Daily Papers

The Transformer architecture, despite its widespread success, struggles with long-context scenarios due to quadratic computation and linear memory growth. While various linear attention variants mitigate these efficiency constraints by compressing context into fixed-size states, they often degrade performance in tasks such as in-context retrieval and reasoning. To address this limitation and achieve more effective context compression, we propose two key innovations. First, we introduce a row-sparse update formulation for linear attention by conceptualizing state updating as information classification. This enables sparse state updates via softmax-based top-k hard classification, thereby extending receptive fields and reducing inter-class interference. Second, we present Sparse State Expansion (SSE) within the sparse framework, which expands the contextual state into multiple partitions, effectively decoupling parameter size from state capacity while maintaining the sparse classification paradigm. Our design, supported by efficient parallelized implementations, yields effective classification and discriminative state representations. We extensively validate SSE in both pure linear and hybrid (SSE-H) architectures across language modeling, in-context retrieval, and mathematical reasoning benchmarks. SSE demonstrates strong retrieval performance and scales favorably with state size. Moreover, after reinforcement learning (RL) training, our 2B SSE-H model achieves state-of-the-art mathematical reasoning performance among small reasoning models, scoring 64.7 on AIME24 and 51.3 on AIME25, significantly outperforming similarly sized open-source Transformers. These results highlight SSE as a promising and efficient architecture for long-context modeling.

Scalable Vector Graphics (SVG) animation generation is pivotal for professional design due to their structural editability and resolution independence. However, this task remains challenging as it requires bridging discrete code representations with continuous visual dynamics. Existing optimization-based methods often destroy topological consistency, while general-purpose LLMs rely on rigid CSS/SMIL transformations, failing to model geometry-level non-rigid deformations. To address these limitations, we present VAnim, the first LLM-based framework for open-domain text-to-SVG animation. We reconceptualize animation not as sequence generation, but as Sparse State Updates (SSU) on a persistent SVG DOM tree. This paradigm compresses sequence length by over 9.8x while preserving the SVG DOM structure and non-participating elements by construction. To enable precise control, we propose an Identification-First Motion Planning mechanism that grounds textual instructions in explicit visual entities. Furthermore, to overcome the non-differentiable nature of SVG rendering, we employ Rendering-Aware Reinforcement Learning via Group Relative Policy Optimization (GRPO). By leveraging a hybrid reward from a state-of-the-art video perception encoder, we align discrete code updates with high-fidelity visual feedback. We also introduce SVGAnim-134k, the first benchmark for vector animation. Extensive experiments demonstrate that VAnim significantly outperforms state-of-the-art baselines in semantic alignment and structural validity, with additional appendix metrics further validating motion quality and identity preservation.

We study whether a structured recurrent state can serve as a compact associative backbone for language modeling while still supporting exact retrieval. We introduce UniMatrix, a Universal Transformer style family that reuses a shared recurrent block across depth and augments it with hybrid state updates, a ROSA-style residual path, and token-conditioned embedding modulation. We evaluate these models on byte-level WikiText-2, synthetic associative recall, throughput profiling on Apple MPS, and a corrected benchmark for triple-token interactions. At small scale, UniMatrix-Core and UniMatrix-ROSA slightly outperform a parameter-matched Transformer on WikiText-2 while using many fewer parameters, reaching 5.084 and 5.083 bits-per-byte versus 5.124. The main negative result is equally important: on associative recall, the original UniMatrix family remains near chance while the Transformer reaches 25.4 percent, showing that compressed recurrent state alone is not enough for exact lookup. A retrieval-oriented follow-up, UniMatrix-Assoc, helps only marginally. By contrast, UniMatrix-SparsePointer, which adds sparse slot routing and direct pointer-logit fusion, reaches 75.6 percent on the original pilot recipe and 99.2 percent on a no-dropout follow-up while using 53.8 percent fewer parameters than the Transformer baseline. Ablations show that the gain comes from sufficient slot capacity and exact pointer-level output routing. Overall, structured recurrent state is promising and parameter-efficient, but strong long-range behavior still requires explicit sparse retrieval and better kernels.

Current Unified Large Multimodal Models (ULMMs) support interleaved multimodal reasoning through textual reasoning and intermediate visual states, but typically generate each visual state as a full image. This full-image generation paradigm introduces substantial visual-token redundancy and dilutes supervision on sparse yet reasoning-critical state transitions. We propose DeltaV, a ULMM that replaces full-image generation with visual updates. Conditioned on historical visual states, DeltaV incrementally predicts compact update tokens that capture the visual changes across reasoning steps, avoiding repeated modeling of unchanged content. To align the token budget of each update with the magnitude of visual change, DeltaV introduces a temporal similarity (TSIM) Router, which stops allocating tokens once the marginal reconstruction gain falls below a threshold. To support more diverse and generalizable reasoning, we further construct StructCoT, a large-scale interleaved multimodal reasoning dataset with 1.05M samples spanning 44 task domains. Experiments show that the visual-update paradigm reduces newly generated visual tokens by 55.6\% on average without compromising reconstruction fidelity, and improves multimodal reasoning by 3.3\% over full-image generation. Trained with StructCoT and large-scale multimodal data, DeltaV-2B further outperforms substantially larger open-source models by 8.4\% on in-domain multimodal reasoning evaluations and surpasses the comparable-scale Qwen3-VL-2B by 5.9\% on external multimodal reasoning and understanding benchmarks. Code, models, and StructCoT will be released at https://github.com/Pengjie-W/DeltaV.

Event cameras provide sequential visual data with spatial sparsity and high temporal resolution, making them attractive for low-latency object detection. Existing asynchronous event-based neural networks exploit this low-latency advantage by updating predictions event by event, but still suffer from two bottlenecks: recurrent architectures are difficult to train efficiently on long sequences, and improving accuracy often increases per-event computation and latency. Linear attention is appealing because it enables parallel training and recurrent inference. However, its dense state updates make per-event computation scale with the state size, yielding a poor accuracy-efficiency trade-off for object detection, where accurate localization requires fine-grained spatial states. The key challenge is therefore to introduce sparse state activation that exploits the spatial sparsity of events while preserving efficient parallel training. We propose Spatially-Sparse Linear Attention (SSLA), which introduces a mixture-of-spaces state decomposition and a scatter-compute-gather training procedure, enabling state-level sparsity as well as training parallelism. Building on SSLA, we develop an end-to-end asynchronous linear attention model, SSLA-Det, for low-latency event-based object detection. On Gen1 and N-Caltech101, SSLA-Det achieves state-of-the-art accuracy among asynchronous methods, reaching 0.375 mAP and 0.515 mAP, respectively, while reducing per-event computation by over 20 times compared with the strongest prior asynchronous baseline, demonstrating the potential of linear attention for low-latency event-based vision.

We introduce WriteSAE, the first sparse autoencoder that decomposes and edits the matrix cache write of state-space and hybrid recurrent language models, where residual SAEs cannot reach. Existing SAEs read residual streams, but Gated DeltaNet, Mamba-2, and RWKV-7 write to a d_k times d_v cache through rank-1 updates k_t v_t^top that no vector atom can replace. WriteSAE factors each decoder atom into the native write shape, exposes a closed form for the per-token logit shift, and trains under matched Frobenius norm so atoms swap one cache slot at a time. Atom substitution beats matched-norm ablation on 92.4% of n=4{,}851 firings at Qwen3.5-0.8B L9 H4, the 87-atom population test holds at 89.8%, the closed form predicts measured effects at R^2=0.98, and Mamba-2-370M substitutes at 88.1% over 2,500 firings. Sustained three-position installs at 3times lift midrank target-in-continuation from 33.3% to 100% under greedy decoding, the first behavioral install at the matrix-recurrent write site.

We present StateSMix, a fully self-contained lossless compressor that couples an online-trained Mamba-style State Space Model (SSM) with sparse n-gram context mixing and arithmetic coding. The model is initialised from scratch and trained token-by-token on the file being compressed, requiring no pre-trained weights, no GPU, and no external dependencies. The SSM (DM=32, NL=2, approximately 120K active parameters per file) provides a continuously-updated probability estimate over BPE tokens, while nine sparse n-gram hash tables (bigram through 32-gram, 16M slots each) add exact local and long-range pattern memorisation via a softmax-invariant logit-bias mechanism that updates only non-zero-count tokens. An entropy-adaptive scaling mechanism modulates the n-gram contribution based on the SSM's predictive confidence, preventing over-correction when the neural model is already well-calibrated. On the standard enwik8 benchmark, StateSMix achieves 2.123 bpb on 1 MB, 2.149 bpb on 3 MB, and 2.162 bpb on 10 MB, beating xz -9e (LZMA2) by 8.7%, 5.4%, and 0.7% respectively. Ablation experiments establish the SSM as the dominant compression engine: it alone accounts for a 46.6% size reduction over a frequency-count baseline and beats xz without any n-gram component, while n-gram tables provide a complementary 4.1% gain through exact context memorisation. OpenMP parallelisation of the training loop yields 1.9x speedup on 4 cores. The system is implemented in pure C with AVX2 SIMD and processes approximately 2,000 tokens per second on commodity x86-64 hardware.

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, FlashLoop delivers lossless accuracy while achieving up to 1.64times end-to-end speedup and up to 6times KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.

World models are essential for autonomous robotic planning. However, the substantial computational overhead of existing dense Transformerbased models significantly hinders real-time deployment. To address this efficiency-performance bottleneck, we introduce DDP-WM, a novel world model centered on the principle of Disentangled Dynamics Prediction (DDP). We hypothesize that latent state evolution in observed scenes is heterogeneous and can be decomposed into sparse primary dynamics driven by physical interactions and secondary context-driven background updates. DDP-WM realizes this decomposition through an architecture that integrates efficient historical processing with dynamic localization to isolate primary dynamics. By employing a crossattention mechanism for background updates, the framework optimizes resource allocation and provides a smooth optimization landscape for planners. Extensive experiments demonstrate that DDP-WM achieves significant efficiency and performance across diverse tasks, including navigation, precise tabletop manipulation, and complex deformable or multi-body interactions. Specifically, on the challenging Push-T task, DDP-WM achieves an approximately 9 times inference speedup and improves the MPC success rate from 90% to98% compared to state-of-the-art dense models. The results establish a promising path for developing efficient, high-fidelity world models. Codes will be available at https://github.com/HCPLab-SYSU/DDP-WM.

Reinforcement learning (RL) yields substantial improvements in large language models (LLMs) downstream task performance and alignment with human values. Surprisingly, such large gains result from updating only a small subnetwork comprising just 5 percent to 30 percent of the parameters, with the rest effectively unchanged. We refer to this phenomenon as parameter update sparsity induced by RL. It is observed across all 7 widely used RL algorithms (e.g., PPO, GRPO, DPO) and all 10 LLMs from different families in our experiments. This sparsity is intrinsic and occurs without any explicit sparsity promoting regularizations or architectural constraints. Finetuning the subnetwork alone recovers the test accuracy, and, remarkably, produces a model nearly identical to the one obtained via full finetuning. The subnetworks from different random seeds, training data, and even RL algorithms show substantially greater overlap than expected by chance. Our analysis suggests that this sparsity is not due to updating only a subset of layers, instead, nearly all parameter matrices receive similarly sparse updates. Moreover, the updates to almost all parameter matrices are nearly full-rank, suggesting RL updates a small subset of parameters that nevertheless span almost the full subspaces that the parameter matrices can represent. We conjecture that the this update sparsity can be primarily attributed to training on data that is near the policy distribution, techniques that encourage the policy to remain close to the pretrained model, such as the KL regularization and gradient clipping, have limited impact.

Reinforcement Learning (RL) has become essential for eliciting complex reasoning capabilities in Large Language Models (LLMs). However, the substantial memory overhead of storing Key-Value (KV) caches during long-horizon rollouts acts as a critical bottleneck, often prohibiting efficient training on limited hardware. While existing KV compression techniques offer a remedy for inference, directly applying them to RL training induces a severe policy mismatch, leading to catastrophic performance collapse. To address this, we introduce Sparse-RL empowers stable RL training under sparse rollouts. We show that instability arises from a fundamental policy mismatch among the dense old policy, the sparse sampler policy, and the learner policy. To mitigate this issue, Sparse-RL incorporates Sparsity-Aware Rejection Sampling and Importance-based Reweighting to correct the off-policy bias introduced by compression-induced information loss. Experimental results show that Sparse-RL reduces rollout overhead compared to dense baselines while preserving the performance. Furthermore, Sparse-RL inherently implements sparsity-aware training, significantly enhancing model robustness during sparse inference deployment.

In large-scale reinforcement learning (RL) systems with decoupled Trainer-Rollout execution, the Trainer must regularly synchronize policy weights to the Rollout side to limit policy staleness. When inter-node bandwidth is abundant, such synchronization is usually only a small fraction of end-to-end cost. As model size grows, however, the communication demand rises rapidly. In bandwidth-constrained or network-variable deployments -- for example, cross-datacenter or cross-cluster settings, heterogeneous resource pools, and online RL -- weight synchronization can become a dominant bottleneck for throughput and tail latency. We observe that, in mainstream large-model RL training, the locations where parameters actually change are highly sparse at the element level (often 99%+ sparsity). Building on this observation, we propose and implement SparseRL-Sync, which replaces full-weight transfers with a lossless sparse update payload (indices and values) that can be exactly reconstructed on the inference side, thereby preserving 100% fidelity. Under a simplified cost model, sparse synchronization reduces the per-update communication volume from S to approximately S/X; with 99% sparsity (X ~ 100), this yields about a 100x reduction in transmitted data. Combined with appropriate bucketing, SparseRL-Sync also reduces launch and control-plane overhead, significantly improving scalability and end-to-end efficiency in bandwidth-limited and highly asynchronous RL settings.

Hybrid-attention models replace most softmax attention layers with linear attention, reducing KV-cache growth and enabling larger decode batches where recurrent-state access becomes a major bottleneck. ReplaySSM amortizes state updates by buffering keys and values, but each new query still requires a full-state read even though the state remains unchanged between state updates. We observe that low-rank state-weighted query approximation accurately preserves state-read outputs. Although future queries are unknown, the basis vectors used to approximate them can be fixed offline. Based on this observation, we introduce SketchSSM, which preserves full-state updates while approximating reads. At each state update, SketchSSM reads the full state once to precompute outputs for these basis vectors, storing them in a compact sketch. Each subsequent decode step combines the sketch vectors with query-dependent coefficients to reconstruct the output without a full-state read. Across four Mamba-2-, GDN-, and KDA-based models, SketchSSM at a mean sketch rank of 8 reduces state-access traffic by approximately 10times while matching the average accuracy of the FP32 full-state baseline across four decode benchmarks, and preserves recall on four RULER retrieval tasks. At this rank on one NVIDIA B300, linear-attention kernel speedups over the Standard vLLM baseline reach 7.30times, 5.02times, and 5.24times for Mamba-2, GDN, and KDA, respectively, with up to 2.77times higher decode throughput on Nemotron 3 Super.

Radio maps and channel knowledge maps provide reusable propagation knowledge, but a stored map can become locally outdated after persistent changes to doors, partitions, furniture, large equipment, or infrastructure. Motivated by digital-twin state synchronization, we develop an electromagnetic twin that recurrently converts sparse channel measurements into a persistent wireless state, exposes that state to communication queries, and uses its uncertainty to request subsequent measurements. The twin tracks persistent or semi-persistent propagation changes rather than transient human motion or fast fading. Each update is a constrained inverse problem that combines the previous map, a scene graph, and an imperfect physics prior. Measurement consistency with a confidence-calibrated radius and physical gain bounds enforce feasibility, while scene-aware spatial regularization and selective temporal memory preserve propagation boundaries and unchanged regions. Successive convex approximation (SCA), majorization--minimization alternating direction method of multipliers (MM-ADMM), and a low-complexity primal--dual hybrid gradient (LC-PDHG) mode realize the framework at different computational scales, and a local perturbation analysis gives an explicit multi-update tracking recursion. The updated state supports access-point association and codebook beam selection, while change-weighted A-optimal design closes the measurement--update--query loop. Over 500 realizations, the recurrent update remains stable through eight persistent scene events and raises best-beam accuracy from 76.64% to 90.83% as measured-location density grows from 2% to 16%.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

State-space models (SSMs) offer a promising architecture for sequence modeling, providing an alternative to Transformers by replacing expensive self-attention with linear recurrences. In this paper, we propose a simple yet effective trick to enhance SSMs within given computational budgets by sparsifying them. Our intuition is that tokens in SSMs are highly redundant due to gradual recurrent updates, and dense recurrence operations block the delivery of past information. In particular, we observe that upper layers of SSMs tend to be more redundant as they encode global information, while lower layers encode local information. Motivated by this, we introduce Simba, a hierarchical sparsification method for SSMs based on token pruning. Simba sparsifies upper layers more than lower layers, encouraging the upper layers to behave like highways. To achieve this, we propose a novel token pruning criterion for SSMs, measuring the global impact of tokens on the final output by accumulating local recurrences. We demonstrate that Simba outperforms the baseline model, Mamba, with the same FLOPS in various natural language tasks. Moreover, we illustrate the effect of highways, showing that Simba not only enhances efficiency but also improves the information flow across long sequences. Code is available at https://github.com/woominsong/Simba.

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

Dynamic Sparse Training (DST) methods achieve state-of-the-art results in sparse neural network training, matching the generalization of dense models while enabling sparse training and inference. Although the resulting models are highly sparse and theoretically less computationally expensive, achieving speedups with unstructured sparsity on real-world hardware is challenging. In this work, we propose a sparse-to-sparse DST method, Structured RigL (SRigL), to learn a variant of fine-grained structured N:M sparsity by imposing a constant fan-in constraint. Using our empirical analysis of existing DST methods at high sparsity, we additionally employ a neuron ablation method which enables SRigL to achieve state-of-the-art sparse-to-sparse structured DST performance on a variety of Neural Network (NN) architectures. We demonstrate reduced real-world timings on CPU for online inference -- 3.6x/2x faster at 90% sparsity than equivalent dense/unstructured sparse layers, respectively. Our source code is available at https://github.com/calgaryml/condensed-sparsity

Linear attention models allow a fixed state size and a fixed amount of compute per token. However, due to their limited state size, linear attention models fall behind in long-context recall compared to softmax-attention-based transformer architectures. Increasing the state size of linear attention improves recall performance but at the cost of higher FLOPs. In this work, we introduce Sparse Delta Memory (SDM), an architecture that scales the hidden state of gated linear RNNs to orders of magnitude higher capacity using a sparse addressing scheme. SDM extends the Gated DeltaNet architecture by replacing the dense key-value outer product with sparse reads and writes to a large explicit memory. We show that, under an isoFLOP constraint and with an identical number of parameters, a higher state memory capacity significantly improves performance on in-context learning and long-context retrieval tasks. Moreover, by learning the initial state of the SDM memory and therefore using it as a parametric memory, we show that the model further improves on a wide range of common-knowledge and reasoning tasks.

Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a scaling law that models loss as a function of active parameters, unique tokens, data repetition, and sparsity, accurately predicting performance across compute and data budgets. 2. Delayed data saturation: sparse training postpones diminishing returns from repeated data, making multi-epoch training more effective. 3. Resource trade-offs: With fixed data, loss-optimal sparsity is moderate ~ 50%, while compute-optimal sparsity is higher and grows with data scale. Overall, sparsity is not just a tool for efficiency, but a mechanism for improving scaling trade-offs under data scarcity. Our code is available at: https://github.com/boqian333/sparse-dc-scaling.

A continual learning agent should be able to build on top of existing knowledge to learn on new data quickly while minimizing forgetting. Current intelligent systems based on neural network function approximators arguably do the opposite---they are highly prone to forgetting and rarely trained to facilitate future learning. One reason for this poor behavior is that they learn from a representation that is not explicitly trained for these two goals. In this paper, we propose OML, an objective that directly minimizes catastrophic interference by learning representations that accelerate future learning and are robust to forgetting under online updates in continual learning. We show that it is possible to learn naturally sparse representations that are more effective for online updating. Moreover, our algorithm is complementary to existing continual learning strategies, such as MER and GEM. Finally, we demonstrate that a basic online updating strategy on representations learned by OML is competitive with rehearsal based methods for continual learning. We release an implementation of our method at https://github.com/khurramjaved96/mrcl .

Latent reasoning compresses the chain-of-thought (CoT) into continuous hidden states, yet existing methods rely on dense latent transitions that remain difficult to interpret and control. Meanwhile, sparse representation models uncover human-interpretable semantic features but remain largely confined to post-hoc analysis. We reconcile this tension by proposing LSTR (Latent Sparse Transcoder Reasoning), a latent reasoning framework that elevates functional sparse transcoders into active reasoning operators to perform multi-step computation through sparse semantic transitions. At its core, LSTR employs a Latent Transition Transcoder (LTT) with a residual skip architecture that decouples linear manifold transport from sparse semantic updates, enabling controllable semantic resolution via explicit sparsity constraints. Extensive experiments show that LSTR preserves reasoning accuracy and compression efficiency while substantially improving interpretability over dense latent baselines. Causal interventions and trajectory analyses further demonstrate that these sparse features act as both interpretable and causally effective operators in the reasoning process.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Sparse roadmaps are important to compactly represent state spaces, to determine problems to be infeasible and to terminate in finite time. However, sparse roadmaps do not scale well to high-dimensional planning problems. In prior work, we showed improved planning performance on high-dimensional planning problems by using multilevel abstractions to simplify state spaces. In this work, we generalize sparse roadmaps to multilevel abstractions by developing a novel algorithm, the sparse multilevel roadmap planner (SMLR). To this end, we represent multilevel abstractions using the language of fiber bundles, and generalize sparse roadmap planners by using the concept of restriction sampling with visibility regions. We argue SMLR to be probabilistically complete and asymptotically near-optimal by inheritance from sparse roadmap planners. In evaluations, we outperform sparse roadmap planners on challenging planning problems, in particular problems which are high-dimensional, contain narrow passages or are infeasible. We thereby demonstrate sparse multilevel roadmaps as an efficient tool for feasible and infeasible high-dimensional planning problems.

In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

Long-context LLM agents accumulate interaction histories that strain KV-cache memory and attention computation. Although sparse attention reduces these costs, heterogeneous cache representations and workflows hinder integration with existing inference engines, while prior sparse-serving abstractions support only specific layouts or workflows. We present SparseEngine, a ground-up, sparse-first inference engine whose shared lifecycle contract lets each method control its KV representation and computation while coordinating state transitions with common serving infrastructure. SparseEngine supports 15 methods across four categories and enables cross-request state management through Chain Cache, which resumes KV-eviction methods from retained history, and controllable Prefix-Cache Pruning, which removes KV from selected history regions while preserving logical-prefix matching. While maintaining method quality, SparseEngine delivers over 10x higher throughput with KV eviction, over 2.5x faster decoding at matched concurrency than vLLM, and over 2x end-to-end speedup on agent benchmarks. The code is available at https://github.com/CURRENTF/SparseEngine.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

The emergence of long-context text applications utilizing large language models (LLMs) has presented significant scalability challenges, particularly in memory footprint. The linear growth of the Key-Value (KV) cache responsible for storing attention keys and values to minimize redundant computations can lead to substantial increases in memory consumption, potentially causing models to fail to serve with limited memory resources. To address this issue, we propose a novel approach called Cache Sparse Representation (CSR), which converts the KV cache by transforming the dense Key-Value cache tensor into sparse indexes and weights, offering a more memory-efficient representation during LLM inference. Furthermore, we introduce NeuralDict, a novel neural network-based method for automatically generating the dictionary used in our sparse representation. Our extensive experiments demonstrate that CSR achieves performance comparable to state-of-the-art KV cache quantization algorithms while maintaining robust functionality in memory-constrained environments.

Modern language models are powerful, but typically static after deployment. A major obstacle to building models that continually learn over time is catastrophic forgetting, where updating on new data erases previously acquired capabilities. Motivated by the intuition that mitigating forgetting is challenging because trainable parameters are shared across all tasks, we investigate whether sparse parameter updates can enable learning without catastrophic forgetting. We introduce sparse memory finetuning, leveraging memory layer models (Berges et al., 2024), which are sparsely updated by design. By updating only the memory slots that are highly activated by a new piece of knowledge relative to usage on pretraining data, we reduce interference between new knowledge and the model's existing capabilities. We evaluate learning and forgetting compared to full finetuning and parameter-efficient finetuning with LoRA on two question answering tasks. We find that sparse memory finetuning learns new knowledge while exhibiting substantially less forgetting: while NaturalQuestions F1 drops by 89% after full finetuning on new facts and 71% with LoRA, sparse memory finetuning yields only an 11% drop with the same level of new knowledge acquisition. Our results suggest sparsity in memory layers offers a promising path toward continual learning in large language models.

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable features are embedded in hidden states. Our experiments reveal high probing accuracy, indicating latent space regularities with functionally important directions. Building on this, we use the directions between hidden states with opposing features to fit control vectors. At inference, we add our control vectors to hidden states and evaluate their impact on predictions. Remarkably, such modifications preserve the feasibility of predictions. We further refine our control vectors using sparse autoencoders (SAEs). This leads to more linear changes in predictions when scaling control vectors. Our approach enables mechanistic interpretation as well as zero-shot generalization to unseen dataset characteristics with negligible computational overhead.

Dynamic sparse attention (DSA) accelerates long-context LLM decoding by attending to only the top-K KV blocks relevant to each query, but it introduces a serialized selection-to-attention dependency that emerges as a new latency bottleneck. We present PRR, a speculate-reuse-repair runtime that exploits temporal locality in DSA selections to predict likely blocks, speculate the attention over them while selection is in flight, and incrementally repair missed blocks once the true selected set is known. PRR uses a lightweight EMA-based predictor, a profiling-guided speculation budget that keeps speculative work off the critical path, and a FlashAttention-based repair kernel that folds missed blocks into the partial attention state using online-softmax statistics. Across long-context benchmarks and representative DSA methods, PRR reduces per-token decoding latency by up to 40% while preserving downstream task accuracy. Github: https://github.com/Tianyu9748/Incremental_FlashAttention

Recent works have successfully demonstrated that sparse deep reinforcement learning agents can be competitive against their dense counterparts. This opens up opportunities for reinforcement learning applications in fields where inference time and memory requirements are cost-sensitive or limited by hardware. Until now, dense-to-sparse methods have relied on hand-designed sparsity schedules that are not synchronized with the agent's learning pace. Crucially, the final sparsity level is chosen as a hyperparameter, which requires careful tuning as setting it too high might lead to poor performances. In this work, we address these shortcomings by crafting a dense-to-sparse algorithm that we name Eau De Q-Network (EauDeQN). To increase sparsity at the agent's learning pace, we consider multiple online networks with different sparsity levels, where each online network is trained from a shared target network. At each target update, the online network with the smallest loss is chosen as the next target network, while the other networks are replaced by a pruned version of the chosen network. We evaluate the proposed approach on the Atari 2600 benchmark and the MuJoCo physics simulator, showing that EauDeQN reaches high sparsity levels while keeping performances high.

On-policy distillation (OPD) has recently become a prominent post-training recipe as it combines two desirable ingredients: on-policy student trajectories and dense teacher supervision, yet how this hybrid changes a model's parameters remains unclear. Across several language and vision-language model pairs and use cases, our analysis yields two main findings. On sparsity, OPD-style updates are small and coordinate-sparse. They are distributed across layers and are usually FFN-heavy. This sparse structure is operationally useful: training only the discovered subnetwork recovers nearly the same performance as full OPD. However, the sparsity-inducing SGD optimizer underperforms AdamW in our optimizer ablation, likely because dense teacher supervision preserves heterogeneous coordinate-wise gradient scales where AdamW's adaptive scaling remains useful. On geometry, the updates are numerically full-rank but spectrally concentrated; they lie mostly away from the principal singular subspaces of the source weights and fall disproportionately on coordinates where the source weights are close to zero. These findings suggest that dense teacher supervision does not turn OPD into ordinary dense parameter rewriting; instead, OPD retains important geometric signatures of on-policy post-training.

Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented without any locking. We present an update scheme called HOGWILD! which allows processors access to shared memory with the possibility of overwriting each other's work. We show that when the associated optimization problem is sparse, meaning most gradient updates only modify small parts of the decision variable, then HOGWILD! achieves a nearly optimal rate of convergence. We demonstrate experimentally that HOGWILD! outperforms alternative schemes that use locking by an order of magnitude.

With the increase in the number of parameters in large language models, the process of pre-training and fine-tuning increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA (Hu et al., 2021)), low-rank gradient projection (GaLore (Zhao et al., 2024)), and blockwise optimization (BAdam (Luo et al., 2024)) have been proposed. However, in all these algorithms, the effective rank of the weight updates remains low-rank, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce FRUGAL (Full-Rank Updates with GrAdient spLitting), a new memory-efficient optimization framework. FRUGAL leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD (Bernstein et al., 2018). Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches across various fixed memory budgets, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

Existing work in continual learning (CL) focuses on mitigating catastrophic forgetting, i.e., model performance deterioration on past tasks when learning a new task. However, the training efficiency of a CL system is under-investigated, which limits the real-world application of CL systems under resource-limited scenarios. In this work, we propose a novel framework called Sparse Continual Learning(SparCL), which is the first study that leverages sparsity to enable cost-effective continual learning on edge devices. SparCL achieves both training acceleration and accuracy preservation through the synergy of three aspects: weight sparsity, data efficiency, and gradient sparsity. Specifically, we propose task-aware dynamic masking (TDM) to learn a sparse network throughout the entire CL process, dynamic data removal (DDR) to remove less informative training data, and dynamic gradient masking (DGM) to sparsify the gradient updates. Each of them not only improves efficiency, but also further mitigates catastrophic forgetting. SparCL consistently improves the training efficiency of existing state-of-the-art (SOTA) CL methods by at most 23X less training FLOPs, and, surprisingly, further improves the SOTA accuracy by at most 1.7%. SparCL also outperforms competitive baselines obtained from adapting SOTA sparse training methods to the CL setting in both efficiency and accuracy. We also evaluate the effectiveness of SparCL on a real mobile phone, further indicating the practical potential of our method.

Recent works have explored the use of weight sparsity to improve the training efficiency (test accuracy w.r.t training FLOPs) of deep neural networks (DNNs). These works aim to reduce training FLOPs but training with sparse weights often leads to accuracy loss or requires longer training schedules, making the resulting training efficiency less clear. In contrast, we focus on using sparsity to increase accuracy while using the same FLOPs as the dense model and show training efficiency gains through higher accuracy. In this work, we introduce Sparse-IFT, a family of Sparse Iso-FLOP Transformations which are used as drop-in replacements for dense layers to improve their representational capacity and FLOP efficiency. Each transformation is parameterized by a single hyperparameter (sparsity level) and provides a larger search space to find optimal sparse masks. Without changing any training hyperparameters, replacing dense layers with Sparse-IFT leads to significant improvements across computer vision (CV) and natural language processing (NLP) tasks, including ResNet-18 on ImageNet (+3.5%) and GPT-3 Small on WikiText-103 (-0.4 PPL), both matching larger dense model variants that use 2x or more FLOPs. To our knowledge, this is the first work to demonstrate the use of sparsity for improving the accuracy of dense models via a simple-to-use set of sparse transformations. Code is available at: https://github.com/CerebrasResearch/Sparse-IFT.

Multispectral fusion object detection is a critical task for edge-based maritime surveillance and remote sensing, demanding both high inference efficiency and robust feature representation for high-resolution inputs. However, current State Space Models (SSMs) like Mamba suffer from significant parameter redundancy in their standard 2D Selective Scan (SS2D) blocks, which hinders deployment on resource-constrained hardware and leads to the loss of fine-grained structural information during conventional compression. To address these challenges, we propose the Low-Rank Two-Dimensional Selective Structured State Space Model (Low-Rank SS2D), which reformulates state transitions via matrix factorization to exploit intrinsic feature sparsity. Furthermore, we introduce a Structure-Aware Distillation strategy that aligns the internal latent state dynamics of the student with a full-rank teacher model to compensate for potential representation degradation. This approach substantially reduces computational complexity and memory footprint while preserving the high-fidelity spatial modeling required for object recognition. Extensive experiments on five benchmark datasets and real-world edge platforms, such as Raspberry Pi 5, demonstrate that our method achieves a superior efficiency-accuracy trade-off, significantly outperforming existing lightweight architectures in practical deployment scenarios.

Linear-time sequence models typically store long-context information in a recurrent state. A fixed-size state limits how much information can be stored, while hybrid architectures that add full attention for better recall incur quadratic sequence cost. Alternatively, sparse attention with continued pretraining (CPT) can extend the effective context length. Generalization beyond the trained length remains challenging, however, and CPT can be costly. We introduce FreeSolo, a native sparse attention mechanism with a short-range sliding window branch and a long-range branch that selects keypoint cells for direct token attention. Its linear-time variant, FS-L, learns to prune the prefix before query-dependent selection through short CPT. FS-B searches balanced trees with O(Nlog^2 N) algorithmic cost including radix-sort construction. FreeSolo demonstrates better zero-shot length extrapolation than the baselines without long-context fine-tuning.

Streaming recurrent models enable efficient 3D reconstruction by maintaining persistent state representations. However, they suffer from catastrophic forgetting over long sequences due to balancing historical information with new observations. Recent methods alleviate this by deriving adaptive signals from attention perspective, but they operate on single dimensions without considering temporal and spatial consistency. To this end, we propose a training-free framework termed TTSA3R that leverages both temporal state evolution and spatial observation quality for adaptive state updates in 3D reconstruction. In particular, we devise a Temporal Adaptive Update Module that regulates update magnitude by analyzing temporal state evolution patterns. Then, a Spatial Contextual Update Module is introduced to localize spatial regions that require updates through observation-state alignment and scene dynamics. These complementary signals are finally fused to determine the state updating strategies. Extensive experiments demonstrate the effectiveness of TTSA3R in diverse 3D tasks. Moreover, our method exhibits only 1.33x error increase compared to over 4x degradation in the baseline model on extended sequences of 3D reconstruction, significantly improving long-term reconstruction stability. Our codes are available at https://github.com/anonus2357/ttsa3r.

Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces Lattice, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of K-V matrices to efficiently compress the cache into a fixed number of memory slots, achieving sub-quadratic complexity. We formulate this compression as an online optimization problem and derive a dynamic memory update rule based on a single gradient descent step. The resulting recurrence features a state- and input-dependent gating mechanism, offering an interpretable memory update process. The core innovation is the orthogonal update: each memory slot is updated exclusively with information orthogonal to its current state hence incorporation of only novel, non-redundant data, which minimizes the interference with previously stored information. The experimental results show that Lattice achieves the best perplexity compared to all baselines across diverse context lengths, with performance improvement becoming more pronounced as the context length increases.

Deep State Space Models (SSMs), such as Mamba (Gu & Dao, 2024), have become powerful tools for language modeling, offering high performance and linear scalability with sequence length. However, the application of parameter-efficient fine-tuning (PEFT) methods to SSM-based models remains largely underexplored. We start by investigating two fundamental questions on existing PEFT methods: (i) How do they perform on SSM-based models? (ii) Which parameters should they target for optimal results? Our analysis shows that LoRA and its variants consistently outperform all other PEFT methods. While LoRA is effective for linear projection matrices, it fails on SSM modules-yet still outperforms other methods applicable to SSMs, indicating their limitations. This underscores the need for a specialized SSM tuning approach. To address this, we propose Sparse Dimension Tuning (SDT), a PEFT method tailored for SSM modules. Combining SDT for SSMs with LoRA for linear projection matrices, we achieve state-of-the-art performance across extensive experiments.

State-space models (SSMs) maintain a fixed-size recurrent state, but reading and writing it at every decoding step can bottleneck hybrid models. This eager state management causes large state I/O with low arithmetic intensity, leaves speculative decoding no cheap rollback, and feeds state quantization error into subsequent recurrent updates. We introduce ReplaySSM, which unrolls the recurrence to represent the state as a checkpoint and a buffer of recent SSM inputs. This separates output computation from checkpoint updates. By updating the checkpoint periodically, ReplaySSM avoids state writes on most steps and roughly halves the dominant state memory traffic. Keeping recent inputs also makes speculative rollback a buffer-pointer operation and enables output-only verification without materializing intermediate states. The same separation allows a low-precision checkpoint to serve output computation on most steps while a higher-precision checkpoint serves recurrent updates, so rounding error in the low-precision copy never enters later updates. We implement ReplaySSM in vLLM for Mamba-2 and Gated DeltaNet. At serving batch size 256, it accelerates standard decoding by 1.20--1.47times over a tuned vLLM baseline across four hybrid models, and delivers about 1.8times the throughput of vLLM's speculative decoding on the two 120B-class models. Separate state precisions also reduce output KL divergence and downstream accuracy losses compared with a shared low-precision checkpoint.

Neural networks can be significantly compressed by pruning, yielding sparse models with reduced storage and computational demands while preserving predictive performance. Model soups (Wortsman et al., 2022) enhance generalization and out-of-distribution (OOD) performance by averaging the parameters of multiple models into a single one, without increasing inference time. However, achieving both sparsity and parameter averaging is challenging as averaging arbitrary sparse models reduces the overall sparsity due to differing sparse connectivities. This work addresses these challenges by demonstrating that exploring a single retraining phase of Iterative Magnitude Pruning (IMP) with varied hyperparameter configurations such as batch ordering or weight decay yields models suitable for averaging, sharing identical sparse connectivity by design. Averaging these models significantly enhances generalization and OOD performance over their individual counterparts. Building on this, we introduce Sparse Model Soups (SMS), a novel method for merging sparse models by initiating each prune-retrain cycle with the averaged model from the previous phase. SMS preserves sparsity, exploits sparse network benefits, is modular and fully parallelizable, and substantially improves IMP's performance. We further demonstrate that SMS can be adapted to enhance state-of-the-art pruning-during-training approaches.

On-device training enables the model to adapt to new data collected from the sensors by fine-tuning a pre-trained model. Users can benefit from customized AI models without having to transfer the data to the cloud, protecting the privacy. However, the training memory consumption is prohibitive for IoT devices that have tiny memory resources. We propose an algorithm-system co-design framework to make on-device training possible with only 256KB of memory. On-device training faces two unique challenges: (1) the quantized graphs of neural networks are hard to optimize due to low bit-precision and the lack of normalization; (2) the limited hardware resource does not allow full back-propagation. To cope with the optimization difficulty, we propose Quantization-Aware Scaling to calibrate the gradient scales and stabilize 8-bit quantized training. To reduce the memory footprint, we propose Sparse Update to skip the gradient computation of less important layers and sub-tensors. The algorithm innovation is implemented by a lightweight training system, Tiny Training Engine, which prunes the backward computation graph to support sparse updates and offload the runtime auto-differentiation to compile time. Our framework is the first solution to enable tiny on-device training of convolutional neural networks under 256KB SRAM and 1MB Flash without auxiliary memory, using less than 1/1000 of the memory of PyTorch and TensorFlow while matching the accuracy on tinyML application VWW. Our study enables IoT devices not only to perform inference but also to continuously adapt to new data for on-device lifelong learning. A video demo can be found here: https://youtu.be/XaDCO8YtmBw.

We present a novel network pruning algorithm called Dynamic Sparse Training that can jointly find the optimal network parameters and sparse network structure in a unified optimization process with trainable pruning thresholds. These thresholds can have fine-grained layer-wise adjustments dynamically via backpropagation. We demonstrate that our dynamic sparse training algorithm can easily train very sparse neural network models with little performance loss using the same number of training epochs as dense models. Dynamic Sparse Training achieves the state of the art performance compared with other sparse training algorithms on various network architectures. Additionally, we have several surprising observations that provide strong evidence for the effectiveness and efficiency of our algorithm. These observations reveal the underlying problems of traditional three-stage pruning algorithms and present the potential guidance provided by our algorithm to the design of more compact network architectures.

Long-horizon agents continuously accumulate interaction history during task execution, yet the importance of past interactions changes as the agent state evolves. Existing context management methods largely compress history based on fixed windows, periodic schedules, or current relevance, overlooking a more fundamental question: when has a past interaction become safe to replace? Premature compression may remove information still needed for future actions, while overly conservative retention leads to substantial context overhead. To address this, we propose State Conditioned Compression (StateComp), a framework that determines when historical interactions can be safely compressed according to the current agent state. StateComp constructs KEEP and READY supervision through a two-stage annotation procedure and trains an imbalance-aware router on hidden representations from a frozen language model. A bounded state representation further reduces the cost of evaluating long histories, while adjacent READY interactions are grouped into continuous spans and replaced with compact summaries during execution. Experiments on WorkBuddyBench show that StateComp reduces total agent and summarization tokens by 52.27% while maintaining task performance, and achieves a 12.67-fold speedup in representation extraction.

Large language models rely on KV caching to reduce repeated prefill computation in long context and interactive applications. As lightweight adapters evolve, cached states reflect earlier versions, so stale reuse distorts current model outputs, while complete affected suffix recomputation restores fidelity at substantial cost. We seek minimal recomputation that recovers current adapter behavior. Existing systems track token, context, or stable adapter identity, but neither represent caches from earlier adapter versions nor distinguish update propagation from the recomputation required for behavioral recovery. To address these gaps, we introduce CacheReforge, which represents stale KV caches as layerwise mixed-version objects. It combines per-layer adapter anchors, calibrated sensitivity, accumulated drift, and executable restart boundaries to select direct reuse, bounded recomputation, or complete affected-suffix recovery. We distinguish dependency depth from the functional recomputation horizon and use cumulative tail influence to characterize when bounded recovery preserves current-model behavior. We evaluate CacheReforge on Qwen2.5-1.5B and Qwen2.5-7B with continual LoRA updates, including 16K HotpotQA and 2WikiMQA workloads. CacheReforge reduces mean KL divergence by 92.4% relative to stale reuse, while recomputing only 5.44% of layers and reducing cache-maintenance time by 93.2% relative to fresh full prefill. These results show that version-aware recovery preserves model fidelity and most KV caching gains.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated K-step unrolling pipeline to learn multi-step dynamics. MetaState adds only {sim}0.6% trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5% across all evaluations.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

To address the challenge of increasing network size, researchers have developed sparse models through network pruning. However, maintaining model accuracy while achieving significant speedups on general computing devices remains an open problem. In this paper, we present a novel mobile inference acceleration framework SparseByteNN, which leverages fine-grained kernel sparsity to achieve real-time execution as well as high accuracy. Our framework consists of two parts: (a) A fine-grained kernel sparsity schema with a sparsity granularity between structured pruning and unstructured pruning. It designs multiple sparse patterns for different operators. Combined with our proposed whole network rearrangement strategy, the schema achieves a high compression rate and high precision at the same time. (b) Inference engine co-optimized with the sparse pattern. The conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet-v1 outperform strong dense baselines on the efficiency-accuracy curve. Experimental results on Qualcomm 855 show that for 30% sparse MobileNet-v1, SparseByteNN achieves 1.27x speedup over the dense version and 1.29x speedup over the state-of-the-art sparse inference engine MNN with a slight accuracy drop of 0.224%. The source code of SparseByteNN will be available at https://github.com/lswzjuer/SparseByteNN

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map h+BAh adds a low-rank correction to a hidden representation. A slow state ρ learns starting factors across tasks; a private fast state Φ copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.

The ever-increasing large language models (LLMs), though opening a potential path for the upcoming artificial general intelligence, sadly drops a daunting obstacle on the way towards their on-device deployment. As one of the most well-established pre-LLMs approaches in reducing model complexity, network pruning appears to lag behind in the era of LLMs, due mostly to its costly fine-tuning (or re-training) necessity under the massive volumes of model parameter and training data. To close this industry-academia gap, we introduce Dynamic Sparse No Training (DSnoT), a training-free fine-tuning approach that slightly updates sparse LLMs without the expensive backpropagation and any weight updates. Inspired by the Dynamic Sparse Training, DSnoT minimizes the reconstruction error between the dense and sparse LLMs, in the fashion of performing iterative weight pruning-and-growing on top of sparse LLMs. To accomplish this purpose, DSnoT particularly takes into account the anticipated reduction in reconstruction error for pruning and growing, as well as the variance w.r.t. different input data for growing each weight. This practice can be executed efficiently in linear time since its obviates the need of backpropagation for fine-tuning LLMs. Extensive experiments on LLaMA-V1/V2, Vicuna, and OPT across various benchmarks demonstrate the effectiveness of DSnoT in enhancing the performance of sparse LLMs, especially at high sparsity levels. For instance, DSnoT is able to outperform the state-of-the-art Wanda by 26.79 perplexity at 70% sparsity with LLaMA-7B. Our paper offers fresh insights into how to fine-tune sparse LLMs in an efficient training-free manner and open new venues to scale the great potential of sparsity to LLMs. Codes are available at https://github.com/zyxxmu/DSnoT.

We study nonlinear filtering with misspecified initial distributions and dynamics, but a correctly specified observation model. Observations are treated as a random process generated by the true model, rather than as fixed realizations, and both the correct filter and the misspecified filter are analyzed under this common observation law. Our main result is a Bayesian total variation balance identity for the expected change in total variation distance under a Bayesian update: a covariance term minus a non-negative remainder. The identity characterizes conditional and averaged update non-expansivity. Combined with prediction contraction, it yields finite-time bounds separating the initialization error from accumulated dynamical discrepancies, while allowing expansive updates. When the averaged updates are non-expansive and a uniform joint prediction--update coefficient is less than one, a persistent dynamical misspecification yields an asymptotic error bound proportional to the one-step discrepancy. When the conditional updates are non-expansive, we characterize an accumulated joint contraction that implies almost-sure and \(L^1\) coalescence of the true and misspecified filters. Finally, we verify update non-expansivity for scalar Gaussian predictive laws under a variance-ordering condition and, separately, derive explicit prediction contraction bounds for truncated kernels and bounded transition functions with elliptically symmetric noise.

We introduce Sparse Forcing, a training-and-inference paradigm for autoregressive video diffusion models that improves long-horizon generation quality while reducing decoding latency. Sparse Forcing is motivated by an empirical observation in autoregressive diffusion rollouts: attention concentrates on a persistent subset of salient visual blocks, forming an implicit spatiotemporal memory in the KV cache, and exhibits a locally structured block-sparse pattern within sliding windows. Building on this observation, we propose a trainable native sparsity mechanism that learns to compress, preserve, and update these persistent blocks while restricting computation within each local window to a dynamically selected local neighborhood. To make the approach practical at scale for both training and inference, we further propose Persistent Block-Sparse Attention (PBSA), an efficient GPU kernel that accelerates sparse attention and memory updates for low-latency, memory-efficient decoding. Experiments show that Sparse Forcing improves the VBench score by +0.26 over Self-Forcing on 5-second text-to-video generation while delivering a 1.11-1.17x decoding speedup and 42% lower peak KV-cache footprint. The gains are more pronounced on longer-horizon rollouts, delivering improved visual quality with +0.68 and +2.74 VBench improvements, and 1.22x and 1.27x speedups on 20-second and 1-minute generations, respectively.

The Lottery Ticket Hypothesis demonstrated that sparse subnetworks can match full-model performance, suggesting parameter redundancy. Meanwhile, in Reinforcement Learning with Verifiable Rewards (RLVR), recent work has shown that updates concentrate on a sparse subset of parameters, which further lends evidence to this underlying redundancy. We study the simplest possible way to exploit this redundancy: training only a randomly selected subset of parameters at extreme sparsities. Empirically, we find that training just 1\% of parameters matches or exceeds full-parameter RLVR finetuning across 3 models and 2 task domains. Moreover, different random masks show minimal overlap (leq 0.005 Jaccard similarity) and yet all succeed, suggesting pretrained models contain many viable sparse subnetworks rather than one privileged set. We term this the Multiple Ticket Hypothesis. We explain this phenomenon through the implicit per-step KL constraint in RLVR, which restricts updates to a low-dimensional subspace, enabling arbitrary sparse masks to succeed.

Fine-tuning LLMs is both computationally and memory-intensive. While parameter-efficient fine-tuning methods, such as QLoRA and DoRA, reduce the number of trainable parameters and lower memory usage, they do not decrease computational cost. In some cases, they may even slow down fine-tuning. In this paper, we introduce SparseLoRA, a method that accelerates LLM fine-tuning through contextual sparsity. We propose a lightweight, training-free SVD sparsity estimator that dynamically selects a sparse subset of weights for loss and gradient computation. Also, we systematically analyze and address sensitivity across layers, tokens, and training steps. Our experimental results show that SparseLoRA reduces computational cost by up to 2.2 times and a measured speedup of up to 1.6 times while maintaining accuracy across various downstream tasks, including commonsense and arithmetic reasoning, code generation, and instruction following.

Linear-attention language models keep their context in a recurrent state of fixed size, where an inference system stores one copy of this state for every sequence it decodes at the same time. Storing the state at lower precision therefore lets more sequences share an accelerator. Existing state quantizers round the state after every generated token and report that four bits lose accuracy unless the bit width is raised or the model is fine-tuned.\par We introduce PACE, a post-hoc four-bit state quantizer. PACE rounds the state only once every few generated tokens, as chunked kernels already do once per chunk during prefill, and keeps the tokens generated in between in a small buffer. Rounding less often reduces the error that accumulates in the state. Additionally, we find that the large entries of the gated-delta state gather in columns, because some channels of the update written at each token remain large across many tokens. PACE therefore shares each quantization scale within one column. It also keeps the heads that retain rounding error longest at eight bits. On four hybrid models from 4B to 35B parameters, PACE with mixed four- and eight-bit heads is competitive with eight-bit DAMP on the three larger models at about two thirds of its memory, PACE with four-bit heads throughout scores higher than Q-Mamba at equal memory, and rounding every few tokens preserves the decoding speedup of the buffer.

Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates. In this work, we show that the naive use of standard Adam-based optimizers leads to a cold-start issue for newly regrown parameters, resulting in excessively large updates and disrupted training dynamics. To address this issue, we propose Sparse Memory-Efficient Training (SMET), which stabilizes DST with optimizer warm-up and improves training progress through density-aware learning-rate scaling. SMET further reduces memory consumption by storing gradients and optimizer states only for active parameters. We provide a theoretical analysis of the update behaviors under SMET, showing improved optimization stability. Extensive experiments demonstrate that SMET enables stable, scalable, and memory-efficient sparse pre-training of LLMs, paving the way for sparse training as a practical alternative to dense training. Our code is publicly available at: https://github.com/QiaoXiao7282/SMET.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide array of text-centric tasks. However, their `large' scale introduces significant computational and storage challenges, particularly in managing the key-value states of the transformer, which limits their wider applicability. Therefore, we propose to adaptively release resources from caches and rebuild the necessary key-value states. Particularly, we accomplish this by a lightweight controller module to approximate an ideal top-K sparse attention. This module retains the tokens with the highest top-K attention weights and simultaneously rebuilds the discarded but necessary tokens, which may become essential for future decoding. Comprehensive experiments in natural language generation and modeling reveal that our method is not only competitive with full attention in terms of performance but also achieves a significant throughput improvement of up to 221.8%. The code for replication is available on the https://github.com/WHUIR/ADORE.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

Current PEFT methods for LLMs can achieve either high quality, efficient training, or scalable serving, but not all three simultaneously. To address this limitation, we investigate sparse fine-tuning and observe a remarkable improvement in generalization ability. Utilizing this key insight, we propose a family of Structured Sparse Fine-Tuning (S^{2}FT) methods for LLMs, which concurrently achieve state-of-the-art fine-tuning performance, training efficiency, and inference scalability. S^{2}FT accomplishes this by "selecting sparsely and computing densely". It selects a few heads and channels in the MHA and FFN modules for each Transformer block, respectively. Next, it co-permutes weight matrices on both sides of the coupled structures in LLMs to connect the selected components in each layer into a dense submatrix. Finally, S^{2}FT performs in-place gradient updates on all submatrices. Through theoretical analysis and empirical results, our method prevents forgetting while simplifying optimization, delivers SOTA performance on both commonsense and arithmetic reasoning with 4.6% and 1.3% average improvements compared to LoRA, and surpasses full FT by 11.5% when generalizing to various domains after instruction tuning. Using our partial backpropagation algorithm, S^{2}FT saves training memory up to 3times and improves latency by 1.5-2.7times compared to full FT, while delivering an average 10% improvement over LoRA on both metrics. We further demonstrate that the weight updates in S^{2}FT can be decoupled into adapters, enabling effective fusion, fast switch, and efficient parallelism for serving multiple fine-tuned models.

Branch prediction is arguably one of the most important speculative mechanisms within a high-performance processor architecture. A common approach to improve branch prediction accuracy is to employ lengthy history records of previously seen branch directions to capture distant correlations between branches. The larger the history, the richer the information that the predictor can exploit for discovering predictive patterns. However, without appropriate filtering, such an approach may also heavily disorganize the predictor's internal mechanisms, leading to diminishing returns. This paper studies a fundamental control-flow property: the sparsity in the correlation between branches and recent history. First, we show that sparse branch correlations exist in standard applications and, more importantly, such correlations can be computed efficiently using sparse modeling methods. Second, we introduce a sparsity-aware branch prediction mechanism that can compactly encode and store sparse models to unlock essential performance opportunities. We evaluated our approach for various design parameters demonstrating MPKI improvements of up to 42% (2.3% on average) with 2KB of additional storage overhead. Our circuit-level evaluation of the design showed that it can operate within accepted branch prediction latencies, and under reasonable power and area limitations.

Acquiring an accurate world model online for model-based reinforcement learning (MBRL) is challenging due to data nonstationarity, which typically causes catastrophic forgetting for neural networks (NNs). From the online learning perspective, a Follow-The-Leader (FTL) world model is desirable, which optimally fits all previous experiences at each round. Unfortunately, NN-based models need re-training on all accumulated data at every interaction step to achieve FTL, which is computationally expensive for lifelong agents. In this paper, we revisit models that can achieve FTL with incremental updates. Specifically, our world model is a linear regression model supported by nonlinear random features. The linear part ensures efficient FTL update while the nonlinear random feature empowers the fitting of complex environments. To best trade off model capacity and computation efficiency, we introduce a locality sensitive sparse encoding, which allows us to conduct efficient sparse updates even with very high dimensional nonlinear features. We validate the representation power of our encoding and verify that it allows efficient online learning under data covariate shift. We also show, in the Dyna MBRL setting, that our world models learned online using a single pass of trajectory data either surpass or match the performance of deep world models trained with replay and other continual learning methods.

Activation sparsity can enable practical inference speedups in large language models (LLMs) by reducing the compute and memory-movement required for matrix multiplications during the forward pass. However, existing methods face limitations that inhibit widespread adoption. Some approaches are tailored towards older models with ReLU-based sparsity, while others require extensive continued pre-training on up to hundreds of billions of tokens. This paper describes TEAL, a simple training-free method that applies magnitude-based activation sparsity to hidden states throughout the entire model. TEAL achieves 40-50% model-wide sparsity with minimal performance degradation across Llama-2, Llama-3, and Mistral families, with sizes varying from 7B to 70B. We improve existing sparse kernels and demonstrate wall-clock decoding speed-ups of up to 1.53times and 1.8times at 40% and 50% model-wide sparsity. TEAL is compatible with weight quantization, enabling further efficiency gains.

While diffusion language models (DLMs) offer a promising alternative to autoregressive models (ARs), existing open-source DLMs suffer from high inference latency. This bottleneck is mainly due to the attention's quadratic complexity with respect to context length in computing all query-key pairs. Intuitively, to reduce this complexity, a natural strategy is to restrict attention to sparse patterns that retain only the most relevant connections. Such approaches are well-established in ARs, where attention follows fixed and clearly defined sparse patterns. However, in DLMs, we observe distinct sparsity behaviors: (1) attention patterns vary across heads, (2) attention patterns in each head remain highly similar across denoising steps, and (3) early denoising steps are critical for generation. These findings render sparse attention methods designed for ARs largely incompatible with DLMs, as they fail to capture head-specific structures and risk degrading generation when applied in early denoising steps. To address these challenges, we propose SparseD, a novel sparse attention method for DLMs. Leveraging the observations, SparseD only requires pre-computing head-specific sparse patterns one time, and reuses them across all steps. This prevents recomputing sparse patterns at each denoising step. Meanwhile, SparseD uses full attention in the early steps, then switches to sparse attention later to maintain generation quality. Together, these establish SparseD as a practical and efficient solution for deploying DLMs in long-context applications. Experimental results demonstrate that SparseD achieves lossless acceleration, delivering up to 1.50times speedup over FlashAttention at a 64k context length with 1,024 denoising steps.

In reinforcement learning for large language models, Proximal Policy Optimization (PPO) commonly uses a critic to estimate state values and reduce the variance of policy updates. However, we uncover a systematic failure mode in PPO critics, which we call Value Flattening: state values, estimated from multiple Monte Carlo continuations, change sharply across intermediate states while critic predictions remain comparatively flat. We further observe this phenomenon in a controlled FrozenLake environment and find that it becomes more pronounced as the state space grows. Our theoretical and empirical analyses relate Value Flattening to an implicit variance penalty in the critic loss and redundant updates from temporally correlated states with similar gradients. Motivated by these findings, we introduce SParse Proximal Policy Optimization (SP^3O), which applies the value loss to only a few well-separated states in each response to mitigate both effects. Experiments on Qwen3-Base show that SP^3O with only three states supervised per response can mitigate Value Flattening and consistently improve the learned policy across model sizes and evaluation suites. Together, our results identify Value Flattening as an important yet overlooked failure mode of critic learning in standard PPO and show that a simple sparse supervision strategy can mitigate it.

We introduce the Graph Machine (GM), an architecture that maintains an O(n)-sized state and accesses it through sparse, dynamic routing. Unlike methods with fixed-size states or sparse but static routing, GM preserves O(n) complexity in its sparse layers without restricting the potentially accessible state size to O(1). Instead, GM uses edges - pointer-like objects updated differentiably by a referral mechanism resembling pointer chasing. We replace 75% of the dense Transformer layers in Qwen3-0.6B with GM sparse layers and pretrain from scratch on 15.7B tokens. With only 2 of 4,096 tokens retrieved per KV head in each sparse layer, loss degrades only slightly; with 4, the best model marginally improves loss.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Deploying large language models (LLMs) for long-context inference remains challenging due to their substantial memory and computational demands. While techniques such as Key-Value (KV) cache compression are designed to reduce memory usage, they often neglect the structured sparsity inherent in the relationship between hidden states and their corresponding KV cache. In this work, we explore the role of uncertainty as a potential indicator of sparsity within LLMs. We propose UNComp, an uncertainty-aware framework that leverages truncated matrix entropy to identify areas of low information content, thereby revealing sparsity patterns that can be used for adaptive compression. Unlike traditional methods that apply uniform compression, UNComp dynamically adjusts its approach to compression, guided by uncertainty measures that reflect the importance of various model components. Our analysis shows that sparsity patterns, when derived from uncertainty estimates, can be exploited to reveal special long-range dependencies, such as retrieval heads and retrieval layers. This perspective not only enhances our understanding of how compression can be optimized but also provides new insights into the inherent sparsity of LLMs during long-context inference. By focusing on uncertainty to analyze the sparsity pattern in detail, UNComp reduces the KV cache size to 4.74% of the original, achieves a 6% prefill speedup, and improves throughput by 6.4x - not only delivering strong lossless compression performance, but also validating the effectiveness of the underlying theoretical tool. We release the code at https://github.com/menik1126/UNComp.

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Speculative decoding accelerates autoregressive generation by drafting multiple tokens per step, yet feature-based drafters rely on target hidden features whose contextual emphasis may not align with the needs of subsequent draft positions. Hybrid linear attention (HLA) models maintain compact recurrent states that accumulate historical associations, offering an efficient source of complementary context for speculative drafting. We introduce ReaDy, the first speculative decoding method, to the best of our knowledge, to leverage HLA recurrent states for position-specific context retrieval during drafting. ReaDy equips each draft position with a learned query to retrieve supplementary context directly from the target's committed recurrent states. A lightweight state reader integrates this context into draft representations through residual updates, while low-rank state reads and fused operators keep additional computation and I/O overhead low. Building on DSpark's parallel backbone and sequential prediction head, ReaDy employs a lightweight two-stage adaptation strategy, with reader capacity, state sources, and residual placement examined through ablation studies. Across seven benchmarks spanning mathematics, code generation, and dialogue, ReaDy achieves an average 3.16times decoding speedup over autoregressive decoding with Qwen3.8-27B on a single NVIDIA B200 GPU. It outperforms DSpark on every benchmark, improving throughput by 7.97% and acceptance length by 8.50% on average. Our code is available at https://github.com/StartLuxLabs/ReaDy.

Recent advancements in State Space Models (SSMs) have attracted significant interest, particularly in models optimized for parallel training and handling long-range dependencies. Architectures like Mamba have scaled to billions of parameters with selective SSM. To facilitate broader applications using Mamba, exploring its efficiency is crucial. While token reduction techniques offer a straightforward post-training strategy, we find that applying existing methods directly to SSMs leads to substantial performance drops. Through insightful analysis, we identify the reasons for this failure and the limitations of current techniques. In response, we propose a tailored, unified post-training token reduction method for SSMs. Our approach integrates token importance and similarity, thus taking advantage of both pruning and merging, to devise a fine-grained intra-layer token reduction strategy. Extensive experiments show that our method improves the average accuracy by 5.7% to 13.1% on six benchmarks with Mamba-2 compared to existing methods, while significantly reducing computational demands and memory requirements.

Long-horizon tasks require LLM agents to continually draw on information from earlier interactions. However, retaining the full history increases context costs, while compressing it risks losing details needed later, and the relevance of historical information often becomes apparent as the task progresses. To address these challenges, we propose FlowState, which treats execution state as memory that can be retained and revisited across requests, unifying current decision-making with the reuse of historical information. FlowState preserves semantically typed state nodes, their relations, and references to raw tool observations, separating persistent retention from on-demand access. Within a single execution loop, Incremental State Update (ISU) maintains the current state based on new inputs and feedback, while Progressive State Access (PSA) progressively reveals historical states and supporting evidence as needed during reasoning. Together, these mechanisms enable agents to reassess prior decisions in light of new information and guide subsequent actions. Compared with a full-context baseline using the same DeepSeek-V4-Flash model, FlowState improves the average success rate on MemoryArena and the average pass rate on τ^3-Bench by 4.55 and 13.95 percentage points, respectively, while reducing total token consumption by 43.2% and 40.6%. These results demonstrate the performance and efficiency advantages of FlowState on long-horizon tasks.

A high-performance image compression algorithm is crucial for real-time information transmission across numerous fields. Despite rapid progress in image compression, computational inefficiency and poor redundancy modeling still pose significant bottlenecks, limiting practical applications. Inspired by the effectiveness of state space models (SSMs) in capturing long-range dependencies, we leverage SSMs to address computational inefficiency in existing methods and improve image compression from multiple perspectives. In this paper, we integrate the advantages of SSMs for better efficiency-performance trade-off and propose an enhanced image compression approach through refined context modeling, which we term MambaIC. Specifically, we explore context modeling to adaptively refine the representation of hidden states. Additionally, we introduce window-based local attention into channel-spatial entropy modeling to reduce potential spatial redundancy during compression, thereby increasing efficiency. Comprehensive qualitative and quantitative results validate the effectiveness and efficiency of our approach, particularly for high-resolution image compression. Code is released at https://github.com/AuroraZengfh/MambaIC.

We introduce MoS (Mixture of States), a novel fusion paradigm for multimodal diffusion models that merges modalities using flexible, state-based interactions. The core of MoS is a learnable, token-wise router that creates denoising timestep- and input-dependent interactions between modalities' hidden states, precisely aligning token-level features with the diffusion trajectory. This router sparsely selects the top-k hidden states and is trained with an ε-greedy strategy, efficiently selecting contextual features with minimal learnable parameters and negligible computational overhead. We validate our design with text-to-image generation (MoS-Image) and editing (MoS-Editing), which achieve state-of-the-art results. With only 3B to 5B parameters, our models match or surpass counterparts up to 4times larger. These findings establish MoS as a flexible and compute-efficient paradigm for scaling multimodal diffusion models.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

The rapid growth of Large Transformer-based models, specifically Large Language Models (LLMs), now scaling to trillions of parameters, has necessitated training across thousands of GPUs using complex hybrid parallelism strategies (e.g., data, tensor, and pipeline parallelism). Checkpointing this massive, distributed state is critical for a wide range of use cases, such as resilience, suspend-resume, investigating undesirable training trajectories, and explaining model evolution. However, existing checkpointing solutions typically treat model state as opaque binary blobs, ignoring the ``3D heterogeneity'' of the underlying data structures--varying by memory location (GPU vs. Host), number of ``logical'' objects sharded and split across multiple files, data types (tensors vs. Python objects), and their serialization requirements. This results in significant runtime overheads due to blocking device-to-host transfers, data-oblivious serialization, and storage I/O contention. In this paper, we introduce DataStates-LLM, a novel checkpointing architecture that leverages State Providers to decouple state abstraction from data movement. DataStates-LLM exploits the immutability of model parameters during the forward and backward passes to perform ``lazy'', non-blocking asynchronous snapshots. By introducing State Providers, we efficiently coalesce fragmented, heterogeneous shards and overlap the serialization of metadata with bulk tensor I/O. We evaluate DataStates-LLM on models up to 70B parameters on 256 A100-40GB GPUs. Our results demonstrate that DataStates-LLM achieves up to 4times higher checkpointing throughput and reduces end-to-end training time by up to 2.2times compared to state-of-the-art solutions, effectively mitigating the serialization and heterogeneity bottlenecks in extreme-scale LLM training.

Diffusion Large Language Models (dLLMs) enable breakthroughs in reasoning and parallel decoding but suffer from prohibitive quadratic computational complexity and memory overhead during inference. Current caching techniques accelerate decoding by storing full-layer states, yet impose substantial memory usage that limit long-context applications. Our analysis of attention patterns in dLLMs reveals persistent cross-layer sparsity, with pivotal tokens remaining salient across decoding steps and low-relevance tokens staying unimportant, motivating selective cache eviction. We propose Sparse-dLLM, the first training-free framework integrating dynamic cache eviction with sparse attention via delayed bidirectional sparse caching. By leveraging the stability of token saliency over steps, it retains critical tokens and dynamically evicts unimportant prefix/suffix entries using an attention-guided strategy. Extensive experiments on LLaDA and Dream series demonstrate Sparse-dLLM achieves up to 10times higher throughput than vanilla dLLMs, with comparable performance and similar peak memory costs, outperforming previous methods in efficiency and effectiveness.

Diffusion language models (DLMs) iteratively refine a sequence, allowing earlier predictions to be revised as context evolves. This rollback capability distinguishes them from irreversible autoregressive generation, but makes inference costly. Every denoising update alters the global context, forcing both prompt and response states to be recomputed even though only response tokens are revisable. Key-value (KV) caching could reduce this cost, yet conventional caching assumes immutable historical states and is therefore difficult to reconcile with rollback. In this paper, we introduce Adaptive Reuse of Cached Hidden States for Efficient Rollback (Archer), a training-free KV caching method for rollback-capable DLMs. Archer asymmetrically keeps the mutable response synchronized with the current hypothesis while reusing prompt K/V within a bounded state neighborhood. Although prompt representations also change under bidirectional attention, their token identities remain fixed; bounded reuse therefore amortizes repeated prompt computation without caching mutable response states. It also delays feedback from tentative tokens, reducing premature reinforcement of transient high-confidence errors and giving rollback more opportunity to correct them. Our analysis characterizes prompt reuse as a reversibility-aligned cache boundary, bounds its state-dependent approximation error, and gives a decoder-margin condition for preserving full-refresh decisions. Existing DLM acceleration often trades quality for speed. Archer shifts this frontier, attaining the best mean performance of 33.63% together with a 2.57x mean speedup on the main suite. Across evaluated settings, it improves Pass@1 by up to 3.05 points and reaches up to 2.95x speedup. Controlled analyses connect the quality gain to delayed prompt feedback and validate state-aware refresh. Our code is available at https://github.com/Hxnng/Archer.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

The deployment of efficient long-context LLMs in applications like autonomous agents, long-chain reasoning, and creative writing is fundamentally bottlenecked by the linear growth of KV cache memory. Existing compression and eviction methods often struggle to balance accuracy, compression ratio, and hardware efficiency. We propose DeltaKV, a residual-based KV cache compression framework motivated by two empirical findings: long-range inter-token similarity and highly shared latent components in KV representations. Instead of discarding tokens, DeltaKV encodes semantic residuals relative to retrieved historical references, preserving fidelity while substantially reducing storage. To translate compression gains into real system speedups, we further introduce Sparse-vLLM, a high-performance inference engine with decoupled memory management and kernels optimized for sparse and irregular KV layouts. Experiments show that DeltaKV reduces KV cache memory to 29\% of the original while maintaining near-lossless accuracy on LongBench, SCBench, and AIME. When integrated with Sparse-vLLM, it achieves up to 2times throughput improvement over vLLM in long-context scenarios, demonstrating a practical path toward scalable long-context LLM deployment. Code, model checkpoints, and datasets are available at https://github.com/CURRENTF/Sparse-vLLM.

Memory is a fundamental component for enabling long-context LLM agents, supporting persistent state across interactions through a continuous serve-and-update lifecycle. Despite substantial prior work, existing systems suffer from significant maintenance overhead due to two key limitations: coarse-grained state management and inherently sequential update pipelines. In particular, updates are often tightly coupled with LLM inference and require full-state rewrites, leading to poor scalability and growing latency as memory accumulates. To address these challenges, we present MemForest, a memory framework that reformulates agent memory as a write-efficient temporal data management problem. MemForest breaks the sequential bottleneck via parallel chunk extraction, decoupling memory construction into concurrent, independent operations. To further eliminate coarse-grained maintenance, we introduce MemTree, a hierarchical temporal index that organizes memory as time-ordered trees rather than flat global summaries. This design replaces full-state rewrites with localized per-node updates, reducing maintenance cost to the affected tree paths while naturally preserving temporally evolving states. We evaluate MemForest on two long-context memory benchmarks, LongMemEval-S and LoCoMo. On LongMemEval-S, MemForest achieves the best overall performance among stateful baselines, reaching 79.8% pass@1 accuracy while sustaining a memory construction throughput approximately 6x higher than state-of-the-art approaches including EverMemOS.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

Autoregressive (AR) video diffusion is a powerful paradigm for streaming and interactive video generation. However, its reliance on softmax self-attention leads to quadratic compute complexity in sequence length and memory usage due to key-value caching, which limits its scalability to long video horizons. Existing remedies (e.g., sparse attention and KV-cache compression) reduce per-step cost but still rely on a linearly growing cache or irreversibly discard past context, and thus fail to address linear memory growth and streaming context management. To address this scalability bottleneck, we propose ARL2 (Attend Locally, Remember Linearly), a hybrid attention module that replaces quadratic cross-frame attention with a fixed-size recurrent state. We decompose self-attention into two branches: an intra-frame softmax branch for spatial detail and local dependencies, and an inter-frame gated recurrent linear branch that maintains a fixed-size state for streaming context. Our key insight is that softmax attention captures fine-grained local interactions, while a recurrent state provides controllable long-range memory. This design achieves linear-time scaling with constant memory while improving temporal consistency over the full-softmax model. To prevent noisy intermediate states from corrupting memory, we update the recurrent state only after the denoised pass. To avoid within-frame information asymmetry, all tokens share the same pre-update state rather than sequential updates. To the best of our knowledge, this is the first work to convert a pretrained AR video diffusion model into a hybrid linear attention architecture, through an efficient two-stage training scheme for AR video. With 75% of layers replaced by hybrid linear attention, the model achieves up to 2.26 wall-clock speedup and 54% memory reduction, while maintaining comparable quality with improving temporal consistency.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

Sparse sketches such as the sparse Johnson-Lindenstrauss transform are a core primitive in randomized numerical linear algebra because they leverage random sparsity to reduce the arithmetic cost of sketching, while still offering strong approximation guarantees. Their random sparsity, however, is at odds with efficient implementations on modern GPUs, since it leads to irregular memory access patterns that degrade memory bandwidth utilization. Motivated by this tension, we pursue a sketch-kernel co-design approach: we design a new family of sparse sketches, BlockPerm-SJLT, whose sparsity structure is chosen to enable FlashSketch, a corresponding optimized CUDA kernel that implements these sketches efficiently. The design of BlockPerm-SJLT introduces a tunable parameter that explicitly trades off the tension between GPU-efficiency and sketching robustness. We provide theoretical guarantees for BlockPerm-SJLT under the oblivious subspace embedding (OSE) framework, and also analyze the effect of the tunable parameter on sketching quality. We empirically evaluate FlashSketch on standard RandNLA benchmarks, as well as an end-to-end ML data attribution pipeline called GraSS. FlashSketch pushes the Pareto frontier of sketching quality versus speed, across a range of regimes and tasks, and achieves a global geomean speedup of roughly 1.7x over the prior state-of-the-art GPU sketches.

During image editing, existing deep generative models tend to re-synthesize the entire output from scratch, including the unedited regions. This leads to a significant waste of computation, especially for minor editing operations. In this work, we present Spatially Sparse Inference (SSI), a general-purpose technique that selectively performs computation for edited regions and accelerates various generative models, including both conditional GANs and diffusion models. Our key observation is that users prone to gradually edit the input image. This motivates us to cache and reuse the feature maps of the original image. Given an edited image, we sparsely apply the convolutional filters to the edited regions while reusing the cached features for the unedited areas. Based on our algorithm, we further propose Sparse Incremental Generative Engine (SIGE) to convert the computation reduction to latency reduction on off-the-shelf hardware. With about 1%-area edits, SIGE accelerates DDPM by 3.0times on NVIDIA RTX 3090 and 4.6times on Apple M1 Pro GPU, Stable Diffusion by 7.2times on 3090, and GauGAN by 5.6times on 3090 and 5.2times on M1 Pro GPU. Compared to our conference version, we extend SIGE to accommodate attention layers and apply it to Stable Diffusion. Additionally, we offer support for Apple M1 Pro GPU and include more results with large and sequential edits.

This is an extended version of our publication Learning state machines from data streams: A generic strategy and an improved heuristic, International Conference on Grammatical Inference (ICGI) 2023, Rabat, Morocco. It has been extended with a formal proof on PAC-bounds, and the discussion and analysis of a similar approach has been moved from the appendix and now has a full dedicated section. State machine models are models that simulate the behavior of discrete event systems, capable of representing systems such as software systems, network interactions, and control systems, and have been researched extensively. The nature of most learning algorithms however is the assumption that all data be available at the beginning of the algorithm, and little research has been done in learning state machines from streaming data. In this paper, we want to close this gap further by presenting a generic method for learning state machines from data streams, as well as a merge heuristic that uses sketches to account for incomplete prefix trees. We implement our approach in an open-source state merging library and compare it with existing methods. We show the effectiveness of our approach with respect to run-time, memory consumption, and quality of results on a well known open dataset. Additionally, we provide a formal analysis of our algorithm, showing that it is capable of learning within the PAC framework, and show a theoretical improvement to increase run-time, without sacrificing correctness of the algorithm in larger sample sizes.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

State Space Models (SSMs) have emerged as efficient alternatives to Transformers, mitigating their quadratic computational cost. However, the application of Parameter-Efficient Fine-Tuning (PEFT) methods to SSMs remains largely unexplored. In particular, prompt-based methods like Prompt Tuning and Prefix-Tuning, which are widely used in Transformers, do not perform well on SSMs. To address this, we propose state-based methods as a superior alternative to prompt-based methods. This new family of methods naturally stems from the architectural characteristics of SSMs. State-based methods adjust state-related features directly instead of depending on external prompts. Furthermore, we introduce a novel state-based PEFT method: State-offset Tuning. At every timestep, our method directly affects the state at the current step, leading to more effective adaptation. Through extensive experiments across diverse datasets, we demonstrate the effectiveness of our method. Code is available at https://github.com/furiosa-ai/ssm-state-tuning.

Feed-forward transformer models have driven rapid progress in 3D vision, but state-of-the-art methods such as VGGT and π^3 have a computational cost that scales quadratically with the number of input images, making them inefficient when applied to large image collections. Sequential-reconstruction approaches reduce this cost but sacrifice reconstruction quality. We introduce ZipMap, a stateful feed-forward model that achieves linear-time, bidirectional 3D reconstruction while matching or surpassing the accuracy of quadratic-time methods. ZipMap employs test-time training layers to zip an entire image collection into a compact hidden scene state in a single forward pass, enabling reconstruction of over 700 frames in under 10 seconds on a single H100 GPU, more than 20times faster than state-of-the-art methods such as VGGT. Moreover, we demonstrate the benefits of having a stateful representation in real-time scene-state querying and its extension to sequential streaming reconstruction.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

Transformers achieve strong language modeling performance by providing direct token-to-token communication paths, but causal self-attention scales quadratically with context length. Recurrent and state-space models reduce this cost, yet compress history into sequentially updated fixed-size states. This paper studies a third primitive: a parallel content-addressed memory over causal successor records. The proposed Parallel Causal Associative Field (PCAF) writes local records from a context window into hash buckets, retrieves a bounded candidate set for the current query, forms a sparse cache distribution over successor tokens, and mixes that cache with a parametric local language model through a learned gate. The resulting model maintains sparse long-context access while avoiding a single fixed recurrent state bottleneck. We evaluate PCAF under full autoregressive pretraining on WikiText-103 and PG-19 using a distributed Google Cloud TPU v4-32 pod. At 303M parameters and context length T = 2048, PCAF-semantic reaches 36.31 perplexity on WikiText-103 and 52.45 perplexity on PG-19, compared with 47.49 and 53.84 for a matched dense Transformer. PCAF-semantic simultaneously processes 0.61-0.62M tokens/s across the TPU pod, versus 0.43M tokens/s for dense and local attention baselines. Supporting 41M-parameter multi-seed sweeps and single-GPU component ablations show that the associative cache, retrieval capacity, and learned gate materially affect the speed-quality trade-off.

In this work, we investigate how Large Language Models (LLMs) adapt their internal representations when encountering inputs of increasing difficulty, quantified as the degree of out-of-distribution (OOD) shift. We reveal a consistent and quantifiable phenomenon: as task difficulty increases, whether through harder reasoning questions, longer contexts, or adding answer choices, the last hidden states of LLMs become substantially sparser. In short, \textit{the farther the shift, the sparser the representations}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that language models respond to unfamiliar or complex inputs by concentrating computation into specialized subspaces in the last hidden state. Through a series of controlled analyses with a learning dynamic explanation, we demonstrate that this sparsity is not incidental but an adaptive mechanism for stabilizing reasoning under OOD. Leveraging this insight, we design Sparsity-Guided Curriculum In-Context Learning (SG-ICL), a strategy that explicitly uses representation sparsity to schedule few-shot demonstrations, leading to considerable performance enhancements. Our study provides new mechanistic insights into how LLMs internalize OOD challenges. The source code is available at the URL: https://github.com/MingyuJ666/sparsityLLM.

Large language model (LLM) agents require long-term user memory for consistent personalization, but limited context windows hinder tracking evolving preferences over long interactions. Existing memory systems mainly rely on static, hand-crafted update rules; although reinforcement learning (RL)-based agents learn memory updates, sparse outcome rewards provide weak supervision, resulting in unstable long-horizon optimization. Drawing on memory schema theory and the functional division between prefrontal regions and hippocampus regions, we introduce MemCoE, a cognition-inspired two-stage optimization framework that learns how memory should be organized and what information to update. In the first stage, we propose Memory Guideline Induction to optimize a global guideline via contrastive feedback interpreted as textual gradients; in the second stage, Guideline-Aligned Memory Policy Optimization uses the induced guideline to define structured process rewards and performs multi-turn RL to learn a guideline-following memory evolution policy. We evaluate on three personalization memory benchmarks, covering explicit/implicit preference and different sizes and noise, and observe consistent improvements over strong baselines with favorable robustness, transferability, and efficiency.

Block-wise sparse attention offers significant efficiency gains for long-context modeling, yet existing methods often suffer from low selection fidelity and cumulative contextual loss by completely discarding unselected blocks. To address these limitations, we introduce Sparse Plus Linear Attention (SPLA), a framework that utilizes a selection metric derived from second-order Taylor expansions to accurately identify relevant blocks for exact attention. Instead of discarding the remaining "long tail," SPLA compresses unselected blocks into a compact recurrent state via a residual linear attention (RLA) module. Crucially, to avoid IO overhead, we derive an optimized subtraction-based formulation for RLA -- calculating the residual as the difference between global and selected linear attention -- ensuring that unselected blocks are never explicitly accessed during inference. Our experiments demonstrate that SPLA closes the performance gap in continual pretraining, surpassing dense attention models on long-context benchmarks like RULER while maintaining competitive general knowledge and reasoning capabilities.

State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs.

The attention prefilling phase of long-context LLM inference scales quadratically, making self-attention a severe computational bottleneck. Traditional sparse attention methods mitigate this through fixed patterns or offline profiling, but lack the flexibility to adapt to input-dependent attention structure. Recent dynamic methods address this by routing heads to sparse patterns in real-time, but rely on indirect routing proxies with overhead and budget allocation mechanisms that overlook the post-softmax mass hierarchy. We present CRISP (Cliff-awaRe Input-adaptive Sparse Prefilling), which identifies and addresses two structural challenges in this dynamic routing paradigm. First, we show that the routing decision can be read directly off the structure of the proxy attention map. We replace the Jensen-Shannon Divergence (JSD) routing with C_struct, a structural proxy that measures mass at Vertical-Slash compatible positions and reproduces JSD's routing decisions while eliminating both the pooled matmul and subsequent KL divergence overhead. Second, we formalize the post-softmax mass cliff and demonstrate theoretically that strictly cumulative coverage thresholds accumulate O(n) background noise at long contexts. CRISP navigates this via a sink-aware threshold grounded in the noise floor. Empirically, across InfiniteBench, RULER and LongBench on two model families, CRISP is the strongest sparse method overall and matches or exceeds exact dense attention on retrieval-heavy benchmarks, recovering up to +28.0 pp on retrieval tasks over baselines and achieving up to a 5.30x attention speedup at 512k tokens, driven primarily by our O(n) noise elimination during selection while preserving structural integrity.

Semi-structured N:M sparsity and low-bit quantization (e.g., 1.58-bit BitNet) are two promising approaches for improving the efficiency of large language models (LLMs), yet they have largely been studied in isolation. In this work, we investigate their interaction and show that 1.58-bit BitNet is naturally more compatible with N:M sparsity than full-precision models. To study this effect, we propose Sparse-BitNet, a unified framework that jointly applies 1.58-bit quantization and dynamic N:M sparsification while ensuring stable training for the first time. Across multiple model scales and training regimes (sparse pretraining and dense-to-sparse schedules), 1.58-bit BitNet consistently exhibits smaller performance degradation than full-precision baselines at the same sparsity levels and can tolerate higher structured sparsity before accuracy collapse. Moreover, using our custom sparse tensor core, Sparse-BitNet achieves substantial speedups in both training and inference, reaching up to 1.30X. These results highlight that combining extremely low-bit quantization with semi-structured N:M sparsity is a promising direction for efficient LLMs. Code available at https://github.com/AAzdi/Sparse-BitNet

This work presents dyGRASS, an efficient dynamic algorithm for spectral sparsification of large undirected graphs that undergo streaming edge insertions and deletions. At its core, dyGRASS employs a random-walk-based method to efficiently estimate node-to-node distances in both the original graph (for decremental update) and its sparsifier (for incremental update). For incremental updates, dyGRASS enables the identification of spectrally critical edges among the updates to capture the latest structural changes. For decremental updates, dyGRASS facilitates the recovery of important edges from the original graph back into the sparsifier. To further enhance computational efficiency, dyGRASS employs a GPU-based non-backtracking random walk scheme that allows multiple walkers to operate simultaneously across various target updates. This parallelization significantly improves both the performance and scalability of the proposed dyGRASS framework. Our comprehensive experimental evaluations reveal that dyGRASS achieves approximately a 10x speedup compared to the state-of-the-art incremental sparsification (inGRASS) algorithm while eliminating the setup overhead and improving solution quality in incremental spectral sparsification tasks. Moreover, dyGRASS delivers high efficiency and superior solution quality for fully dynamic graph sparsification, accommodating both edge insertions and deletions across a diverse range of graph instances originating from integrated circuit simulations, finite element analysis, and social networks.

Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the community. Yet, much less is known about the interaction between sparsity and the standard stochastic optimization techniques used for training sparse networks, and most existing work uses standard dense schedules and hyperparameters for training sparse networks. In this work, we examine the impact of high sparsity on model training using the standard computer vision and natural language processing sparsity benchmarks. We begin by showing that using standard dense training recipes for sparse training is suboptimal, and results in under-training. We provide new approaches for mitigating this issue for both sparse pre-training of vision models (e.g. ResNet50/ImageNet) and sparse fine-tuning of language models (e.g. BERT/GLUE), achieving state-of-the-art results in both settings in the high-sparsity regime, and providing detailed analyses for the difficulty of sparse training in both scenarios. Our work sets a new threshold in terms of the accuracies that can be achieved under high sparsity, and should inspire further research into improving sparse model training, to reach higher accuracies under high sparsity, but also to do so efficiently.

RLVR has substantially improved the reasoning capabilities of LLMs. However, existing methods typically parameterize temporal progression in the Markov Decision Process by token-by-token generation, despite the highly non-uniform information flow along autoregressive trajectories. In this paper, we propose InfoPPO, which reparameterizes temporal progression using information density rather than raw token count. This reparameterization induces a common state-dependent structure for both temporal credit propagation and policy updates. InfoPPO restores the effectiveness of non-trivial discounting in long-horizon reasoning, retaining effective-horizon contraction while avoiding excessive attenuation of terminal supervision over long token sequences. Moreover, the information-time policy-improvement analysis naturally leads to a state-dependent update constraint, which we implement through adaptive clipping. By adapting the clipping threshold at each token position to the information density of its corresponding state, this mechanism enables more targeted policy updates while preserving proximal control. Theoretically, we extend performance-difference and policy-improvement analyses to the information-time MDP, deriving a policy-improvement lower bound when policy changes are regulated by information density. We further connect the general information-time analysis to practical LLM policy optimization by relating state-wise information density to local policy movement, while also providing theoretical grounding for the adaptive update mechanism. Experiments on Qwen3 models demonstrate consistent gains over competitive baselines across five challenging competition-style mathematical reasoning benchmarks. InfoPPO also maintains stable accuracy and response length across non-trivial discount settings under which token-time PPO deteriorates.

Sparse dictionary learning has been a rapidly growing technique in mechanistic interpretability to attack superposition and extract more human-understandable features from model activations. We ask a further question based on the extracted more monosemantic features: How do we recognize circuits connecting the enormous amount of dictionary features? We propose a circuit discovery framework alternative to activation patching. Our framework suffers less from out-of-distribution and proves to be more efficient in terms of asymptotic complexity. The basic unit in our framework is dictionary features decomposed from all modules writing to the residual stream, including embedding, attention output and MLP output. Starting from any logit, dictionary feature or attention score, we manage to trace down to lower-level dictionary features of all tokens and compute their contribution to these more interpretable and local model behaviors. We dig in a small transformer trained on a synthetic task named Othello and find a number of human-understandable fine-grained circuits inside of it.

Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM computation via convolution. To overcome compatibility limitations in parallel convolutional computation, this paper proposes a novel non-recursive non-uniform sample processing strategy. Theoretical analysis of SSMs through the lens of Event-Triggered Control (ETC) theory reveals the Non-Stable State (NSS) problem, where deviations from sampling point requirements lead to error transmission and accumulation, causing the divergence of the SSM's hidden state. Our analysis further reveals that adjustments of input sequences with early memories can mitigate the NSS problem, achieving Sampling Step Adaptation (SSA). Building on this insight, we introduce a simple yet effective plug-and-play mechanism, State Memory Replay (SMR), which utilizes learnable memories to adjust the current state with multi-step information for generalization at sampling points different from those in the training data. This enables SSMs to stably model varying sampling points. Experiments on long-range modeling tasks in autoregressive language modeling and Long Range Arena demonstrate the general effectiveness of the SMR mechanism for a series of SSM models.

Training large, deep neural networks to convergence can be prohibitively expensive. As a result, often only a small selection of popular, dense models are reused across different contexts and tasks. Increasingly, sparsely activated models, which seek to decouple model size from computation costs, are becoming an attractive alternative to dense models. Although more efficient in terms of quality and computation cost, sparse models remain data-hungry and costly to train from scratch in the large scale regime. In this work, we propose sparse upcycling -- a simple way to reuse sunk training costs by initializing a sparsely activated Mixture-of-Experts model from a dense checkpoint. We show that sparsely upcycled T5 Base, Large, and XL language models and Vision Transformer Base and Large models, respectively, significantly outperform their dense counterparts on SuperGLUE and ImageNet, using only ~50% of the initial dense pretraining sunk cost. The upcycled models also outperform sparse models trained from scratch on 100% of the initial dense pretraining computation budget.

Leveraging attention sparsity to accelerate long-context large language models (LLMs) has been a hot research topic. However, current algorithms such as sparse attention or key-value (KV) cache compression tend to use a fixed budget, which presents a significant challenge during deployment because it fails to account for the dynamic nature of real-world scenarios, where the optimal balance between accuracy and efficiency can vary greatly. In this paper, we find that borrowing top-p sampling (nucleus sampling) to sparse attention can surprisingly achieve adaptive budgeting. Based on this, we propose Twilight, a framework to bring adaptive sparsity to any existing sparse attention algorithm without sacrificing their accuracy. Empirical results show that Twilight can adaptively prune at most 98% of redundant tokens, leading to 15.4times acceleration in self-attention operations and 3.9times acceleration in end-to-end per token latency in long context LLM decoding.

We propose a sparsity-aware evolutionary (SAE) framework for model merging that involves iterative pruning-merging cycles to act as a novel mutation operator. We incorporate the sparsity constraints into the score function, which steers the evolutionary process to favor more sparse models, in addition to other conventional performance scores. Interestingly, the by-product of competition for sparsity introduces an extra local attraction and interplay into the evolutionary process: if one competitor has more zero elements, the other competitor's non-zero elements will occupy those positions, even though the less sparse competitor loses to the more sparse competitor in other positions. The proposed pipeline is evaluated on a variety of large-scale LLM benchmarks. Experiments demonstrate that our approach can improve model merging reliability across multiple benchmarks, and is easy to incorporate due to its simplicity and being orthogonal to most existing approaches.

Joint-embedding predictive architectures (JEPAs) learn latent dynamics for planning and avoid representation collapse by matching features to maximum-entropy distributions such as isotropic Gaussians, yielding dense representations. However, it is unclear whether dense representations are the most favorable geometry for modeling dynamics. In this work, we ask whether a different geometry, sparse representations, can make action-conditioned latent dynamics easier to model, and what dynamical structure emerges from such representations. We first show that nonlinear Lipschitz dynamics can be approximated arbitrarily well by action-conditioned linear dynamics in a sufficiently high-dimensional one-hot latent space, with rollout error vanishing as the dimension grows. This motivates distributed sparse representations as a practical relaxation of one-hot sparsity. We introduce LpWorldModel (LpWM), a JEPA model regularized with Rectified Distribution Matching Regularization (RDMReg) to match encoder features to a Rectified Generalized Gaussian distribution, yielding non-negative sparse codes. Empirically, sparsity lowers the predictor complexity required for successful planning: on PushT, sparse LpWM outperforms dense LeWM by up to 57% in planning success at intermediate predictor capacities. This advantage also extends beyond Gaussian distribution matching, with LpWM outperforming dense VICReg representations across multiple predictor families. We further find that the learned sparse representations are mode-factored, with support encoding discrete dynamical regimes and feature magnitudes capturing continuous within-regime state. Together, these results suggest that sparse representations can reduce the predictor complexity required for control while revealing interpretable structure.

We demonstrate that unstructured sparsity significantly improves KV cache compression for LLMs, enabling sparsity levels up to 70% without compromising accuracy or requiring fine-tuning. We conduct a systematic exploration of pruning strategies and find per-token magnitude-based pruning as highly effective for both Key and Value caches under unstructured sparsity, surpassing prior structured pruning schemes. The Key cache benefits from prominent outlier elements, while the Value cache surprisingly benefits from a simple magnitude-based pruning despite its uniform distribution. KV cache size is the major bottleneck in decode performance due to high memory overhead for large context lengths. To address this, we use a bitmap-based sparse format and a custom attention kernel capable of compressing and directly computing over compressed caches pruned to arbitrary sparsity patterns, significantly accelerating memory-bound operations in decode computations and thereby compensating for the overhead of runtime pruning and compression. Our custom attention kernel coupled with the bitmap-based format delivers substantial compression of KV cache upto 45% of dense inference and thereby enables longer context length and increased tokens/sec throughput of upto 2.23x compared to dense inference. Our pruning mechanism and sparse attention kernel is available at https://github.com/dhjoo98/mustafar.

A critical approach for efficiently deploying computationally demanding large language models (LLMs) is Key-Value (KV) caching. The KV cache stores key-value states of previously generated tokens, significantly reducing the need for repetitive computations and thereby lowering latency in autoregressive generation. However, the size of the KV cache grows linearly with sequence length, posing challenges for applications requiring long context input and extensive sequence generation. In this paper, we present a simple yet effective approach, called MiniCache, to compress the KV cache across layers from a novel depth perspective, significantly reducing the memory footprint for LLM inference. Our approach is based on the observation that KV cache states exhibit high similarity between the adjacent layers in the middle-to-deep portion of LLMs. To facilitate merging, we propose disentangling the states into the magnitude and direction components, interpolating the directions of the state vectors while preserving their lengths unchanged. Furthermore, we introduce a token retention strategy to keep highly distinct state pairs unmerged, thus preserving the information with minimal additional storage overhead. Our MiniCache is training-free and general, complementing existing KV cache compression strategies, such as quantization and sparsity. We conduct a comprehensive evaluation of MiniCache utilizing various models including LLaMA-2, LLaMA-3, Phi-3, Mistral, and Mixtral across multiple benchmarks, demonstrating its exceptional performance in achieving superior compression ratios and high throughput. On the ShareGPT dataset, LLaMA-2-7B with 4-bit MiniCache achieves a remarkable compression ratio of up to 5.02x, enhances inference throughput by approximately 5x, and reduces the memory footprint by 41% compared to the FP16 full cache baseline, all while maintaining near-lossless performance.

Sparse autoencoders (SAEs) have emerged as powerful techniques for interpretability of large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the ell_0 sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method, a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

Self-attention gives LLMs fine-grained, query-dependent access to context, but dense token interactions incur quadratic prefill cost and a key--value cache growing with context length. Research thus spans explicit-memory compression, sparse access, recurrent state construction, structured state dynamics, and heterogeneous mechanism composition. This survey analyzes these developments as model-internal contextual memory. We introduce a five-dimensional lens---Memory Representation, Memory Update, Access, Readout, and Integration---describing what is represented, how it changes, what is query-eligible, how it is read, and how readouts form outputs. This lens compares overlapping research lines without imposing one computational model. We reconstruct mechanism-level developments and architectural adoption using 59 release-level records from 14 major model lineages and 11 high-performing open-weight endpoints. First, explicit-memory and recurrent-state methods retain distinct interfaces but increasingly control overlapping memory functions. Second, heterogeneous architectures increasingly coordinate across network depth: layer-wise composition distributes complementary memory processing across representational stages, while cross-layer reuse carries selected memory and routing artifacts forward. Depth thus becomes a dimension along which contextual memory is constructed and managed. Third, these developments motivate a stateful multidimensional memory-routing hypothesis: persistent memory is organized across temporal scope, network depth, substrate type, and representation granularity, while coordinated Sparse Write and Sparse Read determine what is maintained and what contributes to each query. Overall, efficient sequence architecture design increasingly concerns the organization, lifecycle, and selective use of contextual memory rather than an isolated Attention operator.

Asynchronous reinforcement learning improves throughput by decoupling rollout generation from optimization, but staleness is an inevitable byproduct compounded by policy lag, engine delays, and mixture-of-experts routing. From a trust-region perspective, this mismatch is critical: training-inference divergence governs approximation error in finite-horizon bounds, whereas PPO clipping only gates sampled outward updates, acting as a sampled surrogate rather than a full-policy constraint. As a result, high-staleness updates remain weakly controlled in the asynchronous regime where stale rollouts matter most. We introduce the Staleness-Adaptive Trust Region (SAT), which uses the detached sampled log-ratio as a practical staleness proxy, identifies high-mismatch tails within each batch via staleness-based kernel scaling, and contracts only the sign-selected endpoint of the nominal PPO interval. This preserves baseline behavior on ordinary tokens while enforcing more conservative updates on newly intercepted outward bands. We prove local interval containment and pointwise pessimism relative to PPO, showing how the adaptive rule reshapes update geometry under heterogeneous staleness. We evaluate SAT in a decoupled asynchronous RL setup built on Qwen3-30B-A3B-Base, using SGLang as the inference engine and Megatron for training. In this setting, SAT-GSPO w/ R3 achieves the best observed AIME24 avg@8, reaching 35.83 at lag 1 and 34.79 at lag 8, while SAT-GSPO reaches 34.17 at lag 1. Adaptive clipping and routing replay act as complementary stabilizers targeting mismatch tails and routing inconsistency, respectively. Overall, aligning clip intervals with staleness heterogeneity effectively stabilizes asynchronous RL.

Sparse attention reduces compute and memory bandwidth for long-context LLM inference. However, two key challenges remain: (1) KV cache capacity still grows with sequence length, and offloading to CPU memory introduces a PCIe transfer bottleneck; (2) the sparse selection step itself retains O(T^2) complexity and can dominate attention cost at long contexts. We propose SparDA, a decoupled sparse attention architecture that introduces a fourth per-layer projection, the Forecast, alongside Query, Key, and Value. The Forecast predicts the KV blocks needed by the next layer, enabling lookahead selection that overlaps CPU-to-GPU prefetch with current-layer execution. Because Forecast is decoupled from the attention query, our GQA implementation uses one Forecast head per GQA group, reducing selection overhead versus the original multi-head selector. SparDA adds <0.5% parameters and trains only the Forecast projections by matching the original selector's attention distribution. On two sparse-pretrained 8B models, SparDA matches or slightly improves accuracy and delivers up to 1.25times prefill speedup and 1.7times decode speedup over the sparse-attention offload baseline. By enabling larger feasible batch sizes on a single GPU, SparDA further reaches up to 5.3times higher decode throughput than the non-offload sparse baseline. Our source code is available at https://github.com/NVlabs/SparDA.

A user's movie, news, and dialogue histories differ in their native actions and outputs, yet each interaction supplies evidence that can update user memory. We study whether these histories can train one reusable update mechanism. An action-on-item schema pairs a mapped interaction role with a content embedding, allowing shared update parameters to operate on separate user states. We establish invariance to native relabeling, bounded state changes under item-embedding perturbations, and a pooled-training bound under explicit compatibility conditions. The Multi-Timescale State Hypothesis (MTSH) specifies how this evidence enters, persists, and is consumed; PerTIDE implements it with action gating, three state-space traces, fusion, and command-conditioned readout. On PENS, the same history encoder supports both next-news prediction and personalized headline generation. In a controlled PENS-to-MovieLens experiment, a frozen source-trained core exceeds an identically structured random core by 15.23 MRR points after fitting the same target consumer. On MIND, PerTIDE retains a 4.12-point MRR advantage over a same-input three-branch state-space control. Action, readout, and trace interventions identify complementary contributions to these gains. Together, the theory and experiments support learning history updates across compatible sources and reusing them through predictive and generative consumers.