Daily Papers

Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer. We study the finite computation obtained by releasing the N-th iterate of deterministic gradient descent on wmapsto F(w;S)+langle z,wrangle, where zsimmathcal N(0,σ^2I_d) is drawn once before optimization. For strongly convex and smooth objectives with Lipschitz Hessian, we prove an explicit condition under which the map zmapsto w_N is a C^1-diffeomorphism on the bounded domains used in the privacy argument, with a quantitative lower bound on the smallest singular value of its Jacobian. This permits a direct change-of-variables analysis of the finite iterate. For generalized linear models, the resulting privacy-profile bound has no explicit ambient-dimension factor once the iteration condition holds, and its finite-iteration correction decreases geometrically. By letting the free truncation parameter grow slowly with N, we recover the corresponding exact-minimizer certificate in the limit. We also bound the expected excess empirical risk by dσ^2/(2μ) plus a geometrically decreasing optimization term, and transfer the result to population risk without an additional multiplicative condition-number factor in the leading statistical terms.

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the ε-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.

Adversarial optimization under a shared ell_1 budget requires deciding not only how much perturbation to use, but also where that limited budget should be spent. This allocation problem becomes particularly important when individual input coordinates are subject to local magnitude constraints, which restrict the extent to which perturbation can be concentrated on a small number of locations. We introduce an importance-guided allocation mechanism that uses a fixed clean-gradient prior to steer perturbation toward model-sensitive regions while leaving the feasible perturbation set unchanged. A centered allocation objective encourages perturbation at above-average importance locations and discourages unnecessary expenditure elsewhere, thereby redistributing rather than enlarging the available budget. Across ten robust model--dataset configurations under a common capacity-limited threat setting, the proposed method improves attack success over matched APGD- and PMA-based baselines by 2.52 to 17.70 percentage points. Allocation analysis shows that these gains are accompanied by substantially greater perturbation mass in high-importance regions without increased global ell_1 consumption. Mechanism ablations further show that centered non-uniform redistribution provides part of the benefit, while model-derived importance yields an additional improvement. These results identify perturbation allocation as a distinct and practically relevant dimension of adversarial optimization under shared-budget, locally constrained threat models.

Most adversarial attacks on deep reinforcement learning (DRL) assume white-box access to the victim policy, which rarely holds in practice. This paper studies transfer-based black-box attacks on DRL: the attacker crafts observation perturbations on a white-box surrogate agent and feeds them to an unknown victim. We formulate the attack as return minimization under a per-step perturbation budget. We first show that transplanting transferable image-classification attacks (FGSM, MI-FGSM, and NI-FGSM) with a per-step objective yields perturbations that transfer but are no stronger than random noise of the same budget. We then propose a trajectory-level attack that optimizes a sequence of perturbations over a receding horizon through a differentiable model of the environment and a temperature-smoothed surrogate policy, with the same optimizers. On CartPole-v1 with ten DQN and DDQN agents and 100 surrogate--victim pairs, the trajectory-level attack outperforms per-step attacks and random noise in the white-box, cross-model, and cross-algorithm settings.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Learning informative representations from tabular data in remote sensing and environmental science is challenging due to heterogeneity, scarce labels, and redundancy among features. We present ZAYAN (Zero-Anchor dYnamic feAture eNcoding), a self-supervised, feature-centric contrastive framework for tabular data. ZAYAN performs contrastive learning at the feature rather than sample level, removing the need for explicit anchor selection and any reliance on class labels, while encouraging a redundancy-minimized, disentangled embedding space. The framework has two modules: ZAYAN-CL, which pretrains feature embeddings via a zero-anchor contrastive objective with dynamic perturbations and masking, and ZAYAN-T, a Transformer that conditions on these embeddings for downstream classification. Across eight datasets, including six remote-sensing tabular benchmarks and two remote-sensing-driven flood-prediction tables from satellite and GIS products, ZAYAN achieves superior accuracy, robustness, and generalization over tabular deep learning baselines, with consistent gains under label scarcity and distribution shift. These results indicate that feature-level contrastive learning and dynamic feature encoding provide an effective recipe for learning from tabular sensing data.

Machine learning models are susceptible to adversarial perturbations: small changes to input that can cause large changes in output. It is also demonstrated that there exist input-agnostic perturbations, called universal adversarial perturbations, which can change the inference of target model on most of the data samples. However, existing methods to craft universal perturbations are (i) task specific, (ii) require samples from the training data distribution, and (iii) perform complex optimizations. Additionally, because of the data dependence, fooling ability of the crafted perturbations is proportional to the available training data. In this paper, we present a novel, generalizable and data-free approaches for crafting universal adversarial perturbations. Independent of the underlying task, our objective achieves fooling via corrupting the extracted features at multiple layers. Therefore, the proposed objective is generalizable to craft image-agnostic perturbations across multiple vision tasks such as object recognition, semantic segmentation, and depth estimation. In the practical setting of black-box attack scenario (when the attacker does not have access to the target model and it's training data), we show that our objective outperforms the data dependent objectives to fool the learned models. Further, via exploiting simple priors related to the data distribution, our objective remarkably boosts the fooling ability of the crafted perturbations. Significant fooling rates achieved by our objective emphasize that the current deep learning models are now at an increased risk, since our objective generalizes across multiple tasks without the requirement of training data for crafting the perturbations. To encourage reproducible research, we have released the codes for our proposed algorithm.

Speech deepfake detectors often lose accuracy when the distribution of the test data differs from that of the training data. Meta-learning for domain generalization (MLDG) shows promise by simulating domain shifts with episodic meta-train and meta-test splits. However, the MLDG meta-objective considers only a single clean adaptation trajectory and does not account for the local loss landscape around its endpoints. To address this limitation, we first propose an explicit worst-case MLDG variant, dubbed WC-MLDG-4P, which perturbs both the meta-train and meta-test states but requires four gradient evaluations per episode. We then introduce WC-MLDG-2P, a source-directed alternative to the explicit robust objective. It shifts the clean MLDG endpoint toward a locally higher source-loss state and evaluates the meta-test gradient there, retaining the two-evaluation cost of the first-order MLDG. A first-order expansion relates the resulting gradient change to meta-test directional curvature along the source gradient without explicitly computing a Hessian. Relative to MLDG, WC-MLDG-2P achieves relative mean-EER reductions of 23.4% with XLSR-AASIST and 7.6% with XLSR-Conformer-TCM, respectively.

Vision-Language-Action (VLA) models have advanced robotic control by enabling end-to-end decision-making directly from multimodal inputs. However, their tightly coupled architectures expose novel security vulnerabilities. Unlike traditional adversarial perturbations, backdoor attacks represent a stealthier, persistent, and practically significant threat-particularly under the emerging Training-as-a-Service paradigm-but remain largely unexplored in the context of VLA models. To address this gap, we propose BadVLA, a backdoor attack method based on Objective-Decoupled Optimization, which for the first time exposes the backdoor vulnerabilities of VLA models. Specifically, it consists of a two-stage process: (1) explicit feature-space separation to isolate trigger representations from benign inputs, and (2) conditional control deviations that activate only in the presence of the trigger, while preserving clean-task performance. Empirical results on multiple VLA benchmarks demonstrate that BadVLA consistently achieves near-100% attack success rates with minimal impact on clean task accuracy. Further analyses confirm its robustness against common input perturbations, task transfers, and model fine-tuning, underscoring critical security vulnerabilities in current VLA deployments. Our work offers the first systematic investigation of backdoor vulnerabilities in VLA models, highlighting an urgent need for secure and trustworthy embodied model design practices. We have released the project page at https://badvla-project.github.io/.

A central goal in systems biology and drug discovery is to predict the transcriptional response of cells to perturbations. This task is challenging due to the noisy and sparse nature of single-cell measurements, as well as the fact that perturbations often induce population-level shifts rather than changes in individual cells. Existing deep learning methods typically assume cell-level correspondences, limiting their ability to capture such global effects. We present scDFM, a generative framework based on conditional flow matching that models the full distribution of perturbed cells conditioned on control states. By incorporating a maximum mean discrepancy (MMD) objective, our method aligns perturbed and control populations beyond cell-level correspondences. To further improve robustness to sparsity and noise, we introduce the Perturbation-Aware Differential Transformer (PAD-Transformer), a backbone architecture that leverages gene interaction graphs and differential attention to capture context-specific expression changes. Across multiple genetic and drug perturbation benchmarks, scDFM consistently outperforms prior methods, demonstrating strong generalization in both unseen and combinatorial settings. In the combinatorial setting, it reduces mean squared error by 19.6% relative to the strongest baseline. These results highlight the importance of distribution-level generative modeling for robust in silico perturbation prediction. The code is available at https://github.com/AI4Science-WestlakeU/scDFM

This paper presents a collection of audio transforms that introduce perceptually irrelevant distortions and demonstrates their use as perceptual stress tests for audio quality models. We refer to these methods as Perceptual Audio Data Perturbation (PADP). PADP exploits the insensitivity of the human auditory system to certain fine-grained signal variations to substantially alter the waveform while preserving perceived audio quality and content. The audibility of PADP and the selection of its parameters are evaluated through controlled listening tests, ensuring that the transformations achieve transparent or near-transparent quality for both non-critical and critical items. We further probe the robustness of state-of-the-art (SOTA) perception-motivated objective audio quality models and foundation models. The results reveal a misalignment between model responses and human auditory perception, highlighting the limited perceptual awareness of these models for certain proposed transforms.

Successive cancellation perturbation-enhanced (SCP) decoding improves the performance of finite-length polar codes by performing multiple SC decoding attempts with receiver-side perturbations. However, many existing perturbation schemes generate or update subsequent perturbations according to the outcomes of previous decoding attempts, resulting in additional decoding latency. In this paper, we propose an offline variance design (OVD) method for parallel SCP (PSCP) decoding of short- and medium-length polar codes. First, we formulate the exact recovery objective conditioned on ordinary SC failure and classify failed frames by the position of the first genie-aided intrinsic error and the number of subsequent intrinsic errors. We also derive a consistent Gaussian representation of the perturbed channel that preserves min-sum SC hard decisions. Second, we construct a class-based approximation of the recovery objective using Gaussian approximation and backward recursions, accounting for both error correction and new errors introduced by perturbations. We prove that both the exact and analytical objectives are nondecreasing and exhibit diminishing marginal gains as independent branches are added. Third, we develop a greedy algorithm to select variances from a finite candidate set for a given code, signal-to-noise ratio (SNR), and number of perturbation branches. All variances are determined offline, allowing the original SC branch and all perturbation branches to start simultaneously. Simulations for rate-1/2 polar codes of lengths 64, 128, 256, and 512 show that OVD-PSCP achieves lower block error rates (BLERs) than conventional SCP with the same number of perturbation branches. The gains are larger for shorter codes and increase as the number of perturbation branches grows.

The study on improving the robustness of deep neural networks against adversarial examples grows rapidly in recent years. Among them, adversarial training is the most promising one, which flattens the input loss landscape (loss change with respect to input) via training on adversarially perturbed examples. However, how the widely used weight loss landscape (loss change with respect to weight) performs in adversarial training is rarely explored. In this paper, we investigate the weight loss landscape from a new perspective, and identify a clear correlation between the flatness of weight loss landscape and robust generalization gap. Several well-recognized adversarial training improvements, such as early stopping, designing new objective functions, or leveraging unlabeled data, all implicitly flatten the weight loss landscape. Based on these observations, we propose a simple yet effective Adversarial Weight Perturbation (AWP) to explicitly regularize the flatness of weight loss landscape, forming a double-perturbation mechanism in the adversarial training framework that adversarially perturbs both inputs and weights. Extensive experiments demonstrate that AWP indeed brings flatter weight loss landscape and can be easily incorporated into various existing adversarial training methods to further boost their adversarial robustness.

Predicting how cells respond to genetic perturbations is fundamental to understanding gene function, disease mechanisms, and therapeutic development. While recent deep learning approaches have shown promise in modeling single-cell perturbation responses, they struggle to generalize across cell types and perturbation contexts due to limited contextual information during generation. We introduce PT-RAG (Perturbation-aware Two-stage Retrieval-Augmented Generation), a novel framework that extends Retrieval-Augmented Generation beyond traditional language-model applications to cellular biology. Unlike standard RAG systems designed for text retrieval with pre-trained LLMs, perturbation retrieval lacks established similarity metrics and requires learning what constitutes relevant context, making differentiable retrieval essential. PT-RAG addresses this through a two-stage pipeline: first, retrieving candidate perturbations K using GenePT embeddings, then adaptively refining the selection through Gumbel-Softmax discrete sampling conditioned on both the cell state and the input perturbation. This cell-type-aware differentiable retrieval enables end-to-end optimization of the retrieval objective jointly with generation. On the Replogle-Nadig single-gene perturbation dataset, we demonstrate that PT-RAG outperforms both STATE and vanilla RAG under identical experimental conditions, with the strongest gains in distributional similarity metrics (W_1, W_2). Notably, vanilla RAG's dramatic failure is itself a key finding: it demonstrates that differentiable, cell-type-aware retrieval is essential in this domain, and that naive retrieval can actively harm performance. Our results establish retrieval-augmented generation as a promising paradigm for modelling cellular responses to gene perturbation. The code to reproduce our experiments is available at https://github.com/difra100/PT-RAG_ICLR.

Masked image modeling (MIM) methods typically operate in either raw pixel space (reconstructing masked patches) or latent feature space (aligning with a pre-trained teacher). We present MEDiC (Multi-objective Exploration of Distillation from CLIP), a framework that combines both spaces in a single pipeline through three complementary objectives: patch-level token distillation from a frozen CLIP encoder, global CLS alignment, and pixel reconstruction via a lightweight decoder. We conduct a systematic investigation of the design space surrounding this multi-objective framework. First, we show that all three objectives provide complementary information, with the full combination reaching 73.9% kNN accuracy on ImageNet-1K. Second, we introduce hierarchical clustering with relative position bias for evolved masking and find that, despite producing more semantically coherent masks than prior methods, evolved masking does not outperform simple block masking in the teacher-guided distillation setting, a finding we attribute to the teacher's inherent semantic awareness. Third, we reveal that optimal scalar loss weights are extremely fragile, with small perturbations causing drops of up to 17 percentage points in kNN accuracy. Our framework achieves 73.9% kNN and 85.1% fine-tuning accuracy with ViT-Base at 300 epochs.

Robustness evaluation must examine diverse visual perturbations, while benchmarks cover only some real-world conditions and physical testing is costly. Paired evaluations link clean and perturbed predictions for the same image, capturing changes in correctness, confidence, and acceptance beyond aggregate accuracy. We investigate how this image correspondence supports two needs in robustness evaluation: interpreting paired evaluation results and prioritizing samples for physical testing. To interpret paired evaluation results, we fix both sets of prediction records and vary their correspondence within each class. We prove that classwise correct-correct counts give the same sharp bounds on lost acceptance and mean true-class probability decrease among retained-correct inputs as any feasible five-state refinement. Distinguishing persistent from changed wrong answers can further constrain accepted-error transitions, while shared correspondence can establish policy orderings left unresolved by separate cost intervals. To prioritize samples for physical testing, we retain each image's synthetic responses and rank clean-correct images by their mean true-class probability under corruption. Across 44 classifiers, testing the highest-risk 20% finds 67% and 45% of failures under mild screen and print recaptures, versus 58% and 36% for clean confidence and 60% and 37% for an equal-size natural-transformation average. With both probability averaging and an A3Rank scoring adaptation, the tested corruption set yields higher mean failure recall than the natural-transform set; differences between scores depend on the source and budget. Together, these findings show that the value of correspondence depends on the evaluation objective: classwise counts suffice for specified reliability bounds, while image-specific synthetic responses improve the allocation of physical tests within the evaluated pool.

A central task in virtual cell modeling is predicting single-cell transcriptional responses to unseen genetic perturbations and drug combinations, and biological networks provide valuable priors on gene relationships. Existing graph-based models commonly use the same network to structure gene representations and mediate intergene interactions, thereby implicitly treating stable associations as perturbation-response pathways. Gene Ontology and control-derived coexpression networks encode relatively stable relationships rather than intervention-specific response directions or magnitudes. We therefore propose GeneGeoFlow, which conditions a control-anchored residual flow on gene-wise geometry derived from biological networks to learn intervention-specific transcriptional responses. GeneGeoFlow derives multi-scale spectral coordinates from Gene Ontology and control-derived coexpression networks. A perturbation-conditioned, gene-wise gating module selects relevant structural scales and network sources, yielding intervention-specific gene geometry. The resulting geometry conditions a control-anchored residual flow without explicitly propagating target-derived signals along the graph. Condition-wise optimal transport couples unpaired control and perturbed populations for training, while a Delta-correlation objective aligns the predicted and observed condition-level expression-shift directions. GeneGeoFlow achieves Pearson Delta scores of 0.8979 on the Norman additive benchmark and 0.9088 on five held-out drug combinations in the fixed ComboSciPlex test split. These results support perturbation-conditioned gene geometry as an effective structural prior for intervention-specific response prediction, without conflating stable gene relationships with response propagation.

Recent multimodal large language models have demonstrated strong reasoning ability, yet their reliability as automated evaluators remains limited by a critical weakness: when visual evidence conflicts with textual cues, MLLM judges tend to reward plausible narratives over perceptually correct answers. We identify and systematically analyze this phenomenon, which we term Perceptual Judgment Bias. Through controlled visual perturbations, existing multimodal judges frequently anchor on the response text instead of their own visual perception, leading to inconsistent and non-verifiable evaluations. To address this issue, we introduce the Perceptually Perturbed Judgment Dataset, which constructs minimally edited counterfactual responses that isolate perceptual errors and enable verifiable supervision. Building on this dataset, we develop a unified training framework that combines a structured GRPO-based reward with a batch-ranking objective, achieving coherent global ordering without explicit pairwise labels. Experiments across diverse MLLM-as-a-Judge benchmarks show that our approach substantially improves perceptual fidelity, ranking coherence, and alignment with human evaluation. Our results establish a scalable and generalizable pathway for training multimodal judges that are perceptually grounded, interpretable, and robust to visual-reasoning conflicts.

In time-varying D-optimal subset selection, the number of replaced coordinates does not measure physical displacement: when the optimal selection for a set of mobile sensors changes, a single sensor may have to cross the entire graph. We therefore measure movement by a bottleneck matching distance on a fixed mobility graph, and define the distance margin at radius P as the smallest old-objective loss among configurations farther than P from the current maximizer. Our main result shows that if the projector drift is small and the distance margin at a chosen radius exceeds an explicit threshold, then every maximizer of the new objective lies within that radius, without tie-breaking rules or uniform conditioning assumptions over subsets. Moreover, we show that separation information of this kind is genuinely needed: a weighted-path construction shows that, at a fixed baseline eigengap, an arbitrarily small perturbation can move an optimal sensor from one end of the graph to the other, so no bound depending only on perturbation size and eigengap can vanish with the perturbation. We also give a finite certificate, conditions under which local and Voronoi restrictions retain a global optimum, and oversampled and regularized extensions, and we identify the learned dictionary criteria to which the results apply.

Large language models achieve strong scores on medical benchmarks, yet these benchmarks evaluate each question in isolation, providing no measure of whether a system can distinguish clinically similar presentations requiring different interventions. We introduce MamaBench, the first counterfactual benchmark for maternal and paediatric AI: 434 expert-authored clinical narratives in 217 pairs across 371 pathologies, evaluated via the Bias Trap Rate (BTR), the conditional probability that a model fails the counterfactual given success on the base case. We propose Evidence-Anchored RAG (EA-RAG), a three-stage retrieval method that replaces aggregate similarity with an evidence coverage objective through clinical parameter extraction, coverage auditing, and contrastive sub-queries. Across eight configurations of four frontier LLMs, base accuracy overstates robust accuracy by 16-28 percentage points in every model. EA-RAG achieves 20.3% BTR and 65.0% robust accuracy on Claude Sonnet 4.6, a 5.5 percentage point BTR reduction without degrading base accuracy. The residual 20% BTR confirms that counterfactual robustness in clinical AI remains an open challenge. Keywords: counterfactual evaluation, clinical AI, maternal healthcare, retrieval-augmented generation, diagnostic robustness

Motivated by the open question of Bianchi, Hachem, and Schechtman (Bianchi et al., 2024, Remark 4), we show that in the non-weakly convex definable setting, omnidirectional noise with conditional fourth-moment control does not suffice for universal almost-sure avoidance of sharply repulsive critical points. We demonstrate this failure by constructing a globally Lipschitz, coercive, definable objective that is not weakly convex. For this objective and its sufficiently small linear perturbations, stochastic subgradient descent with independent noise uniformly distributed on a ball in R^2 converges with probability 1 to a nonminimal sharply repulsive critical point from every initial point in a specified ball. A two-cycle argument establishes uniform bounds on the rescaled iterates, yielding convergence to the sharply repulsive critical point. In contrast, for locally Lipschitz definable objectives, Gaussian noise ensures simultaneous almost-sure avoidance of any finite collection of sharply repulsive points. Through a construction of difference quotient functions, we show that convergence to any such point with positive probability would produce a stationary distribution with expected descent 0, whereas a global positive lower bound on the Fréchet subgradient norms of the limiting functions forces strictly positive expected descent under the same distribution. This contradiction proves avoidance, with the everywhere positive Gaussian density playing a key role.

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not.

Self-supervised speech representation learning has become essential for extracting meaningful features from untranscribed audio. Recent advances highlight the potential of deriving discrete symbols from the features correlated with linguistic units, which enables text-less training across diverse tasks. In particular, sentence-level Self-Distillation of the pretrained HuBERT (SD-HuBERT) induces syllabic structures within latent speech frame representations extracted from an intermediate Transformer layer. In SD-HuBERT, sentence-level representation is accumulated from speech frame features through self-attention layers using a special CLS token. However, we observe that the information aggregated in the CLS token correlates more with speaker identity than with linguistic content. To address this, we propose a speech-only self-supervised fine-tuning approach that separates syllabic units from speaker information. Our method introduces speaker perturbation as data augmentation and adopts a frame-level training objective to prevent the CLS token from aggregating paralinguistic information. Experimental results show that our approach surpasses the current state-of-the-art method in most syllable segmentation and syllabic unit quality metrics on Librispeech, underscoring its effectiveness in promoting syllabic organization within speech-only models.

We develop a model-free policy gradient method for discrete-time mean-field control (MFC). In MFC, the policy affects the objective both through the controlled dynamics and through the population distribution. Standard REINFORCE estimators capture the first effect but not the second. We introduce Transport REINFORCE, a transport map-based approach that perturbs a suitable transformation of the population distribution to estimate this missing mean-field contribution. The method applies to both finite and continuous state spaces. In finite state spaces, we perturb the population distribution directly on the probability simplex through a convex combination of the current population weights and random weights. In continuous state spaces, we project the population distribution onto the manifold of Gaussian mixtures, and then randomize it via a transport map that ensures the perturbed law remains within this manifold. We prove consistency of the perturbed objective and gradient as the perturbation vanishes, and derive bias and mean-square error bounds for the resulting sample-based gradient estimator. Numerical experiments on several MFC benchmarks show that Transport REINFORCE improves over standard REINFORCE.

Autonomous LLM agents generate multi-step action plans that can fail due to contextual misalignment or structural incoherence. Existing anomaly detection methods are ill-suited for this challenge: mean-pooling embeddings dilutes anomalous steps, while contrastive-only approaches ignore sequential structure. Standard unsupervised methods on pre-trained embeddings achieve F1-scores no higher than 0.69. We introduce Trajectory Guard, a Siamese Recurrent Autoencoder with a hybrid loss function that jointly learns task-trajectory alignment via contrastive learning and sequential validity via reconstruction. This dual objective enables unified detection of both "wrong plan for this task" and "malformed plan structure." On benchmarks spanning synthetic perturbations and real-world failures from security audits (RAS-Eval) and multi-agent systems (Who\&When), we achieve F1-scores of 0.88-0.94 on balanced sets and recall of 0.86-0.92 on imbalanced external benchmarks. At 32 ms inference latency, our approach runs 17-27times faster than LLM Judge baselines, enabling real-time safety verification in production deployments.

Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population to follow specific attribute distributions (e.g., demographic balance or semantic proportions). We formalize this setting as the inference-time attribute distributional alignment problem for pretrained unconditional diffusion models. To address this, we cast inference-time attribute distributional alignment as an optimal control problem over the reverse diffusion process, viewing the process as the rollout of a dynamical system and augmenting it with additive, time-dependent perturbations as control. We solve for the perturbations using an optimal-control-based algorithm to optimize a differentiable distribution-matching objective while penalizing control effort to preserve data fidelity. Experiment results in image generation demonstrate that our proposed plug-and-play approach can better align attribute distributions to diverse and flexible test-time targets compared to baselines, without retraining or finetuning the pretrained diffusion model.

Reasoning Vision-Language Models (VLMs) have shown promising performance on complex multimodal tasks. However, they still face significant challenges: they are highly sensitive to reasoning errors, require large volumes of annotated data or accurate verifiers, and struggle to generalize beyond specific domains. To address these limitations, we explore self-correction as a strategy to enhance reasoning VLMs. We first conduct an in-depth analysis of reasoning VLMs' self-correction abilities and identify key gaps. Based on our findings, we introduce Sherlock, a self-correction and self-improvement training framework. Sherlock introduces a trajectory-level self-correction objective, a preference data construction method based on visual perturbation, and a dynamic beta for preference tuning. Once the model acquires self-correction capabilities using only 20k randomly sampled annotated data, it continues to self-improve without external supervision. Built on the Llama3.2-Vision-11B model, Sherlock achieves remarkable results across eight benchmarks, reaching an average accuracy of 64.1 with direct generation and 65.4 after self-correction. It outperforms LLaVA-CoT (63.2), Mulberry (63.9), and LlamaV-o1 (63.4) while using less than 20% of the annotated data.

Verification and validation of autonomous driving (AD) systems and components is of increasing importance, as such technology increases in real-world prevalence. Safety-critical scenario generation is a key approach to robustify AD policies through closed-loop training. However, existing approaches for scenario generation rely on simplistic objectives, resulting in overly-aggressive or non-reactive adversarial behaviors. To generate diverse adversarial yet realistic scenarios, we propose SEAL, a scenario perturbation approach which leverages learned objective functions and adversarial, human-like skills. SEAL-perturbed scenarios are more realistic than SOTA baselines, leading to improved ego task success across real-world, in-distribution, and out-of-distribution scenarios, of more than 20%. To facilitate future research, we release our code and tools: https://github.com/cmubig/SEAL

Wasserstein gradient flow extends gradient descent to probability measures. Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems. We investigate when its approximation by finitely many interacting particles remains accurate over growing time horizons. Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence. This captures favorable scenarios in which temporary instability is compatible with accurate tracking over growing horizons. Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature. To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison. We verify the conditions in a variance-plus-cosine model, where curvature recovery yields a growing-horizon tracking guarantee. We also establish local attraction, transverse descent, and positive second variation in two regions of a regularized matrix-factorization model, motivating a positive-negative-positive curvature pattern.

We introduce CPPO, a Contrastive Perception Policy Optimization method for finetuning vision-language models (VLMs). While reinforcement learning (RL) has advanced reasoning in language models, extending it to multimodal reasoning requires improving both the perception and reasoning aspects. Prior works tackle this challenge mainly with explicit perception rewards, but disentangling perception tokens from reasoning tokens is difficult, requiring extra LLMs, ground-truth data, forced separation of perception from reasoning by policy model, or applying rewards indiscriminately to all output tokens. CPPO addresses this problem by detecting perception tokens via entropy shifts in the model outputs under perturbed input images. CPPO then extends the RL objective function with a Contrastive Perception Loss (CPL) that enforces consistency under information-preserving perturbations and sensitivity under information-removing ones. Experiments show that CPPO surpasses previous perception-rewarding methods, while avoiding extra models, making training more efficient and scalable.

Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.

It is well-known that the performance of well-trained deep neural networks may degrade significantly when they are applied to data with even slightly shifted distributions. Recent studies have shown that introducing certain perturbation on feature statistics (\eg, mean and standard deviation) during training can enhance the cross-domain generalization ability. Existing methods typically conduct such perturbation by utilizing the feature statistics within a mini-batch, limiting their representation capability. Inspired by the domain generalization objective, we introduce a novel Adversarial Style Augmentation (ASA) method, which explores broader style spaces by generating more effective statistics perturbation via adversarial training. Specifically, we first search for the most sensitive direction and intensity for statistics perturbation by maximizing the task loss. By updating the model against the adversarial statistics perturbation during training, we allow the model to explore the worst-case domain and hence improve its generalization performance. To facilitate the application of ASA, we design a simple yet effective module, namely AdvStyle, which instantiates the ASA method in a plug-and-play manner. We justify the efficacy of AdvStyle on tasks of cross-domain classification and instance retrieval. It achieves higher mean accuracy and lower performance fluctuation. Especially, our method significantly outperforms its competitors on the PACS dataset under the single source generalization setting, \eg, boosting the classification accuracy from 61.2\% to 67.1\% with a ResNet50 backbone. Our code will be available at https://github.com/YBZh/AdvStyle.

Self-attention is usually described as a flexible, content-adaptive way to mix a token with information from its past. We reinterpret causal self-attention transformers, the backbone of modern foundation models, within a probabilistic framework, much as classical PCA is extended to probabilistic PCA. This reformulation reveals a key structural consequence of the underlying change of variables: a barrier constraint emerges on the parameters of self-attention. The resulting geometry exposes a degeneracy boundary where the attention-induced mapping becomes locally ill-conditioned, yielding a stability-margin interpretation analogous to the margin in support vector machines. This, in turn, naturally gives rise to the concept of support tokens. We further show that causal transformers define a consistent stochastic process over infinite token sequences, providing a rigorous probabilistic foundation for sequence modeling. Building on this view, we derive a Bayesian MAP training objective that requires only a minimal modification to standard LLM training: adding a smooth log-barrier penalty to the usual cross-entropy loss. Empirically, the resulting training objective improves robustness to input perturbations and sharpens the margin geometry of the learned representations without sacrificing out-of-sample accuracy.

Vision-Language-Action (VLA) models are vulnerable to adversarial attacks, yet universal and transferable attacks remain underexplored, as most existing patches overfit to a single model and fail in black-box settings. To address this gap, we present a systematic study of universal, transferable adversarial patches against VLA-driven robots under unknown architectures, finetuned variants, and sim-to-real shifts. We introduce UPA-RFAS (Universal Patch Attack via Robust Feature, Attention, and Semantics), a unified framework that learns a single physical patch in a shared feature space while promoting cross-model transfer. UPA-RFAS combines (i) a feature-space objective with an ell_1 deviation prior and repulsive InfoNCE loss to induce transferable representation shifts, (ii) a robustness-augmented two-phase min-max procedure where an inner loop learns invisible sample-wise perturbations and an outer loop optimizes the universal patch against this hardened neighborhood, and (iii) two VLA-specific losses: Patch Attention Dominance to hijack texttovision attention and Patch Semantic Misalignment to induce image-text mismatch without labels. Experiments across diverse VLA models, manipulation suites, and physical executions show that UPA-RFAS consistently transfers across models, tasks, and viewpoints, exposing a practical patch-based attack surface and establishing a strong baseline for future defenses.

Globalization and multiculturalism continue to produce increasingly diverse speech varieties. Yet current spoken dialogue systems frequently fail on under-represented dialects and accents, often misidentifying the input language and causing cascading failures in downstream dialogue tasks. Addressing this dialectal variance under low-resource constraints remains an open challenge, as standard fine-tuning is computationally expensive and prone to overfitting on high-dimensional speech data. We propose Convex Language Detection (CLD), a novel framework that integrates theoretically grounded convex optimization techniques into the spoken dialogue systems pipeline. Our method is efficiently implemented via multi-GPU Alternating Direction Method of Multipliers (ADMM) in JAX, thus providing global optimality guarantees and fast training in polynomial time. Theoretically, we prove that our convex objective induces certified margin stability and provide guarantees against feature perturbations. Empirically, we demonstrate sample efficiency and robustness to input dialectical variation, achieving 97-98% accuracy in challenging low-resource regimes. Our open-source package is available at https://pypi.org/project/jaxcld/

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as the standard paradigm for improving reasoning capability of large language models, while Multi-Token Prediction (MTP) has been a widely adopted module in pretraining. Combining them is a natural approach, yet current RL practices detach MTP gradients because joint training degrades the performance. We revisit this failure from an optimization perspective. We show that the per-step effect of MTP on the RL objective can be decomposed into two terms: a first-order correlation and a second-order perturbation penalty. This decomposition unifies three MTP training regimes: Detach, Cross-Entropy loss, and Policy loss, and explains why each succeeds or fails. Further analysis of policy loss reveals that, although it aligns with intuition, performance still degrades: the correlation term decays while the quadratic penalty persists. Guided by the analysis, we propose Optimal Coefficient Calibration (OCC), an adaptive scheme that tracks the optimal coefficient online via a log-probability proxy at negligible cost. Across six competition-level mathematical reasoning benchmarks, OCC consistently matches or exceeds the detach baseline, delivering improved joint MTP-RL training performance.

Due to the potential for exploratory reasoning of Latent Visual Reasoning, recent works tend to enable MLLMs (Multimodal Large Language Models) to perform visual reasoning by propagating continuous hidden states instead of decoding intermediate steps into discrete tokens. However, existing works typically rely on hard alignment objectives to force latent representations to match predefined visual features, thereby severely limiting the exploratory of latent reasoning process. To address this problem, we propose CoLVR (Contrastive Optimization for Latent Visual Reasoning). To obtain a more exploratory visual reasoning, CoLVR introduces a latent contrastive training framework. Firstly, CoLVR learns diverse and exploratory representations with a latent contrastive objective guided by angle-based perturbation, which expands the semantic latent space and avoids over-constrained embedding. Then, CoLVR employs a latent trajectory contrastive reward for RL (Reinforcement Learning) post-training to enable fine-grained optimization of latent visual reasoning process and thus fostering diverse reasoning behaviors. Experiments demonstrate that CoLVR significantly enhances the exploratory capability of latent representations, achieving average improvements of 5.83% on VSP and 8.00% on Jigsaw, while also outperforming existing latent models on out of domain benchmarks, with a 3.40% gain on MMStar. The data, codes, and models are released at https://github.com/Oscar-dzy/CoLVR.

Quantile-based reinforcement learning provides an interpretable approach to risk-sensitive decision-making by optimizing a prescribed quantile of the cumulative-return distribution. Despite this appeal, learning under a point quantile objective is challenging: quantiles can change abruptly under small perturbations of the return distribution, and exact quantile-sensitive planning requires computationally demanding distributional optimization. Lower-buffered quantiles alleviate the former difficulty by averaging neighboring quantiles immediately below the target level, providing a smoother surrogate while preserving the underlying point-quantile objective. Existing methods based on this principle, however, remain model-based and rely on explicit return-law planning, limiting their applicability beyond small tabular problems. We develop Deep-BQRL, a model-free distributional reinforcement-learning framework that extends buffered-quantile learning to neural function approximation. The method learns conditional return quantiles directly from sampled transitions, constructs buffered action scores from the relevant region of the learned quantile function, and uses ensemble disagreement to guide exploration. An augmented input representation allows the learned policy to respond to trajectory information without explicitly reproducing the quantile-state recursion required by exact planning. Experiments on an asset-selling optimal-stopping problem and slippery FrozenLake compare Deep-BQRL with model-based UCB-BQRL and tabular PPO and TRPO implementations. In asset selling, Deep-BQRL attains smaller mean cumulative point-quantile policy gaps than PPO and TRPO at the reported target levels, while UCB-BQRL retains the smallest gaps. The learned stopping decisions also vary with the target quantile, providing an interpretable illustration of the method's risk-sensitive behavior.

This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.

The standard quadratic program (StQP) minimizes a quadratic form over nonnegative variables that sum to one. We compose classical graph reductions with regularized Motzkin--Straus clique formulations to express discrete optimization problems in this continuous domain. The graph matrix has diagonal entries τ, zeros on edges, and ones on nonedges. For 0<τ<1, its minimum is τ/ω(G), where ω(G) is the clique number. Its strict local minimizers are precisely the uniform distributions on maximal cliques, and its global minimizers encode maximum cliques. At τ=1/2, integer scaling gives coefficients in {0,1,2} and minimum 1/ω(G), yielding an NP-complete StQP threshold problem with a restricted coefficient alphabet. We give explicit formulations for satisfiability, coloring, Hamiltonian cycles, independent set, vertex cover, set packing, three-dimensional matching, and graph isomorphism. A regularized weighted clique formulation combined with local-state compatibility graphs gives an exact compiler for finite-domain factor models specified by complete local tables, including QUBO, with at most four simplex coordinates per binary pair factor. The catalog covers Karp's 21 problems: twelve use direct graph formulations, and nine use factor-state formulations, including six obtained through binary-linear feasibility. For each route we record dimensions, coefficient structure, and recovery rules. We analyze interaction count, coefficient range, objective separation, perturbation tolerance, support recovery, and decoding overhead. The separation bounds quantify the effects of clique size, factor weights, and offsets. In the complete factor-state construction, every assignment, including each suboptimal assignment, is a strict local minimum.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

Generative systems of musical accompaniments are rapidly growing, yet there are no standardized metrics to evaluate how well generations align with the conditional audio prompt. We introduce a distribution-based measure called "Accompaniment Prompt Adherence" (APA), and validate it through objective experiments on synthetic data perturbations, and human listening tests. Results show that APA aligns well with human judgments of adherence and is discriminative to transformations that degrade adherence. We release a Python implementation of the metric using the widely adopted pre-trained CLAP embedding model, offering a valuable tool for evaluating and comparing accompaniment generation systems.

Code generation models have achieved impressive performance. However, they tend to be brittle as slight edits to a prompt could lead to very different generations; these robustness properties, critical for user experience when deployed in real-life applications, are not well understood. Most existing works on robustness in text or code tasks have focused on classification, while robustness in generation tasks is an uncharted area and to date there is no comprehensive benchmark for robustness in code generation. In this paper, we propose ReCode, a comprehensive robustness evaluation benchmark for code generation models. We customize over 30 transformations specifically for code on docstrings, function and variable names, code syntax, and code format. They are carefully designed to be natural in real-life coding practice, preserve the original semantic meaning, and thus provide multifaceted assessments of a model's robustness performance. With human annotators, we verified that over 90% of the perturbed prompts do not alter the semantic meaning of the original prompt. In addition, we define robustness metrics for code generation models considering the worst-case behavior under each type of perturbation, taking advantage of the fact that executing the generated code can serve as objective evaluation. We demonstrate ReCode on SOTA models using HumanEval, MBPP, as well as function completion tasks derived from them. Interesting observations include: better robustness for CodeGen over InCoder and GPT-J; models are most sensitive to syntax perturbations; more challenging robustness evaluation on MBPP over HumanEval.

The wide-ranging applications of large language models (LLMs), especially in safety-critical domains, necessitate the proper evaluation of the LLM's adversarial robustness. This paper proposes an efficient tool to audit the LLM's adversarial robustness via a prompt-based adversarial attack (PromptAttack). PromptAttack converts adversarial textual attacks into an attack prompt that can cause the victim LLM to output the adversarial sample to fool itself. The attack prompt is composed of three important components: (1) original input (OI) including the original sample and its ground-truth label, (2) attack objective (AO) illustrating a task description of generating a new sample that can fool itself without changing the semantic meaning, and (3) attack guidance (AG) containing the perturbation instructions to guide the LLM on how to complete the task by perturbing the original sample at character, word, and sentence levels, respectively. Besides, we use a fidelity filter to ensure that PromptAttack maintains the original semantic meanings of the adversarial examples. Further, we enhance the attack power of PromptAttack by ensembling adversarial examples at different perturbation levels. Comprehensive empirical results using Llama2 and GPT-3.5 validate that PromptAttack consistently yields a much higher attack success rate compared to AdvGLUE and AdvGLUE++. Interesting findings include that a simple emoji can easily mislead GPT-3.5 to make wrong predictions.

Transferable adversarial attacks are arguably the most practical black-box threat model. Under the same perturbation budget, stronger transfer attacks attain higher attack success rate (ASR), yet their imperceptibility also tends to degrade. Under such a fixed-budget protocol, transferability and imperceptibility therefore appear to trade off against each other. We argue that this conflict is an artifact of fixed-budget evaluation, not an intrinsic trade-off. When attacks are compared on the ASR--imperceptibility Pareto frontier obtained by sweeping ε, stronger transfer attacks already attain better imperceptibility at matched ASR than weaker ones. To exploit this latent advantage, we introduce the stealthy transfer attack ST, a plug-in primal-dual wrapper that adds an L_infty saturation regularizer to the standard constrained objective and resolves it through a two-step primal-dual update: a projected primal step on the perturbation coupled with an L_1-ball projection on a dual variable that absorbs the regularizer through Fenchel duality, requiring no auxiliary models or handcrafted perceptual priors. Empirically, ST extends the Pareto frontier across different base attacks and additional surrogate architectures. At ε{=}16/255, average imperceptibility gains over each base attack are 17% on LPIPS and 14% on NIQE while ASR is preserved or improved. At matched high-ASR levels, the strongest ST variants further Pareto-dominate dedicated stealth-oriented transfer attacks, confirming that the latent imperceptibility advantage of strong transfer attacks can be unlocked by a primal-dual optimization wrapper without sacrificing transferability. Code will be made available at https://github.com/AndssY/ST.

We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method converges to a nonminimizing Clarke critical point. For suitable power-law stepsizes, this convergence holds for open sets of initial points and linear tilts of the objective, uniformly over all perturbation sequences within a prescribed bound.

Recent years have witnessed major progress in joint audio-video generation. Existing models still suffer from limited per-modality fidelity, insufficient text-modality alignment and weak cross-modal synchronization. While reinforcement-learning post-training offers a promising remedy, directly adapting it to joint audio-video generation is challenging. Heterogeneous multimodal rewards entangle learning signals and complicate credit assignment. Joint optimization of two modality towers is computationally expensive given their divergent dynamics. Moreover, synchronization evaluation difficulty depends on paired samples, preventing fair reward comparisons. We propose AV-GRPO, a modality-anchored online diffusion RL framework, and 5DAV, a decoupled, difficulty-controllable training dataset. AV-GRPO includes three key modules: (1) modality-anchored rollouts to disentangle learning signals and stabilize difficulty; (2) trajectory-locked frozen-tower optimization to reduce cost and reassign credit; (3) adaptive objectives and perturbation strengths tailored to modality-specific dynamics. This converts coupled multimodal preference learning into unimodal subproblems for precise reward attribution and better synchronization. Our 5DAV dataset decouples samples across five dimensions for systematic training. Experiments on JavisBench and VABench demonstrate AV-GRPO outperforms LTX-2.3 in generation quality, semantic alignment and cross-modal synchronization under LoRA and full fine-tuning. Ablations confirm our designs. Code and data: https://github.com/zhiyuxu03/AV-GRPO

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to perturbation analysis and address them by introducing the concept of extremal perturbations, which are theoretically grounded and interpretable. We also introduce a number of technical innovations to compute extremal perturbations, including a new area constraint and a parametric family of smooth perturbations, which allow us to remove all tunable hyper-parameters from the optimization problem. We analyze the effect of perturbations as a function of their area, demonstrating excellent sensitivity to the spatial properties of the deep neural network under stimulation. We also extend perturbation analysis to the intermediate layers of a network. This application allows us to identify the salient channels necessary for classification, which, when visualized using feature inversion, can be used to elucidate model behavior. Lastly, we introduce TorchRay, an interpretability library built on PyTorch.

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the collected data can actually reveal. Although reinforcement learning (RL) can optimize a given objective, constructing objectives that reflect parametric learnability is difficult in high-dimensional robotic systems. Many parameter directions are weakly observable or unidentifiable, and even when identifiable directions are selected, omitted directions can still influence exploration and distort information measures. To address this challenge, we propose Quasi-Optimal Experimental Design (Q{\footnotesize OED}), an adaptive information objective grounded in optimal experimental design. Q{\footnotesize OED} (i) performs eigenspace analysis of the Fisher information matrix to identify an observable subspace and select identifiable parameter directions, and (ii) modifies the exploration objective to emphasize these directions while suppressing nuisance effects from non-critical parameters. Under bounded nuisance influence and limited coupling between critical and nuisance directions, Q{\footnotesize OED} provides a constant-factor approximation to the ideal information objective that explores all parameters. We evaluate Q{\footnotesize OED} on simulated and real-world navigation and manipulation tasks, where identifiable-direction selection and nuisance suppression yield performance improvements of 35.23{\percent} and 21.98{\percent}, respectively. When integrated as an exploration objective in model-based policy optimization, Q{\footnotesize OED} further improves policy performance over established RL baselines.

Overfitting widely exists in adversarial robust training of deep networks. An effective remedy is adversarial weight perturbation, which injects the worst-case weight perturbation during network training by maximizing the classification loss on adversarial examples. Adversarial weight perturbation helps reduce the robust generalization gap; however, it also undermines the robustness improvement. A criterion that regulates the weight perturbation is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find that it is essential to conduct weight perturbation on adversarial data with small classification loss to eliminate robust overfitting. Weight perturbation on adversarial data with large classification loss is not necessary and may even lead to poor robustness. Based on these observations, we propose a robust perturbation strategy to constrain the extent of weight perturbation. The perturbation strategy prevents deep networks from overfitting while avoiding the side effect of excessive weight perturbation, significantly improving the robustness of adversarial training. Extensive experiments demonstrate the superiority of the proposed method over the state-of-the-art adversarial training methods.

Predicting cellular responses to perturbations supports the study of gene function, disease mechanisms, and therapeutic strategies. Despite advances in single-cell perturbation modeling, existing models typically optimize surrogate losses that do not directly reflect the biological criteria used for evaluation, so better data fitting need not yield better biological predictions. To address this mismatch, we introduce CellRFT, a reinforcement fine-tuning framework that uses biological evaluation as direct training feedback. CellRFT uses policy-gradient optimization to learn from non-differentiable evaluations of generated cell populations and integrates multiple biological rewards through hierarchical reward aggregation. Comprehensive experiments demonstrate CellRFT's applicability across different pretrained models and effectiveness in improving perturbation prediction, reveal that optimizing one biological criterion can help or hinder others, and show that complementary rewards can improve criteria beyond those directly optimized, offering a way to probe how biological metrics shape model behavior, with the potential to inform evaluation design. Code will be made available.

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

Offline reinforcement learning (offline RL) can benefit from nearby out-of-distribution (OOD) actions, but estimation errors at these actions may be amplified by bootstrapping. Existing regularization and local-generalization methods control either the admissible OOD region or the influence of generalized targets, often through separate mechanisms. We propose Convex Hull Neighborhood Smooth Dual Generalization (CSDG), which expresses the Bellman backup as an in-sample value target plus a CHN-local correction. This formulation makes the generalized contribution explicit and separates it from the in-sample reference path. The correction is obtained by smoothing in-sample-oriented and OOD-oriented candidates sampled at different perturbation radii. A mixture coefficient lambda scales its contribution to each backup, while the recursive discount remains gamma. Under boundedness and fixed perturbation kernels, we derive an exact one-step correction identity, a time-varying iterate bound, and a fixed-point bound that depends only on the branch discrepancy at the fixed point. We further characterize the implicit policies induced by the idealized operators and give a conditional non-degradation criterion. The practical algorithm approximates these quantities using asymmetric bounded noise and expectile regression, without exact support classification or an additional pessimistic OOD penalty. Experiments on Gym-MuJoCo and AntMaze show strong aggregate performance and stable value estimation. Code is available at: https://github.com/YOUNG-fnxm/CSDG

Policy-based reinforcement learning algorithms are widely used in various fields. Among them, mainstream policy optimization algorithms such as TRPO and PPO introduce importance sampling into policy iteration, which allows the reuse of historical data. However, this can also lead to a high variance of the surrogate objective and indirectly affects the stability and convergence of the algorithm. In this paper, we first derived an upper bound of the surrogate objective variance, which can grow quadratically with the increase of the surrogate objective. Next, we proposed the dropout technique to avoid the excessive increase of the surrogate objective variance caused by importance sampling. Then, we introduced a general reinforcement learning framework applicable to mainstream policy optimization methods, and applied the dropout technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct comparative experiments between D-PPO and PPO algorithms in the Atari 2600 environment, and the results show that D-PPO achieved significant performance improvements compared to PPO, and effectively limited the excessive increase of the surrogate objective variance during training.

We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We also extend our analysis to dynamic regret, obtaining the first guarantees with optimal P_T path-length dependencies without prior knowledge of P_T. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore Ω(dT) rate for adversarial linear bandits on the Euclidean ball, which is of independent interest.

Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and discusses some issues raised due to "complexity" and "stochasticity". These unresolved issues call for a new practical methodology. For stochastic systems, a degree of observability may be defined and the observability problem is not a binary (i.e., yes-no) question anymore. Here, we propose to employ a goal-seeking system to play a supervisory role in the network. Hence, improving the degree of observability would be a valid objective for the supervisory system. Towards this goal, the supervisor dynamically optimizes the observation process by reconfiguring the sensory parts in the network. A cognitive dynamic system is suggested as a proper choice for the supervisory system. In this framework, the network itself is viewed as the environment with which the cognitive dynamic system interacts. Computer experiments confirm the potential of the proposed approach for addressing some of the issues raised in networks due to complexity and stochasticity.

Deep learning problems rarely involve objectives that are equal in importance. A primary objective defines the goal, whilst secondary objectives, such as sparsity, compression, or robustness constrain the solution. While existing multi-objective methods have proven effective in practice, they have a clear symmetry problem and neglect the inherent objective hierarchy built into these objective spaces. We introduce Priority-Constrained Descent (PCD), a gradient-based optimization framework designed to explicitly exploit hierarchical objective structures. PCD preserves the direction of primary descent whilst allowing for the minimal distortion necessary to guarantee progress on secondary objectives, controlled by a single τin [0, 1] that dictates the strength of the distortion. The resulting formulation is invariant to objective scaling and admits exact closed-form solutions for problems with two and three objectives. We evaluate PCD within structured network compression settings, unstructured sparsity and low-rankness, and across a variety of synthetic experiments, showing Pareto dominance and better per-objective performance with secondary progress guarantees over existing methods, further exhibiting the interpretable trade-off that τ provides.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Virtual cell models should capture phenotypes induced by specific perturbations. However, image-based models are typically trained and evaluated to match real-image distributions, which alone does not explicitly prioritize perturbation-specific biological responses. Recent approaches add biological signals through reinforcement-learning post-training or inference-time steering, raising a central question: where should biological response information enter the generative pipeline? We introduce PerturbBridge, a stochastic data-to-data bridge model that directly supervises perturbation-specific phenotypes in predicted perturbed images during training. PerturbBridge jointly optimizes bridge regression and differentiable biological response losses, with biological gradients passing through a frozen image encoder. We further introduce perturbation-response evaluations based on downstream classification and retrieval. Across three microscopy benchmarks for perturbation profiling and subcellular imaging, PerturbBridge surpasses CellFlux in biological fidelity, image quality, and sampling efficiency. On BBBC021, mechanism-of-action classification improves by 5.66 and 7.5 percentage points with morphological and learned visual features, respectively. On JUMP and AllenCell, retrieval Hit@10 and Hit@1 improve by 1.77 and 7.15 percentage points, respectively. On BBBC021 and JUMP, PerturbBridge achieves lower FID with 80% fewer model evaluations than CellFlux. Overall, these results show that directly supervising perturbation responses during training improves phenotypic fidelity while enabling efficient cellular image generation. Code is available at https://github.com/yyc1215lll-creator/PerturbBridge.

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter sigma > 0. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be O(sigma)-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as O(sigma)-approximation of the original BO, we propose first-order algorithms that find an epsilon-stationary solution by optimizing the penalty formulation with sigma = O(epsilon). When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an epsilon-stationary point of the penalty function, using in total O(epsilon^{-3}) and O(epsilon^{-7}) accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with O(1) samples per iteration, and achieves the improved oracle-complexity of O(epsilon^{-3}) and O(epsilon^{-5}), respectively.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Guided diffusion samplers are increasingly used to reconstruct physical fields from sparse observations, but standard diagnostics do not say how much of the reconstruction was actually determined by the data. We introduce effective data resolution for black-box generative posteriors: a comparison between the resolution warranted by the inverse problem, dof_{ref}, and the resolution realised by the sampler, dof_{samp}. A perturbation estimator measures dof_{samp} and the spatial map R(x,x) from sampler queries alone. We validate the estimator against exact references and use it to study guided diffusion. The resulting measurements show that guidance weight can strongly alter apparent information transfer, that mean, spread and resolution are not jointly corrected by one weight even with an exact prior and score, and that resolution fidelity does not follow reliably from the apparent principledness of a guidance rule.

The Perturbation Discrimination Score (PDS) is increasingly used to evaluate whether predicted perturbation effects remain distinguishable, including in Systema and the Virtual Cell Challenge. However, its behavior in high-dimensional gene-expression settings has not been examined in detail. We show that PDS is highly sensitive to the choice of similarity or distance measure and to the scale of predicted effects. Analysis of observed perturbation responses reveals that ell_1 and ell_2-based PDS behave very differently from cosine-based measures, even after norm matching. We provide geometric insight and discuss implications for future discrimination-based evaluation metrics.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Building Virtual Cells that can accurately simulate cellular responses to perturbations is a long-standing goal in systems biology. A fundamental challenge is that high-throughput single-cell sequencing is destructive: the same cell cannot be observed both before and after a perturbation. Thus, perturbation prediction requires mapping unpaired control and perturbed populations. Existing models address this by learning maps between distributions, but typically assume a single fixed response distribution when conditioned on observed cellular context (e.g., cell type) and the perturbation type. In reality, responses vary systematically due to unobservable latent factors such as microenvironmental fluctuations and complex batch effects, forming a manifold of possible distributions for the same observed conditions. To account for this variability, we introduce PerturbDiff, which shifts modeling from individual cells to entire distributions. By embedding distributions as points in a Hilbert space, we define a diffusion-based generative process operating directly over probability distributions. This allows PerturbDiff to capture population-level response shifts across hidden factors. Benchmarks on established datasets show that PerturbDiff achieves state-of-the-art performance in single-cell response prediction and generalizes substantially better to unseen perturbations. See our project page (https://katarinayuan.github.io/PerturbDiff-ProjectPage/), where code and data will be made publicly available (https://github.com/DeepGraphLearning/PerturbDiff).

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

Inverse inequalities are essential for controlling derivative growth and ensuring stable sampling in kernel approximation. Existing whole-space and single-scale estimates provide an established analytical basis, but their extension to multiscale analytic spaces on finite intervals requires uniform control of boundary effects and cross-scale cancellation. This paper establishes unweighted interval \(L^2\) inverse inequalities for spaces generated by primitives of kernels with positive exponential spectra. By retaining exterior diagonal energy and controlling off-diagonal interactions through one-sided estimates with endpoint-distance weights, we derive uniform coefficient bounds for normalized high derivatives. A synthesis-operator perturbation argument extends these bounds to positive spectral mixtures, while adjacent-derivative comparison and interval interpolation yield an inverse bound of order \(h_*^{-1}\), where \(h_*\) is the smallest scale. Under geometric scale separation and within-scale centre separation, the constant is independent of the number of scales and centres and their distances from the endpoints, allowing endpoint centres and coincident centres across scales. The coefficient lower bound approaches the optimal limit \(1/2\). Two-centre constructions establish the sharpness of the scale exponent for every fixed kernel in the class and, for a single exponential spectrum, a sharp deficit of order \(q^{-1/2}\) from \(1/2\) for the best uniform coefficient lower bound, where \(q\) is the derivative order. Numerical illustrations for Cauchy and logistic kernels demonstrate coefficient stability in several multiscale configurations. These results extend interval inverse estimates to multiscale analytic kernel spaces with endpoint centres and provide quantitative conditions for deterministic sampling stability.

The antenna-elements that make up a radio interferometer form a spatial filter that samples components of the Fourier transform of a target radio astronomical source brightness. Along the signal path, there are multiplicative and additive perturbation effects that alter the signal and that should be corrected. The process of mitigating these perturbation effects is called calibration. In this work, we develop a new and fast Maximum Likelihood based estimator of these perturbation effects using the Exponential Map and Lie groups. To evaluate its performance, we compare it to the Cramér-Rao Lower Bound and, to test the estimation time, we compare it with the Expectation Maximization algorithm, another fast Maximum Likelihood estimator. Finally, we apply our estimator to a real observation of the protoplanetary disk AS 209 made with the Submillimeter Array. We found that our proposed estimator meets the Cramér-Rao Lower Bound and it was approximately 40 times faster than the Expectation Maximization algorithm.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems.In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

We study a persistent failure mode in multi-objective alignment for large language models (LLMs): training improves performance on only a subset of objectives while causing others to degrade. We formalize this phenomenon as cross-objective interference and conduct the first systematic study across classic scalarization algorithms, showing that interference is pervasive and exhibits strong model dependence. To explain this phenomenon, we derive a local covariance law showing that an objective improves at first order when its reward exhibits positive covariance with the scalarized score. We extend this analysis to clipped surrogate objectives used in modern alignment, demonstrating that the covariance law remains valid under mild conditions despite clipping. Building on this analysis, we propose Covariance Targeted Weight Adaptation (CTWA), a plug-and-play method that maintains positive covariance between objective rewards and the training signal to effectively mitigate cross-objective interference. Finally, we complement these local improvement conditions with a global convergence analysis under the Polyak--Łojasiewicz condition, establishing when non-convex scalarized optimization achieves global convergence and how cross-objective interference depends on specific model geometric properties.

Many modern deep learning applications require balancing multiple objectives that are often conflicting. Examples include multi-task learning, fairness-aware learning, and the alignment of Large Language Models (LLMs). This leads to multi-objective deep learning, which tries to find optimal trade-offs or Pareto-optimal solutions by adapting mathematical principles from the field of Multi-Objective Optimization (MOO). However, directly applying gradient-based MOO techniques to deep neural networks presents unique challenges, including high computational costs, optimization instability, and the difficulty of effectively incorporating user preferences. This paper provides a comprehensive survey of gradient-based techniques for multi-objective deep learning. We systematically categorize existing algorithms based on their outputs: (i) methods that find a single, well-balanced solution, (ii) methods that generate a finite set of diverse Pareto-optimal solutions, and (iii) methods that learn a continuous Pareto set of solutions. In addition to this taxonomy, the survey covers theoretical analyses, key applications, practical resources, and highlights open challenges and promising directions for future research. A comprehensive list of multi-objective deep learning algorithms is available at https://github.com/Baijiong-Lin/Awesome-Multi-Objective-Deep-Learning.

While reinforcement learning algorithms can learn effective policies for complex tasks, these policies are often brittle to even minor task variations, especially when variations are not explicitly provided during training. One natural approach to this problem is to train agents with manually specified variation in the training task or environment. However, this may be infeasible in practical situations, either because making perturbations is not possible, or because it is unclear how to choose suitable perturbation strategies without sacrificing performance. The key insight of this work is that learning diverse behaviors for accomplishing a task can directly lead to behavior that generalizes to varying environments, without needing to perform explicit perturbations during training. By identifying multiple solutions for the task in a single environment during training, our approach can generalize to new situations by abandoning solutions that are no longer effective and adopting those that are. We theoretically characterize a robustness set of environments that arises from our algorithm and empirically find that our diversity-driven approach can extrapolate to various changes in the environment and task.

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning schemes, with little development of the general framework. In this paper, we identify a fundamental issue of the standard MBRL framework -- what we call the objective mismatch issue. Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized. In the context of MBRL, we characterize the objective mismatch between training the forward dynamics model w.r.t.~the likelihood of the one-step ahead prediction, and the overall goal of improving performance on a downstream control task. For example, this issue can emerge with the realization that dynamics models effective for a specific task do not necessarily need to be globally accurate, and vice versa globally accurate models might not be sufficiently accurate locally to obtain good control performance on a specific task. In our experiments, we study this objective mismatch issue and demonstrate that the likelihood of one-step ahead predictions is not always correlated with control performance. This observation highlights a critical limitation in the MBRL framework which will require further research to be fully understood and addressed. We propose an initial method to mitigate the mismatch issue by re-weighting dynamics model training. Building on it, we conclude with a discussion about other potential directions of research for addressing this issue.

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., N!approx!30), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph structure and, if available, an observational dataset; and then solves the restricted optimization problem by modelling target and constraint quantities using Gaussian processes and by sequentially selecting interventions via a constrained expected improvement acquisition function. We propose different surrogate models that enable to integrate observational and interventional data while capturing correlation among effects with increasing levels of sophistication. We evaluate cCBO on artificial and real-world causal graphs showing successful trade off between fast convergence and percentage of feasible interventions.

We investigate an experiential learning paradigm for acquiring an internal model of intuitive physics. Our model is evaluated on a real-world robotic manipulation task that requires displacing objects to target locations by poking. The robot gathered over 400 hours of experience by executing more than 100K pokes on different objects. We propose a novel approach based on deep neural networks for modeling the dynamics of robot's interactions directly from images, by jointly estimating forward and inverse models of dynamics. The inverse model objective provides supervision to construct informative visual features, which the forward model can then predict and in turn regularize the feature space for the inverse model. The interplay between these two objectives creates useful, accurate models that can then be used for multi-step decision making. This formulation has the additional benefit that it is possible to learn forward models in an abstract feature space and thus alleviate the need of predicting pixels. Our experiments show that this joint modeling approach outperforms alternative methods.

In this paper, we study the problem of sampling from a probability distribution using Langevin-type dynamics. We consider overdamped Langevin dynamics perturbed by adding a Stratonovich perturbation that preserves reversibility. We prove an optimal scaling for the Stratonovich perturbation applied to Gaussian target distributions and derive an algorithm to construct such perturbation. Our theoretical results are supplemented by numerical experiments in which we compare our proposed method with nonreversible samplers and overdamped Langevin dynamics. Our numerical experiments demonstrate the efficiency of the approach beyond the quadratic case.

We formulate gene regulatory network reconstruction from RNA velocity as a sparse dynamical inverse problem. We show that control-only data can be structurally nonidentifying and characterize excitation conditions under which controlled perturbations restore identifiability by generating complementary regulator trajectories. To enable stable reconstruction from noisy data, we develop an integral sparse estimator that avoids numerical differentiation and derive recovery bounds separating stochastic error from systematic contributions due to latent-time uncertainty, kinetic-parameter error, numerical quadrature, and model misspecification. Synthetic experiments illustrate perturbation-assisted identifiability, improved conditioning, and the robustness of integral reconstruction. Applied to perturbation-resolved RPE1 RNA-velocity data, the framework yields an empirically full-rank design whose conditioning improves with perturbational diversity and a reconstructed network core stable under perturbation subsampling. Held-out evaluation further shows that identifiability and reconstruction stability do not imply uniform predictive improvement. These results connect perturbational excitation, identifiability, and stable sparse recovery in regulatory dynamical systems.

Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback--Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.

This paper derives necessary optimality conditions for free end-time optimal control problems governed by sweeping process dynamics. In contrast to classical optimal control problems, the presence of the normal cone term in the state equation introduces discontinuities with respect to the state variable and prevents the standard Lipschitz regularity assumptions typically used in optimal control theory. As a result, both the analysis of trajectories and the formulation of optimality conditions require refined tools. We address problems with general endpoint constraints and time-dependent data, considering both the case in which the dynamics are Lipschitz continuous in time and the more challenging setting of merely measurable time dependence. Special attention is devoted to the additional transversality conditions associated with the free end-time variable. In the Lipschitz case, these conditions are expressed in terms of a function of bounded variation that coincides almost everywhere with the maximized Hamiltonian. In the measurable case, we show that a suitable interpretation can be obtained via the notions of sub- and super-essential values of the maximized Hamiltonian, recently introduced in the literature, leading to strengthened transversality conditions. These conditions also involve an additional term reflecting the interaction between the costate arc and the normal cone to the moving set at the optimal endpoints. Our approach combines suitable perturbation techniques with a penalization method tailored to sweeping processes. The moving set is modelled as a finite intersection of inequality-defined sets satisfying suitable constraint qualifications, including a positive linear independence condition and a diagonal dominance property of the associated Gramian matrix. We also introduce a local version of the constraint qualification condition. Our results apply to a broad class of problems, including those involving unbounded moving sets such as polyhedra. The resulting optimality system extends and sharpens recent results for classical free end-time problems to the non-Lipschitz, discontinuous framework of sweeping processes. The relevance of the transversality conditions obtained in this article is illustrated through two simple examples.

Sharpness Aware Minimization (SAM) enhances performance across various neural architectures and datasets. As models are continually scaled up to improve performance, a rigorous understanding of SAM's scaling behaviour is paramount. To this end, we study the infinite-width limit of neural networks trained with SAM, using the Tensor Programs framework. Our findings reveal that the dynamics of standard SAM effectively reduce to applying SAM solely in the last layer in wide neural networks, even with optimal hyperparameters. In contrast, we identify a stable parameterization with layerwise perturbation scaling, which we call Maximal Update and Perturbation Parameterization (μP^2), that ensures all layers are both feature learning and effectively perturbed in the limit. Through experiments with MLPs, ResNets and Vision Transformers, we empirically demonstrate that μP^2 achieves hyperparameter transfer of the joint optimum of learning rate and perturbation radius across model scales. Moreover, we provide an intuitive condition to derive μP^2 for other perturbation rules like Adaptive SAM and SAM-ON, also ensuring balanced perturbation effects across all layers.

Existing works have extensively studied adversarial examples, which are minimal perturbations that can mislead the output of deep neural networks (DNNs) while remaining imperceptible to humans. However, in this work, we reveal the existence of a harmless perturbation space, in which perturbations drawn from this space, regardless of their magnitudes, leave the network output unchanged when applied to inputs. Essentially, the harmless perturbation space emerges from the usage of non-injective functions (linear or non-linear layers) within DNNs, enabling multiple distinct inputs to be mapped to the same output. For linear layers with input dimensions exceeding output dimensions, any linear combination of the orthogonal bases of the nullspace of the parameter consistently yields no change in their output. For non-linear layers, the harmless perturbation space may expand, depending on the properties of the layers and input samples. Inspired by this property of DNNs, we solve for a family of general perturbation spaces that are redundant for the DNN's decision, and can be used to hide sensitive data and serve as a means of model identification. Our work highlights the distinctive robustness of DNNs (i.e., consistency under large magnitude perturbations) in contrast to adversarial examples (vulnerability for small imperceptible noises).

Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL). While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. To this end, we study a general family of probability-based objectives and characterize their effectiveness under different conditions. Through comprehensive experiments and extensive ablation studies across 7 model backbones, 14 benchmarks, and 3 domains, we uncover a critical dimension that governs objective behavior: the model-capability continuum. Near the model-strong end, prior-leaning objectives that downweight low-probability tokens (e.g., -p, -p^{10}, thresholded variants) consistently outperform NLL; toward the model-weak end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability. Our code is available at https://github.com/GaotangLi/Beyond-Log-Likelihood.

AI-based cellular perturbation prediction is essential to accelerate drug discovery and therapeutic identification. However, perturbation-specific signals are generally obscured by cellular complexity, making it difficult for existing methods to correctly capture perturbation effects. To address this problem, we propose PerturbEnergy, which introduces a conditional energy-based prior over perturbation representations. It assigns lower energy (higher probability) to representations compatible with the given perturbation and higher energy to others, thereby explicitly tilting the latent space toward perturbation-preferred regions. Besides, PerturbEnergy can be integrated into autoencoder architectures as we find its Evidence Lower Bound (ELBO) is equivalent to the ELBO of the complete autoencoder. We further prove that optimizing PerturbEnergy increases the lower bound on the conditional mutual information between representation and perturbation. Extensive experiments on four benchmark datasets demonstrate the effectiveness of our PerturbEnergy: it improves perturbation recognition especially in latent space with improvement of up to 83.2\%; It also achieves state-of-the-art performance for predicting top-50/100/200 differentially expressed gene(DEG) response and remaining competitive on highly variable gene(HVG) prediction. The code is provided: https://github.com/BlueWhaleLab/PerturbEnergy

We study the relation between equal-weight circle quadrature, Gauss--Chebyshev quadrature, and planar Minkowski reconstruction. The regular N-point grid is an mathbb S^1-design of strength N-1; a half-step rotation of the 2M-point grid projects to the classical M-point Gauss--Chebyshev rule. A common family of quadrature-error functionals gives exact identities for integration error, mixed-area error, and support-function error. For Nge3, the centered Minkowski polygon P_N with perimeter 2π has the exact Hausdorff distance from the unit disk B^2 \[ d_H(P_N,B^2)=1-\fracπ{N}\cot\fracπ{N} =π^2{3N^2}+O(N^{-4}). \] With Steiner centering, we obtain d_H(K_μ,K_ν)leπW_1(μ,ν) for balanced, nondegenerate probability measures, where W_1 uses geodesic distance. Its exponent is sharp even for smooth positive densities near the uniform measure. The identity W_1(ν_N,σ)=π/(2N) yields a general O(N^{-1}) bound for the regular grid. The sharper O(N^{-2}) rate follows from the sparse discrepancy spectrum and the inverse multiplier (1-k^2)^{-1}. Finally, a perturbation estimate gives sufficient conditions for preserving the quadratic rate and its leading constant.

Recent benchmarks reveal that models for single-cell perturbation response are often outperformed by simply predicting the dataset mean. We trace this anomaly to a metric artifact: control-referenced deltas and unweighted error metrics reward mode collapse whenever the control is biased or the biological signal is sparse. Large-scale in silico simulations and analysis of two real-world perturbation datasets confirm that shared reference shifts, not genuine biological change, drives high performance in these evaluations. We introduce differentially expressed gene (DEG)-aware metrics, weighted mean-squared error (WMSE) and weighted delta R^{2} (R^{2}_{w}(Δ)) with respect to all perturbations, that measure error in niche signals with high sensitivity. We further introduce negative and positive performance baselines to calibrate these metrics. With these improvements, the mean baseline sinks to null performance while genuine predictors are correctly rewarded. Finally, we show that using WMSE as a loss function reduces mode collapse and improves model performance.

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of distributed alignment search (DAS), the standard for causal variable localization, to propose a new steering method: Concept DAS (CDAS). While we adopt the core mechanism of DAS, distributed interchange intervention (DII), we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering. Our code is available at https://github.com/colored-dye/concept_das.

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. Its continuous-time formulation can be interpreted as an interacting particle system driven by a Kalman-type preconditioned descent direction. A well-known limitation of this dynamics is the possible premature collapse of the covariance of the ensemble, which makes the method sensitive to the initial ensemble. We introduce a second-order particle system in which the particles evolve according to an inertial dynamics. The model combines a Kalman-type relaxation force with damping, attraction towards the ensemble mean, and a short-range repulsive interaction designed to counteract ensemble collapse. The resulting dynamics can be interpreted as a heavy-ball reformulation of continuous-time EKI enriched by competing attractive and repulsive mechanisms. For linear inverse problems, we analyze the induced mean and fluctuation dynamics and identify a parameter regime in which fully collapsed configurations are linearly unstable. We further characterize asymptotic equilibria through a constrained optimality condition on the subspace retained by the limiting ensemble covariance and derive an exponential decay estimate. Numerical experiments illustrate the effect of inertia and repulsion on the ensemble dynamics and compare the proposed second-order method with first-order EKI-type

As LLM-based agents continue to advance, their evaluation has become increasingly multifaceted: a capable agent must not only achieve high task completion accuracy but also perform well in interaction quality, safety, and efficiency, raising a central question: can these objectives be optimized simultaneously? Existing methods have considered multiple objectives, but many collapse heterogeneous measurements into a fixed scalar score. Such scalarization depends on metric normalization and preference weights and may discard candidates that represent useful deployment trade-offs. We introduce Multi-Objective Agent Evolution (MOAE), which organizes iterative in-context refinement as a Pareto-preserving evolutionary search over complete agent rollouts. Given a limited rollout budget, MOAE maintains an empirical archive of non-dominated candidates, uses objective-specific diagnostics to guide offspring generation, and applies constraint-aware selection only at deployment. This separates candidate preservation during search from the preference used to return a final solution. The procedure requires no parameter updates and allows each objective to be replaced by any measurable property, which we instantiate as task performance, trajectory quality, and safety. Experiments on TravelPlanner and AgentDojo show that MOAE consistently improves task performance and trajectory quality while maintaining strong safety under matched rollout budgets. Search-behavior analysis further shows that Pareto preservation expands the attainable objective region and increases the frequency of joint improvement. These results demonstrate the potential of Pareto-preserving in-context evolution for optimizing multiple agent properties without committing to a fixed scalarization during search.

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

We construct an odd smooth initial density for the unforced incompressible porous media (IPM) equation on mathbb T^2 whose solution develops a finite-time blowup. The components partial_{x_2}ρ(t,0) and partial_{x_1}u_1(t,0) tend to +infty as the maximal smooth existence time is approached, while the density and velocity remain bounded in L^2. Starting from a stationary solution, we iterate the angular amplification of localized oscillations with rapidly growing frequencies, adapting the mechanism of Córdoba and Martínez-Zoroa [7] for forced IPM. Each perturbation is constructed from time zero and creates the geometry configuration for the next iteration stage. A one-sided upper bound for the pressure Hessian is applied to control backward preparation and initial perturbations, following an idea from the Euler construction of OpenAI [14].

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under intermittent androgen suppression (IAS) to study a threshold-based policy for therapy design. IAS is currently one of the most widely used treatments for advanced prostate cancer. Patients undergoing IAS are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. One of the main challenges in IAS is to optimally design a therapy scheme, i.e., to determine when to discontinue and recommence androgen suppression. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. The threshold-based policy we propose is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. Using Infinitesimal Perturbation Analysis (IPA), we derive unbiased gradient estimators of this cost metric with respect to the controllable PSA threshold values based on actual data and show how these estimators can be used to adaptively adjust controllable parameters so as to improve therapy outcomes based on the cost metric defined.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

Learning from preference labels plays a crucial role in fine-tuning large language models. There are several distinct approaches for preference fine-tuning, including supervised learning, on-policy reinforcement learning (RL), and contrastive learning. Different methods come with different implementation tradeoffs and performance differences, and existing empirical findings present different conclusions, for instance, some results show that online RL is quite important to attain good fine-tuning results, while others find (offline) contrastive or even purely supervised methods sufficient. This raises a natural question: what kind of approaches are important for fine-tuning with preference data and why? In this paper, we answer this question by performing a rigorous analysis of a number of fine-tuning techniques on didactic and full-scale LLM problems. Our main finding is that, in general, approaches that use on-policy sampling or attempt to push down the likelihood on certain responses (i.e., employ a "negative gradient") outperform offline and maximum likelihood objectives. We conceptualize our insights and unify methods that use on-policy sampling or negative gradient under a notion of mode-seeking objectives for categorical distributions. Mode-seeking objectives are able to alter probability mass on specific bins of a categorical distribution at a fast rate compared to maximum likelihood, allowing them to relocate masses across bins more effectively. Our analysis prescribes actionable insights for preference fine-tuning of LLMs and informs how data should be collected for maximal improvement.

Reinforcement Learning (RL) post-training has become the standard for aligning generative models with human preferences, yet most methods rely on a single scalar reward. When multiple criteria matter, the prevailing practice of ``early scalarization'' collapses rewards into a fixed weighted sum. This commits the model to a single trade-off point at training time, providing no inference-time control over inherently conflicting goals -- such as prompt adherence versus source fidelity in image editing. We introduce ParetoSlider, a multi-objective RL (MORL) framework that trains a single diffusion model to approximate the entire Pareto front. By training the model with continuously varying preference weights as a conditioning signal, we enable users to navigate optimal trade-offs at inference time without retraining or maintaining multiple checkpoints. We evaluate ParetoSlider across three state-of-the-art flow-matching backbones: SD3.5, FluxKontext, and LTX-2. Our single preference-conditioned model matches or exceeds the performance of baselines trained separately for fixed reward trade-offs, while uniquely providing fine-grained control over competing generative goals.

Predicting cellular responses to perturbations is a central problem in cellular biology, with broad applications in systems biology and drug discovery. This task is challenging because cellular responses can be complex and cell-state dependent, intrinsic cell-to-cell variability can be confounded with perturbation effects, and destructive single-cell RNA sequencing precludes paired measurements of the same cell before and after treatment. Flow matching transports control cells to perturbed states flexibly, but acting on the full cell state can confound perturbation effects with pre-existing cell-to-cell variability. Disentangled approaches separate responsive from invariant components, but model perturbations through prescribed mechanisms, such as latent shifts or graph edits, limiting their flexibility. We address both limitations in a unified framework. A variational encoder disentangles each cell into an invariant block, capturing state unaffected by the perturbation, and a responsive block, capturing state it changes, through conditional priors and an information-theoretic invariance constraint. Conditional flow matching transports only the responsive block, conditioned on the perturbation and invariant state, yielding a flexible, data-driven model of perturbation effects without confounding pre-existing variability. Across several benchmarks, our method outperforms the strongest published method in settings involving combinatorial and unseen perturbation prediction.

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.

Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem may be high-dimensional and/or time-varying. Most problems in these applications are nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing Omega(d) function valuations per iteration (with d denoting the problem dimension) can escape saddle points efficiently, it remains an open question if zeroth-order methods based on two-point estimators can escape saddle points. In this paper, we show that by adding an appropriate isotropic perturbation at each iteration, a zeroth-order algorithm based on 2m (for any 1 leq m leq d) function evaluations per iteration can not only find epsilon-second order stationary points polynomially fast, but do so using only Oleft(d{mepsilon^{2}psi}right) function evaluations, where psi geq Omegaleft(epsilonright) is a parameter capturing the extent to which the function of interest exhibits the strict saddle property.

In this paper, by introducing Generalized Bernstein condition, we propose the first Obig(sqrt{p}{nepsilon}big) high probability excess population risk bound for differentially private algorithms under the assumptions G-Lipschitz, L-smooth, and Polyak-{\L}ojasiewicz condition, based on gradient perturbation method. If we replace the properties G-Lipschitz and L-smooth by alpha-H{\"o}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to Obig(n^{-alpha{1+2alpha}}big) w.r.t n, which cannot achieve Oleft(1/nright) when alphain(0,1]. To solve this problem, we propose a variant of gradient perturbation method, max{1,g-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions alpha-H{\"o}lder smooth and Polyak-{\L}ojasiewicz condition can achieve Obig(sqrt{p}{nepsilon}big), which is the first Oleft(1/nright) high probability excess population risk bound w.r.t n for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

Generative modeling has shown increasing promise for predicting cellular perturbation effects under chemical compound treatments. Existing approaches either model perturbation as a distribution-to-distribution mapping without explicit concentration handling, or treat concentration as a discrete class label, precluding continuous dose control. We introduce a joint flow matching approach that simultaneously models cell latents and drug concentration via a dual-timestep formulation, enabling dose-conditioned single-cell morphing through the invertibility of flow matching. The joint formulation induces a monotonic dose-response geometry in latent space and additionally supports concentration estimation from cell morphology. As proof of concept, we further demonstrate generalization to an unseen dose held out during training. Empirically, our method achieves competitive or improved per-concentration metrics on two compounds compared with representative baselines, while enabling capabilities structurally unavailable to discrete-class methods.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

Multi-Objective Reinforcement Learning (MORL) is a generalization of traditional Reinforcement Learning (RL) that aims to optimize multiple, often conflicting objectives simultaneously rather than focusing on a single reward. This approach is crucial in complex decision-making scenarios where agents must balance trade-offs between various goals, such as maximizing performance while minimizing costs. We consider the problem of MORL where the objectives are combined using a non-linear scalarization function. Just like in standard RL, policy gradient methods (PGMs) are amongst the most effective for handling large and continuous state-action spaces in MORL. However, existing PGMs for MORL suffer from high sample inefficiency, requiring large amounts of data to be effective. Previous attempts to solve this problem rely on overly strict assumptions, losing PGMs' benefits in scalability to large state-action spaces. In this work, we address the issue of sample efficiency by implementing variance-reduction techniques to reduce the sample complexity of policy gradients while maintaining general assumptions.

Predicting high-dimensional transcriptional responses to genetic perturbations is challenging due to severe experimental noise and sparse gene-level effects. Existing methods often suffer from mean collapse, where high correlation is achieved by predicting global average expression rather than perturbation-specific responses, leading to many false positives and limited biological interpretability. Recent approaches incorporate biological knowledge graphs into perturbation models, but these graphs are typically treated as dense and static, which can propagate noise and obscure true perturbation signals. We propose AdaPert, a perturbation-conditioned framework that addresses mean collapse by explicitly modeling sparsity and biological structure. AdaPert learns perturbation-specific subgraphs from biological knowledge graphs and applies adaptive learning to separate true signals from noise. Across multiple genetic perturbation benchmarks, AdaPert consistently outperforms existing baselines and achieves substantial improvements on DEG-aware evaluation metrics, indicating more accurate recovery of perturbation-specific transcriptional changes.