Sparse
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On the Sparsity-Storage-Accuracy Tradeoff in Parsimoniously Activated Dictionary Learning
2026-10-12 14:26:17Zihui Zhao, Yuanbo Tang, Yang LiAbstract
Dictionary learning has long been studied from both optimization and probabilistic perspectives. While formulations with element-wise sparsity regularization (e.g., L1-based sparse coding) admit well-established probabilistic interpretations, many structured variants that impose global constraints lack a clear and tractable generative view. In this paper, we revisit a class of practically effective yet theoretically under-explored dictionary learning methods that impose a simple global regularization on the number of activated dictionary atoms, which we term parsimoniously activated dictionary learning (PADL). We show that PADL admits an equivalent formulation as maximum a posteriori estimation under a structured generative model, with auxiliary latent variables that govern global activation patterns. This formulation allows us to derive generalization guarantees that are difficult to obtain under the original formulation. More importantly, it yields an analytical characterization of the tradeoff between sparsity, storage cost, and reconstruction accuracy, enabling data-driven estimation of optimal hyperparameters. Based on this connection, we develop an efficient and interpretable PADL algorithm that eliminates manual hyperparameter tuning, achieving improved reconstruction performance under comparable sparsity levels on visual benchmarks. We further demonstrate its practical utility in accelerating inference for vision-language models.
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URL
https://arxiv.org/abs/2606.22352
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Relational Learning as World Modeling
2026-10-12 13:24:37Zheyu Zhang, Gjergji KasneciAbstract
Relational learning typically predicts from a database state, but decision making asks a different question: how will that state change under an action? In operational systems, the answer depends on system-specific dynamics that may not be visible in the database itself. We view each such system as a relational "world" and ask whether a model can infer how it behaves from observed executions. We introduce TabWM (Tabular World Model) and WorldRel, a generator of executable relational worlds for pretraining. Given executions from an unseen world, TabWM uses them as context to predict the sparse structured edits caused by a new action without parameter updates. Across 512 held-out worlds, complete-edit F1 rises from 0.016 with no observed executions to 0.685 with 64, where a correct edit must match its operation, relational location, and value. Because these predictions are explicit relational edits, they can be applied recursively to imagine candidate futures and compare actions before they are taken. Broader search over these predicted futures improves the realized return of selected action sequences. Together, these results suggest that relational dynamics can be learned in context, broadening relational learning from modeling system state to modeling how that state changes under action.
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URL
https://arxiv.org/abs/2610.16763
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Learning Incompressible 3D Flows from Sparse Samples: A Set Transformer Approach to Divergence-Free Kernel Fitting
2026-10-12 12:06:44Ramzi Idoughi, Radouan Boukharfane, Peter WonkaAbstract
Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representations, and robustness to missing data. We introduce DFK-Former, a set-to-field transformer that reconstructs divergence-free velocity fields from sparse, noisy, and irregularly sampled 3D observations. The model is inherently invariant to the number and ordering of input samples and predicts the parameters of a divergence-free kernel representation, producing continuous, mesh-free velocity fields that satisfy incompressibility exactly by construction rather than approximately through soft constraints or projection operators. Unlike existing divergence-free kernel approaches, which estimate kernel coefficients via a separate optimization for each field, DFK-Former predicts these coefficients directly in a single forward pass. This eliminates costly iterative fitting while providing a learned prior that enables accurate reconstruction even when observations are insufficient to uniquely determine the field. To enhance representational power, we introduce adaptive and anisotropic divergence-free kernels that preserve exact incompressibility guarantees while capturing more complex flow structures. Extensive experiments across varying levels of sparsity, noise, and occlusion, including transfer to real Direct Numerical Simulation (DNS) turbulence data, demonstrate substantial gains in both accuracy and efficiency. DFK-Former reduces endpoint error by up to 4.6x compared to per-field divergence-free-kernel optimization, while reconstructing each field in 7.5 ms instead of 9.8 s, yielding a speedup of more than three orders of magnitude. These results establish direct, feed-forward prediction of divergence-free kernel parameters as a practical and effective paradigm for physically consistent velocity-field reconstruction from sparse observations.
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URL
https://arxiv.org/abs/2610.16645
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Large language model-generated patterns for epidemiological modeling: a multi-benchmark evaluation framework
2026-10-11 23:48:02Sophia Mao, Keshav Gandhi, Alexander GutfraindAbstract
Representing individual-level behavioral heterogeneity is challenging in epidemiological modeling, particularly when empirical behavioral data are sparse. We assess the potential of large language model (LLM)-generated behavioral outputs in addressing this challenge, using hepatitis C virus-related behaviors among people who inject drugs as a case study. Correspondence with epidemiological patterns was evaluated using external benchmarks: literature-informed association directions, correlations from an agent-based model (ABM), and survey associations. Across three LLMs, unconditional directional recovery across 28 retained literature-informed associations was 46-68%, compared with 82-93% agreement when LLMs were directly asked to classify the same associations. Mean absolute differences from ABM and survey correlation patterns were 0.11-0.13 and 0.15-0.18, respectively. Together, these findings show partial alignment between LLM-generated behavioral relationships and epidemiological evidence, despite higher knowledge-probe agreement. More systematic evaluation is needed before incorporating LLM-generated behavioral outputs into epidemiological models that simulate transmission dynamics.
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URL
https://arxiv.org/abs/2610.15994
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Small but Mighty: Test Suites as Improvement Signals for Self-Evolving Agents
2026-10-11 22:36:54Yutong Cheng, Wei Cheng, Wenchao Yu, Dawei Zhou, Haifeng ChenAbstract
A self-evolving agent rewrites its own harness and must decide which rewrites to keep, so its improvement signal is the check a rewrite has to pass. Verifying a rewrite by agent rollout is expensive and subjective, while executable checks such as the repository's own tests are too sparse to catch behavior-changing rewrites, rejecting only a quarter of them. We instead take test feedback as the executable signal, and search for test suites that are both small and strong with a quality-diversity evolutionary algorithm, so that the signal is dense and informative. TeSearch treats suite size as a behavior descriptor, so that quality is pursued at every size and a small, strong suite is reachable, and learns a transition kernel during the search that denoises the LLM as an actuator on that descriptor. Across 129 real-world modules and three backbones, TeSearch delivers the highest-quality suites of any method compared, LLM-driven evolutionary search included, and the smallest of any LLM-based one. Used as the improvement signal of a self-evolving agent, it rejects 59.9% of behavior-changing rewrites against 25.3% for the repository's tests, at a 4.0% false-alarm rate and 3.5 s per decision. The code and data are available at this https URL.
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URL
https://arxiv.org/abs/2610.15964
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LLM Value Functions for Credit Assignment in Agentic RL
2026-10-11 18:46:50Kaijie Zhu, Weixiang Yan, Omar Attia, Abbas Kazerouni, Alexander Toshev, Andrew SzotAbstract
Reinforcement learning (RL) for large language model (LLM) agents remains challenging in long-horizon tasks with sparse outcome rewards, where assigning credit to individual actions is difficult. Methods such as GRPO assign the same trajectory-level advantage to all actions, while critic-based methods require learning an additional value function that can be costly and unstable. We introduce LLM Value Function RL (LVRL), which uses the pretrained knowledge and in-context learning ability of an LLM to estimate policy-aware state values without finetuning a separate critic. LVRL conditions the value model on group context and calibrates its predictions using known values at the initial and terminal states, enabling step-level credit assignment from estimated value differences. We further extend this idea to learning from an expert policy through on-policy distillation (OPD), introducing LLM Value Function OPD (LVOPD), which focuses teacher supervision on actions associated with decreases in estimated value. We evaluate our approach across diverse agentic benchmarks: AppWorld, BabyAI, and SWE-bench Verified. Across policy scales (4B to 32B), LVRL consistently and substantially outperforms both GRPO and PPO. On AppWorld and SWE-bench Verified, LVRL yields absolute improvements of up to 13.6 and 8.6 percentage points over GRPO. Notably, on tasks requiring extended exploration like BabyAI, LVRL bridges the gap from total failure to 75.0% success. Furthermore, LVOPD yields consistent improvements over standard distillation baselines on AppWorld. Finally, Monte-Carlo analysis confirms that our frozen critic accurately identifies semantic pitfalls and recoveries, proving that LVRL extracts robust, policy-aware step-level credit from sparse terminal outcomes.
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URL
https://arxiv.org/abs/2610.15840
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History Replays Itself: Unleashing Long-Context Capability in Linear Attention
2026-10-11 15:58:04Li Nanbo, Firas Laakom, Yilan Zhang, Piotr Pi\k{e}kos, Yimeng Chen, Liangyu Wang, Yifan Xu, Mateusz Ostaszewski, Dandan Guo, Wenyi Wang, Yanning Dai, Yuhui Wang, J\"{u}rgen SchmidhuberAbstract
Linear attention promises the efficiency needed for long-context language modelling, yet its fixed-size recurrent state must simultaneously support ongoing computation and preserve information from an ever-growing history. This coupling has reinforced a prevailing view that the state's memory capacity defines the model's long-context capability. We challenge this presumed ceiling: \emph{recurrent computation need not bear the full burden of long-term storage}. We introduce NoteBank, a sparse episodic memory that archives selected text before future queries are known, uses the backbone's native features for writing and addressing, and reads retrieved evidence through its native forward computation via replay. This \emph{training-free, plug-and-play} interface requires no external embedding model, separately trained retriever, or separate neural reader. At one million tokens, it raises Gated DeltaNet's mean accuracy across six RULER retrieval tasks from 1.7% to 70.3%, with no observed significant retrieval degradation from 4K to 1M tokens. This recovery adds $\leqslant$0.025% to analytical FLOPs, with persistent context storage approximately 1/2,600 that of a Transformer's full MHA KV cache at matched width, depth, and precision. Experiments extend from three 1.3B recurrent backbones to Mamba-2-8B and post-trained Qwen3.5-9B, demonstrating gains on LongBench v1/v2 and MemoryAgentBench. Together, these results show that sparse evidence storage and native replay can substantially expand the long-context capability of pretrained linear attention models while retaining the efficiency of recurrent computation.
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URL
https://arxiv.org/abs/2610.15715
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Recall What Is Missing: Composing Evidence from Long-Term Agent Memory
2026-10-11 14:18:11Qi Feng, Jicong FanAbstract
Under a limited context budget, a long-term agent must recall not merely memories that are individually relevant, but evidence that is collectively sufficient for the current query. Conventional memory access retrieves, scores, and truncates memories, often spending multiple context slots on redundant facts while leaving complementary evidence behind. We cast the read phase of long-term memory as query-conditioned evidence composition: each memory is valued by what it adds beyond the evidence already selected. We instantiate this operation with MemPursuit, a training-free mechanism that uses the residual of a sparse convex query reconstruction as a representation-space proxy for what the current memory set is missing. By reusing the query and candidate embeddings already available from retrieval, MemPursuit progressively composes nested evidence contexts without invoking a language model or cross-encoder to score each query--memory pair. The effectiveness of our method is verified on 3 popular benchmarks in comparison to strong baselines. In fixed-budget LoCoMo experiments, MemPursuit improves end-to-end accuracy by 7.2 percentage points at Top-10 and 5.5 percentage points at Top-20, with consistent gains across multiple memory frameworks, while achieving a 32.9$\times$ speedup in median reranking latency over fully batched BGE-v2-m3. Our implementation is available at this https URL.
Abstract (translated)
URL
https://arxiv.org/abs/2610.15642
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Fitting Every Hint Is Not Enough: Premature Floods in Recurrent Algorithmic Reasoners
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Recurrent algorithmic reasoners are trained with per-step hints on small graphs and run for many more steps on large ones. On breadth-first search in SALSA-CLRS, we find that a reasoner can reproduce every training hint and still fail on deep graphs: after some exact steps, it declares nodes reached before the search gets there. We call this a premature flood and trace two routes to it. In our GRU processor with a degree input, the flood is carried in the hidden state and set off when that input is in the tail of the training distribution. Setting the input higher at inference brings the flood sooner, and none of the six flooding models counts steps. Without the input, summing the neighbors' states instead of averaging them also breaks the processor. In the benchmark's own GIN and PGN, trained with its code, some seeds instead flood from a fixed step, on sparse and dense graphs alike. Clamping the degree input or adding 200 dense training graphs removes every failure of the GRU processor. Detaching the state between steps avoids the flood in that processor (0 of 23 seeds, against 6 under full backpropagation) but not with sums or a residual update, and two published remedies leave floods. None of the benchmark's test sets is both deep and dense, but its deepest one shows the second route: on its Delaunay graphs at 1,600 nodes, one GIN seed floods from step 18. We therefore recommend auditing the range of every input and aggregate, which catches the first route, and testing on deep graphs, which catches both.
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URL
https://arxiv.org/abs/2610.14982
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FleetPilot: Fine-Grained Steering Empowers Real-World LLM Personalization
2026-10-10 14:44:50Kounianhua Du, Jianxing Liu, Kangning Zhang, Wenxiang Jiao, Yuan Lu, Jiarui Jin, Jianghao Lin, Weiwen Liu, Yong Yu, Weinan ZhangAbstract
With the rapid evolution of large language models (LLMs), there is an increasing demand for effective personalization techniques that can adapt model behavior to individual user preferences. Personalized LLMs must infer a user's query-dependent preferences from limited, heterogeneous, and evolving interaction histories. Existing approaches rely primarily on in-context personalization, parametric adaptation, or personalized reward modeling, but respectively incur recurring costs in context management, model optimization and deployment, or multi-candidate generation and scoring. These limitations become particularly restrictive when user observations are sparse and the preference evidence relevant to each query varies across contexts and over time. To address these challenges, we propose \modelname, a fine-grained and instance-tailored steering framework that dynamically generates sample-level interference vectors from user data and injects them into the model's forward pass for personalized adaptation. Our approach introduces: match contrast that produces user-relevant signals, fine-grained steering component that captures nuanced signals by hooking activations from attention and MLP layers, and query-conditioned aggregation module that synthesizes these signals into contextually relevant enhancements. Extensive experiments across diverse scenarios, including short-to-long text generation, and web function calling, validate the effectiveness and compatibility of \modelname. Results show that our method consistently brings significant performance gains, and show extreme superiority in fast-shifting and data-sparse environments. Additionally, \modelname rids us of training cycles and incurs light overhead of storage or inference latency. These make \modelname a strong and real-world deployable method. Implementation is available \footnote{this https URL}.
Abstract (translated)
URL
https://arxiv.org/abs/2610.14970
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Bridging Risk Approximation Gaps in Model Predictive Task Sampling via In-Context Modeling
2026-10-10 13:35:02Jiarong Wen, Qi Tao, Kaiyu Zhang, Yun Qu, Lizhou Cai, Heming Zou, Yuhang Jiang, Qi WangAbstract
Reinforcement learning (RL) is essential for adaptive decision-making, e.g., robust Meta-RL and domain randomization (DR), and efficient post-training of large language models (LLMs), where tasks are commonly structured as Markov decision processes or prompts. A central bottleneck in all these settings is the cost of agent-environment interactions required for task selection and policy optimization. Model predictive task sampling (MPTS) has emerged as a promising approach to improve sample efficiency by querying informative tasks via a risk predictive model (RPM) trained on optimization history. However, existing RPMs suffer from two failure modes: (i) sparse optimization histories, which limit RPMs' generalization across the task space, and (ii) a one-step lag in risk approximation, which causes biased difficulty estimation as the policy evolves. This work formalizes these failure modes, derives lagged-risk decompositions that expose the resulting temporal bias, and recasts risk prediction as an in-context sequence modeling problem. The developed RPM integrates a one-step look-ahead mechanism with a temporal-weighted sliding window to mitigate data non-stationarity and scarcity, without requiring additional rollouts. Empirically, our approach yields more reliable difficulty estimates and consistent performance gains across robust Meta-RL, DR, and prompt curriculum RL post-training of LLMs.
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URL
https://arxiv.org/abs/2610.14913
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GateSight: Recurrent Memory Anticipates Attention Memory for Query-Agnostic KV Eviction in Hybrid LLMs
2026-10-10 09:19:05Junjie Li, Jiong Lou, Jie LiAbstract
Hybrid language models interleave Gated DeltaNet (GDN) layers, whose recurrent memory has a fixed size, with full-attention layers, whose key-value (KV) cache grows with the context and dominates serving memory. In this paper, we ask whether the recurrent memory already knows what the attention memory will need. We first show that which GDN heads of Qwen3.8-27B keep long memories is fixed by the weights rather than by the document. Next, we define the future utility of a KV entry by how much removing it changes the attention output over the model's own continuations, and find that the write gate, decay and write magnitude that GDN layers emit during prefill anticipate this utility before any query is seen. Because the relation is spread across many GDN heads and layers, and a linear map recovers its trend but less of its high-utility tail than a nonlinear one, we propose GateSight, which learns it with lightweight per-head multilayer perceptrons that read these signals and no attention score. Their predicted utility decides which entries each attention layer keeps, and how much each layer keeps is set by the model's native attention output gate, whose mean differs by more than an order of magnitude across layers. Finally, at serving time, GateSight scores the cache once after prefill and physically releases discarded KV entries. Experimental results on SCBench and RULER-4096 with Qwen3.8-27B and, with the same recipe, the sparse-attention model Qwen3.8-Flash-Next, up to the 262K-token limit of the models, show that with a tenth of the attention KV cache, GateSight is the most accurate of five query-agnostic methods on three of the four model-benchmark pairs and leads KVzip on all four, by 9.5 to 47.2 points. Notably, it scores a full-length context with negligible overhead relative to prefill.
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URL
https://arxiv.org/abs/2610.14754
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PTGPO: Prefix Tree Group Policy Optimization
2026-10-10 08:57:33Ruolin Chen, Yang Li, Jihang Wang, Zhuoya Zhao, Yuchen Liu, Jiaming Xu, Qian ZhangAbstract
Training language agents on long-horizon interactive tasks is challenging because sparse terminal rewards provide weak credit signals for intermediate actions. Existing group-based methods either assign a shared trajectory-level advantage or estimate step-level advantages from state groups, which may conflate the current action with subsequent decisions. We propose Prefix Tree Group Policy Optimization (PTGPO), a critic-free method that constructs prefix trees over trajectory suffixes within anchor-state groups. PTGPO assigns each tree edge a credit given by the difference between its child and parent empirical mean returns, capturing the conditional return change revealed by each additional action. These prefix-tree credits provide fine-grained learning signals without requiring a critic or additional rollouts. Experiments on interactive benchmarks ALFWorld, WebShop and Sokoban show that PTGPO consistently improves over RL baselines, demonstrating its effectiveness.
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URL
https://arxiv.org/abs/2610.14737
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PsyMemBehav: Psychology-Informed and Memory-Grounded Two-Level Identity-to-Action Reasoning for Social-Media Behavior Simulation
2026-10-10 04:38:44Wenji Zhang, Xilong Cheng, Yunxiao Qin, Mai Tu, Tongye Zhu, Yuhao Zhou, JingBo Ji, Yuting Tan, Duoyin Li, Hongjiang Xiao, Yuan ZhangAbstract
Large language models (LLMs) support social simulation, but faithfully reproducing real users requires grounding both structured platform decisions and language in sparse, noisy behavioral evidence. We introduce PsyMemBehav, which maps psychology-informed profiles and retrieved memories to target-first platform behavior through two-level identity-to-action reasoning. To support this approach with comprehensive behavioral traces, we construct a dataset PsyMemBehav-bench from 5.57M observed behaviors of 5,862 real users (approximately 950 per user) across Reddit, Bluesky, and Twitter. Each recorded engagement is modeled as target selection followed by Comment, Like, or Repost and optional response generation. PsyMemBehav combines 41-dimensional user descriptors, top-5 BM25 memories, reverse-CoT supervision, and rubric-guided DPO over complete reasoning-action trajectories. Experiments show that PsyMemBehav 27B ranks first in 11 of 12 reported individual-level metrics, improving average response quality over GPT-5.4 from 54.28 to 59.68 (9.95% relative), and obtains the lowest group-level MAE (0.081) and MSE (0.009) among simulated systems. These results support evidence-grounded user modeling for observed-thread continuation; the benchmark remains conditional on recorded engagement and does not model no-action decisions.
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URL
https://arxiv.org/abs/2610.14570
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LASER: Defeasible Certificate Search for Long-Range Protocol Dependencies
Abstract
Protocol specifications rarely justify executable behavior in one place: a transition may inherit its source state from a remote control block, name its events only by number, and remain subject to a later correction. Recovering the nearby clause is therefore insufficient; the system must assemble a source-linked certificate and determine whether any stronger rule applies. We introduce LASER, a proof-carrying search method for sparse, defeasible protocol evidence. LASER represents missing support and unresolved corrections as explicit obligations, searches typed evidence routes, and lets an occurrence-aware symbolic checker alone decide whether a certificate warrants, refutes, or leaves a behavior unresolved. On 91 BehaviorCheck families under a matched 2K budget, LASER improves Joint Edge+Proof over the strongest local reader on two model families ($\Delta=+.132$, $p=.017$; $\Delta=+.198$, $p<.001$) while cutting false discoveries by 2--3$\times$. Controlled replays attribute the gain and its limits: neither reference routing nor deterministic citation expansion alone exceeds the local baseline; whole-document reading (29--65K tokens), two-round iterative retrieval, and even oracle minimal-certificate evidence all fail to reach LASER, localizing the bottleneck in typed obligation closure rather than evidence access. An authority-corruption replay shows source-link errors only cause abstention, while the only unsafe-warrant mechanism is mis-recording a Held erratum as Verified, confined to that erratum's family. LASER thus improves long-range dependency recovery while converting incomplete evidence and uncertain authority into explicit residual obligations rather than unsupported behavior.
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URL
https://arxiv.org/abs/2610.14552
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LLM-based User-Product Relevance Evaluation for Dynamic Product Advertising
2026-10-10 04:15:08Wen Zhang, Xiao Bai, Hsiang-wei Chao, Mengfan Zhu, Tong Zhao, Mingxuan Ju, Xiaodong Liu, Congfei Zhang, Yunzhi Zhou, Yajun Wang, Jinchao Li, Yu ZhangAbstract
Dynamic Product Advertising (DPA) retrieval systems are a core component of modern e-commerce advertising; however, their evaluation remains challenging. Conventional offline engagement metrics are limited by sparse, biased feedback, while online evaluation is costly and time-consuming. In this work, we propose a user--product relevance metric for offline evaluation of DPA retrieval systems. The metric first compresses the engagement history into a compact set of intent representatives via Semantic-ID-grouped, event-stratified segmentation, then assesses the relevance of a recommended product to each individual intent and aggregates them as a user-level relevance score, yielding a stable and interpretable measure of retrieval quality. To compute this metric at scale, we leverage large language models (LLMs) as semantic relevance judges, capturing nuanced functional and semantic relationships that heuristic methods often miss. We propose an agentic, human-aligned prompting framework that generates multi-category relevance guidelines and distills teacher-model judgments into an efficient student model for scalable evaluation. The resulting metric strongly correlates with offline and online business metrics, enabling faster and more reliable DPA retrieval iteration before A/B testing.
Abstract (translated)
URL
https://arxiv.org/abs/2610.14550
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Akule: Fast and Scalable Multi-Robot Motion Planning via Sparse Interaction Diffusion
2026-10-09 19:10:23Manav Vora, Gokul Puthumanaillam, Aditya Penumarti, Jane Shin, Melkior OrnikAbstract
Diffusion models provide expressive trajectory priors for multi-robot motion planning (MRMP), but scaling them to large teams requires coordinating individual motions without expensive joint computation. We introduce Akule, a sparse interaction diffusion framework that augments a frozen single-robot prior with three learned modules: a reusable pairwise correction model $R_{\phi}$, a contextual selector $U_{\psi}$ that determines which corrections to evaluate, and a composer $G_{\omega}$ that combines their effects through context-dependent signed weights. This decomposition separates which interactions merit computation from how their effects should be combined into coordinated denoising updates. We train $R_{\phi}$ using matched pairwise trajectory optimizations, then learn $G_{\omega}$ and $U_{\psi}$ from physically optimized joint trajectories without requiring a prescribed ground-truth interaction graph. The resulting joint proposals are passed to a downstream search-based planner for validation and repair. Across diverse MRMP benchmarks, Akule achieves competitive planning success, complete-planner speedups of up to $25\times$, zero-shot population transfer, and successful planning with up to $256$ robots. Ablations further demonstrate that learned selection and composition reduce pre-repair conflicts and downstream repair effort relative to heuristic selection and uniform summation.
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URL
https://arxiv.org/abs/2610.14248
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Learnable Low-Rank Polynomial Sketch for Effective Linear Attention
2026-10-09 18:30:52Zongyue Qin, Haoran Deng, Jason Cong, Yizhou SunAbstract
Softmax attention in Transformers suffers from quadratic complexity in sequence length, making it impractical for long-context applications. Linear attention alleviates this issue by replacing the exponential kernel with alternative functions that enable linear-time computation. Among existing linear attention approaches, recent studies have shown that polynomial kernels are particularly effective, as they exhibit sparse and spiky behavior similar to softmax attention, which emphasizes large dot products while suppressing irrelevant interactions. However, the exact computation of high-degree polynomial kernels is infeasible for high-dimensional representations. As a result, prior work relies on approximate polynomial kernels. This introduces a non-negligible approximation error. In this paper, we show that, from the perspective of polynomial kernel approximation, existing linear attention methods are still suboptimal. We propose \textbf{L}earnable \textbf{Lo}w-Rank \textbf{P}olynomial \textbf{S}ketch (LLoPS), a principled and flexible framework for approximating polynomial kernels with linear attention. Our method learns a low-rank polynomial sketch that provably achieves a strictly smaller approximation error than existing approaches. Experiment results show that LLoPS achieves the highest performance across extensive benchmarks, comparing with various linear attention baselines.
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URL
https://arxiv.org/abs/2610.14219
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Cross-Modal Latent Influence: Patch-Level Training Sample Attribution for Vision-Language Models
2026-10-09 18:04:04Laura Yao, Shixing Yu, Jie Peng, Promit Ghosal, Kyra Gan, Tianlong ChenAbstract
Explaining a vision--language model (VLM) prediction requires tracing training-example influence to the multimodal evidence that mediates it, yet existing attribution methods largely operate only at the sample level. Recent latent-mediated influence methods provide feature-level attribution in language models, but lack the multimodal and spatial structure needed to ground influence in VLMs. We introduce MOSAIC (Multimodal Orthogonalized Sparse Autoencoders for Influence Characterization). It learns a shared sparse image--text latent space whose concepts are 1) sparse within each modality, 2) supported on contiguous image regions, 3) aligned to the phrases that describe them, and 4) approximately decorrelated. It then applies EK-FAC to decompose training-example influence through these concepts and localize their contributions to specific text phrases and image regions. We evaluate MOSAIC on Qwen and Gemma across captioning, chest X-ray understanding, and visual question answering. The learned features are more localized and coherent without degrading task behavior, and ablating influence-ranked latents changes model outputs more than ablating latents ranked by activation or frequency. We find that visual evidence can substantially reorganize training-data attribution while preserving more of the shared latent structure. MOSAIC thus connects where model behavior comes from with what multimodal evidence carries that influence.
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URL
https://arxiv.org/abs/2610.14190
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Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning
2026-10-09 16:24:23Teo Deveney, Lea Bogensperger, Hok Shing WongAbstract
Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes $\beta$-Flow: a general plug-and-play method indexed by a correlation parameter $\beta$ that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter $\kappa$ that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4 datasets in terms of PSNR and SSIM. Moreover, we demonstrate the utility of this prior control, by showing that confident high correlations (strict priors) work best when observations are less informative, while low correlation is preferred when observations are more informative, reflecting the complementary roles of the prior and likelihood in Bayesian inference.
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URL
https://arxiv.org/abs/2610.13812
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