[40] Shaobin Zhuang, Kunchang Li, Xinyuan Chen, Yaohui Wang, Ziwei Liu, Yu Qiao, and Yali Wang. Vlogger: Make your dream a vlog. arXiv preprint arXiv:2401.09414, 2024.  
+[41] Chenliang Chang, Kiseung Bang, Gordon Wetzstein, Byoungho Lee, and Liang Gao. Toward the next-generation vr/ar optics: a review of holographic near-eye displays from a human-centric perspective. Optica, 7(11):1563-1578, 2020.  
+[42] Yichun Shi, Peng Wang, Jianglong Ye, Mai Long, Kejie Li, and Xiao Yang. Mvdream: Multiview diffusion for 3d generation. arXiv preprint arXiv:2308.16512, 2023.
+
+[43] Xiangyu Yue, Bichen Wu, Sanjit A Seshia, Kurt Keutzer, and Alberto L Sangiovanni-Vincentelli. A lidar point cloud generator: from a virtual world to autonomous driving. In Proceedings of the 2018 ACM on International Conference on Multimedia Retrieval, pages 458-464, 2018.  
+[44] Ajay Jain, Ben Mildenhall, Jonathan T Barron, Pieter Abbeel, and Ben Poole. Zero-shot text-guided object generation with dream fields. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 867-876, 2022.  
+[45] Zhengyi Wang, Cheng Lu, Yikai Wang, Fan Bao, Chongxuan Li, Hang Su, and Jun Zhu. Prolificdreamer: High-fidelity and diverse text-to-3d generation with variational score distillation. Advances in Neural Information Processing Systems, 36, 2024.  
+[46] Yukun Huang, Jianan Wang, Yukai Shi, Xianbiao Qi, Zheng-Jun Zha, and Lei Zhang. Dreamtime: An improved optimization strategy for text-to-3d content creation. arXiv preprint arXiv:2306.12422, 2023.  
+[47] Yixun Liang, Xin Yang, Jiantao Lin, Haodong Li, Xiaogang Xu, and Yingcong Chen. Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284, 2023.  
+[48] Ryan Po and Gordon Wetzstein. Compositional 3d scene generation using locally conditioned diffusion. arXiv preprint arXiv:2303.12218, 2023.  
+[49] Gege Gao, Weiyang Liu, Anpei Chen, Andreas Geiger, and Bernhard Scholkopf. Graphdreamer: Compositional 3d scene synthesis from scene graphs. arXiv preprint arXiv:2312.00093, 2023.  
+[50] Xiaoyu Zhou, Xingjian Ran, Yajiao Xiong, Jinlin He, Zhiwei Lin, Yongtao Wang, Deqing Sun, and Ming-Hsuan Yang. Gala3d: Towards text-to-3d complex scene generation via layout-guided generative gaussian splatting. arXiv preprint arXiv:2402.07207, 2024.  
+[51] Dejia Xu, Hanwen Liang, Neel P Bhatt, Hezhen Hu, Hanxue Liang, Konstantinos N Plataniotis, and Zhangyang Wang. Comp4d: Llm-guided compositional 4d scene generation. arXiv preprint arXiv:2403.16993, 2024.  
+[52] Sherwin Bahmani, Xian Liu, Yifan Wang, Ivan Skorokhodov, Victor Rong, Ziwei Liu, Xihui Liu, Jeong Joon Park, Sergey Tulyakov, Gordon Wetzstein, et al. Tc4d: Trajectory-conditioned text-to-4d generation. arXiv preprint arXiv:2403.17920, 2024.  
+[53] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600-612, 2004.  
+[54] Urvashi Khandelwal, Omer Levy, Dan Jurafsky, Luke Zettlemoyer, and Mike Lewis. Generalization through memorization: Nearest neighbor language models. In International Conference on Learning Representations, 2020.  
+[55] Georgios Pavlakos, Vasileios Choutas, Nima Ghorbani, Timo Bolkart, Ahmed AA Osman, Dimitrios Tzionas, and Michael J Black. Expressive body capture: 3d hands, face, and body from a single image. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10975-10985, 2019.  
+[56] Jing Lin, Ailing Zeng, Shunlin Lu, Yuanhao Cai, Ruimao Zhang, Haoqian Wang, and Lei Zhang. Motion-x: A large-scale 3d expressive whole-body human motion dataset. Advances in Neural Information Processing Systems, 36, 2024.  
+[57] René Ranftl, Alexey Bochkovskiy, and Vladlen Koltun. Vision transformers for dense prediction. In Proceedings of the IEEE/CVF international conference on computer vision, pages 12179-12188, 2021.  
+[58] Sherwin Bahmani, Ivan Skorokhodov, Victor Rong, Gordon Wetzstein, Leonidas Guibas, Peter Wonka, Sergey Tulyakov, Jeong Joon Park, Andrea Tagliasacchi, and David B Lindell. 4d-fy: Text-to-4d generation using hybrid score distillation sampling. arXiv preprint arXiv:2311.17984, 2023.
+
+[59] Haoxin Chen, Yong Zhang, Xiaodong Cun, Menghan Xia, Xintao Wang, Chao Weng, and Ying Shan. Videocrafter2: Overcoming data limitations for high-quality video diffusion models. arXiv preprint arXiv:2401.09047, 2024.  
+[60] Jaeyoung Chung, Suyoung Lee, Hyeongjin Nam, Jaerin Lee, and Kyoung Mu Lee. *Luciddreamer: Domain-free generation of 3d gaussian splattering scenes.* arXiv preprint arXiv:2311.13384, 2023.  
+[61] Xian Liu, Xiaohang Zhan, Jiaxiang Tang, Ying Shan, Gang Zeng, Dahua Lin, Xihui Liu, and Ziwei Liu. Humangaussian: Text-driven 3d human generation with gaussian splatting. arXiv preprint arXiv:2311.17061, 2023.  
+[62] Haoning Wu, Zicheng Zhang, Weixia Zhang, Chaofeng Chen, Liang Liao, Chunyi Li, Yixuan Gao, Annan Wang, Erli Zhang, Wenxiu Sun, et al. Q-align: Teaching Imms for visual scoring via discrete text-defined levels. arXiv preprint arXiv:2312.17090, 2023.  
+[63] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International conference on machine learning, pages 8748-8763. PMLR, 2021.  
+[64] Wilson Yan, Andrew Brown, Pieter Abbeel, Rohit Girdhar, and Samaneh Azadi. Motion-conditioned image animation for video editing. arXiv preprint arXiv:2311.18827, 2023.  
+[65] Jianhong Bai, Tianyu He, Yuchi Wang, Junliang Guo, Haoji Hu, Zuozhu Liu, and Jiang Bian. Uniedit: A unified tuning-free framework for video motion and appearance editing. arXiv preprint arXiv:2402.13185, 2024.  
+[66] Tianyi Xie, Zeshun Zong, Yuxin Qiu, Xuan Li, Yutao Feng, Yin Yang, and Chenfanfu Jiang. Physgaussian: Physics-integrated 3d gaussians for generative dynamics. arXiv preprint arXiv:2311.12198, 2023.
+
+# A Implementation Details
+
+# A.1 Experimental Settings
+
+During the process of multi-modal LLMs-based trajectory estimation, we use 20 locations by default to indicate the trajectory between the starting point and the ending point, (i.e.,  $N = 20$  in Eq. 4), where the path between adjacent locations is assumed as a straight line. For scale refinement (Eq. 6),  $\tau_{s}$  is set to 0.1. For location refinement (Eq. 7), we apply it to refine all the twenty locations. The training iterations for each location is 1000 and  $\tau_{L}$  is set to 0.1. All experiments are conducted using a single NVIDIA A100 GPU.
+
+# A.2 Pre-trained Expert Models
+
+LucidDreamer [60]. As a powerful 3D scene generation method, LucidDreamer adopts an iterative view generation strategy, where a series of views are dreamed and aligned via depth-warping based inpainting networks. After obtaining these multiview-consistent images, 3D gaussians are optimized to construct a high-quality 3D scene, by means of typical training pipeline of 3DGS.
+
+HumanGaussian [61]. We choose HumanGaussian as the method for human generation due to its capability of producing drivable avatars on the basis of 3DGS. Specifically, HumanGaussian starts with SMPL-X prior to densely sample Gaussians on the human mesh surface as initial center positions, followed by a texture-structure joint model and an annealed negative prompt guidance strategy to obtain high-fidelity outputs.
+
+Motion-X [56]. Motion-X is a large-scale 3D expressive whole-body human motion dataset which comprises 15.6M precise 3D whole-body pose annotations (i.e., SMPL-X) covering 81.1K motion sequences from massive scenes with sequence-level semantic labels. By calculating the similarity of text embeddings between the motion-related sub-prompt and sequence labels, we find the most matching sequence and acquire motion data in the form of SMPL-X parameters [55].
+
+# A.3 Metrics
+
+Given the lack of ground truth videos for specific text queries, we utilize pre-trained quality-assessment models to evaluate the generated videos and their individual frames. In line with Comp4D [51], we employ Q-Align [62] as the benchmarking tool to assess the quality and aesthetics of the videos. The Q-Align rating, which ranges from 1 (worst) to 5 (best), is considered state-of-the-art, closely aligning with human judgments across established quality assessment benchmarks. Additionally, we include the CLIP score [63] to measure the alignment between the generated videos and the input texts, where higher scores signify better alignment.
+
+# B Results of Different Stages
+
+As shown in Fig. 6, Fig. 7 and Fig. 8, we provide a detailed visualization of results obtained during different stages, including results of LLM-based task decomposition, results of coarse-grained trajectory generation with GPT-4V, and results of the final rendered videos.
+
+# C More Results of Controllable Generation
+
+In this section, we present additional results on controllable generation. As demonstrated in Fig. 9, Fig. 10 and Fig. 11, we can achieve fine-grained control of the target without affecting other concepts in the 3D space.
+
+Prompt: In a Magician's magical cabin alone in a serene forest, an alien walking on the floor, starting from the cabin's door to the mow near the bottom right corner of this image.
+
+# Task Decomposition with LLM
+
+a Magician's magical cabin alone in a serene forest
+
+![](images/5075507e4f347f57ba3fb1658f1106ae5665befed1f4eb03f4ea653d42eb9dcf.jpg)
+
+![](images/8abd03aa12d92037ab03db75f694742e585e24fc9ded191e9f2642a89afa3ea4.jpg)
+
+![](images/bc9f03bf96140e1cd8c61df9d2f8547d6eef6aab5814364edeab7ec25775684b.jpg)
+
+![](images/912836f7825651ffdde0f284caaa7d0f3cca75b5b97191fadfb8c5149950d32b.jpg)
+
+![](images/98cb1b018ab61b94db62890b494c55a708ce6754a24274451eda9c2b75774461.jpg)
+
+an alien
+
+![](images/3b795e7729a499409325540bfebc23e450e08e4ae9056518e100f259e11e872b.jpg)
+
+![](images/e89584e1e07382d0b0346bbe92109dda4d889bcc1221828c630939899bdc2e6d.jpg)
+
+![](images/e093b02e3f35ff7365ae2e3626ea868d070b785b3e5ea005f01dd2c8d2af4046.jpg)
+
+![](images/ed6533942d7e46fdc6c9c7c6509cc0bcca2c6069a9bf64163eff0be1d7a255ed.jpg)
+
+![](images/029b7f3106269a562271c29dc42df73d4b7367a4c77c03bc882f934ac6ba7151.jpg)
+
+walking on the floor
+
+![](images/f55bf25ed4cf3170e7e39f47532ce0bd6d471773a53a1cc14c1a2272b3ae3350.jpg)
+
+![](images/8a2f4f2c372f1c7e74bc4c0cd3929019d946aee143a44668fc20df1e7823cec7.jpg)
+
+![](images/b3c1c2414c2d22d3338aac94586a8912fcb22756534b8bc6b3b9beb283a0af49.jpg)
+
+![](images/87535d703cf90a0f4b940c39027ad44c7ab3752743bc7712f9a123117c7e27c2.jpg)
+
+![](images/e3ff95faa95af9d2dcb40ae924a2401317f183c478aef01b7f6bdb96562f25bc.jpg)
+
+# Trajectory Generation with LLM
+
+![](images/1dc484cfc4fa6813bbb045a4ae70c50f0148da5590eb96fbf64c11b535ff1e92.jpg)  
+Use a bounding box to represent the cabin's door, what is the pixel coordinate of the center of the bounding box?
+
+![](images/ce6f562423eb58dfe1c46779b67b77a0751c0142e6120c7a548e79795a23806a.jpg)  
+Use a bounding box to represent the mow near the bottom right corner of this image, what is the pixel coordinate of the center of the bounding box?
+
+![](images/cf10de9fc626aba7048736dcaaa27eeaae20d1e07d49b450a2aeefd349aeeca9.jpg)  
+Estimated trajectory
+
+# Rendered Video
+
+![](images/ecb1d9b374365d42a569d716c72ebd006f71582a152798e3e0e517222937a62b.jpg)
+
+![](images/03edb6a8aa29c6f82225bfa520202b7401b8beeb2c6013bb0d65badd9bbc6ef4.jpg)
+
+![](images/1924b89c3b8e2cab0e960d971f7b8e27eb9f7a20a215d27170ee478176c75d3c.jpg)  
+Figure 6: Results of different stages given the textual prompt: "In a Magician's magical cabin alone in a serene forest, an alien walking on the floor, starting from the cabin's door to the mow near the bottom right corner of this image."
+
+![](images/650851f5599773f5de248829a7f237dd1532d766b3be9fd87a0545918fd000d2.jpg)
+
+![](images/da0f8da3ebb6ff6a5699fc7788c65ff72c5df4ba486fa343edff943c51da9b55.jpg)
+
+![](images/84b8e586abfd1df28b5b62b4064460b5ca038ef683b4ff30ec5442512353ca03.jpg)
+
+![](images/532c04f230480a01ccebcf79661e417dbcdf28683c3a0c061f991019e72fb513.jpg)
+
+![](images/79a9bf4fe852e309ae5b0b0d2b6e9f56a7a5d3bd161090cc34ac64ed44d26dd9.jpg)
+
+![](images/59f62d8f80b7eaedef67ba95478dcaef025a8f9c13f1ecc81480a9a2c054d505.jpg)
+
+![](images/30b63cae5fb82f8ce09c6ae4ca7835341613a4d6f46a1ecf841199978559b6f3.jpg)
+
+![](images/ab09314e6fabcc02e87352e461b513db91c1548876c563300abfdd0920b7c327.jpg)
+
+![](images/c7967b8b487f16f9aadfb7d54b0bbf077325c7984a4ce4d26576b878b90beb2a.jpg)
+
+![](images/b6f97cce3c2907514d517c1718a8afe233796175fc5095825ccf4d45e12884f3.jpg)
+
+![](images/d1990a8ce6fb8f7d6cdd1ed56037e53973e971b8dd76b82903d3dadebe799265.jpg)
+
+![](images/cab664a63b22ccf0475cc93abd263d9813e56a6d4323b32c9e2a8d59fb620d9d.jpg)
+
+![](images/2818bccef8ae69cd7130283ef32e705d72f8e60e6089de5e5ae348d5db965464.jpg)
+
+![](images/071bb1820d7dcaa57489113a5ebe94ef825234169dac15a2f0faccd138d35d74.jpg)
+
+![](images/9d02066fa36b8b44f36cdefd4aa70245bed80d2a679365f332cea6a07759beea.jpg)
+
+Prompt: Inside a cozy livingroom in Christmas, a astrologer performing ballet on the floor, starting from wooden floor behind the red armchair near the bottom left of this image to the sofa in the bottom right corner of this image.
+
+# Task Decomposition with LLM
+
+a cozy livingroom in Christmas
+
+![](images/ee337c740f55ef10bf3da46e2e1aca725af4c3e85b2309f05dc0329a70040ffe.jpg)
+
+![](images/5db2cea85d578b80e61d2e59f177fd7bd43a78dd38429108a4a2191e0581b8ba.jpg)
+
+![](images/d9971fa1a6c5cbaa35dee0cd4e43587e4d7e8d263d9a25c729d464a79926f129.jpg)
+
+![](images/a75f7ab22f827154d6c95ad6bb57da332c5d32e5aa921e76e2147b6c79ec75a5.jpg)
+
+![](images/0f323b89491fc5d0da720f1b1193d25d23d4ac81f4369222da9cb0abd4377944.jpg)
+
+a astrologer
+
+![](images/4d45c6ecbae84ec52241d3f94f50507d2a5c69bb80f4f972b9d0efd99fdbccb1.jpg)
+
+![](images/212564d1cfd81da2d0a6af2f2793f9aa3d9d8768a00472db12f737a4ca312d79.jpg)
+
+![](images/e104c3586ceab42795c7843495beb5f296bf48ec1c190d7610d8c34696d125b5.jpg)
+
+![](images/ec5eed0d49624e4818c7050c56bcca6e3d3306ec39627f25c8125ab257563e04.jpg)
+
+![](images/f8d0961c3aa1abb9f1a95b36ac75cef5d7a3e2c2370c42177eb08d7350aeb8e5.jpg)
+
+performing ballet on the floor
+
+![](images/bca9c62908812468a49e6c2f40afe7f8eecbe6d4a1568cf42681d2fe65ff3479.jpg)
+
+![](images/b13bfb5558d94960e03c8a8209a2f0f57a26ebf97a0a8bf0e2bf896d81b652c7.jpg)
+
+![](images/5a32391304c155e24a1f0383b852d6b1b27c7a017a592d9ff496a33a0666d43b.jpg)
+
+![](images/3c3b6bf052dfefc21f6a42975750b600dc0774073945e6d3d641973a70686390.jpg)
+
+![](images/f2d00031e62d140693c2ae79c57e6c385817317b1cea790cb419fe64c007bd92.jpg)
+
+# Trajectory Generation with LLM
+
+![](images/7878f595eb6916283ed93738da90af9681f64387a6f7eacdf1d28c0bf8efab3e.jpg)
+
+![](images/b6127f4944642ed4b7e0491f0b5386224ddd4868c8be397ff5d91c9d1e26ebd7.jpg)
+
+![](images/46bbb5c0d2ee3f839a6c695409454dc1619d5418e785b2c0cf17ee059f2109b6.jpg)
+
+Use a bounding box to represent wooden floor behind the red armchair near the bottom left of this image, what is the pixel coordinate of the center of the bounding box?
+
+Use a bounding box to represent the sofa in the bottom right corner of this image, what is the pixel coordinate of the center of the bounding box?
+
+Estimated trajectory
+
+# Rendered Video
+
+![](images/9aa2cb5e7bd6c87cc9ceb88be477fa328ad651a8bff4105904e03164b16a6b3f.jpg)
+
+![](images/624b73cf2ac6792e25a0116fd2ee5a59d7e0be779839af58c75e53fe1d6581b1.jpg)
+
+![](images/f82c99631fb6162a08afb7bff87c054436faa8af5aab4360d4c1441f33d559f8.jpg)
+
+![](images/c7e6139936d3e0d7e849df90cbb9b8402e80b73d23709c76f434f98b8e1d0e3d.jpg)
+
+![](images/57fc64e4b0bedca66dd71a6345f318c59bab2a7ffbf053bfd11e5cba30e1891c.jpg)
+
+![](images/d223385538e991cd177acdcdb59d1ea8492f3f8f8fa4de968ca611978e34fd06.jpg)
+
+![](images/8ee1dbdaa1bb2a2272934ad19311073ffe8ef14980c739936ef15f35630101af.jpg)
+
+![](images/f444ee449eede5ad607dda567b5fef0f3085623f83bdcefd13ca60549fb6a74e.jpg)
+
+![](images/638c37a0bc30fa9757977824a4e2dce42d0a594aa152a83bea551f5aaac12e0f.jpg)
+
+![](images/ace21e5a783abc07cf5a4cd1e57e327bd3ce8ce6df3b31e105ed232cff6b3ddd.jpg)
+
+![](images/4685906f28dc854c67c95fa9960963df13f7e83c7ad61681a6b5f50578567664.jpg)
+
+![](images/2f086a270c332f9141aaaa51ac59bccd404aa838d92132f6068bb5feda407c9f.jpg)
+
+![](images/9d23105655be8c0fa7ef0a14e114ed7eff41f17840a51f61e90aee8ac2cd45dd.jpg)  
+Figure 7: Results of different stages given the textual prompt: "Inside a cozy livingroom in Christmas, a astrologer performing ballet on the floor, starting from wooden floor behind the red armchair near the bottom left of this image to the sofa in the bottom right corner of this image."
+
+![](images/66ce4bc0ee7e94932ba74fb933e51374bc43cf240ed0a15ec510ab697eeb2b41.jpg)
+
+![](images/4e711156a35270639875d56030008802db38db121a3d78cdf553568bbbe74a57.jpg)
+
+![](images/33cc5afc2d810eb59e806467dcd334b6526b57eb8a220e135cac58ff1cca3726.jpg)
+
+![](images/bdaabda0f8195a232a7c6b4ef677da6306d90d0201e8d3e50a0983632af203b3.jpg)
+
+![](images/48a9423e14597d8bb061c63fb6580b31bc2013d0d100b7dd0dc1e7b4ea472c96.jpg)
+
+Prompt: On a simple stage, a man with a black fedora and a denim jacket and a woman wearing ski clothes are performing Kungfu and dancing respectively, on the left side and right side of this stage.
+
+a simple stage
+
+![](images/7497b9d2daba3517cc268c4fa1114d6ace45312e0b4c4913a9e51c364c0df847.jpg)  
+Task Decomposition with LLM
+
+![](images/57189ee878dedefc05b7cdf43e580fcc44daf32b8e6dfd699e4f6134c8996e01.jpg)
+
+![](images/26f222808d0d63afef6157a82741a4b89be7a7c4da71301126a20726536e651f.jpg)
+
+![](images/8cc3818357f23232298c0b639655e0c5c1e0bc48ed26d111a10007c68fa0a752.jpg)
+
+![](images/c699bbc903f889af889dd0414b9e34e15b082df36c25f539ff7dac1164c9f6a1.jpg)
+
+a man with a black fedora and a denim jacket
+
+![](images/307131406cce880d5b4dd648e2ab4305ea0ceb16a943df9d66595bafd7185991.jpg)
+
+![](images/cc35bffce389df65200f85c4412a051f2f841928ea38eec3f1b6f70150b89c27.jpg)
+
+![](images/d29598fef8976bee8f1b3d075a6f623ca07ed3406d9512d9ca32c6bc7647d7f4.jpg)
+
+![](images/e2d5d6134ab76864bec56fae1392ab63950d941e2f6136560679d5b953747ebd.jpg)
+
+![](images/de8746d9fcd505d81c7940b4ba795faedb3707fb453554f695b6b70a1ea4763b.jpg)
+
+performing Kungfu
+
+![](images/4bb4ed25e59bc77e7f40f33481572988d71c4ee0e587225877fe64ae285bf4be.jpg)
+
+![](images/a032c3d4b84cc8cf9c5bb9f3f771ddd0635c98225c0002a1aad2d23d57498a10.jpg)
+
+![](images/e501df735879280b62047a69c7f19b5095ec262379d02f9e42f07772d07f644a.jpg)
+
+![](images/fc47da2364c2211797d67d6cdcbd388123455e1b5cdff48a0491422043e81687.jpg)
+
+![](images/6116f847ed7ccc4b3f8d3f4fb61db960c94972f16998d361c0bc17cc2091cac6.jpg)
+
+![](images/176740bcbcf8274abef8263792f561dc5f05ef7c8b0321ac99d3063c893ca592.jpg)  
+Trajectory Generation with LLM  
+Use a bounding box to represent left side of the stage in this image, what is the pixel coordinate of the center of the bounding box?
+
+![](images/31d769ebcc83608164881e63345b078507978921c692c375fb65bc99ec9e6d15.jpg)  
+Use a bounding box to represent right side of the stage in this image, what is the pixel coordinate of the center of the bounding box?
+
+![](images/8aedc9dfe26cead5635c09fcd696fc9e726ce1bb775abda6d019c14f1066488a.jpg)  
+Estimated trajectory
+
+![](images/fea741d4f3150718e9fb0301b3dde244054ce013bc5053212864c480e2a00014.jpg)
+
+![](images/ba6a4a1a261f0af0c3a7b2679146a5316f1a29464da47ed7206395aa6eb166ac.jpg)
+
+![](images/130a92630187dc8fdf6302184073d91a2288892b267a63f5fede37e34c29dac1.jpg)  
+Rendered Video
+
+![](images/4184059b8f1774e2b77d458838ed19c415cf2f1c3469ee511de336f097b4756e.jpg)
+
+![](images/f021e0ef8f34feb9acd35da31958ae8b5eeef5a2b30c93d2fc2615198fa7dce5.jpg)
+
+![](images/5c7c06809a30baceceef28cd50d5fad4be21ee926d1683ba5e493389d7aa7358.jpg)
+
+![](images/4cb1c06a90fcaf55223e7a66e75ebd5f3144019e6b461a141c42b9a8887811b2.jpg)
+
+![](images/f8df4bbb2084a01d63aed7f2fd730993d8438b4c700eda12a1883ef6bf3bbed0.jpg)
+
+![](images/4b4323cbdd00819ca7b9eb7daca6a5de21a9e16b55baa992fc4173ec3e905360.jpg)
+
+![](images/466a4fc783cc38831700849f11ca722be978016a506882a65c729fc46f70a3ae.jpg)
+
+![](images/81684a46049c17196bba61363f55363a1f73ce701ec2f1acb63caa195b6b15f7.jpg)
+
+![](images/a1306bfa5bd42495c292a423fa4987c0865e87eca43998fbbc3f76d2f53ebbc2.jpg)
+
+![](images/603530256b37a1a57499483b89cb5908c9ad61ab393cbadc48ec2c098444a6e5.jpg)  
+Figure 8: Results of different stages given the textual prompt: "On a simple stage, a man with a black fedora and a denim jacket and a woman wearing ski clothes are performing Kungfu and dancing respectively, on the left side and right side of this stage."
+
+![](images/29cb54c5a7253b38f0f86a0843dd1f8e73e9788ca7781a3c4be6b1b197b871ea.jpg)
+
+![](images/a19c6a9485a24743a71144c59f08d66f2e1934e5f27d901d1e83e6b7fbf0f47e.jpg)
+
+![](images/85370b765d9245374b1fb1686252a9b6c1dee1e5f4614476fac8a38a0e41dea4.jpg)
+
+![](images/694c9904da90066a0f84ac2eb976f6d7b191c99fa77b23ec13939150abbaed76.jpg)
+
+![](images/0f753e76cf9a95d8929d8fdb425b8629d7b2bc82d17734b2102abb76f7f0e81d.jpg)
+
+![](images/e2ab2b0239afc1faa2f3e04e0f9dffc9b332e6a79f2f59eba39fca52a49666af.jpg)  
+(a) Prompt: A black man wearing a green t-shirt playing Kungfu on the stage.
+
+![](images/ad7c4b61d4d697903c1519f0c8b054b452d61b3be2c4e3a5a6b78797f3d75743.jpg)  
+(b) Prompt: Turn the character into a fairy.
+
+![](images/37befa98c3f56d40eed93cf9ee21ce77f175b181bf03e0c3893b34a5c717d18d.jpg)  
+(c) Prompt: Turn the character into a warlock.
+
+![](images/863d0861cdee7da4d10907cb0ab63b29d4875c1351340a68cb76879e261bab25.jpg)  
+Figure 9: Results of actor's appearance editing.  
+(a) Prompt: A demon slayer performing a han and tang dance on the stage.
+
+![](images/020e08c756d98d2313ad7ee841d79151b58042b506b85a37d3487b7a0df7445c.jpg)  
+(b) Prompt: Turn the motion of the character into a ballet.
+
+![](images/c94749eeafca00a80c14699fd5ba17c47dc0d7493131c367aec8ed717d636ceb.jpg)  
+(c) Prompt: Turn the motion of the character into a kin kong exotic dance.  
+Figure 10: Results of actor's motion editing
+
+![](images/7a1d66f8e92052ae901a635626f8633b0dab1f91d55ded3154f6388b8f70dd09.jpg)  
+(a) Prompt: A revenant dancing Daily Lovedive in a ultra-modern mega villa by the sea with swimming pool.
+
+![](images/c0961aab23075d34e2d49bb0098a38cba9181757f8243782c95f2977545bb074.jpg)
+
+![](images/b9dde7e3191707033506b6c7ab4cae351847802bced8fd5000e8624d9c3108df.jpg)
+
+![](images/569bc418ae157ef6a94806e8b0618f2cf89003e0f36715ae64480ebc89bde259.jpg)
+
+![](images/fdcf9e4d93dfb47b5cccfec99a2bb9a83cbed203e34e00d80b0e6e9f7e4a78c8.jpg)
+
+![](images/2f2dae6253d9f28c327b10db47c21ef802308ee64252182f67d796e81d674485.jpg)  
+(b) Prompt: Turn the scene into a long anime-style road with anime-blocks and little anime-grass.
+
+![](images/b3c39f64338b692cdfef512aa044a1f9ca6e36d0ba72131a5c118dc6bb1af989.jpg)
+
+![](images/cdaa0ac723f3438ef55abd285d4fd7f3b2dcb7e896458eb693d6c1633da32280.jpg)
+
+![](images/640f867df579121911fe11367f6619a4278e3606c8cc6ef0527410f0e664778d.jpg)
+
+![](images/c9d71c310c96bb94fb33b0d5db2e9782a03596956922fa16dd9332fecdf8dbf0.jpg)
+
+![](images/b3981f145b1256a85a6c80e082567e574f3a3bab97730929d00b0cfbe5dc4cc6.jpg)  
+(c) Prompt: Turn the character into a postapocalyptic city in desert.
+
+![](images/55585362c8049bf98fdcd72750f81adee6156df19c4774d984ddd68f6214cffb.jpg)  
+Figure 11: Results of scene editing.
+
+![](images/0d988b5202eaacc1786a82e1a5e54a50f1fdf274214c232fa30315654a5542cd.jpg)
+
+![](images/eba1370fe50d965034a26a3da6f6de238675903b30fe33e5b5a4fa04a046c364.jpg)
+
+![](images/f8fa3b3f86a403bfac8a283cc881026819a4521c4645165ec2c3d19362094d16.jpg)
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: We clarify our contributions in Sec. 1.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: We clarify our limitations in Sec. 6.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory Assumptions and Proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [NA]
+
+Justification: This paper does not include theoretical results.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental Result Reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+Answer: [Yes]
+
+Justification: We provide implementation details in Sec. 5 and Sec. A.1.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.  
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.  
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.  
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example  
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).  
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+# Answer: [No]
+
+Justification: We do not provide open access to the data and code in supplemental material.
+
+# Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental Setting/Details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+# Answer: [Yes]
+
+Justification: We provide implementation details in Sec. 5 and Sec. A.1.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment Statistical Significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+# Answer: [No]
+
+Justification: Error bars are not reported because they would be too computationally expensive.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).  
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).
+
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments Compute Resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: We provide computer resources used in Sec. A.1.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code Of Ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: We have reviewed the NeurIPS Code of Ethics.
+
+# Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader Impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: We report possible impacts of our method in Sec. 1 and Sec. 6.
+
+# Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.  
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
+
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: The paper poses no such risks.
+
+Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: We cite all models and datasets mentioned in the paper.
+
+Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URL.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.  
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
+
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New Assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [Yes]
+
+Justification: The paper proposes a novel paradigm for text-to-video generation, named C3V. We plan to release the model's code along with comprehensive documentation to facilitate its use and replication.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and Research with Human Subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: The human avatars showed in this paper are all virtual humans that have no relationships with real human beings.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The human avatars showed in this paper are all virtual humans that have no relationships with real human beings.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
+
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

2024/Compositional 3D-aware Video Generation with LLM Director/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0af2be4fd4e8b56cd9f74a03e35345737774cd2ad748f631a8a02894cff58b63
+size 1756568

2024/Compositional Automata Embeddings for Goal-Conditioned Reinforcement Learning/efed71db-e1cf-4991-9669-febad5d9f10a_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8d8c86e74929ca241c34c30e5b417db2d7f2f1198d2541afbdfe0fd5e7b4f83b
+size 5278014

2024/Compositional Automata Embeddings for Goal-Conditioned Reinforcement Learning/full.md

@@ -0,0 +1,671 @@
+# Compositional Automata Embeddings for Goal-Conditioned Reinforcement Learning
+
+Beyazit Yalcinkaya*
+
+University of California, Berkeley
+
+beyazit@berkeley.edu
+
+Niklas Lauffer*
+
+University of California, Berkeley
+
+nlauffer@berkeley.edu
+
+Marcell Vazquez-Chanlatte*
+
+Nissan Advanced Technology Center marcell.chanlatte@nissan-usa.com
+
+Sanjit A. Seshia
+
+University of California, Berkeley seshia@berkeley.edu
+
+# Abstract
+
+Goal-conditioned reinforcement learning is a powerful way to control an AI agent's behavior at runtime. That said, popular goal representations, e.g., target states or natural language, are either limited to Markovian tasks or rely on ambiguous task semantics. We propose representing temporal goals using compositions of deterministic finite automata (cDFAs) and use cDFAs to guide RL agents. cDFAs balance the need for formal temporal semantics with ease of interpretation: if one can understand a flow chart, one can understand a cDFA. On the other hand, cDFAs form a countably infinite concept class with Boolean semantics, and subtle changes to the automaton can result in very different tasks, making them difficult to condition agent behavior on. To address this, we observe that all paths through a DFA correspond to a series of reach-avoid tasks and propose pre-training graph neural network embeddings on "reach-avoid derived" DFAs. Through empirical evaluation, we demonstrate that the proposed pre-training method enables zero-shot generalization to various cDFA task classes and accelerated policy specialization without the myopic suboptimality of hierarchical methods.
+
+![](images/cff8bd7afb73db28cdadeb5ae084fb5265856c9a3e0e2c9fcac00f06919b84b2.jpg)  
+Figure 1: Given a (conjunctive) composition of deterministic finite automata (shown on the left), we construct its embedding using a graph neural network (GATv2) and use this embedding as a goal to condition the reinforcement learning policy.
+
+# 1 Introduction
+
+Goal-conditioned reinforcement learning (RL) [33] has proven to be a powerful way to create AI agents whose task (or goal) can be specified (conditioned on) at runtime. In practice, this is done by learning a goal encoder, i.e., a mapping to dense vectors, and passing the encoded goals as inputs to a policy, e.g., a feedforward neural network. This expressive framework enables the development of flexible agents that can be deployed in a priori unknown ways, e.g., visiting states never targeted during training. The rise of large language models has popularized leveraging natural language as an ergonomic means to specify a task, e.g., "pick up the onions, chop them, and take them to stove."
+
+While incredibly powerful, tasks specified by target states or natural language have a number of shortcomings. First and foremost, target states are necessarily limited to non-temporal tasks. On the other hand, natural language is, by definition, ambiguous, providing little in the way of formal guarantees or analysis of what task is being asked of the AI agent.
+
+To this end, we consider conditioning on tasks in the form of Boolean combinations of deterministic finite automata (DFAs). We refer to this concept class as compositional DFAs (cDFAs). The choice of cDFAs as the concept class is motivated by three observations. First and foremost, DFAs offer simple and intuitive semantics that require only a cursory familiarity with formal languages—if one can understand a flow chart, one can understand a DFA. Moreover, recent works have demonstrated that DFA and cDFA can be learned in a few shot manner from expert demonstrations and natural language descriptions [41]. As such, DFAs offer a balance between the accessibility of natural language and rigid formal semantics. The addition of Boolean combinations to cDFA, e.g., perform task 1 AND task 2 AND task 3, provides a simple mechanism to build complicated tasks from smaller ones.
+
+Second, DFAs represent temporal tasks that become Markovian by augmenting the state-space with finite memory. Further, they are the "simplest" family to do so since their finite states are equivalent to having a finite number of sub-tasks, formally Nerode congruences [19]. This is particularly important for goal-conditioned RL which necessarily treats temporal tasks differently than traditional RL. For traditional RL, because the task is fixed, one can simply augment the state space with the corresponding memory to make the task Markovian. In goal-conditioned RL, this is not, in general, possible as it is unclear what history will be important until the task is provided. Instead, the encoded task must relay to the policy this temporal information. Third, existing formulations like temporal logics over finite traces and series of reach-avoid tasks are regular languages and thus are expressible as DFAs [11]. This makes DFAs a natural target for conditioning an RL policy on temporal tasks.
+
+The expressivity of DFAs introduces a number of challenges for goal-conditioned RL. First, DFAs form a countably infinite and exponentially growing concept class where subtle changes in the DFA can result in large changes in an agent's behavior. Notably, this means that any distribution over DFAs is necessarily biased with many "similar" DFAs having drastically different probability. Thus, to generally work with DFAs, one cannot simply match finite patterns, but need to learn to encode details necessary for planning. Second, as with traditional goal-based objectives, DFAs provide a very sparse binary reward signal—did you reach the accepting state or not? Together with non-trivial dynamics, naive applications of RL become infeasible due to the lack of dense reward signal. Finally, the exponentially-expanding concept class presents computational limitations for encoding. For example, many interesting DFAs may be too large to be feasibly processed by a graph neural network.
+
+To address these issues of reward sparsity and the need to encode planning, we introduce a distribution of DFAs, called reach-avoid derived (RAD). This concept class is inspired by the observation that all paths through a DFA correspond to a series of (local) reach-avoid problems. We argue in Section 4 that RAD encourages learning to navigate a DFA's structure. Our first key result is that pre-training DFA encoders on RAD DFAs enables zero-shot generalization to other DFAs. Next, we treat the problem of DFA size. Many problems are naturally expressed compositionally, e.g., a sequence of rules that must all hold or a set of tasks of which at least one must be accomplished. Due to their Boolean semantics, i.e., did you reach the accepting state or not, DFAs offer well-defined semantics under Boolean compositions. Our second key insight is to encode conjunctions $^2$  of DFAs (called cDFAs). This is done by using a graph attention network [9] (GATv2) to encode the individual DFA graph structure as well as the conjunction (AND) relationships between a collection of tasks. Recalling that the conjunction of any two DFAs grows (worst-case) quadratically, we observe that cDFAs offer an exponential reduction in the size of temporal tasks passed to GATv2.
+
+1.1 Contributions. Our main contributions are: (1) we propose compositional DFAs (cDFAs), which balance formal semantics, accessibility, and expressivity, as a goal representation for temporal tasks in goal-conditioned RL; (2) we propose encoding cDFAs using graph attention networks (GATv2); (3) we propose pre-training the cDFA encoder on reach-avoid derived (RAD) DFAs, and (4) we perform experiments demonstrating strong zero-shot generalization of pre-training on RAD DFAs.
+
+1.2 Related Work. Our work explores a temporal variant of goal-conditioned RL [33] where goals are represented as automata. While traditionally focused on goals as future target states, this has since been extended to tasks such as natural language [7, 21, 26, 37] and temporal logic [38]. While not as expressive as natural language, we believe cDFAs offer a balance between the ergonomics of language while maintaining unambiguous semantics—something of increasing importance due to the seemingly inevitable proliferation of AI agents to safety-critical systems. Moreover, DFA inference has a rich literature [6, 15, 17, 24, 27, 28, 45] with recent works have even shown the ability to learn DFA and cDFA from natural language and expert demonstrations—bridging the gap even more between natural language and automata specified goals [41, 42, 43].
+
+Operating in a similar space, previous work, LTL2Action [38], has shown success with using (finite) linear temporal logic (LTL), a modal extension of propositional logic, to condition RL policies on. In fact, the pre-training and test domains used in this paper are directly derived from that work.
+
+Our choice to focus on DFA rather than LTL is two-fold. First and foremost, over finite traces, LTL is strictly less expressive than DFA. For example, LTL cannot express tasks such as "the number of times the light switch is toggled should be even." Second, like DFA, LTL tasks constitute a countably infinite set of tasks. This again means that any distribution over LTL is necessarily biased to certain subclasses. On the one hand, the syntactic structure makes separation of subclasses very easy. On the other, it remains unclear how to generalize to "common" LTL formula. By contrast, we argue that the local reach-avoid structure of DFAs offers a direct mechanism for generalization. Finally, we note that while LTL is exponentially more succinct than DFA, this is largely mitigated by supporting boolean combinations of DFAs (cDFAs).
+
+Moving away from goal-conditioned RL, recent works have proposed performing symbolic planning on the DFA and cleverly stringing together policies to realize proposed paths [16, 22, 23, 30]. However, their method can still suffer from sub-optimality due to their goal-conditioned value functions being myopic. Specifically, if there are multiple ways to reach the next sub-goal of a temporal task, the optimality of the next action depends on the entire plan, not just the next sub-goal—destroying the compositional structure used for planning. For example, Figure 4 shows a simple example in which hierarchical approaches will find a suboptimal solution due to their myopia. In contrast, conditioning on cDFA embeddings allows our policies to account for the entire task.
+
+On the single-task LTL-constrained policy optimization side, several works have tackled the problem in varying settings [10, 13, 36, 44]. Adjacent to these efforts, various approaches have explored LTL specifications and automaton-like models as objectives in RL [2, 3, 8, 12, 14, 20, 29, 32, 46, 48]. A different line of work considers leveraging quantitative semantics of specifications to shape the reward [1, 22, 25, 36]. However, all of these lines of work are limited to learning a single, fixed goal.
+
+Finally, in a previous work [47], we used hindsight experience replay [5] to solve the reward sparsity problem for DFA-conditioned off-policy learning of DFA task classes. We observe that our RAD pre-training pipeline has similar sample efficiency while generalizing to larger classes of DFAs.
+
+# 2 Preliminaries
+
+In the next sections, we will develop a formalism for conditioning agent behavior on temporal tasks represented as DFAs. To facilitate this exposition, we quickly review goal-conditioned RL and DFA.
+
+# 2.1 Goal-Conditioned RL. We start with technical machinery for goal-conditioned RL.
+
+Definition 2.1. A Markov Decision Process $^3$  (MDP) is a tuple  $\mathcal{M} = (S, A, T)$ , where  $S$  is a set of states,  $A$  is a set of actions, and  $T$  is a map determining the conditional transition probabilities, i.e.  $\operatorname*{Pr}(s' \mid s, a) \stackrel{\mathrm{def}}{=} T(s', a, s)$  for  $s, s' \in S$  and  $a \in A$ . We assume that  $\mathcal{M}$  contains a sink
+
+state, $, denoting the end of an episode. Any MDP, $\mathcal{M}$, can be given γ-temporal discounting semantics by asserting that each transition can end the episode with probability 1 - γ. Formally,  $T'(s', a, s) = (1 - \gamma) \cdot T(s', a, s)$ , for s, s' ≠ $
+
+Definition 2.2. Let  $\mathcal{G}$  be a set of states called goals. A goal-conditioned policy,  $\pi : S \times \mathcal{G} \to \Delta A$ , is a map from state-goal pairs to distributions over actions. Together, an MDP  $\mathcal{M}$  and a goal-conditioned policy,  $\pi$ , define a distribution of sequences of states, called paths.
+
+A goal-conditioned reinforcement learning problem is a tuple consisting of a (possibly unknown) MDP and a distribution over goals,  $\operatorname{Pr}(g)$  for  $g \in \mathcal{G}$ . The objective of goal-conditioned RL is to maximize the probability of generating a path containing  $g$ .
+
+2.2 Deterministic Finite Automata. Next, we provide a brief refresher on automata.
+
+Definition 2.3. A Deterministic Finite Automaton (DFA) is a tuple  $\mathcal{A} = (Q, \Sigma, \delta, q_0, F)$ , where  $Q$  is a finite set of states,  $\Sigma$  is a finite alphabet,  $\delta: Q \times \Sigma \to Q$  is the transition function,  $q_0 \in Q$  is the initial state, and  $F \subseteq Q$  are the accepting states. The transition function can be lifted to strings via repeated application,  $\delta^*: Q \times \Sigma^* \to Q$ . One says  $\mathcal{A}$  accepts  $x$  if  $\delta^*(q_0, x) \in F$ . Finally for simplicity, we abuse notation and denote by DFA the set of all DFA.
+
+Visually, we represent DFAs as multi-graphs whose nodes represent states and whose edges are annotated with a symbol that triggers the corresponding transition. Omitted transitions are assumed to stutter, i.e., transition back to the same state. DFAs have a number of interesting properties.
+
+Up to a state isomorphism, all DFAs can be minimized to a canonical form, e.g., using Hopcroft's algorithm [18], denoted by minimize  $(\mathcal{A})$ . Further, DFAs are closed under Boolean combinations. For example, the conjunction of two DFAs,  $\mathcal{A}_1$  and  $\mathcal{A}_2$ , denoted  $\mathcal{A}_1 \wedge \mathcal{A}_2$ , is constructed by taking the product of the states,  $Q = Q_1 \times Q_2$ , and evaluating the transition functions element-wise,  $\delta((q_1, q_2), \sigma) = (\delta_1(q_1, \sigma), \delta_2(q_2, \sigma))$ . Also,  $(q_1, q_2) \in F$  if  $q_1 \in F_1$  and  $q_2 \in F_2$ . While DFAs are closed under conjunction, each pair-wise operation results in a  $O(n^2)$  increase in the number of states.
+
+Definition 2.4. A compositional DFA (cDFA) is a finite set of DFA,  $\mathcal{C} = \{\mathcal{A}_1,\dots ,\mathcal{A}_n\}$ . The monolithic DFA associated to cDFA,  $\mathcal{C}$ , is given by monolithic  $(\mathcal{C})\stackrel {\mathrm{def}}{=}\bigwedge_{\mathcal{A}\in \mathcal{C}}\mathcal{A}$ . The semantics of a cDFA are inherited from its monolithic DFA, i.e., a string  $x$  is accepted by cDFA  $\mathcal{C}$  if and only if it is accepted by monolithic  $(\mathcal{C})$ . Graphically, cDFA are represented as trees of depth 1 where the root corresponds to conjunction and each leaf is itself a DFA.
+
+2.3 Augmenting MDPs with cDFAs. Observe that DFAs can be viewed as deterministic MDPs leading to a natural cascading composition we refer to as DFA-augmentation of a MDP. Informally, one imagines that the MDP and DFA transitions are interleaved. First, the MDP transitions given an action. The new state is then mapped to the DFA's alphabet. This symbol then transitions the DFA. The goal is to reach an accepting state in the DFA before the MDP reaches its end-of-episode state.
+
+Formally, let \(\mathcal{A}\) and \(\mathcal{M}\) be a DFA and MDP, respectively and let \(L: S \to \Sigma\) denote a labelling function mapping states to symbols in the DFAs alphabet. The new MDP is constructed as a quotient of the cascading composition of \(\mathcal{A}\) and \(\mathcal{M}\). First, take the product of the state spaces, \(S \times Q\). The action space is \(\mathcal{M}\)'s action set. The transition of the MDPs state is as before and the DFA transitions are given by: \(\delta(q, L(s))\). In order for there to be a unique goal and end-of-episode state, we quotient \(S \times Q\) as follows: (i) \((\\), q)\) are treated as a single end of episode state and (ii) for all accepting states, \(q \in F\), the product states \((s, q)\) are treated as a single accepting (goal) state.
+
+# 3 Compositional Automata-Conditioned Reinforcement Learning
+
+We are now ready to formally define (compositional) automata-conditioned RL as a variant of goal-conditioned RL where goals are defined in the augmented MDPs.
+
+Definition 3.1. A DFA-conditioned policy,  $\pi : S \times \mathrm{DFA} \to \Delta A$  is a mapping from state-DFA pairs to action distributions. A DFA-conditioned RL problem is a tuple  $(\mathcal{M}, P)$ , where  $\mathcal{M}$  is an MDP and  $P$  is a distribution over DFAs. The objective is to maximize the probability of generating a path containing the accepting state. cDFA-conditioned RL is defined via the underlying monolithic DFA.
+
+![](images/99b60992dc63e67926e85ec45873fe8e819bce23c79cb40a406e592d0247ee90.jpg)  
+Figure 2: Message passing illustration on the featurization of the cDFA given in Figure 1.
+
+The proposed architecture for conditioning RL policies on temporal tasks encoded as cDFA is given in Figure 1. At step  $t$ , given an observation  $o_t$  and a cDFA  $\mathcal{C}_t$ , we compute an embedding  $s_t$  of the observation  $o_t$  using a convolutional neural network and embedding  $g_t$  of  $\mathcal{C}_t$  (constituting a goal) using a message-passing neural network (MPNN). We then concatenate  $s_t$  and  $g_t$  and feed it to a policy network to get an action  $a_t$ . After taking  $a_t$ , we use the next observation  $o_{t+1}$  to update the initial state of each  $\mathcal{A}_t \in \mathcal{C}_t$  based on the transition taken. We then minimize each updated DFA to form the next cDFA  $\mathcal{C}_{t+1}$ , which is used to get the next action  $a_{t+1}$ .
+
+3.1 cDFA Featurization. In order to pass a cDFA  $\mathcal{C}_t$  to an MPNN, we construct a featurization  $\hat{\mathcal{G}}_{\mathcal{C}_t} = (\hat{\mathcal{V}}_{\mathcal{C}_t},\hat{\mathcal{E}}_{\mathcal{C}_t},h_{\mathcal{C}_t})$ . Details of this process are given in Appendix A. Essentially, we apply four sequential modifications to the graph structure trivially induced by  $\mathcal{C}_t$ : (i) add new nodes for every transition in each DFA in the composition, remove these transitions to connect the new nodes to the source and target nodes of the removed transitions, and in the feature vectors of the new nodes, encode all symbols triggering that transition using positional one-hot encodings, (ii) reverse all the edges, (iii) add self-loops to all nodes, and (iv) add edges from the nodes corresponding to the initial states of DFAs to the "AND" node. Figure 2 shows the featurization of the cDFA given in Figure 1.  
+3.2 cDFA Embedding. Given a cDFA featurization  $\hat{\mathcal{G}}_{\mathcal{C}_t} = (\hat{\mathcal{V}}_{\mathcal{C}_t},\hat{\mathcal{E}}_{\mathcal{C}_t},h_{\mathcal{C}_t})$ , we construct an embedding of the cDFA using a graph attention network (GATv2) [9] performing a sequence of message passing steps to map each node to a vector. For ease of notation, we refer to the features of a node  $v\in \hat{\mathcal{V}}_{\mathcal{C}_t}$  as  $h_v\stackrel {\mathrm{def}}{=}h_{\mathcal{C}_t}(v)$ . At each message passing step, node features are updated as:
+
+$$
+h _ {v} ^ {\prime} = \sum_ {u \in \mathcal {N} (v)} \alpha_ {v u} W _ {t g t} h _ {u},
+$$
+
+where  $\mathcal{N}(v)$  denotes neighbors of  $v$ ,  $W_{tgt}$  is a linear map, and  $\alpha_{vu}$  is the attention score between  $v$  and  $u$  computed as:
+
+$$
+\alpha_ {v u} = \mathrm {s o f t m a x} _ {\mathrm {i}} (e _ {v u}) \qquad e _ {v u} = a \cdot \mathrm {L e a k y R e L U} \left(W _ {s r c} h _ {v} + W _ {t g t} h _ {u}\right),
+$$
+
+where  $a$  is a vector and  $W_{src}$  is a linear map. After message passing steps, the feature vector of the cDFA's "AND" node (which has received messages from all  $\mathcal{A}_t\in \mathcal{C}_t$ ) represents the latent space encoding  $g_{t}$  of the temporal task given by  $\mathcal{C}_t$ .
+
+# 4 Pre-training on Reach-Avoid Derived (RAD) Compositional Automata
+
+In this section, we introduce pre-training on reach-avoid derived (RAD) cDFAs. This pre-training is designed to solve three important problems. First, we wish to avoid simultaneously learning a control policy and embeddings for the cDFAs. Second, we wish to learn a domain-independent cDFA encoder that performs well across cDFA distributions. Third, we wish to have either a domain-specific or a general cDFA-conditioned policy that performs well across different cDFA distributions.
+
+To alleviate the first problem, i.e., decoupling of learning of control and cDFA embeddings, we follow [38] and pre-train our cDFA encoding GNN on a "dummy" MDP containing a single non-end-of-episode state. To solve this dummy MDP, we connect a single linear layer to the output of the GNN which maps cDFA embeddings to the symbols in its alphabet. We then take these symbols and
+
+![](images/e1dab8c9cca836ac4bf1af77ab3f20cce306667b7eb77d7b5c03e47e6bb37197.jpg)  
+Figure 3: An example of a sequence of local reach-avoid problems and a RAD DFA obtained from it.
+
+take a transition (either a stuttering one or one that changes the state of the DFA) in each DFA of the composition. The episode ends either when all DFAs end up in their corresponding accepting states (reward 1) or when one of the DFAs in the composition ends up in a non-accepting sink state (reward  $-1$ ). The cDFA-augmentation then only models the dynamics of the cDFA being conditioned on. The resulting cDFA-conditioned RL problem can thus focus on only learning to encode the cDFAs.
+
+4.1 Sequential reach-avoid as the basis for planning. What remains then is to support generalization to other cDFA distributions. In particular, recall that cDFAs (and DFAs) lack a canonical "unbiased" distribution making it a priori difficult to pre-select a cDFA distribution. To begin, observe that realizing any individual state transition  $q \rightarrow q'$  through a DFA corresponds to a reach-avoid task: (i) eventually transition to state  $q'$  and (ii) avoid symbols that transition to a state different than  $q$  and  $q'$ . Further, a path through a DFA,  $q_1, \ldots, q_n$ , corresponds to a sequence of reach-avoid (SRA) tasks. Notably, as illustrated in Figure 3, SRA tasks can be represented as DFA. Thus, in order to generally reason about satisfying a DFA, our neural encoding must be able to solve SRA tasks.
+
+4.2 Reach-avoid derived DFAs. For general DFAs, there can be arbitrarily many (often infinitely many) paths leading to an accepting state, resulting in multiple SRA tasks interacting and interleaving. Thus, the overall structure of a DFA might be much richer than an SRA task even though it consists of local reach-avoid problems. Building on the observation that paths of a DFA correspond to SRA tasks, we define reach-avoid derived DFAs as a generalization of SRA.
+
+Definition 4.1. We define a mutation of a DFA  $\mathcal{A}$  to be the process of randomly changing a transition of  $\mathcal{A}$ , removing the outgoing edges of the accepting state, and then minimizing. To change a transition, we uniformly sample a state-symbol-state triplet  $(q,\sigma,q')$  and define  $\delta(q,\sigma)\stackrel{\mathrm{def}}{=}q'$ . A DFA  $\mathcal{A}$  is said to be  $m$ -reach-avoid derived ( $m$ -RAD) if it can be constructed by mutating an SRA DFA  $m$ -times.
+
+We define the  $(m,p)$ -RAD distribution over DFAs as follows: (i) sample a SRA DFA,  $\mathcal{A}$ , with  $k + 2$  states where  $k\sim \mathrm{Geometric}(p)$ ; each transition stutters with probability 0.9 and is otherwise made a reach or avoid transition with equal probability; (ii) sequentially apply  $m$  mutations where mutations leading to trivial one-state DFAs are rejected. To avoid notational clutter, we shall often suppress  $m,p$  and say RAD DFAs. Finally, we define the RAD cDFA distribution by sampling  $n$  RAD DFAs, where  $n$  is also drawn from a geometric distribution. See Appendix B for the pseudocode. Figure 3 demonstrates how mutations and minimization can turn an SRA DFA into a RAD DFA. To get the RAD DFA, we apply two mutations to the SRA DFA, adding two new transitions: (i) from  $q_{0}$  to  $q_{3}$  on green and (ii) from  $q_{4}$  to  $q_{1}$  on blue, and then the minimization collapses  $q_{0}$  and  $q_{4}$  to a single state.
+
+# 5 Experiments
+
+We explore the following 6 questions on several task classes in discrete and continuous environments:
+
+RQ1 Do our policies overcome the limitations of hierarchical approaches?  
+RQ2 Does pre-training of the cDFA encoder on RAD cDFAs accelerate cDFA-conditioned RL?  
+RQ3 Does freezing the cDFA encoder negatively impact cDFA-conditioned RL performance?  
+RQ4 Do the cDFA-embeddings pre-trained on RAD generalize to other task classes?  
+RQ5 How does the RAD pre-trained cDFA encoder represent the corresponding cDFA?  
+RQ6 Do RAD pre-trained cDFA-conditioned policies generalize across task classes?
+
+![](images/7ddd59dd24e0a8521858f634eaa054b86ed74d2fa47813c05ded3ee112f566c2.jpg)  
+Figure 4: An example in which the myopia of hierarchical approaches causes them to find a suboptimal solution. If the task is to first go to orange and then green, the hierarchical approaches will choose the closest orange which takes them further from green whereas our approach finds the optimal solution.
+
+![](images/c9e4172f8055874003d9114dd0cce0277e5352d619120995bb5976a3f14e8854.jpg)
+
+Letterworld Environment. Introduced in [4, 38], Letterworld is a 7x7 grid where the agent occupies one square at a time. Some squares have randomly assigned letters which cDFA tasks are defined over. The agent can move in the four cardinal directions to adjacent squares. Moving into a square with a letter satisfies the corresponding symbol. The agent observes its position and the letters in each grid. Each layout has 12 unique letters (each appearing twice) and a horizon of 75.
+
+Zones environment. Introduced in [38] (building on Safety Gym [31]), Zones is as an extension to Letterworld with continuous state and action spaces. There are 8 colored (2 of each color) circles randomly positioned in the environment. cDFA tasks are defined over colors. The agent's action space allows it to steer left and right and accelerate forward and backward while observing lidar, accelerometer, and velocimeter data. The environment has a horizon of 1000.
+
+Task classes. In addition to RAD, we consider the following task classes in our experiments.
+
+- Reach (R): Defines a total order over  $k \sim \operatorname{Uniform}(1, K)$  symbols, e.g.,  $q_0$  and  $q_1$  in Figure 1.  
+- Reach-Avoid (RA): Defines an SRA task of length  $k \sim \text{Uniform}(1, K)$ , e.g., first DFA in Figure 1.  
+- Reach-Avoid with Redemption (RAR): Similar to RA, but they have transitions from their avoid state to the previous state, e.g., the sub-DFA with states  $q_{0}, q_{1}, q_{3}$  in Figure 3.  
+- Parity: A sub-class of RAR where the symbol that leads to the avoid state also triggers a transition back to the previous state, e.g., the DFA on the right in Figure 1. These tasks are not expressible in LTL due to their languages not being star-free regular [40].
+
+Given a bound  $N$ , using these task classes, we generate their compositional counterparts by sampling  $n \sim \mathrm{Uniform}(1, N)$  many DFAs to form a cDFA. As a short-hand notation, for example, we refer to RAR cDFAs with a maximum number of conjunctions 3 where each DFA has a task length of also 2 as cRAR.1.2.1.3 and refer to its associated monolithic (see Definition 2.4) class as RAR.1.2.1.3, i.e., without the "c" prefix. We use the same abbreviation convention for other task classes as well. We use cRAD for RAD cDFAs with truncated distributions and NT-cRAD for the not-truncated version.
+
+Finally, for comparisons with [38], we include the task classes defined in that work, i.e., partially ordered (PO) and avoidance (AV) finite LTL tasks, represented as cDFAs.
+
+Pre-training procedure. We pre-train GATv2 on RAD cDFAs in the dummy MDP as described in Section 4. We set both geometric distribution parameters of the RAD cDFA sampler to 0.5 and truncate these distributions so that  $n \leq 5$  and  $2 + k \leq 10$ , i.e., we make sure that the maximum number of DFAs in a composition is 5, and the maximum number of states of each DFA is 10. As a baseline for GATv2, we also pre-train a relational graph convolutional network (RGCN) [34].
+
+Training procedure. We experiment with training policies three ways: Training without pretraining (no pretraining), with frozen MPNNs pre-trained on RAD as described in Section 4 (pretraining (frozen)), and allowing the pre-trained MPNN to continue receiving gradient updates (pretraining).
+
+We use proximal policy optimization (PPO) [35] for all reinforcement learning setups, giving a reward of  $+1$  when a rollout reaches the accepting state of the cDFA task,  $-1$  when a rollout reaches
+
+![](images/faabeecb6c6d8b6ea3f164a73211307df16108704138c6dbd42d842793d9e862.jpg)  
+Figure 5: Training curves (error bars show a  $90\%$  confidence interval over 10 seeds) in Letterworld (discrete) and Zones (continuous) for policies trained on RAD cDFAs, showing that frozen pre-trained cDFA encoders perform better than non-frozen ones while no pre-training barely learns the tasks.
+
+![](images/2edba0ca65399b2d42b54a92c1458ca290bdcbbfc5284b487e0744d18390498f.jpg)
+
+![](images/e52ac6ba7834cafec07e1af6a84e9e7fd0858599965abac7798ec4f3f7bf5fb5.jpg)
+
+a rejecting sink state of the cDFA task, and 0 if the environment reaches the timeout horizon without achieving the cDFA task. See Appendix D for the hyperparameters and compute used.
+
+RQ1 cDFA-conditioned policies do not suffer from myopia. First, we present the experiment results highlighting the myopia of hierarchical approaches. To this end, we construct a simplified variation of the Letterworld environment, given in Figure 4, where the task is to visit the orange square before the green one. Observe that any hierarchical approach, like [23, 30], based on high-level planning over some automaton-like structure suffers from myopia. Specifically, such approaches do not account for the overall task while planning for the intermediate goals. In this example, hierarchical approaches fail to differentiate between the two orange squares in the context of the given task. On the other hand, our approach quickly converges to the optimal policy as given in Figure 4.
+
+RQ2,RQ3: Pretraining helps policies perform better faster. Figure 5 shows training curves for learning on RAD tasks using RGCN (dashed curves) and GATv2 (solid curves) as the MPNN module in Letterworld. Without pre-training in the dummy environment (blue curves), the policies barely learn how to accomplish the tasks, likely because of the difficulty in trying to simultaneously learn an embedding of the cDFA task and learn the dynamics of the environment required to reach certain symbols. Frozen pre-training (green curve) helps tremendously in learning the RAD task class in the Letterworld regardless of the MPNN module architecture. The policies learned are able to satisfy sampled RAD tasks on average over  $95\%$  of the time and within 5 timesteps. Non-frozen pre-training (red curve) also helps the policies learn more quickly, but with a significant difference between GATv2 and RGCN. Notably, non-frozen pre-training performs significantly worse for RGCN than its frozen counterpart, showing that freezing the MPNN module after pre-training actually helps performance. We further note that the wall clock training time was significantly faster due to not propagating gradients through the MPNN (about  $20\%$  faster).
+
+RQ4: Pretrained cDFA embeddings generalize well. We tested pre-trained GATv2 and RGCN models on various new cDFAs and their associated monolithic task distributions in the dummy DFA environment. Figure 10 in Appendix C.2 presents experiment results averaged over 10 seeds and 50 episodes per seed. The left y-axis illustrates the satisfaction likelihood while the right y-axis presents the number of steps needed to complete the task. The figure shows that GATv2 achieves approximately  $90\%$  accuracy across all tasks, with nearly  $100\%$  accuracy in most cases. Although RGCN generalizes comparably to GATv2 in most instances, it achieves around  $80\%$  accuracy for both cRA.1.5.1.5 and cRA.1.1.1.10 whereas GATv2 performs at nearly  $90\%$  and  $100\%$ , respectively.
+
+Considering that the maximum number of DFAs in a composition seen during training is 5 (sampled with low probability) and the DFA with the maximum task length is 9 (with a maximum of 10 states, sampled with even lower probability), these generalization results are quite remarkable. GATv2 can generalize to 10 DFAs in composition as well as DFAs with a task length of 10 with nearly  $100\%$  accuracy. Furthermore, Figure 10 shows that the embeddings produced by GATv2 lead to shorter episodes compared to RGCN, indicating that GATv2 learns better representations for cDFAs. Overall, regardless of the MPNN model used, pre-training on the RAD cDFAs provides generalization.
+
+Reach-Avoid Derived  
+Reach-Avoid  
+Reach
+
+Reach-Avoid with Redemption  
+Parity  
+No Op
+
+2-Conjunction Collapse  
+1-Step Advance  
++ 1-Step Advance Leading Accept
+
+![](images/f8c8c7a7db54d7f80396417dfa33b7eb67fd7540654cfc07c564db9e9e99b4e8.jpg)  
+(a) GATv2 - 2-D t-SNE
+
+![](images/4a006f759b1fe5812f81e2a685ede9a3736af56bec8aa287f8273571c8385c54.jpg)  
+(b) GATv2 - Cosine similarity heat map
+
+![](images/bed41be1e2bddaec0dcb50daab9c0b0c3dc8d4cfa0a892d7769a0480e316deb2.jpg)  
+(c) GATv2 - Euclidean distance heat map  
+Figure 6: Visualizations of the embeddings generated by GATv2 pre-trained on RAD cDFAs, illustrating that the learned embedding space reflects the similarities between different task classes.
+
+RQ5: cDFA embedding space is well-clustered. Our GATv2 cDFA encoders learn 32-dimensional embeddings, and, as shown in the previous answer, generalize well to other cDFA classes. To study the cDFA embeddings, we sample cDFAs from RAD, RA, RAR, reach, and parity task classes. For each class, we also introduce two variants: 2-conjunction collapse and 1-step advance. The former randomly selects two DFAs of a cDFA and collapses them down to a single DFA, and the latter takes a random non-stuttering transition on the cDFA. We study the embedding space in two different ways. One projects the embeddings down to 2D using t-SNE [39]. The other computes pairwise cosine similarities and Euclidean distances of the embeddings. See Appendix C.3 for the RGCN results.
+
+The results are given in Figure 6. We first observe that modifications like 2-conjunction collapse and 1-step advance result in similar embeddings, showcasing the robustness provided by pre-training GATv2 on RAD. Moreover, due to the 1-step advance operation, some cDFAs end up in their accepting states, and we see that accepting cDFAs are well-isolated inside the green region in Figure 6a. Similarly, we observe that parity samples are mapped very close to RAR samples (its parent class).
+
+The same figure also demonstrates that GATv2 successfully separates different cDFA classes into distinct clusters. This separation is further confirmed by the cosine similarity (c.f. Figure 6b) and Euclidean distance heat maps (c.f. Figure 6c). On the other hand, both heat maps also show that the RAD cDFA class is very rich in terms of various DFAs it contains since it has both similar and different samples compared to other task classes. Notably, we see that the vast majority of RAD cDFA we sample are out-of-distribution for the other classes implying robust generalization.
+
+RQ6: Policies Trained on RAD generalize well. Figure 7 (blue) shows how well the policies trained on RAD generalize to other task distributions. Both frozen and non-frozen (see Appendix C.4) pre-trained policies generalize well across the board with a slight edge to frozen pre-training. Notably, the policies suffers almost no performance loss on non-truncated RAD tasks even though it was only trained on the truncated distribution. The policy sees the largest dip in satisfaction likelihood on
+
+![](images/f442e62cdd4cb021f9d1448f5559c80322877a87c106178eb8b4293ef8d46429.jpg)  
+Figure 7: Pre-training the cDFA encoder lets policies trained in Letterworld on subclasses to generalize OOD. All policies were trained using frozen GATv2. See Appendix C.5 for training curves.
+
+![](images/ed57017cdb2e071508edd1303d0e39e056202dabf7c16e08f5bafc41135ad2db.jpg)  
+Figure 8: Satisfaction generalization capabilities on LTL tasks (from [38]) of LTL2Action [38] policies vs policies trained on RAD cDFAs. See Appendix C.8 for training curves of policies.
+
+longer compositional reach avoid (cRA) tasks. Interestingly, even very long cRA tasks of up to 10 symbols can be satisfied above  $90\%$  of the time, even though such long tasks put the satisfying state in cDFA past the depth that the message passing in our MPNNs reach. Overall, the performance of the non-pre-trained models (see Appendix C.4) follows a similar (albeit dramatically worse) trend as the pre-trained models. They do see some success in the easier task classes such as reach and parity but perform poorly in more difficult task classes that contain rejecting sink states. Our generalization experiments comparing GATv2 to RGCN show that even though RGCN performs comparably, GATv2 outperforms it in all cases (see Appendix C.6).
+
+Figure 7 shows that RAD pre-training allows policies trained in Letterworld to zero-shot generalize far out of distribution. If you take a RAD pre-trained cDFA encoder and train a policy on some small subclass (cRA.1.1.1.5 and cRAR.1.2.1.2), the policies can still handle much longer tasks within their class and even tasks outside of their class. In the case of cRA.1.1.1.5, the training of the policy module never gets to see a multistage task, only multiple conjunctions, yet it's able to satisfy tasks from the full RAD distribution  $90\%$  of the time.
+
+We also compare against policies trained using LTL syntax embeddings [38]. Figure 21 in Appendix C.8 shows training curves for these policies where pre-training was performed similar to RAD pre-training except only on the specialized class that randomly samples between PO.1.5.1.4 and AV.1.3.1.2 (task classes from [38]). Figure 8 shows how well these policies and our RAD pre-trained policy generalize in the Letterworld to harder version of PO and AV. The results show that our method generalizes well across all tasks. Furthermore, in some cases, it outperforms the LTL policy on the task it is specifically trained on, e.g., even though the LTL policy shown by the green bar is trained on cAV.1.3.1.2, our method outperforms it. Similarly, observe that although our method was not specifically trained on cPO.1.5.1.4 tasks, it achieves  $100\%$  accuracy just like the LTL policy that is specifically trained on this task class. In addition to all of the earlier generalization results, this figure shows that RAD pre-training generalizes to these out of distribution tasks just as well as the policies from [38] even though it is not specifically trained on these tasks.
+
+# 6 Conclusion
+
+We introduced compositional deterministic finite automata (cDFA) as an expressive and robust goal representation for temporal tasks in goal-conditioned reinforcement learning (RL). Addressing the limitations of hierarchical approaches and the challenge of extending goal-conditioned RL to non-Markovian tasks, we proposed using cDFAs to leverage formal semantics, accessibility, and expressivity. By employing graph attention networks (GATv2) to construct embeddings for cDFA tasks and conditioning the RL policy on these representations, our method encourages the policy to take the entire temporal task into account during decision-making. Additionally, we introduced reach-avoid derived (RAD) cDFAs to enable the learning of rich task embeddings and policies that generalize to unseen task classes. Our experiments show that pre-training on RAD cDFAs provides strong zero-shot generalization and robustness. Using cDFAs to encode temporal tasks enhances explainability and enables automated reasoning for interpretable and safe AI systems.
+
+6.1 Limitations. A limitation of this work is the assumption of a labeling function mapping MDP states to the task alphabet. Also, further research is needed to understand how cDFA-encoders learn to represent tasks and how much further their generalization capabilities can be pushed.
+
+# Acknowledgments and Disclosure of Funding
+
+This work is partially supported by DARPA contracts FA8750-18-C-0101 (AA) and FA8750-23-C-0080 (ANSR), by Nissan and Toyota under the iCyPhy Center, and by C3DTI. Niklas Lauffer is supported by an NSF graduate research fellowship.
+
+# References
+
+[1] Derya Aksaray, Austin Jones, Zhaodan Kong, Mac Schwager, and Calin Belta. Q-learning for robust satisfaction of signal temporal logic specifications. In 2016 IEEE 55th Conference on Decision and Control (CDC), pages 6565-6570. IEEE, 2016.  
+[2] Rajeev Alur, Suguman Bansal, Osbert Bastani, and Kishor Jothimurugan. A framework for transforming specifications in reinforcement learning. In *Principles of Systems Design: Essays Dedicated to Thomas A. Henzinger on the Occasion of His 60th Birthday*, pages 604–624. Springer, 2022.  
+[3] Rajeev Alur, Osbert Bastani, Kishor Jothimurugan, Mateo Perez, Fabio Somenzi, and Ashutosh Trivedi. Policy synthesis and reinforcement learning for discounted ltl. In International Conference on Computer Aided Verification, pages 415-435. Springer, 2023.  
+[4] Jacob Andreas, Dan Klein, and Sergey Levine. Modular multitask reinforcement learning with policy sketches. In International conference on machine learning, pages 166-175. PMLR, 2017.  
+[5] Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, OpenAI Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. Advances in neural information processing systems, 30, 2017.  
+[6] Dana Angluin. Learning regular sets from queries and counterexamples. Inf. Comput., 75(2):87-106, 1987.  
+[7] Dzmitry Bahdanau, Felix Hill, Jan Leike, Edward Hughes, Arian Hosseini, Pushmeet Kohli, and Edward Grefenstette. Learning to understand goal specifications by modelling reward. arXiv preprint arXiv:1806.01946, 2018.  
+[8] Alper Kamil Bozkurt, Yu Wang, Michael M Zavlanos, and Miroslav Pajic. Control synthesis from linear temporal logic specifications using model-free reinforcement learning. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 10349-10355. IEEE, 2020.  
+[9] Shaked Brody, Uri Alon, and Eran Yahav. How attentive are graph attention networks? arXiv preprint arXiv:2105.14491, 2021.  
+[10] Mingyu Cai, Shaoping Xiao, Zhijun Li, and Zhen Kan. Optimal probabilistic motion planning with potential infeasible ltl constraints. IEEE transactions on automatic control, 68(1):301-316, 2021.  
+[11] Alberto Camacho, Meghyn Bienvenu, and Sheila A McIlraith. Finite ltl synthesis with environment assumptions and quality measures. In Sixteenth International Conference on Principles of Knowledge Representation and Reasoning, 2018.  
+[12] Alberto Camacho, Rodrigo Toro Icarte, Toryn Q Klassen, Richard Anthony Valenzano, and Sheila A McIlraith. Ltl and beyond: Formal languages for reward function specification in reinforcement learning. In *IJCAI*, volume 19, pages 6065–6073, 2019.  
+[13] Xuchu Ding, Stephen L Smith, Calin Belta, and Daniela Rus. Optimal control of markov decision processes with linear temporal logic constraints. IEEE Transactions on Automatic Control, 59(5):1244-1257, 2014.  
+[14] Jie Fu and Ufuk Topcu. Probably approximately correct mdp learning and control with temporal logic constraints. arXiv preprint arXiv:1404.7073, 2014.
+
+[15] E Mark Gold. Language identification in the limit. Information and control, 10(5):447-474, 1967.  
+[16] Mohammadhosein Hasanbeig, Daniel Kroening, and Alessandro Abate. Deep reinforcement learning with temporal logics. In Formal Modeling and Analysis of Timed Systems: 18th International Conference, FORMATS 2020, Vienna, Austria, September 1–3, 2020, Proceedings 18, pages 1–22. Springer, 2020.  
+[17] Marijn Heule and Simco Verwer. Exact DFA identification using SAT solvers. In ICGI, volume 6339 of Lecture Notes in Computer Science, pages 66-79. Springer, 2010.  
+[18] John Hopcroft. An n log n algorithm for minimizing states in a finite automaton. In Theory of machines and computations, pages 189-196. Elsevier, 1971.  
+[19] John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.  
+[20] Rodrigo Toro Icarte, Toryn Q Klassen, Richard Valenzano, and Sheila A McIlraith. Reward machines: Exploiting reward function structure in reinforcement learning. Journal of Artificial Intelligence Research, 73:173-208, 2022.  
+[21] Yiding Jiang, Shixiang Shane Gu, Kevin P Murphy, and Chelsea Finn. Language as an abstraction for hierarchical deep reinforcement learning. Advances in Neural Information Processing Systems, 32, 2019.  
+[22] Kishor Jothimurugan, Rajeev Alur, and Osbert Bastani. A composable specification language for reinforcement learning tasks. Advances in Neural Information Processing Systems, 32, 2019.  
+[23] Kishor Jothimurugan, Suguman Bansal, Osbert Bastani, and Rajeev Alur. Compositional reinforcement learning from logical specifications. Advances in Neural Information Processing Systems, 34:10026-10039, 2021.  
+[24] Niklas Lauffer, Beyazit Yalcinkaya, Marcell Vazquez-Chanlatte, Ameesh Shah, and Sanjit A Sesha. Learning deterministic finite automata decompositions from examples and demonstrations. In Conference on Formal MMethods in Computer-Aided Design-FMCAD 2022, page 325, 2022.  
+[25] Xiao Li, Cristian-Ioan Vasile, and Calin Belta. Reinforcement learning with temporal logic rewards. In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 3834-3839. IEEE, 2017.  
+[26] Jelena Luketina, Nantas Nardelli, Gregory Farquhar, Jakob Foerster, Jacob Andreas, Edward Grefenstette, Shimon Whiteson, and Tim Rocktäschel. A survey of reinforcement learning informed by natural language. arXiv preprint arXiv:1906.03926, 2019.  
+[27] José Oncina and Pedro Garcia. Inferring regular languages in polynomial updated time. In Pattern recognition and image analysis: selected papers from the IVth Spanish Symposium, pages 49-61. World Scientific, 1992.  
+[28] Rajesh Parekh and Vasant Honavar. Learning DFA from simple examples. Machine Learning, 44:9-35, 2001.  
+[29] Mateo Perez, Fabio Somenzi, and Ashutosh Trivedi. A pac learning algorithm for ltl and omega-regular objectives in mdps. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 21510–21517, 2024.  
+[30] Wenjie Qiu, Wensen Mao, and He Zhu. Instructing goal-conditioned reinforcement learning agents with temporal logic objectives. Advances in Neural Information Processing Systems, 36, 2024.  
+[31] Alex Ray, Joshua Achiam, and Dario Amodei. Benchmarking safe exploration in deep reinforcement learning. arXiv preprint arXiv:1910.01708, 7(1):2, 2019.
+
+[32] Dorsa Sadigh, Eric S Kim, Samuel Coogan, S Shankar Sastry, and Sanjit A Seshia. A learning based approach to control synthesis of markov decision processes for linear temporal logic specifications. In 53rd IEEE Conference on Decision and Control, pages 1091-1096. IEEE, 2014.  
+[33] Tom Schaul, Daniel Horgan, Karol Gregor, and David Silver. Universal value function approximators. In International conference on machine learning, pages 1312-1320. PMLR, 2015.  
+[34] Michael Schlichtkrull, Thomas N Kipf, Peter Bloem, Rianne Van Den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. In The semantic web: 15th international conference, ESWC 2018, Heraklion, Crete, Greece, June 3-7, 2018, proceedings 15, pages 593-607. Springer, 2018.  
+[35] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.  
+[36] Ameesh Shah, Cameron Voloshin, Chenxi Yang, Abhinav Verma, Swarat Chaudhuri, and Sanjit A Seshia. Deep policy optimization with temporal logic constraints. arXiv preprint arXiv:2404.11578, 2024.  
+[37] Sumedh Sontakke, Jesse Zhang, Séb Arnold, Karl Pertsch, Erdem Biryik, Dorsa Sadigh, Chelsea Finn, and Laurent Itti. Roboclip: One demonstration is enough to learn robot policies. Advances in Neural Information Processing Systems, 36, 2024.  
+[38] Pashootan Vaezipoor, Andrew C Li, Rodrigo A Toro Icarte, and Sheila A Mcilraith. Ltl2action: Generalizing ltl instructions for multi-task rl. In International Conference on Machine Learning, pages 10497-10508. PMLR, 2021.  
+[39] Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), 2008.  
+[40] Moshe Y Vardi. From church and prior to psl. In 25 Years of Model Checking: History, Achievements, Perspectives, pages 150-171. Springer, 2008.  
+[41] Marcell Vazquez-Chanlatte, Karim Elmaaroufi, Stefan J Witwicki, and Sanjit A Seshia. L\*lm: Learning automata from examples using natural language oracles. arXiv preprint arXiv:2402.07051, 2024.  
+[42] Marcell Vazquez-Chanlatte, Ameesh Shah, Gil Lederman, and Sanjit A Seshia. Demonstration informed specification search. CoRR, vol. abs/2112.10807, 2021.  
+[43] Marcell Jose Vazquez-Chanlatte. *Specifications from Demonstrations: Learning, Teaching, and Control*. University of California, Berkeley, 2022.  
+[44] Cameron Voloshin, Hoang Le, Swarat Chaudhuri, and Yisong Yue. Policy optimization with linear temporal logic constraints. Advances in Neural Information Processing Systems, 35:17690-17702, 2022.  
+[45] Wojciech Wieczorek. Grammatical Inference. Springer, 2017.  
+[46] Eric M Wolff, Ufuk Topcu, and Richard M Murray. Robust control of uncertain markov decision processes with temporal logic specifications. In 2012 IEEE 51st IEEE Conference on decision and control (CDC), pages 3372-3379. IEEE, 2012.  
+[47] Beyazit Yalcinkaya, Niklas Lauffer, Marcell Vazquez-Chanlatte, and Sanjit Seshia. Automata conditioned reinforcement learning with experience replay. In NeurIPS 2023 Workshop on Goal-Conditioned Reinforcement Learning, 2023.  
+[48] Cambridge Yang, Michael Littman, and Michael Carbin. On the (in) tractability of reinforcement learning for ltl objectives. arXiv preprint arXiv:2111.12679, 2021.
+
+# A Details of cDFA Featurization
+
+To construct the featurization of a cDFA  $\mathcal{C}_t$ , we first build individual graph featurizations for each DFA in the composition and then combine them in a single featurization for  $\mathcal{C}_t$ . For each  $\mathcal{A}_t \in \mathcal{C}_t$ , we construct a directed graph  $\mathcal{G}_{\mathcal{A}_t} = (\mathcal{V}_{\mathcal{A}_t}, \mathcal{E}_{\mathcal{A}_t}, \mathcal{P}_{\mathcal{A}_t})$ , where  $v_i \in \mathcal{V}_{\mathcal{A}_t}$  represents the states of  $\mathcal{A}_t$ ,  $e_{vu} = (v, u) \in \mathcal{E}_{\mathcal{A}_t}$  represents the transitions of  $\mathcal{A}_t$ , and  $\mathcal{P}_{\mathcal{A}_t}: \mathcal{E}_{\mathcal{A}_t} \mapsto 2^{\Sigma_t}$  maps each edge  $e_{vu}$  to a set of symbols in  $\mathcal{A}_t$ 's alphabet, denoting different symbols triggering a transition from  $v$  to  $u$ . Using the graph representation  $\mathcal{G}_{\mathcal{A}_t}$ , we construct the DFA featurization  $\hat{\mathcal{G}}_{\mathcal{A}_t} = (\hat{\mathcal{V}}_{\mathcal{A}_t}, \hat{\mathcal{E}}_{\mathcal{A}_t}, h_{\mathcal{A}_t})$ . The sketch of the iterative construction of  $\hat{\mathcal{G}}_{\mathcal{A}_t}$  is given in the following paragraph.
+
+Initially,  $\hat{\mathcal{G}}_{\mathcal{A}_t}$  has all the nodes of  $\mathcal{G}_{\mathcal{A}_t}$ , and it does not have any edges. For each  $e_{vu} = (v,u)\in \mathcal{E}_{\mathcal{A}_t}$ , add a new node  $e_{vu}$  to  $\hat{\mathcal{V}}_{\mathcal{A}_t}$  and two new edges to  $\hat{\mathcal{E}}_{\mathcal{A}_t}$  - one from  $v$  to the new node  $e_{vu}$  and another one from  $e_{vu}$  to  $u$ . Then, add self-loop edges for each node. Once  $\hat{\mathcal{G}}_{\mathcal{A}_t}$  is constructed this way, we reverse its edges to ensure that message passing transmits information to the initial state of the DFA. To include the details of individual nodes, each  $v\in \hat{\mathcal{V}}_{\mathcal{A}_t}$  is associated with an input node feature  $h_{\mathcal{A}_t}(v)$ . For  $v\in \mathcal{V}_{\mathcal{A}_t}$ ,  $h_{\mathcal{A}_t}(v)$  indicates whether  $v$  is the initial, an accepting, or a rejecting state. For each  $e_{vu}\in \hat{\mathcal{V}}_{\mathcal{A}_t}\setminus \mathcal{V}_{\mathcal{A}_t}$ ,  $h_{\mathcal{A}_t}(e_{vu})$  has one-hot positional encodings of each symbol in  $\mathcal{P}_{\mathcal{A}_t}(e_{vu})$ .
+
+Once all featurizations are constructed for each  $\mathcal{A}_t\in \mathcal{C}_t$ , we construct the composition's featurization  $\hat{\mathcal{G}}_{\mathcal{C}_t} = (\hat{\mathcal{V}}_{\mathcal{C}_t},\hat{\mathcal{E}}_{\mathcal{C}_t},h_{\mathcal{C}_t})$ . It is constructed by taking the union of all  $\hat{\mathcal{G}}_{\mathcal{A}_t}$  for each  $\mathcal{A}_t\in \mathcal{C}_t$ , adding an "AND" node  $v_{\mathrm{AND}}$  to the graph, and including new edges from the nodes corresponding to the initial states of all  $\mathcal{A}_t\in \mathcal{C}_t$  to  $v_{\mathrm{AND}}$ . Notice that taking this union is trivial since all nodes and edges of a DFA in the composition are unique. Through one-hot encoding of a unique index in the feature vector  $h_{\mathcal{C}_t}(v_{\mathrm{AND}})$  of  $v_{\mathrm{AND}}$ , the "AND" node is encoded as a different kind of node that does not share any features with other nodes in the graph, making it distinguished compared to nodes representing DFA states and transitions. Figure 2 shows the featurization of the cDFA in Figure 1.
+
+# B RAD cDFA Sampler Algorithm
+
+Algorithm 1 shows the pseudocode for RAD cDFA sampling.
+
+Algorithm 1 RAD cDFA Sampler  
+Require: Geometric distribution parameters  $p_n$  and  $p_k$  and maximum number of mutations  $m$   
+1:  $n \sim \mathrm{Geometric}(p_n)$   
+2:  $\mathcal{C} = \{\}$   
+3: for  $i \gets 1$  to  $n$  do  
+4:  $k \sim \mathrm{Geometric}(p_k)$   
+5:  $\mathcal{A} \gets \mathrm{Sample}$  a reach-avoid DFA with  $k + 2$  states by sampling a reach and an avoid syn uniformly from the alphabet for each state and adding these random transitions; for other sym add a stuttering transition with probability 0.9, or, make it reach or avoid with equal probab  
+6: for  $i \gets 1$  to  $m$  do  
+7:  $\mathcal{A}' \gets \mathcal{A}$   
+8: Mutate  $\mathcal{A}'$  by sampling a state pair  $(s, s')$  and a symbol  $a$  and adding  $s \xrightarrow{a} s'$   
+9: Make  $\mathcal{A}'$ s accepting state a sink by removing its out transitions and minimize  $\mathcal{A}'$   
+10: if  $\mathcal{A}'$  is not a trivially accepting then  $\mathcal{A} \gets \mathcal{A}'$   
+11:  $\mathcal{C} \gets \mathcal{C} \cup \{\mathcal{A}\}$   
+12: Return  $\mathcal{C}$
+
+In the experiments, we bounded the size of sampled cDFAs using truncated geometric distributions for  $n$  and  $k$ , with upper bounds of 5 and 10, respectively, and  $k$  was fixed per rollout environment. Using multiple environments with different sampler instantiations, combined with mutations applied to the sampled DFAs, allowed policies to encounter a diverse range of DFAs of varying sizes during training.
+
+# C Results
+
+C.1 Pretraining learning curves: GATv2 vs RGCN. Figure 9 presents the learning curves for pre-training of GATv2 and RGCN on RAD cDFAs in the dummy MDP. The figure illustrates that GATv2 converges faster than RGCN, potentially highlighting the benefits of the attention mechanism.
+
+Figure 9: Learning curves for pre-training on RAD cDFAs in the dummy MDP.  
+![](images/fe99813958427ada612ca1ec82e5361d71cc93afedc39d6c91b8597c9da31eb5.jpg)  
+Pretraining
+
+![](images/bcda5f3fccfec4ced141a6bbc35a838a500125f49e8c24a9a8ccbed91a57601f.jpg)
+
+C.2 Generalization of pre-trained cDFA embeddings: GATv2 vs RGCN. Figure 10 presents the generalization experiment results in the dummy MDP. It shows that pre-trained GATv2 consistently outperforms RGCN with almost  $100\%$  accuracy in most cases. It also learns to solve the dummy MDP with less steps compared to RGCN. Overall, we observe that pre-training on RAD cDFAs provides good generalization to other cDFA task classes for both GATv2 and RGCN.
+
+![](images/2faa1e650a671636a98215eb23559f467265bc2f8d321c5aaa2d1aab770b99e2.jpg)  
+Figure 10: Generalization results of GATv2 and RGCN pre-trained on RAD cDFAs, where satisfaction likelihood (left) and step count (right) are shown by the solid lines and by cross-hatching, respectively.
+
+C.3 Embedding space analysis: GATv2 vs RGCN. Figure 11 presents the embedding space analysis results for both GATv2 and RGCN. Results show that RGCN demonstrates competence in effectively separating different classes, albeit with certain limitations. While it succeeds in distinguishing reach from other classes, it struggles to differentiate RA tasks from parity and RAR. Even though parity and RAR cDFAs share structural similarities with RA cDFAs, this lack of separation is concerning as there is a semantic difference between these task classes-RA cDFAs have rejecting states but parity and RAR cDFAs do not. However, it still successfully clusters cDFAs that are 2-conjunction collapsed and 1-step advanced while also isolating accepting ones in the green region shown in Figure 11d, illustrating the robustness provided by pre-training on RAD cDFAs.
+
+Another point to note is the scales of the Euclidean distance heat maps given in Figure 11c and Figure 11f. The distance scale for RGCN is from 0 to 1.5 whereas the scale for GATv2 is from 0 to 3. Moreover, we see darker colors in Figure 11c, suggesting that GATv2 captures semantic nuances by effectively leveraging the embedding space for robust representations of cDFAs. The analysis results suggest that GATv2 learns a richer representation of the cDFA embedding space, likely due to its attention mechanism, which enables it to attend to relevant features and relationships within the data.
+
+![](images/638fdc7a9db29ec092c5b76bb7d557a54fcc49f99008cc8644a17823dc6cf5b8.jpg)
+
+![](images/43c4b1dbd39985a9415894f1b5876525fbf94e2755ad384e3f94e94e92e11cff.jpg)
+
+![](images/476f1bee9fcc855ebd3f66fd784933ede05941f15397f6000ef7297bc0ecd344.jpg)
+
+![](images/c2d47b25755744fbfb917f57a0b2fa49d837ba855bda2b83e005fdbb1f0ea2d6.jpg)
+
+![](images/8a2f7ba443fe07f4ead5b1fe5c6c86bd96f4e1875fbb0a0d59f3bfaf920fdad2.jpg)  
+Figure 11: Visualizations of the embeddings generated by GATv2 and RGCN pre-trained on RAD cD-FAs, showing that the learned embedding space reflects the similarities between different task classes.
+
+![](images/0eac4c211e4fa883100dec90891900ba42799c3ffb647057c1d77ee9896ea62e.jpg)
+
+![](images/bfde919c4de71bc18ab0b82dad0012fb13a42e36a4f9b4676457189d42a52634.jpg)
+
+C.4 Generalization of policies: pre-trained vs not pre-trained. Figure 12 compares the generalization strengths of policies with not-pre-trained, pre-trained-and-frozen, and pre-trained GATv2 cDFA encoders. It shows a similar pattern to the learning curves given in Figure 5. Specifically, we see that the frozen one outperforms others while the pre-trained one performs comparably. However, we see that not-pre-trained one does not come close to the others, indicating that learning embedding spaces through pre-training is essential for good performance and generalization to different task classes. Figure 13 presents the number of steps taken in Letterworld to solve the task for the same experiment. We see a similar trend where without pre-training model needs to take a lot of steps to end the episode (either successfully or unsuccessfully). Both pre-trained models take significantly fewer steps while the frozen one solves the task fastest. Combining both figures, we see that the frozen version generalizes well while also learning to solve tasks faster.
+
+![](images/6e33aa440563e38bcd28450b61129bf3c5d7b041d79b5ed3b824e82f0dac0f69.jpg)  
+Figure 12: Effect of pre-training on satisfaction generalization capabilities in Letterworld.
+
+![](images/707fe2f2223ba6175df2c7b9e77761efa65a2fd606ca372559144d742cc29318.jpg)  
+Figure 13: Effect of pre-training on number of steps generalization capabilities in Letterworld.
+
+C.5 Training curves and steps generalization for other task classes. We first present the training curves for RA.1.1.1.5 and RAR.1.2.1.2 using RAD pre-trained cDFA encoders. Figure 14 shows that policies trained on RAD and RAR.1.2.1.2 converge relatively faster than the one trained on RA.1.1.1.5. Notice that RA.1.1.1.5 samples cDFAs with more than 3 DFAs with high probability (since the number of conjunctions sampled uniformly at random from the given interval) whereas the probability of sampling such big compositions is lower in RAD (as it sampled from a geometric distribution). Thus, the figure indicates that it is relatively harder to learn big conjunctions.
+
+In Figure 7, we shared the satisfaction generalization results for these policies, testing how well these policies trained on specialized task distributions generalize to other task distributions. Here, we provide the number of steps taken to finish the episode during the generalization experiments in Figure 15. Observe that training the policy on RAD cDFAs results in shorter episodes. However, it is still worth noting that other policies perform comparably and provide good generalization on unseen tasks.
+
+![](images/b354a3df2708044907077e7571feb67f99f40fd8b1230fe387f0dbf317005cd5.jpg)  
+Figure 14: Training curves for RA and RAR policies with RAD-pre-trained GATv2 in Letterworld.
+
+![](images/553bd0d575ad70d22e027b21fb9fc43229c9db75ac3aa99c4f1bafee02bbbdde.jpg)  
+Figure 15: Number of steps generalization comparison between policies trained on RAD, RA.1.1.1.5 and RAR.1.2.1.2.
+
+C.6 Generalization of pre-trained policies: GATv2 vs RGCN. Figure 16 presents the results. It compares policies with frozen and pre-trained GNNs (both GATv2 and RGCN). In line with the training curves, we can see that GATv2 outperforms RGCN across the board, with the most significant differences on harder task classes with many symbols or many conjunctions. Figure 17 shows the number of steps taken in the same experiments, indicating that GATv2 also learns to complete the tasks with fewer steps compared to RGCN. The results highlight the superior performance of GATv2.
+
+![](images/f693a9bac30a2f173efcceaa79b059f64380bb9cb3980a4f897f78fc9e48f542.jpg)  
+Figure 16: Satisfaction generalization capabilities of policies trained on RAD cDFAs with frozen and pre-trained cDFA encoders in Letterworld, comparing GATv2 and RGCN.
+
+![](images/47de77e2f324a91d92dbba444220e10754327279fd050d7c8dbd334d42e13d8a.jpg)  
+Figure 17: Number of steps generalization capabilities of policies trained on RAD cDFAs with frozen and pre-trained cDFA encoders in Letterworld, comparing GATv2 and RGCN.
+
+C.7 Generalization of pre-trained policies in continuous domains. Figure 18 shows the generalization results for a policy (with a frozen and pre-trained GATv2) trained on RAD DFAs in Zones. The results show that our method can generalize to cDFAs with up to 10 DFAs in the composition as long as each DFA's task length is relatively short. We see that it does not perform as well in tasks with length 5 and more. This is probably due to the fact that control and navigation are much harder in continuous domains compared to discrete ones. Therefore, the low accuracies we are seeing for tasks with more length might be due to timeouts. It is worth noting that the policies can generalize up to 10 conjunctions in a cDFA, which is completely out of distribution for the policy. Overall, the results show that training on RAD DFAs provide zero-shot generalization in continuous domains as well.
+
+![](images/2825563b871ef7f04dc03ae79b4a92d093eba5790dc292aefe3e391dd2641b60.jpg)  
+Figure 18: Satisfaction generalization results of policies trained on RAD cDFAs with frozen and pre-trained GATv2 cDFA encoders in the Zones environment (continuous domain).
+
+Figure 19 shows the number of steps taken to complete the episodes in the same experiment. We see that when the policy satisfies a task class with a high probability, it can also complete it with fewer steps. On the other hand, in almost all cases where it could not satisfy the task with high probability, it also took more steps in those episodes, suggesting that the policy might have timed out.
+
+![](images/b40f150b3d76da77b12fe2695765b64b3be9d5cfe32c547f9674b78f8c3e9292.jpg)  
+Figure 19: Number of steps generalization results of policies trained on RAD cDFAs with frozen and pre-trained GATv2 cDFA encoders in the Zones environment (continuous domain).
+
+C.8 Generalization of pre-trained policies: RAD cDFAs vs LTL2Action. To compare our approach to the closest work in the literature, we design an experiment with LTL2Action [38]. Recall that one of our main contributions is our RAD pre-training procedure that provides generalization across different tasks. Defining such a general LTL task class is not a trivial problem and is a contribution on this own. Moreover, the intuitions used to develop the RAD cDFA class are not applicable to LTL as it is not as easy to generate interesting and satisfiable LTL formulas. Therefore, for LTL2Action, we define a joint task distribution consisting of partially ordered and avoidance tasks, which are task classes defined in [38]. To sample LTL tasks, we flip a coin and pick a samplers.
+
+![](images/e01a2dc6f786124ae6632783e2d40a9dc51cfbac78a8608cce32296350412965.jpg)  
+Figure 20: Learning curve for pre-training LTL policies on the joint distribution of PO and AV.
+
+Figure 20 present LTL2Action's learning curve for the pre-training of an RGCN in the joint LTL task distribution. As the figure shows, the model can easily learn to distinguish these LTL tasks.
+
+Figure 21: Learning curves for training LTL policies on PO and AV LTL tasks.  
+![](images/863ff687bd9d45163eaf6da941e854def21b2eadef5942f77af78b7a99e87263.jpg)  
+No pretraining Pretraining Pretraining (frozen)
+
+![](images/9813db8d5b208577d0c875042b947d8e19632a16389559d77e35c888c4125727.jpg)
+
+We then take the pre-trained RGCN and use it to train a policy that is exclusively trained on one of these task classes, i.e., partially ordered or avoidance LTL tasks. Figure 21 presents the learning curves for this training. The figure shows that if we let the RGCN get gradient updates during training, then pre-training does not help as much as freezing the network. We saw a similar behavior for RGCN in Figure 5, which further justifies our choice of using a network with an attention mechanism. Furthermore, in [38], authors show that pre-training on specific task classes helps training even when we let the RGCN continue getting gradient updates. Combining these results from [38] with what we are seeing on Figure 21 suggests that when pre-trained on rich classes with multiple distinct task patterns, RGCN need to forget about the other task classes it learned during pre-training and has to focus its capacity on the specific task class it is being trained on. We do not see such a gap in the learning curves when we let GATv2 get gradient updates, see Figure 5, suggesting that GATv2 does not suffer from the same issue as RGCN, and it learns more robust cDFA embeddings.
+
+![](images/dc2bb9fd720bd3c3d5bd9effdb77af62ce01bfb42e7e92ec8daf80716939d979.jpg)  
+Figure 22: Number of steps generalization capabilities of LTL policies vs RAD-cDFAs policies.
+
+Figure 22 presents the number of steps taken for the generalization experiments, showing that in all cases our policy trained on RAD cDFAs perform comparably to the specialized LTL policies.
+
+# D Hyperparameters and Compute Usage
+
+Both for the RGCN and GATv2 cDFA encoders, we use a hidden dimension size of 32 and perform 8 message passing steps. Also, for GATv2, we use 4 heads for the multi-head attention.
+
+For both Letterworld and Zones, we implemented the same actor and critic architectures. The actor network comprises three fully connected layers, each with 64 units and ReLU activations, while the critic network has three fully connected layers with 64, 64, and 1 units, using a Tanh activation. For pretraining, we simplified the actor and critic to single-layer models without hidden units, allowing the cDFA encoder to learn a rich embedding space. For environments with discrete actions, the actor's output was passed through a log softmax and a logit layer. In continuous action settings, we used a Gaussian distribution, parameterizing the mean and standard deviation with two separate linear layers from the actor's output. To construct observation embeddings, for Letterworld, we employed a 3-layer convolutional network with 16, 32, and 64 channels,  $2 \times 2$  kernels, and a stride of 1. In Zones, a 2-layer fully connected network with 128 units per layer and ReLU activations was used.
+
+Table 1 shows the hyperparameters used for every training run in the experiments section. Each seed in the experiments section was run as an individual Slurm job with access to 4 cores of an AMD EPYC 7763 running at  $2.45\mathrm{GHz}$  and access to at most  $20\mathrm{gb}$  of memory. RAD pre-training experiments took approximately 14 hours each for 10 million timesteps, policy training in Letterworld took approximately 55 hours (50 hours for the frozen GNN version) for 20 million timesteps, and policy training in Zones took approximately 120 hours (70 hours for the frozen GNN version).
+
+<table><tr><td>Hyperparameter</td><td>Pretraining Env.</td><td>Letterworld Env.</td><td>Zones Env.</td></tr><tr><td>Learning rate</td><td>0.001</td><td>0.0003</td><td>0.0003</td></tr><tr><td>Batch size</td><td>1024</td><td>32</td><td>2048</td></tr><tr><td>Number of epochs</td><td>2</td><td>4</td><td>10</td></tr><tr><td>Discount</td><td>0.9</td><td>0.94</td><td>0.998</td></tr><tr><td>Entropy Coefficient</td><td>0.01</td><td>0.01</td><td>0.003</td></tr><tr><td>GAE(λ)</td><td>0.5</td><td>0.95</td><td>0.95</td></tr><tr><td>Clipping ε</td><td>0.1</td><td>0.2</td><td>0.2</td></tr><tr><td>RMSprop α</td><td>0.99</td><td>0.99</td><td>0.99</td></tr><tr><td>Max. grad. norm.</td><td>0.5</td><td>0.5</td><td>0.5</td></tr><tr><td>Value loss coef.</td><td>0.5</td><td>0.5</td><td>0.5</td></tr></table>
+
+Table 1: PPO pre-training and policy training hyperparameters.
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: In the introduction, we clearly list our contributions, and in the experiments section, we list the research questions we explore. We then relate these research questions and their answers to the listed contributions while discussing the experiment results.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: Throughout the paper and explicitly in the conclusion, we clearly state the limitations of the work.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory Assumptions and Proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+# Answer: [NA]
+
+Justification: The paper does not include any theorems or proofs. But, we still give a rigorous formalism mapping cDFA-conditioned RL to the well-known goal-conditioned RL problem.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental Result Reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: We provide all the information needed to reproduce the main experimental results. In the corresponding section, we define all the RL environments, all the task classes, the pretraining procedure, the training procedure, and the algorithms used in the experiments. We also provide all the hyperparameter values in the appendix.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.  
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.  
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.  
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example  
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
+
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+Answer: [Yes]
+
+Justification: In a footnote on the first page, we include a link to the webpage of the project. This page includes all data and code with instructions to reproduce the experimental results.
+
+# Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental Setting/Details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: We provide all the training and test details in the main body of the paper as well as in the supplementary material included in the appendix.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment Statistical Significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [Yes]
+
+Justification: All plots in the paper report error bars whenever applicable. We also provide other appropriate information (e.g., number of seeds, sample size, etc.) about the statistical significance of the reported experimental results.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).  
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).  
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments Compute Resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: All the details regarding computer resources are given in the appendix.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code Of Ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: We confirm that the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics.
+
+Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader Impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+# Answer: [Yes]
+
+Justification: We discuss the societal impacts of our work in the context of explainable and interpretable AI systems.
+
+# Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.  
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.  
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+# Answer: [NA]
+
+Justification: The paper poses no such risks.
+
+# Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+# Answer: [Yes]
+
+Justification: We clearly credit and cite all the original papers that produced the assets we used as baseline, benchmark, etc.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.
+
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URL.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.  
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.  
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New Assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [Yes]
+
+Justification: The RAD DFAs can be considered a new asset as it is a sampling distribution over DFAs. Its complete definition is given in both the main body and the appendix.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and Research with Human Subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: The paper involves neither crowdsourcing nor research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The paper involves neither crowdsourcing nor research with human subjects.
+
+# Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.  
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

2024/Compositional Automata Embeddings for Goal-Conditioned Reinforcement Learning/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2a64cd3206b3d8fa542ffdf29e9c85e27afe306f3af4542544ffcceb61daa87d
+size 1011212

2024/Compositional Generalization Across Distributional Shifts with Sparse Tree Operations/9c3a27e6-c5e2-4c70-8fb6-7852c705e3bd_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:f25f06ae8a8a82ae75e7d50a492e1f2a53dcca297ae5fa3ccd9775684fd06ea5
+size 1265458

2024/Compositional Generalization Across Distributional Shifts with Sparse Tree Operations/full.md

@@ -0,0 +1,673 @@
+# Compositional Generalization Across Distributional Shifts with Sparse Tree Operations
+
+Paul Soulos*
+
+Johns Hopkins University psoulos1@jh.edu
+
+Henry Conklin*
+
+University of Edinburgh
+
+Mattia Opper*
+
+University of Edinburgh
+
+Paul Smolensky
+
+Johns Hopkins University and Microsoft Research
+
+Jianfeng Gao
+
+Microsoft Research
+
+Roland Fernandez
+
+Microsoft Research
+
+# Abstract
+
+Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional generalization is hybrid neurosymbolic techniques. However, these techniques run into the core issues that plague symbolic approaches to AI: scalability and flexibility. The reason for this failure is that at their core, hybrid neurosymbolic models perform symbolic computation and relegate the scalable and flexible neural computation to parameterizing a symbolic system. We investigate a unified neurosymbolic system where transformations in the network can be interpreted simultaneously as both symbolic and neural computation. We extend a unified neurosymbolic architecture called the Differentiable Tree Machine in two central ways. First, we significantly increase the model's efficiency through the use of sparse vector representations of symbolic structures. Second, we enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems. The improved model retains its prior generalization capabilities and, since there is a fully neural path through the network, avoids the pitfalls of other neurosymbolic techniques that elevate symbolic computation over neural computation.
+
+# 1 Introduction
+
+Deep learning models achieve remarkable performance across a broad range of natural language tasks [71], despite having difficulty generalizing outside of their training data, struggling with new words [36], known words in new contexts [29], and novel syntactic structures, like longer sequences with greater recursive depth [30, 39]. Increasingly this problem is addressed through data augmentation, which tries to make it less likely a model will encounter something unlike what it sees during training — reducing the degree by which it has to generalize [1, 15, 26]. However, even models trained on vast quantities of data struggle when evaluated on examples unlike those seen during training [32].
+
+![](images/eb81395d66f6d5d9fb40292a705b59245b75d840cd8388cb090a8520fe01274d.jpg)  
+Figure 1: Generalization ability of our approach (sDTM) compared with baselines across various out-of-distribution shifts, averaged over different datasets. See §5.
+
+This stands in contrast to how humans process language, which enables robust generalization [51]. By breaking novel sentences into known parts, we can readily interpret phrases and constructions that we have never encountered before (e.g. 'At the airport I smiled myself an upgrade', [22]). Why do models trained on orders of magnitude more language data than a human hears in 200 lifetimes [25] still fail to acquire some of language's most essential properties?
+
+Central to language's generalizability is compositional structure [49] where contentful units, like words, fit together in a structure, like a syntactic tree. Many classical approaches in NLP and Machine Learning attempt to induce a grammar from data in the hope of leveraging the same kinds of generalization seen in natural language [e.g. 34, 33, 68]. However, structured representations are not first-order primitives in most neural networks [44, 63]. Despite theoretical appeal, the strictures of purely discrete symbolic approaches have made them difficult to apply to the breadth of tasks and domains where deep learning models have proven successful [18]. In contrast, purely connectionist models — like Transformers [71] — struggle with the kinds of sample efficiency and robust generalization ubiquitous to human learning.
+
+Neurosymbolic methods attempt to integrate neural and symbolic techniques to arrive at a system that is both compositional and flexible [4, 19, 20, 63]. While some neurosymbolic architectures achieve impressive compositional generalization, they are often brittle due to the symbolic core of their computation [58]. These methods are hybrid neurosymbolic systems, where the primary computation is symbolic, and the neural network serves to parameterize the symbolic space. We take a different approach, one where symbolic operations happen in vector space. In our system, neural and symbolic computations are unified into a single space; we multiply and add vector-embedded symbolic structures instead of multiplying and adding individual neurons.
+
+We introduce a new technique for representing trees in vector space called Sparse Coordinate Trees (SCT). SCT allows us to perform structural operations: transformations which change the structure of an object without changing the content. This is a crucial aspect of compositionality, where the structure and content can be transformed independently. We extend the Differentiable Tree Machine (DTM), a system which operates over binary trees in vector space, into the Sparse Differentiable Tree Machine (sDTM) to improve performance and applicability to a larger variety of tasks<sup>2</sup>. While DTM processes vector-embedded binary trees as the primitive unit of computation, the order of operations and argument selection is governed by a Transformer. We present results showing that this unified approach retains many of the desirable properties of more brittle symbolic models with regards to generalization, while remaining flexible enough to work across a far wider set of tasks. While fully neural architectures or hybrid neurosymbolic techniques excel at certain types of generalization, we find that DTM, with its unified approach, excels across the widest array of shifts.
+
+The main contributions from this paper are:
+
+- Sparse Coordinate Trees (SCT), a method for representing binary trees in vector space as sparse tensors. (§3.1)  
+- Bit-Shift Operating — systematic and parallelized tree operations for SCT. (§3.2)  
+- The introduction of Sparse Differentiable Tree Machine (sDTM), architectural improvements to the DTM to leverage SCT and drastically reduce parameter and memory usage. (\$4)  
+- Techniques to apply DTM to seq2seq tasks by converting sequences into trees. (§4.5)  
+- Empirical comparisons between sDTM and various baselines showing sDTM's strong generalization across a wide variety of tasks. (§5)
+
+# 2 Related Work
+
+Work leveraging the generalizability of tree structures has a long history across Computer Science, Linguistics, and Cognitive Science [9, 45, 57, 64, 68]. Much of classical NLP aims to extract structured representations from text like constituency or dependency parses [for overview: 13, 42]. More recent work has shown the representations learned by sequence-to-sequence models without structural supervision can recover constituency, dependency, and part of speech information from latent representations in machine translation and language models [3, 6]. While those analyses show
+
+![](images/0c54f7ff7666a3036efb993369fc87759ee203551857fdcf2e180362960e41d0.jpg)  
+Figure 2: An example representation using Sparse Coordinate Trees (SCT). The values are N-dimensional vectors, and the tree positional indices are integer representations of positions in the tree. The absent child nodes of "The" (indices 4 and 6) are skipped with SCT.
+
+![](images/a742b9b7b3f236e06e57f7b5c91e17f28d6b9930b21c9a66bc4851b69c145e12.jpg)
+
+structural information is encoded, they stop short of showing that the representations themselves are tree-structured. Analyses inspired by Tensor Product Representations [46, 66] and chart parsing [48] give an account of how representations become somewhat tree-structured over the course of training.
+
+Despite the apparent emergence of semi-structured representations in Transformers and LSTMs, these architectures still appear to struggle with the kinds of structural generalization that come easily to humans [36, 31, 29]. A variety of approaches try to tackle this problem through meta-learning [37, 11], data augmentation [1], or decomposing the task into separate parts [56, 41]. The Relative-Universal Transformer [12] combines relative positional embeddings with a recurrent component, in an effort to emphasize local structures while allowing for unbounded computation.
+
+Explicitly tree structured network architectures have been introduced for RNNs [65], LSTMs [70, 16], and Transformers [72, 61]. However, these variants often do not outperform their unstructured counterpart on out-of-distribution challenges [67]. This may be because generalization requires both structured representations and operations that respect that structure. A separate line of work considers neural architectures that are used to parameterize components of a symbolic system [33, 8] or fuzzy/probabilistic logic [75, 2, 73, 14]. Similar to how vectors are embedded in trees in our work, some work embeds vectors within logical systems [54, 43]. Logic approaches to structure learning are also an active area of research [47, 59]. Other approaches leverage explicit stack operations [17, 24, 27, 76]. NQG from Shaw et al. [58] combines the outputs from neural and symbolic models by inducing a grammar, but deferring to T5 [53] when that grammar fails. However the grammar's induction method has polynomial complexity with both dataset size and sequence length, which limits its application to larger tasks.
+
+Vector Symbolic Architectures (VSAs) implement symbolic algorithms while leveraging high dimensional spaces [52, 21, 28, 35]. VSAs are similar to uniform neurosymbolic approaches, although VSAs commonly lack a learning component. Our work extends that of Soulos et al. [67] which can be viewed as integrating Deep Learning and VSAs. They introduce the Differentiable Tree Machine for Tree-to-Tree transduction. Here we instantiate a sparse Sequence-to-Sequence version with far fewer parameters and improved memory efficiency.
+
+# 3 Differentiable Tree Operations Over Sparse Coordinate Trees
+
+Representing trees in vector space enables us to perform differentiable structural operations on them. Soulos et al. [67] used Tensor Product Representations (TPRs) [64] for this purpose. TPRs use the tensor (or outer) product to represent trees in vector space (§A.1). Use of an outer product leads to a representation dimensionality that is multiplicative with both the embedding dimensionality and the number of possible tree nodes. Additionally, the number of nodes is itself an exponential function of the supported depth. This makes TPRs difficult to use in practice, given available memory is quickly exceeded as tree depth increases.
+
+In this section, we introduce Sparse Coordinate Trees (SCT), a new schema for representing trees in vector space. We then define a library of parallelized tree operations and how to perform these operations on SCT.
+
+![](images/7961d51c0417aad12e94cc8fabbb73c67e369c49d541ced296187e3049393e7a.jpg)  
+Figure 3: Left: Performing left (orange) and right (blue). Right: visualizing the left transformation which results in DP being placed at the root. Tree positional indices of 0 and their corresponding values are discarded.
+
+![](images/3c401c3c260ff71f6973b4ce8b0f10b3e97e5c6cb62d5a2e1e6c845acec64a87.jpg)
+
+# 3.1 Sparse Coordinate Trees (SCT)
+
+Like TPRs, we want an encoding for trees that factorizes the representation into subspaces for structure and content respectively. This approach to representational spaces differs from models like an RNN and Transformer, which represent structure and content jointly in an unfactorized manner. By separating the structure and content subspaces a priori, we can operate over these two spaces independently. This decision is motivated by the fact that distinct treatment of these spaces is an essential aspect of compositionality.
+
+We derive our tree representation scheme from the sparse coordinate list (COO) format. COO stores tensor data in tuples of (indices [integers], values [any format], size [integers]). The indices are N-dimensional to simulate a tensor of arbitrary shape (e.g. including dimensions such as batch or length). When an index is not indicated in indices, it is assumed that the corresponding value is 0.
+
+We give structural meaning to COO representations by defining one dimension of indices as the tree position occupied by a value vector. Our tree addressing scheme is based on Gorn addresses [23]: to get the tree position from an index, convert the index to binary and read from right to left. A left-branch is indicated by a 0 and a right branch by a 1. To distinguish between leading 0s and left-branches (e.g. 010 vs 10), we start our addressing scheme at 1 instead of 0. This indicates that all 0s to the left of the most-significant 1 are unfilled and not left-branches. Figure 2 shows an example encoding of a tree with this approach. SCT can be viewed as a TPR with certain constraints, and Section A.1 defines this equivalence and formally describes the memory savings.
+
+Section 5.2 discusses the performance, memory, and parameter comparison between DTM models which use standard TPRs and SCT.
+
+# 3.2 Differentiable Tree Operations
+
+To operate on the trees defined in the previous section, we need a set of functions. We use a small library of only three: left-child (left), right-child (right), and construct (cons) a new tree from a left and right subtree.<sup>3</sup> Although these three functions are simple, along with the control operations of conditional branching and equality-checking, these five functions are Turing complete [45].
+
+In addition to saving memory, SCT also provides a more efficient method for performing differentiable tree operations. The operations defined in Soulos et al. [67] require precomputing, storing, and applying linear transformations for left, right, and cons. Since our values and tree positional indices are kept separate, we can compute the results of left, right, and cons dramatically more efficiently using indexing, bit-shifts, and addition.
+
+Figure 3 shows how we can perform left directly on SCT. left is performed by indexing the even indices (i.e. those with a 0 in the least significant bit, which targets all of the nodes left of the root) and their corresponding values, then performing a right bit-shift on the indices. right is symmetrical, except that we index for the odd positional indices and ignore position 1 in order to remove the previous root node. cons is performed by left bit-shifting the positional indices from the left- and
+
+right-subtree arguments, then adding 1 to the newly shifted indices for the right argument. A new value  $s$  can be provided for the root node.
+
+Our network also needs to learn a program over multiple operations differentiably. This involves the aforementioned structured operations, as well as differentiable selection of which operation to perform and on which trees. We take weighted sums over the three operations left, right, and cons, as well as over potential trees. Specific details are discussed in the next section. The result of our weighted sum is coalesced, which removes duplicate positional indices by summing together all of the values that share a specific index. Formally, define the trees over which to perform left  $T_{L}$ , right  $T_{R}$ , and cons  $T_{CL}$  &  $T_{CR}$ ;  $\vec{T} = [T_{L}; T_{R}; T_{CL}; T_{CR}]$ . We also take a new value  $s \in \mathbb{R}^{d}$  to be inserted  $(\otimes)$  at the new root node of the cons operation, and a vector of operation weights  $\vec{w} = (w_{L}, w_{R}, w_{C})$  which sum to 1.
+
+$$
+O (\vec {w}, \vec {T}, s) = w _ {L} \operatorname {l e f t} \left(T _ {L}\right) + w _ {R} \operatorname {r i g h t} \left(T _ {R}\right) + w _ {C} \left(\operatorname {c o n s} \left(T _ {C L}, T _ {C R}\right) + s \otimes r _ {1}\right) \tag {1}
+$$
+
+# 4 The Sparse Differentiable Tree Machine (sDTM)
+
+Our work extends the Differentiable Tree Machine (DTM) introduced in Soulos et al. [67] with the Sparse Differentiable Tree Machine (sDTM). While similar to the original at a computational level, sDTM represents a different implementation of these concepts that make it dramatically more parameter and memory efficient. We also introduce techniques to apply sDTM to tasks with sequence input and output (seq2seq).
+
+# 4.1 Overview
+
+sDTM uses our Sparse Coordinate Trees schema across its components. Like the original DTM, our model is comprised of an agent, interpreter, and memory (illustrated in Figure 4). The Interpreter performs Equation 1 by applying the bit-shifting tree operations from Section 3.2 and weighting the result. The output from the interpreter is written to the next available memory slot, and the last memory slot is taken as the output.
+
+The Agent is a Transformer encoder that takes an encoding of the memory as input and produces the inputs for Equation 1:  $\vec{w}$ ,  $\vec{T}$ , and  $s$ . Two special tokens,  $\langle \mathrm{OP} \rangle$  and  $\langle \mathrm{ROOT} \rangle$ , are fed into the Agent
+
+![](images/a930b26baee36fa00b7b6878215afb8b69e1a4aff813d32b89a0919bdfb0a009.jpg)  
+Figure 4: A schematic of how the three core components of the DTM (agent, interpreter, and memory) relate to each other. Adapted from Soulos et al. [67].
+
+to represent  $\vec{w}$  and  $s$ . Each time a tree is written to memory, a fixed-dimensional encoding of that tree is produced and fed as a new token to the agent (§4.2). The agent soft-selects tree arguments for the interpreter,  $\vec{T}$ , by performing a weighted sum over the trees in memory. Figure 6 in the Appendix contains a detailed diagram showing the flow of information for one layer of sDTM.
+
+The agent which implicitly parameterizes the conditional branching and control flow of the program is modeled by a Transformer, and it is possible for sDTM to face some of the generalization pitfalls that plague Transformers. The design of sDTM encourages compositional generalization through differentiable programs, but it does not strictly enforce the constraints of classical symbolic programs. As the results in Section 5 show, sDTM can learn generalizable solutions to some tasks despite the presence of a Transformer, but on some other tasks the issues with generalization are still present.
+
+# 4.2 Pooling by attention
+
+Each tree in memory needs to have a fixed-dimensional encoding to feed into the agent regardless of how many nodes are filled. Commonly this is done via pooling, like taking the means of the elements in the tree, or a linear transformation in the case of the original DTM. Instead, we use Pooling by Multi-headed Attention (PMA) [38], which performs a weighted sum over the elements, where the weight is derived based on query-key attention.
+
+Attention is permutation invariant to the ordering of key and value vectors, but it is important that our pooling considers tree position information. To enforce this, we convert the position indices to their binary vector representation  $\vec{b}$ . This leads to an asymmetrical vector with only positive values, so instead we represent left branches as  $-1$  and keep right branches as  $+1$ . For example, position  $5 \rightarrow [0, 0, 0, 0, 0, 1, 0, 1] \rightarrow [0, 0, 0, 0, 0, 1, -1, 1]$ . The input to our pooling function is the concatenation of this positional encoding  $\vec{b}$  with the token embedding  $\vec{x}$  at that position:  $[\vec{x}; \vec{b}]$ . This method for integrating token and node position is similar to tree positional encoding from Shiv and Quirk [60], except that we use concatenation and a linear transformation to mix the content and position information instead of addition.
+
+Unlike standard self attention, we use a separate learnable parameter for our query vector  $\vec{q} \in \mathbb{R}^{\mathrm{num\_heads} \times \mathrm{key\_dim}}$ . We pass  $[\vec{x}; \vec{b}]$  through linear transformations to generate keys  $\vec{k} \in \mathbb{R}^{\mathrm{num\_heads} \times \mathrm{key\_dim}}$  and values  $\vec{v} \in \mathbb{R}^{\mathrm{num\_heads} \times \mathrm{value\_dim}}$ . The result of this computation is always  $z \in \mathbb{R}^{\mathrm{num\_heads} \times \mathrm{value\_dim}}$  given that  $\vec{q}$  is fixed and does not depend on the input. The rest of the computation is identical to a Transformer with pre-layer normalization [74].
+
+# 4.3 Tree Pruning
+
+While Sparse Coordinate Trees mean that trees with fewer filled nodes take up less memory, the way our model blends operations results in trees becoming dense. The interpreter returns a blend of all three operations at each step, including the cons operation which increases the size of the representation by combining two trees. In practice even as the entropy of the blending distribution drops, the probability of any operation never becomes fully 0. This means that over many steps, trees start to become dense due to repeated use of cons. In order to keep our trees sparse, we use pruning: only keeping the top- $k$  nodes as measured by magnitude.  $k$  is a hyper-parameter that can be set along with the batch size depending on available memory.
+
+# 4.4 Lexical Regularization
+
+To aid lexical generalization, we add noise to our token embeddings. Before feeding an embedded batch into the model, we sample from a multi-variate standard normal for each position in each tree, adding the noise to the embeddings as a form of regularization [5]. Ablation results showing the importance of this regularization are available in Appendix A.3.
+
+# 4.5 Handling Sequential Inputs and Outputs
+
+seq2tree The original DTM can only be applied to tasks where a tree structure is known for both inputs and outputs. Here we provide an extension to allow DTM to process sequence inputs. To do this we treat each input token as a tree with only the root node occupied by the token embedding. We then initialize the tree memory with  $N$  trees, one for each token in the input sequence. Figure 5 left depicts the initial memory state for a sequence. The agent's attention mechanism is permutation-invariant, so in order to distinguish between two sequences which contain the same tokens but in different orders, we apply random sinusoidal positional encodings to the first  $N$  tokens passed to the agent [40, 55]. Random positional encodings sample a set of increasing integers from left-to-right instead of assigning a fixed position to each token. The purpose of left and right is to extract subtrees. Since in our seq2tree setting the input sequence is processed in a completely bottom-up manner, we restrict the agent and interpreter to only have a single operation: cons. Use of a single operation to construct new trees from subtrees aligns the DTM theoretically with the Minimalist Program [10], which addresses natural language's compositionality in terms of a single operation: merge.
+
+seq2seq To handle sequence inputs and outputs we convert the output sequence to a tree. One method to convert the output sequence into a tree is to use a parser. Alternatively, when a parser is not available, we can embed a sequence as the left-aligned leaves at uniform depth (LAUD). Figure 5 right shows how an output sequence can be embedded using LAUD. Since all of the non-terminal nodes are the same, we can hardcode the root argument to cons. We insert a special token <EOB> to signify the end of a branch, similar to an <EOS> token.
+
+![](images/d3c6534b67f68e05e53b4de42f9eed0f341e13b5ef3288c2a3542a61323c9730.jpg)  
+Figure 5: Left: The memory state is initialized as a sequence of trees where only the root node contains a token. Right: An output sequence is embedded in a tree using the left-aligned uniform-depth (LAUD) scheme. <NT> and <EOB> are special tokens not in the original output sequence.
+
+![](images/166dd2576e484e3fac9161bdf1ff7c8c1542034d103d8646248fcc7c3e49b645.jpg)
+
+# 5 Results
+
+# 5.1Baselines
+
+We consider models that are trained from scratch on the datasets they're evaluated on; while the compositional capabilities of large pre-trained models are under active debate [32], we are interested in the compositional abilities of the underlying architecture — rather than those that may result from a pre-training objective. We compare sDTM to two fully neural models, a standard Transformer [71] as well as a relative universal Transformer (RU-Transformer) which was previously shown to improve systematic generalization on a variety of tasks [12]. We also compare our model to a hybrid neurosymbolic system, NQG [58, 69], a model which uses a neural network to learn a quasi-synchronous context-free grammar [62]. NQG was introduced alongside NQG-T5, which is a modular system that uses NQG when the grammar produces an answer and falls back to a fine-tuned large language model T5 [53]. As mentioned at the beginning of this section, we only compare to NQG in this paper since we want to evaluate models that have not undergone significant pre-training. Details related to data preprocessing ( $\S$ A.4), model training ( $\S$ A.6,  $\S$ A.8), compute resources ( $\S$ A.9), and dataset details ( $\S$ A.10) are available in the Appendix. For all datasets, the reported results are the best exact match accuracies on the test set over five random seeds. Additional data on means and standard deviations across the five runs are shown in Section A.7.
+
+For each task, we test whether models generalize to samples drawn from various data distributions. Independent and identically distributed (IID) samples are drawn from a distribution shared with training data. We evaluate several out-of-distribution (OOD) shifts. One-shot lexical samples, while drawn from the same distribution as the training data, contain a word that was only seen in a single training sample. Similarly, Zero-shot lexical samples are those where the model is not exposed to a word at all during training. Structural/length generalization tests whether models can generalize to longer sequences (length) or nodes not encountered during training (structural). Template generalization withstands an abstract n-gram sequence during training, and then each test sample fits the template. Finally, maximum compound divergence (MCD) generates train and test sets with identical uni-gram distributions but maximally divergent n-grams frequencies [29]. Although models are often tested on a single type of generalization, we believe evaluating a model across a broad array of distributional shifts is essential for characterizing the robustness of its generalization performance.
+
+# 5.2 Performance Regression (Active  $\leftrightarrow$  Logical)
+
+Active  $\leftrightarrow$  Logical is a tree2tree task containing input and output trees in active voice and logical forms [67]. Transforming a tree in active voice to its logical form simulates semantic parsing, and transforming a logical form tree to active voice simulates natural language generation. For this dataset, there are three test sets: IID, 0-shot lexical, and structural. In addition to the baselines listed in the previous section, we also compare our modified sDTM to the original DTM. This enables us to confirm that our proposed changes to decrease parameter count and memory usage while increasing inference speed does not lead to a performance regression. The results are show in Table 1.
+
+Table 1: Active  $\leftrightarrow$  Logical accuracy. Results are the best performance over five runs. The test sets are divided into IID, and OOD sets 0-shot lexical and structural. Parameter and memory usage is shown for the original DTM with TPRs and our proposed sparse DTM with and without pruning. Our modifications reduce the parameter count by almost two orders of magnitude. *NQG was trained on a seq2seq version without parentheses because it was not able to learn the tree2tree training set.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Split</td><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2"></td></tr><tr><td>IID</td><td>0-Shot Lexical</td><td>Structural</td></tr><tr><td>Transformer</td><td>1.0</td><td>0.0</td><td>0.0</td><td></td><td></td><td></td></tr><tr><td>RU-Transformer</td><td>1.0</td><td>0.0</td><td>.12</td><td></td><td></td><td></td></tr><tr><td>NQG*</td><td>.45</td><td>0.0</td><td>0.0</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>Parameters</td><td>Memory (GB)</td><td>Relative Speed</td></tr><tr><td>Original DTM</td><td>1.0</td><td>1.0</td><td>1.0</td><td>72M</td><td>12.3</td><td>34</td></tr><tr><td>sDTM</td><td>1.0</td><td>1.0</td><td>1.0</td><td>1M</td><td>9.7</td><td>2.5</td></tr><tr><td>sDTM (pruned k=1024)</td><td>1.0</td><td>1.0</td><td>.95</td><td>1M</td><td>1.8</td><td>1</td></tr></table>
+
+The various DTM models and Transformers all perform perfectly on the IID test set. NQG struggles to learn the Active  $\leftrightarrow$  Logical task, an example of the brittleness of hybrid neurosymbolic systems. Only the DTM variants succeed on the OOD test sets. As anticipated, the RU-Transformer performs better than the standard Transformer with regards to structural generalization.
+
+Comparing the original DTM to sDTM without pruning, we see a 70x reduction in parameter count from pooling by attention, a  $20\%$  reduction in memory usage from fewer parameters and SCT, as well as a roughly 13x speedup. We are able to gain even further memory savings and speed improvements due to the pruning method. The final two rows show that the pruning method has no impact on lexical generalization and a minor impact on structural generalization, while reducing memory usage by 5x and improving speed by 2.5x. The results from this experiment confirm that sDTM is capable of matching DTM performance on a previous baseline. However, since both DTM and sDTM perform near ceiling, it is difficult to isolate the effect of the proposed changes in this paper. We will investigate this question further in Section 5.5. Next, we turn to tasks where the original DTM could not be used.
+
+# 5.3 Scalability (FOR2LAM)
+
+FOR2LAM is a tree2tree program translation task to translate an abstract syntax tree (AST) in an imperative language (FOR) to an AST in a functional language (LAM) [7]. Due to the depth of the trees in this dataset, DTM is unable to fit a batch size of 1 into memory. This makes FOR2LAM a good dataset to test the scalability of sDTM to more complex samples. We augment the FOR2LAM dataset with a 0-shot lexical test set. During training, only two variable names appear: 'x' and 'y'. For the 0-shot test, we replace all occurrences of x in the test set with a new token 'z'. We are unable to test DTM on FOR2LAM because a batch size of 1 does not fit into memory due to the depth of the trees in the dataset.
+
+Results on FOR2LAM are shown on the left side of Table 2. NQG suffers with scale (see A.8), and we were unable to include results for it on FOR2LAM due to training and evaluation exceeding 7 days. All other models do well on the in-distribution test set, but only DTM is able to achieve substantive accuracy on the 0-shot lexical test. DTM's performance is impressive given work on data augmentation has shown the difficulty of few-shot generalization is inversely proportional to vocabulary size [50], with smaller vocabulary tasks being more challenging. This 0-shot challenge is from 2 variables (x, y) to 3 (x, y, z), making it difficult enough that both transformer variants score  $3\%$ .
+
+# 5.4 Seq2Tree (GeoQuery)
+
+GeoQuery is a natural language to SQL dataset [77] where a model needs to map a question stated in natural language to a correctly formatted SQL query, including parentheses to mark functions
+
+Table 2: Accuracies on FOR2LAM and GeoQuery. Results are the best performance over five runs. NQG cannot be evaluated on FOR2LAM because it takes over a week to train. †Results taken from Shaw et al. [58]. *We report the results from a replication study of NQG where the result on the Length split differed substantially from the original result [69].  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">FOR2LAM</td><td colspan="4">GeoQuery</td></tr><tr><td>IID</td><td>0-shot lexical</td><td>IID</td><td>Length</td><td>Template</td><td>TMCD</td></tr><tr><td>Transformer</td><td>1.0</td><td>.03</td><td>.88</td><td>.26</td><td>.79</td><td>.40</td></tr><tr><td>RU-Transformer</td><td>1.0</td><td>.03</td><td>.87</td><td>.25</td><td>.77</td><td>.37</td></tr><tr><td>NQG†</td><td>-</td><td>-</td><td>.76</td><td>.37/.26*</td><td>.62</td><td>.41</td></tr><tr><td>sDTM</td><td>1.0</td><td>.61</td><td>.73</td><td>.20</td><td>.20</td><td>.36</td></tr></table>
+
+and arguments. We use the parentheses and function argument relationship as the tree structure for our output. In this format, GeoQuery is a seq2tree task, and we follow the description from Section 4.5. We use the same preprocessing and data as Shaw et al. [58]. The TMCD split for GeoQuery [58] extends MCD to natural language datasets instead of synthetic languages. GeoQuery is a very small dataset, with a training set containing between 440 and 600 samples, depending on the split. Like FOR2LAM, we are unable to test DTM on GeoQuery because a batch size of 1 does not fit into memory due to the depth of the trees in the dataset.
+
+Results for GeoQuery are shown on the right side of Table 2. This is the most difficult task that we test because of the small training set, and the natural language input is not drawn from a synthetic grammar. Given this, a potential symbolic solution to this task might be quite complex. We find that both NQG and DTM perform worse than the two Transformer variants on the IID test set. This also holds true for the Template split, where Transformers outperform the neurosymbolic models. On the Length and TMCD splits, all of the baselines achieve roughly the same performance while DTM performs slightly worse — the degree of variation in the input space and small training set appear to make it difficult for sDTM to find a compositional solution.
+
+It is worth noting that there is substantial room for improvement across every model on GeoQuery. The small dataset with high variation poses a problem for both compositional methods of sDTM and NQG. It is possible that with sufficient data, GeoQuery's latent compositional structure could be identified by NQG and DTM, but the released GeoQuery dataset has only on the order of 500 training examples. Given all methods struggle to model the IID split, we refrain from drawing substantive conclusions based on minor differences in accuracy on this single task in isolation from the rest of the results.
+
+# 5.5 Seq2Seq (SCAN)
+
+SCAN is a synthetic seq2seq task with training and test variations to examine out-of-distribution generalization [36]. To process seq2seq samples, we follow the description in Section 4.5. We compare two methods for embedding the output sequence into a tree by writing a parser for SCAN's output and comparing this to the left-aligned uniform-depth trees (LAUD). In addition to the standard test splits from SCAN, we introduce a 0-shot lexical test set as well.
+
+Since the trees in SCAN are not very deep, we are able to compare sDTM to DTM to isolate the effect of pooling by attention (§4.2). We modify the original DTM to handle sequential inputs and outputs as described in Section 4.5. Replacing the linear transformation in DTM with pooling by attention in sDTM leads to drastically better results; DTM is unable to perform well even on the simple IID split, whereas sDTM performs well across many of the splits.
+
+All baselines perform well on the IID test set, showing that they have learned the training distribution well. Transformer variants perform poorly on lexical, length, and MCD splits. The Transformers and sDTM perform well on the Template split while NQG completely fails. Along with the results from GeoQuery, which showed weak sDTM performance on the Template split and strong performance from both Transformers, it seems that the Transformer architecture is robust under template shifts between training and testing. sDTM is the only model to perform well on the 0-shot lexical test set, whereas NQG is the only model able to perform well on the MCD test set. The two sDTM rows
+
+Table 3: SCAN accuracy. Results are the best performance over five runs. MCD scores are calculated as the average of the three MCD splits. †Results from Shaw et al. [58]. *Results from Sun et al. [69].  
+
+<table><tr><td rowspan="2">Model</td><td colspan="6">Split</td></tr><tr><td>IID</td><td>1-shot lexical</td><td>0-shot lexical</td><td>Length</td><td>Template</td><td>MCD</td></tr><tr><td>Transformer</td><td>1.0</td><td>.08</td><td>0.0</td><td>.07</td><td>1.0</td><td>.02</td></tr><tr><td>RU-Transformer</td><td>1.0</td><td>.11</td><td>0.0</td><td>.19</td><td>1.0</td><td>.01</td></tr><tr><td>NQG†</td><td>1.0*</td><td>1.0</td><td>0.0</td><td>1.0</td><td>0.0*</td><td>1.0</td></tr><tr><td>sDTM (parse trees)</td><td>1.0</td><td>.99</td><td>.99</td><td>.75</td><td>.95</td><td>.03</td></tr><tr><td>sDTM (LAUD trees)</td><td>1.0</td><td>.87</td><td>.98</td><td>.06</td><td>.98</td><td>0.0</td></tr><tr><td>DTM (parse trees)</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr></table>
+
+compare models trained with output trees from a parser or LAUD encoding. The main performance difference is on the Length split, where the structurally relevant information in the parse trees is necessary for sDTM to perform well. It is not necessary to have structured input for the model to perform well on length generalization as long as the output is structured.
+
+# 6 Conclusions
+
+We introduced the Sparse Differentiable Tree Machine (sDTM) and a novel schema for efficiently representing trees in vector space: Sparse Coordinate Trees (SCT). Unlike the fully neural and hybrid neurosymbolic baselines presented here, sDTM takes a unified approach whereby symbolic operations occur in vector space. While not perfect — sDTM struggles with MCD and Template shifts, as well as the extremely small GeoQuery dataset — the model generalizes robustly across the widest variety of distributional shifts. sDTM is also uniquely capable of zero-shot lexical generalization, likely enabled by its factorization of content and structure.
+
+While these capacities for generalization are shared with the original DTM, our instantiation is computationally efficient (representing a 75x reduction in parameters) and can be applied to seq2seq, seq2tree, and tree2tree tasks. Our work reaffirms the ability of neurosymbolic approaches to bridge the flexibility of connectionist models with the generalization of symbolic systems. We believe continued focus on efficient neurosymbolic implementations can lead to architectures with the kinds of robust generalization, scalability, and flexibility characteristic of human intelligence.
+
+# References
+
+[1] Jacob Andreas. Good-Enough Compositional Data Augmentation. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 7556–7566, Online, 2020. Association for Computational Linguistics. doi: 10.18653/v1/2020.acl-main.676. URL https://www.aclweb.org/anthology/2020.acl-main.676.  
+[2] Samy Badreddine, Artur d'Avila Garcez, Luciano Serafini, and Michael Spranger. Logic tensor networks. Artificial Intelligence, 303:103649, 2022. ISSN 0004-3702. doi: https://doi.org/10.1016/j.artint.2021.103649. URL https://www.sciencedirect.com/science/article/pii/S0004370221002009.  
+[3] Yonatan Belinkov and James Glass. Analysis methods in neural language processing: A survey. Transactions of the Association for Computational Linguistics, 7:49-72, 2019.  
+[4] Tarek R. Besold, Artur S. d'Avila Garcez, Sebastian Bader, Howard Bowman, Pedro M. Domingos, Pascal Hitzler, Kai-Uwe Kühnberger, Luis C. Lamb, Daniel Lowd, Priscila Machado Vieira Lima, Leo de Penning, Gadi Pinkas, Hoifung Poon, and Gerson Zaverucha. Neural-symbolic learning and reasoning: A survey and interpretation. CoRR, abs/1711.03902, 2017. URL http://arxiv.org/abs/1711.03902.  
+[5] Chris M. Bishop. Training with noise is equivalent to tikhonov regularization. Neural Computation, 7(1):108-116, 1995. doi: 10.1162/neco.1995.7.1.108.
+
+[6] Terra Blevins, Omer Levy, and Luke Zettlemoyer. Deep rnns encode soft hierarchical syntax. arXiv preprint arXiv:1805.04218, 2018.  
+[7] Xinyun Chen, Chang Liu, and Dawn Song. Tree-to-tree neural networks for program translation. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018. URL https://proceedings.neurips.cc/paper_files/paper/2018/file/d759175de8ea5b1d9a2660e45554894f-Paper.pdf.  
+[8] Xinyun Chen, Chen Liang, Adams Wei Yu, Dawn Song, and Denny Zhou. Compositional generalization via neural-symbolic stack machines. Advances in Neural Information Processing Systems, 33:1690-1701, 2020.  
+[9] Noam Chomsky. Aspects of the theory of syntax. Number no. 11 in Massachusetts Institute of Technology. Research Laboratory of Electronics. Special technical report. The MIT Press, Cambridge, Massachusetts, 50th anniversary edition edition, 1965. ISBN 978-0-262-52740-8.  
+[10] Noam Chomsky. The Minimalist Program. The MIT Press, 12 2014. ISBN 9780262327282. doi: 10.7551/mitpress/9780262527347.001.0001. URL https://doi.org/10.7551/mitpress/ 9780262527347.001.0001.  
+[11] Henry Conklin, Bailin Wang, Kenny Smith, and Ivan Titov. Meta-learning to compositionally generalize. arXiv preprint arXiv:2106.04252, 2021.  
+[12] Róbert Csordás, Kazuki Irie, and Juergen Schmidhuber. The devil is in the detail: Simple tricks improve systematic generalization of transformers. In Marie-Francine Moens, Xuanjing Huang, Lucia Specia, and Scott Wen-tau Yih, editors, Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 619-634, Online and Punta Cana, Dominican Republic, November 2021. Association for Computational Linguistics. doi: 10.18653/v1/2021.emnlp-main.49. URL https://aclanthology.org/2021.emnlp-main.49.  
+[13] Fernando Cuetos, Don C Mitchell, and Martin MB Corley. Parsing in different languages. In Language processing in Spanish, pages 163-208. Psychology Press, 2013.  
+[14] Lennert De Smet, Pedro Zuidberg Dos Martires, Robin Manhaeve, Giuseppe Marra, Angelika Kimmig, and Luc De Readt. Neural probabilistic logic programming in discrete-continuous domains. In Robin J. Evans and Ilya Shpitser, editors, Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, volume 216 of Proceedings of Machine Learning Research, pages 529-538. PMLR, 31 Jul-04 Aug 2023. URL https://proceedings.mlr.press/v216/de-smet23a.html.  
+[15] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. arXiv:1810.04805 [cs], May 2019. URL http://arxiv.org/abs/1810.04805. arXiv: 1810.04805.  
+[16] Li Dong and Mirella Lapata. Language to logical form with neural attention. arXiv preprint arXiv:1601.01280, 2016.  
+[17] Brian DuSell and David Chiang. Stack attention: Improving the ability of transformers to model hierarchical patterns. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=XVhm3X8Fum.  
+[18] Daniel Furrer, Marc van Zee, Nathan Scales, and Nathanael Scharli. Compositional generalization in semantic parsing: Pre-training vs. specialized architectures. arXiv preprint arXiv:2007.08970, 2020.  
+[19] Artur SD'Avila Garcez, Luis C Lamb, and Dov M Gabbay. Neural-symbolic cognitive reasoning. Springer Science & Business Media, 2008.  
+[20] Marta Garnelo and Murray Shanahan. Reconciling deep learning with symbolic artificial intelligence: representing objects and relations. Current Opinion in Behavioral Sciences, 29: 17-23, 2019. ISSN 2352-1546. doi: https://doi.org/10.1016/j.cobeha.2018.12.010. URL https://www.sciencedirect.com/science/article/pii/S2352154618301943. Artificial Intelligence.  
+[21] Ross W Gayler. Vector symbolic architectures answer jackendoff's challenges for cognitive neuroscience. In Peter Slezak, editor, Proceedings of the ICCS/ASCS Joint International Conference on Cognitive Science (ICCS/ASCS 2003), pages 133-138, Sydney, NSW, AU, jul 2003. University of New South Wales. URL http://arxiv.org/abs/cs/0412059.
+
+[22] Adele E Goldberg. *Constructions at work: the nature of generalization in language*. Oxford University Press, Oxford; New York, 2006. URL http://public.ebookcentral.proquest.com/choice/publicfullrecord.aspx?p=3052348. OCLC: 193697889.  
+[23] Saul Gorn. Explicit Definitions and Linguistic Dominoes, pages 77-115. University of Toronto Press, Toronto, 1967. ISBN 9781487592769. doi: doi:10.3138/9781487592769-008. URL https://doi.org/10.3138/9781487592769-008.  
+[24] Edward Grefenstette, Karl Moritz Hermann, Mustafa Suleyman, and Phil Blunsom. Learning to transduce with unbounded memory. Advances in neural information processing systems, 28, 2015.  
+[25] Thomas L. Griffiths. Understanding human intelligence through human limitations. Trends in Cognitive Sciences, 24:873-883, 2020. URL https://api_semanticscholar.org/CorpusID:221996148.  
+[26] Demi Guo, Yoon Kim, and Alexander M. Rush. Sequence-Level Mixed Sample Data Augmentation. arXiv:2011.09039 [cs], November 2020. URL http://arxiv.org/abs/2011.09039.arXiv:2011.09039.  
+[27] Armand Joulin and Tomas Mikolov. Inferring algorithmic patterns with stack-augmented recurrent nets. Advances in neural information processing systems, 28, 2015.  
+[28] Pentti Kanerva. Hyperdimensional computing: An introduction to computing in distributed representation with high-dimensional random vectors. Cognitive computation, 1:139-159, 2009.  
+[29] Daniel Keysers, Nathanael Scharli, Nathan Scales, Hylke Buisman, Daniel Furrer, Sergii Kashubin, Nikola Momchev, Danila Sinopalnikov, Lukasz Stafiniak, Tibor Tihon, Dmitry Tsarkov, Xiao Wang, Marc van Zee, and Olivier Bousquet. Measuring compositional generalization: A comprehensive method on realistic data. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id=SygcCnNKwrt.  
+[30] Najoung Kim and Tal Linzen. COGS: A compositional generalization challenge based on semantic interpretation. In Bonnie Webber, Trevor Cohn, Yulan He, and Yang Liu, editors, Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 9087-9105, Online, November 2020. Association for Computational Linguistics. doi: 10.18653/v1/2020.emnlp-main.731. URL https://aclanthology.org/2020.emnlp-main.731.  
+[31] Najoung Kim and Tal Linzen. COGS: A Compositional Generalization Challenge Based on Semantic Interpretation. arXiv:2010.05465 [cs], October 2020. URL http://arxiv.org/abs/2010.05465.arXiv:2010.05465.  
+[32] Najoung Kim, Tal Linzen, and Paul Smolensky. Uncontrolled lexical exposure leads to overestimation of compositional generalization in pretrained models. arXiv preprint arXiv:2212.10769, 2022.  
+[33] Yoon Kim, Chris Dyer, and Alexander M Rush. Compound probabilistic context-free grammars for grammar induction. arXiv preprint arXiv:1906.10225, 2019.  
+[34] Dan Klein and Christopher D Manning. A generative constituent-context model for improved grammar induction. In Proceedings of the 40th Annual Meeting of the Association for Computational Linguistics, pages 128-135, 2002.  
+[35] Denis Kleyko, Dmitri A. Rachkovskij, Evgeny Osipov, and Abbas Rahimi. A survey on hyperdimensional computing aka vector symbolic architectures, part i: Models and data transformations. ACM Comput. Surv., 55(6), dec 2022. ISSN 0360-0300. doi: 10.1145/3538531. URL https://doi.org/10.1145/3538531.  
+[36] Brenden Lake and Marco Baroni. Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks. 35th International Conference on Machine Learning, ICML 2018, 7:4487-4499, 2018. arXiv: 1711.00350 ISBN: 9781510867963.  
+[37] Brenden M Lake. Compositional generalization through meta sequence-to-sequence learning. Advances in neural information processing systems, 32, 2019.  
+[38] Juho Lee, Yoonho Lee, Jungtaek Kim, Adam Kosiorek, Seungjin Choi, and Yee Whye Teh. Set transformer: A framework for attention-based permutation-invariant neural networks. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research,
+
+pages 3744-3753. PMLR, 09-15 Jun 2019. URL https://proceedings.mlr.press/v97/lee19d.html.  
+[39] Bingzhi Li, Lucia Donatelli, Alexander Koller, Tal Linzen, Yuekun Yao, and Najoung Kim. SLOG: A Structural Generalization Benchmark for Semantic Parsing, October 2023. URL http://arxiv.org/abs/2310.15040. arXiv:2310.15040 [cs].  
+[40] Yuxuan Li and James McClelland. Representations and computations in transformers that support generalization on structured tasks. Transactions on Machine Learning Research, 2023. ISSN 2835-8856. URL https://openreview.net/forum?id=oFC2LAqS6Z.  
+[41] Matthias Lindemann, Alexander Koller, and Ivan Titov. Compositional generalization without trees using multiset tagging and latent permutations. arXiv preprint arXiv:2305.16954, 2023.  
+[42] Adam Lopez. Statistical machine translation. ACM Computing Surveys (CSUR), 40(3):1-49, 2008.  
+[43] Jaron Maene and Luc De Raedt. Soft-unification in deep probabilistic logic. In A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors, Advances in Neural Information Processing Systems, volume 36, pages 60804-60820. Curran Associates, Inc., 2023. URL https://proceedings.neurips.cc/paper_files/paper/2023/file/bf215fa7fe70a38c5e967e59c44a99d0-Paper-Conference.pdf.  
+[44] Gary F. Marcus. The Algebraic Mind: Integrating Connectionism and Cognitive Science. MIT Press, 2001.  
+[45] John McCarthy. Recursive functions of symbolic expressions and their computation by machine, part i. Communications of the ACM, 3(4):184-195, 1960.  
+[46] R Thomas McCoy, Tal Linzen, Ewan Dunbar, and Paul Smolensky. Rnns implicitly implement tensor product representations. arXiv preprint arXiv:1812.08718, 2018.  
+[47] Stephen Muggleton. Inductive logic programming. New Generation Computing, 8(4):295-318, February 1991. ISSN 1882-7055. doi: 10.1007/BF03037089. URL https://doi.org/10.1007/BF03037089.  
+[48] Shikhar Murty, Pratyusha Sharma, Jacob Andreas, and Christopher D Manning. Characterizing intrinsic compositionality in transformers with tree projections. arXiv preprint arXiv:2211.01288, 2022.  
+[49] Barbara Partee et al. Lexical semantics and compositionality. An invitation to cognitive science: Language, 1:311-360, 1995.  
+[50] Arkil Patel, Satwik Bhattachamishra, Phil Blunsom, and Navin Goyal. Revisiting the compositional generalization abilities of neural sequence models. arXiv preprint arXiv:2203.07402, 2022.  
+[51] Steven Pinker. The language instinct: How the mind creates language. Penguin uK, 2003.  
+[52] Tony A. Plate. Holographic Reduced Representation: Distributed Representation for Cognitive Structures. CSLI Publications, USA, 2003. ISBN 1575864290.  
+[53] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. Exploring the limits of transfer learning with a unified text-to-text transformer. J. Mach. Learn. Res., 21(1), jan 2020. ISSN 1532-4435.  
+[54] Tim Rocktäschel and Sebastian Riedel. Learning knowledge base inference with neural theorem provers. In Jay Pujara, Tim Rocktaschel, Danqi Chen, and Sameer Singh, editors, Proceedings of the 5th Workshop on Automated Knowledge Base Construction, pages 45-50, San Diego, CA, June 2016. Association for Computational Linguistics. doi: 10.18653/v1/W16-1309. URL https://aclanthology.org/W16-1309.  
+[55] Anian Ruoss, Grégoire Delétang, Tim Genewein, Jordi Grau-Moya, Róbert Csordás, Mehdi Bennani, Shane Legg, and Joel Veness. Randomized positional encodings boost length generalization of transformers. In Anna Rogers, Jordan Boyd-Graber, and Naoaki Okazaki, editors, Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pages 1889–1903, Toronto, Canada, July 2023. Association for Computational Linguistics. doi: 10.18653/v1/2023.acl-short.161. URL https://aclanthology.org/2023.acl-short.161.  
+[56] Jake Russian, Jason Jo, Randall C O'Reilly, and Yoshua Bengio. Compositional generalization in a deep seq2seq model by separating syntax and semantics. arXiv preprint arXiv:1904.09708, 2019.
+
+[57] Itiroo Sakai. Syntax in universal translation. In Proceedings of the International Conference on Machine Translation and Applied Language Analysis, 1961.  
+[58] Peter Shaw, Ming-Wei Chang, Panupong Pasupat, and Kristina Toutanova. Compositional generalization and natural language variation: Can a semantic parsing approach handle both? In Chengqing Zong, Fei Xia, Wenjie Li, and Roberto Navigli, editors, Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 922–938, Online, August 2021. Association for Computational Linguistics. doi: 10.18653/v1/2021.acl-long.75. URL https://aclanthology.org/2021.acl-long.75.  
+[59] Hikaru Shindo, Masaaki Nishino, and Akihiro Yamamoto. Differentiable inductive logic programming for structured examples. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6):5034-5041, May 2021. doi: 10.1609/aaai.v35i6.16637. URL https://ojs.aaai.org/index.php/AAAI/article/view/16637.  
+[60] Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. URL https://proceedings.neurips.cc/paper_files/paper/2019/file/6e0917469214d8fbd8c517dcdc6b8DCF-Paper.pdf.  
+[61] Vighnesh Shiv and Chris Quirk. Novel positional encodings to enable tree-based transformers. Advances in neural information processing systems, 32, 2019.  
+[62] David Smith and Jason Eisner. Quasi-synchronous grammars: Alignment by soft projection of syntactic dependencies. In Philipp Koehn and Christof Monz, editors, Proceedings on the Workshop on Statistical Machine Translation, pages 23-30, New York City, June 2006. Association for Computational Linguistics. URL https://aclanthology.org/W06-3104.  
+[63] Paul Smolensky. On the proper treatment of connectionism. Behavioral and Brain Sciences, 11 (1):1-23, 1988. doi: 10.1017/S0140525X00052432.  
+[64] Paul Smolensky. Tensor product variable binding and the representation of symbolic structures in connectionist systems. Artif. Intell., 46:159-216, 1990.  
+[65] Richard Socher, Brody Huval, Christopher D. Manning, and Andrew Y. Ng. Semantic compositionality through recursive matrix-vector spaces. In Jun'ichi Tsujii, James Henderson, and Marius Paşa, editors, Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pages 1201-1211, Jeju Island, Korea, July 2012. Association for Computational Linguistics. URL https://aclanthology.org/D12-1110.  
+[66] Paul Soulos, Tom McCoy, Tal Linzen, and Paul Smolensky. Discovering the compositional structure of vector representations with role learning networks. arXiv preprint arXiv:1910.09113, 2019.  
+[67] Paul Soulos, Edward Hu, Kate McCurdy, Yunmo Chen, Roland Fernandez, Paul Smolensky, and Jianfeng Gao. Differentiable Tree Operations Promote Compositional Generalization, June 2023. URL http://arxiv.org/abs/2306.00751. arXiv:2306.00751 [cs].  
+[68] Mark Steedman. Combinatory grammars and parasitic gaps. *Natural Language & Linguistic Theory*, 5(3):403-439, 1987.  
+[69] Kaiser Sun, Adina Williams, and Dieuwke Hupkes. A Replication Study of Compositional Generalization Works on Semantic Parsing. August 2023. URL https://openreview.net/forum?id=MF9uv95psps.  
+[70] Kai Sheng Tai, Richard Socher, and Christopher D Manning. Improved semantic representations from tree-structured long short-term memory networks. arXiv preprint arXiv:1503.00075, 2015.  
+[71] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017.  
+[72] Yau-Shian Wang, Hung-Yi Lee, and Yun-Nung Chen. Tree transformer: Integrating tree structures into self-attention. arXiv preprint arXiv:1909.06639, 2019.
+
+[73] Thomas Winters, Giuseppe Marra, Robin Manhaeve, and Luc De Raedt. Deepstochlog: Neural stochastic logic programming. Proceedings of the AAAI Conference on Artificial Intelligence, 36(9):10090-10100, Jun. 2022. doi: 10.1609/aaai.v36i9.21248. URL https://ojs.aaaai.org/index.php/AAAI/article/view/21248.  
+[74] Ruibin Xiong, Yunchang Yang, Di He, Kai Zheng, Shuxin Zheng, Chen Xing, Huishuai Zhang, Yanyan Lan, Liwei Wang, and Tieyan Liu. On layer normalization in the transformer architecture. In International Conference on Machine Learning, pages 10524-10533. PMLR, 2020.  
+[75] Zhun Yang, Adam Ishay, and Joohyung Lee. Neurasp: Embracing neural networks into answer set programming. In Christian Bessiere, editor, Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20, pages 1755–1762. International Joint Conferences on Artificial Intelligence Organization, 7 2020. doi: 10.24963/ijcai.2020/243. URL https://doi.org/10.24963/ijcai.2020/243. Main track.  
+[76] Dani Yogatama, Yishu Miao, Gabor Melis, Wang Ling, Adhiguna Kuncoro, Chris Dyer, and Phil Blunsom. Memory architectures in recurrent neural network language models. In International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id=SkFqf01AZ.  
+[77] John M Zelle and Raymond J Mooney. Learning to parse database queries using inductive logic programming. In Proceedings of the national conference on artificial intelligence, pages 1050-1055, 1996.
+
+# A Appendix
+
+# A.1 Sparse Coordinate Trees as Tensor Product Representations
+
+This section shows that Sparse Coordinate Trees is the same as a TPR with the constraint that the role basis is the standard basis. TPRs define structural positions as role vectors  $r_i \in \mathbb{R}^{d_r}$ , and the content that fills these positions is defined by filler vectors  $f_i \in \mathbb{R}^{d_f}$ . For a particular role and filler pair, the filler  $f_i$  is bound to the role  $r_i$  using the tensor/outer product:  $f_i \otimes r_i \in \mathbb{R}^{d_f \times d_r}$ . The representation of an entire structure is the sum over all  $N$  individual filler-role pairs:  $T = \sum_{i=1}^{N} f_i \otimes r_i \in \mathbb{R}^{d_f \times d_r}$ . As shown in the previous two equations, the dimensionality of a single filler-role pair is equal to the dimensionality of an entire structure: both have dimensionality  $\mathbb{R}^{d_f \times d_r}$ . This means that a tree with only a filled root node takes up the same memory as a dense tree with every node filled. An important requirement for TPRs is that the role vectors must be linearly independent; this ensures that a filler can be unbound from a role without introducing noise using the inner product:  $f_j = Tr_j^+$ , where  $\{r_i^+\}_i$  is the basis dual to  $\{r_i\}_i$ . Previous work typically used randomly initialized and frozen orthonormal vectors to define the role basis. By defining our role vectors in a sparse manner as opposed to random initialization, we can greatly reduce the memory used by TPRs.
+
+Classic symbolic data structures grow in memory linearly with the number of filled positions. It is possible to replicate this behavior with TPRs by defining the role vectors to be the standard one-hot basis, which is orthonormal by definition. The  $i$ -th element of role vector  $r_i$  is 1, and the other elements are 0. When a filler and role vector are both dense, the resulting bound vector is also dense. When the role vector is one-hot, the resulting bound vector is 0 everywhere except for column  $i$  which corresponds to the value 1 in  $r_i$ . By using a sparse tensor representation that only keeps track of dimensions that are not equal to 0, we can reduce the memory usage of TPRs to linear growth that scales with the number of filled positions, like a classical symbolic data structure. This however forgoes a motivating desideratum for the design of TPRs, that roles (and not just fillers) have similarity relations that support generalization across structural positions.
+
+We can additionally improve the efficiency by refraining from performing the outer product. Since we are not performing a tensor product, this technique is only implicitly a Tensor Product Representation. Instead, we can keep the filler and role vectors in two aligned lists. A filler is bound to a role by sharing an index in our aligned lists. This is equivalent to the binding and unbinding from classical dense TPRs without having to perform multiplication.
+
+Since we are not performing an outer product, instead of storing sparse role vectors, we can simply store a role integer, where the integer corresponds to the one-hot dimension. We derive a tree addressing scheme based on Gorn addresses [23]. In our scheme, addresses are read from right to left, giving the path from the root where a left-branch is indicated by a 0 and a right-branch is indicated by a 1. We need a way to distinguish between leading 0s and left-branches (e.g., 010 vs. 10), so we start our addressing scheme at 1 instead of 0. This indicates that all 0s to the left of the left-most 1 are unfilled and not left-branches; the left-most 1 and all preceding 0s are ignored when decoding the path-from-root. Figure 2 shows an example encoding of a tree in the sparse implicit approach.
+
+We can compare the memory requirements of the Sparse Coordinate Tree encoding used in the sDTM to the memory requirements of the full TPRs used in the original DTM of Soulos et al. [67]. A TPR uses the same amount of memory regardless of the number of filled nodes. As with all sparse tensor formats, the memory savings arise when there are many zeros. In a dense tree where every node is occupied, the classical dense TPR approach is actually more efficient: the SCT's value list has the same total dimension as the classical TPR, but, in addition, the SCT encoding includes the list of filled-node addresses.
+
+# A.2 Agent Figure
+
+See Figure 6.
+
+# A.3 Lexical Regularization Ablation
+
+To see the importance of adding noise to our input embeddings as defined in Section 4.4, we show the performance of sDTM with and without this regularization in Table 4.
+
+![](images/0820c536fd12d5f8f50de49f3169fce57b699fc661b44385a4f4be3d4dfe55a4.jpg)  
+Figure 6: Adapted from Soulos et al. [67]. One step of DTM is expanded to show how the agent produces the input to the interpreter. The interpreter then writes the output to memory and encodes the output for the agent. Parts of the architecture with learnable parameters are indicated in yellow. The agent uses three linear transformations on top of a standard Transformer encoder layer to parameterize the inputs to the interpreter. The superscript indicates the layer number and refers to parameters and activations that are exclusive to this layer.
+
+Table 4: Comparing sDTM's accuracy on SCAN 1-shot lexical OOD generalization with and without lexical regularization. We use LAUD to embed the output sequence in a tree.  
+
+<table><tr><td>With noise</td><td>.87</td></tr><tr><td>Without noise</td><td>0.0</td></tr></table>
+
+# A.4 Dataset Preprocessing
+
+We preprocessed GeoQuery according to the steps from Shaw et al. [58]. FOR2LAM and GeoQuery both contain non-binary trees, which we convert to binary form using Chomsky normal form. When a new node is inserted to make a branch binary, we use the token  $<\mathrm{NT}>$ . For output sequences with length one embedded according to left-aligned uniform-depth, we make the single token the left child of a new  $<\mathrm{NT}>$  root node.
+
+# A.5 0-shot Lexical Test Generation
+
+For both FOR2LAM and SCAN, we introduce 0-shot lexical tests. For FOR2LAM, we do this by replacing every occurrence of 'x' in the test set with a new token 'z'. For the SCAN 0-shot set, we start with the 1-shot lexical test set and remove the sample containing the 1-shot word 'jump'. We alter the output vocabulary to use the same tokens as the input vocabulary, since it is impossible for a word level model to translate between an input and output word without any exposure to that word.
+
+# A.6 DTM Training Details
+
+When applicable, we adopt the hyperparameters from Soulos et al. [67]. Below we list the newly introduced hyperparameters and changes we made to existing parameters.
+
+Soulos et al. [67] set the dimensionality of the embeddings to be equal to the size of vocabulary. This works for the datasets with small vocabulary examined in the original paper. We keep this setting for
+
+Table 5: Summary statistics for Active  $\leftrightarrow$  Logical. Mean and standard deviation accuracies are shown.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Split</td></tr><tr><td>IID</td><td>0-Shot Lexical</td><td>Structural</td></tr><tr><td>Original DTM</td><td>1.0 ± 0.0</td><td>1.0 ± 0.0</td><td>1.0 ± 0.0</td></tr><tr><td>sDTM</td><td>1.0 ± 0.0</td><td>1.0 ± 0.0</td><td>1.0 ± 0.0</td></tr><tr><td>sDTM (pruned k=1024)</td><td>1.0 ± 0.0</td><td>1.0 ± 0.0</td><td>.86 ± .04</td></tr></table>
+
+Table 6: Summary statistics for FOR2LAM and GeoQuery. Mean and standard deviation accuracies are shown.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">FOR2LAM</td><td colspan="4">GeoQuery</td></tr><tr><td>IID</td><td>0-shot lexical</td><td>IID</td><td>Length</td><td>Template</td><td>TMCD</td></tr><tr><td>sDTM</td><td>1.0±0.0</td><td>.43±.11</td><td>.68±.01</td><td>.19±.01</td><td>.16±.03</td><td>.35±0.0</td></tr></table>
+
+Active  $\leftrightarrow$  Logical, but set the embedding dimension to 64 for FOR2LAM, and 128 for GeoQuery and SCAN. We also changed the loss function from mean-squared error to cross entropy.
+
+For each new task, we need to decide how many layers to use for sDTM. We followed the heuristic of doubling the max tree depth for the models with sequence input and quadrupling the number of layers for tree input. This leads to 56 layers for FOR2LAM, 22 layers for GeoQuery, and 14 layers for SCAN.
+
+Pooling by multi-headed attention 4.2 introduces new hyperparameters such as number of pooling heads and pooling key dimensionality, and we set the value of these to be the same as the Transformer hyperparameters for the agent. Tree pruning 4.3 introduces a new hyperparameter  $k$  for the maximum number of nodes to keep. In general, a larger  $k$  is better but uses more memory. For Active  $\leftrightarrow$  Logical we set  $k = 1024$ , for FOR2LAM  $k = 1024$ , for GeoQuery  $k = 2048$ , and for SCAN  $k = 256$ . With the memory savings from SCT, pooling by multi-headed attention, and pruning, we increase the batch size from 16 to 64. We also increased the agent's model dimension to 256 with 8 heads of attention due to the memory savings except for Active  $\leftrightarrow$  Logical where we matched the original hyperparameters.
+
+Random positional embeddings (RPE) also introduce a new hyperparameter for the max input integer, and we set this to be double the max input length. This leads to an RPE hyperparameter of 44 for GeoQuery and 18 for SCAN.
+
+We noticed that randomly initializing and freezing our embedding vectors was essential for sDTM to achieve 0-shot generalization on SCAN.
+
+For the results, we reported the best run of 5 random seeds. Like DTM, sDTM suffers from high variance. Some runs get stuck in local optima and fail to achieve moderate performance on the training set, which leads to poor performance on the test sets. This is a known issue with models that use superposition data structures, and reporting the best run over a number of random seeds has been previously used [76, 17].
+
+# A.7 DTM Summary Statistics
+
+Mean and standard deviation accuracies are shown in Tables 5, 6, and 7.
+
+# A.8 Baseline Training Details
+
+NQG: Active  $\leftrightarrow$  Logical rule induction used the following hyperparameters: sample size=training set size, terminal code length=8, allow repeated nts=True. The terminal code length setting was
+
+Table 7: Summary statistics for SCAN. Mean and standard deviation accuracies are shown.  
+
+<table><tr><td rowspan="2">Model</td><td colspan="6">Split</td></tr><tr><td>IID</td><td>1-Shot Lexical</td><td>0-Shot Lexical</td><td>Length</td><td>Template</td><td>MCD</td></tr><tr><td>sDTM (parse trees)</td><td>.80±.39</td><td>.51±.39</td><td>.80±.34</td><td>.34±.30</td><td>.19±.38</td><td>.02±.01</td></tr><tr><td>sDTM (LAUD trees)</td><td>1.0±0.0</td><td>.70±.15</td><td>.75±.22</td><td>.04±.01</td><td>.84±.12</td><td>0.0±0.0</td></tr><tr><td>DTM (parse trees)</td><td>0.0±0.0</td><td>0.0±0.0</td><td>0.0±0.0</td><td>0.0±0.0</td><td>0.0±0.0</td><td>0.0±0.0</td></tr></table>
+
+obtained via grid search over the values 1, 8, 32. For the actual training of the model we follow the hyperparameters utilised by [69, 58]. FOR2LAM used the same hyperparameters with the exception of sample size which had to be set to 1000 as additional increases became computationally intractable. Even under these settings rule induction took 42 hours on a machine with 64gb of ram. Writing the training set would take an additional week of processing time, which we considered computationally too expensive.
+
+Transformer: We followed the same hyperparameters obtained via grid search from [67]. Specifically these are: 30,000 steps of which 1000 were warmup and linear learning rate decay; batch size 256; one encoder layer and three decoder layer each with a hidden dimension of 1024 and two attention heads; the optimizer was Adam.
+
+RU-Transformer: We followed the hyperparameters reported by [12]. These are: 128 dimension hidden size with 256 feedforward; 8 attention heads; 3 layers; batch size 256; trained using Adam with learning rate  $10^{-3}$ .
+
+# A.9 Compute resources
+
+All reported sDTM runs could be processed on NVIDIA 16gb V100 GPUs. Depending on availability, we ran some seeds on 80gb H100 GPUs, but this is not necessary. The Transformer baselines were also run on NVIDIA 16gb V100 GPUs. NQG used NVIDIA 40gb A100 GPUs. The GPUs we used were hosted on an internal cluster.
+
+Designing our architecture involved many preliminary experiments that are not reported in the paper.
+
+# A.10 Dataset Statistics and Samples
+
+Example input and output pairs are shown for Active  $\leftrightarrow$  Logical in Figure 7 FOR2LAM in Figure 8, GeoQuery in Figure 9, and SCAN in Figure 5. The memory usage of DTM grows exponentially with tree depth, so we present the max depth of the datasets here:
+
+Active  $\leftrightarrow$  Logical: max tree depth 10  
+FOR2LAM: max tree depth 14  
+- GeoQuery: max tree depth 16  
+- SCAN: max tree depth 8
+
+# A.11 Licenses
+
+# Baselines:
+
+DTM:Permissive 2.0  
+- Transformer: BSD-3 (Pytorch implementation)  
+- RU-Transformer: MIT Licence  
+- NQG: Apache 2.0
+
+# Datasets:
+
+![](images/3b7a0bdb49614b07467aa1dd73a8d146b65bd3d78971f8d863c5deb17b434629.jpg)  
+Figure 7: An input and output pair from Active  $\leftrightarrow$  Logical.
+
+![](images/a04ad8ce1dc81200d8f8c9f4a23c66d448c01c682d815358b4f2212705055798.jpg)  
+Figure 8: An input and output pair from FOR2LAM.
+
+![](images/a13e8686e61c172336382e7f0b33f740e24ba756ea117e819fed8dab12f69143.jpg)  
+Figure 9: An input and output pair from GeoQuery.
+
+- GeoQuery: GLP 2.0  
+- SCAN: BSD  
+Active  $\leftrightarrow$  Logical: Permissive 2.0  
+FOR2LAM: Not public (no licence obtained through email request to original authors)
+
+# NeurIPS Paper Checklist
+
+# 1. Claims
+
+Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
+
+Answer: [Yes]
+
+Justification: At the end of the introduction, we outline the primary contributions of our paper along with the associated section where that content is available.
+
+Guidelines:
+
+- The answer NA means that the abstract and introduction do not include the claims made in the paper.  
+- The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.  
+- The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.  
+- It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
+
+# 2. Limitations
+
+Question: Does the paper discuss the limitations of the work performed by the authors?
+
+Answer: [Yes]
+
+Justification: We address limitations of our approach in Section 6.
+
+Guidelines:
+
+- The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.  
+- The authors are encouraged to create a separate "Limitations" section in their paper.  
+- The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.  
+- The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.  
+- The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.  
+- The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.  
+- If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.  
+- While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
+
+# 3. Theory Assumptions and Proofs
+
+Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
+
+Answer: [NA]
+
+Justification: We provide mathematical descriptions of our model, but we do not introduce any proofs.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include theoretical results.  
+- All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.  
+- All assumptions should be clearly stated or referenced in the statement of any theorems.  
+- The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.  
+- Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.  
+- Theorems and Lemmas that the proof relies upon should be properly referenced.
+
+# 4. Experimental Result Reproducibility
+
+Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
+
+# Answer: [Yes]
+
+Justification: The main content outlines our model and empirical setup. In Appendix A.6 we provide details for training our model, and in Appendix A.8 we outline details for training the baselines. Additionally, we plan to make our code and data open source at the time of publication to facilitate reproducibility.
+
+# Guidelines:
+
+- The answer NA means that the paper does not include experiments.
+
+- If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
+
+- If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
+
+- Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general, releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
+
+- While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
+
+(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.  
+(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.  
+(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).  
+(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
+
+# 5. Open access to data and code
+
+Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
+
+Answer: [Yes]
+
+Justification: we plan to make our code and data open source at the time of publication to facilitate reproducibility.
+
+Guidelines:
+
+- The answer NA means that paper does not include experiments requiring code.  
+- Please see the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).  
+- The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https://nips.cc/public/guides/CodeSubmissionPolicy) for more details.  
+- The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.  
+- The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.  
+- At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).  
+- Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
+
+# 6. Experimental Setting/Details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
+Justification: The data splits are discussed extensively in Section 5. In Appendix A.6 we provide details for training our model, and in Appendix A.8 we outline details for training the baselines.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.  
+- The full details can be provided either with the code, in appendix, or as supplemental material.
+
+# 7. Experiment Statistical Significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
+
+Answer: [No]
+
+Justification: for our results, we report the best run across five random initializations. As discussed in Appendix A.6, neurosymbolic technique can have high variance, and this method of reporting results is common.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.
+
+- The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.  
+- The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).  
+- The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)  
+- The assumptions made should be given (e.g., Normally distributed errors).  
+- It should be clear whether the error bar is the standard deviation or the standard error of the mean.  
+- It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a  $96\%$  CI, if the hypothesis of Normality of errors is not verified.  
+- For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).  
+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments Compute Resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: In Appendix A.9 we discuss the compute resources needed to run our experiments.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
+- The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.  
+- The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.  
+- The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).
+
+# 9. Code Of Ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
+Answer: [Yes]
+
+Justification: This research is upstream of any concrete applications. While there is always a risk of scientific research, we do not believe this work contains risks beyond general scientific research.
+
+Guidelines:
+
+- The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.  
+- If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.  
+- The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).
+
+# 10. Broader Impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [NA]
+
+Justification: This research is upstream of any concrete applications. While there is always a risk of scientific research, we do not believe this work contains risks beyond general scientific research.
+
+# Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.  
+- If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.  
+- Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.  
+- The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.  
+- The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.  
+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
+Justification: This research is upstream of any concrete applications. While there is always a risk of scientific research, we do not believe this work contains risks beyond general scientific research.
+
+# Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
+- Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.  
+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: We cited the papers that introduce the models and datasets that we use. Most of the models and datasets we used are publicly available. Appendix A.11 contains additional information with regards to the licenses of each asset.
+
+# Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
+- The authors should state which version of the asset is used and, if possible, include a URL.  
+- The name of the license (e.g., CC-BY 4.0) should be included for each asset.  
+- For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.  
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
+- For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.  
+- If this information is not available online, the authors are encouraged to reach out to the asset's creators.
+
+# 13. New Assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [Yes]
+
+Justification: we plan to make our code and data open source at the time of publication to facilitate reproducibility.
+
+Guidelines:
+
+- The answer NA means that the paper does not release new assets.  
+- Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.  
+- The paper should discuss whether and how consent was obtained from people whose asset is used.  
+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and Research with Human Subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: Our paper does not involve crowdsourcing nor human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.  
+- According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
+
+# 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+# Answer: [NA]
+
+Justification: Our paper does not involve crowdsourcing nor human subjects.
+
+# Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.  
+- We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.  
+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

2024/Compositional Generalization Across Distributional Shifts with Sparse Tree Operations/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d5c24d9699a85c6b9e1e256a38eb19eb15f030d3babba12177b8b919c36248c9
+size 417246

2024/Compositional PAC-Bayes_ Generalization of GNNs with persistence and beyond/51957fc1-737c-40b8-b340-f596e9d5faca_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9de06ef438a6ea0fc2d52c9fee85f5cc16ce828d991bb2161cec35ab3e791003
+size 882854

2024/Compositional PAC-Bayes_ Generalization of GNNs with persistence and beyond/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cc33045dedd55772242b397ee2062d8167c5c4bbccd1595847125ae74514e5b1
+size 2506326

2024/Compressing Large Language Models using Low Rank and Low Precision Decomposition/fd06d0d7-0c15-4a35-8837-b611ad3cf9d3_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cc48385a1c0829aa303b9cafe4aa1c899cd7fc999c11022772514e340d948cea
+size 1245138

2024/Compressing Large Language Models using Low Rank and Low Precision Decomposition/images.zip

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ce74884280e4bce0784511a61d804f0410aa5a1b84ebc0109581fe49e61641b0
+size 1635453