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10月9日 周五
arXiv cs.LG73

From a Prompt to Repertoires: Evolving Functional REpertoires Enable LLM Continual Learning

arXiv:2610.11373v1 Announce Type: new Abstract: Continual learning remains challenging for large language models, which must enable models to acquire new skills and knowledge without degrading existing capabilities. Existing approaches typically address this challenge by carefully designing how model parameters are updated. In contrast, prompt optimization avoids costly parameter updates while achieving competitive or even superior performance to reinforcement learning methods such as GRPO on individual knowledge-intensive and reasoning tasks. This raises a natural question: \textit{Can prompt optimization, as an efficient adaptation approach, be directly applied to continual learning?} Our analysis shows that, under sequential task adaptation, it suffers from catastrophic forgetting, while optimized prompts accumulate rules that overfit to local task distributions. To address these limitations, we propose \emph{Evolving Functional REpertoires} (EFRE), which replaces a single prompt with a repertoire of functions that evolves as new tasks arrive: compatible updates refine existing functions, while conflicting updates trigger the emergence of new ones. On a three-task continual-learning stream, EFRE achieves a final average performance 7.50 percentage points higher than GRPO. Moreover, after adaptation to the Bio task, its performance on FinQA decreases by only 1.56 percentage points, compared with 25.10 percentage points for the base prompt optimization method. We further instantiate EFRE in a minimal agent system and observe consistent improvements across different backbone models. Overall, these results demonstrate EFRE's strong performance in continual learning for large language models and highlight its substantial potential for continual learning in advanced agent systems.

arXiv cs.LG69

SpatialOPSD: Self-Distilling Spatial Intelligence from Verified Coding Agent Traces

arXiv:2610.11366v1 Announce Type: new Abstract: Spatial coding agents significantly improve spatial reasoning in Multimodal Large Language Models (MLLMs) by using external tools to generate verified execution traces. However, this paradigm inherently suffers from prohibitive inference-time overhead and external dependencies. In this paper, we explore whether an MLLM can internalize this agentic capability to operate entirely tool-free. We begin with a simple observation: prompting an MLLM with summarized execution traces of a spatial coding agent naturally unlocks the model's internal spatial Chain-of-Thought (CoT). Motivated by this, we introduce SpatialOPSD, an on-policy self-distillation framework that internalizes spatial reasoning into a standalone MLLM by formulating verified agent traces as privileged information. To mitigate privileged-information leakage during distillation, we introduce Repetition-Aware Distillation, which combines repetition masking with unlikelihood regularization. Experiments across multiple benchmarks demonstrate that self-distilling SpatialOPSD achieves higher average accuracy than SFT and GRPO on both spatial and OOD datasets, exhibiting superior performance and generalization.

arXiv cs.LG72

Bernoulli Flow Models: Self-Consistent Generative Modeling for Binary Data

arXiv:2610.11362v1 Announce Type: new Abstract: Binary diffusion models typically require a large number of function evaluations (NFEs) to generate high-quality samples, making practical inference computationally expensive. Reducing NFEs while preserving sample quality without distillation or additional training remains a significant challenge. Existing binary diffusion models define a discrete one-step forward path and then derive the reverse posterior. In low-NFE settings requiring cross-step sampling, they approximate the true multi-step likelihood with a single-step likelihood transition, which severely degrades sample quality. To address this fundamental limitation and decouple the generative dynamics from fixed discrete time steps, we propose Bernoulli Flow Models (BFM). Rather than relying on sequential one-step Markov diffusion chains, BFM defines a unified continuous global Bernoulli probability flow path between data distributions and pure noise, from which we derive analytical closed-form posterior transitions over arbitrary time intervals. Consequently, reducing the inference NFE is no longer an approximation based on skipping discrete steps; it only requires re-evaluating the analytical posterior over a new time grid. This eliminates the structural training-inference mismatch inherent to discrete chains and yields self-consistent low-NFE sampling. Experiments show that BFM is highly robust to aggressive NFE reduction. On LSUN Churches 256x256, a BFM trained with 256 steps achieves an FID of 9.22 using only 16 sampling steps, whereas the state-of-the-art discrete baseline degrades to 204.10. BFM also remains competitive with continuous and discrete generative baselines under standard full-step inference. These results establish BFM as a theoretically rigorous, self-consistent, and practically effective framework for fast binary data generation.

arXiv cs.LG73

样本高效的生成式保形预测

arXiv:2610.11349v1 公告类型:新增 摘要:生成式保形预测从条件生成器的样本中构建不确定性集合,但只有当这些样本能够良好地表示响应分布时,这种方法才是高效的。这可能需要大量样本,而每个样本的生成成本都可能很高,例如在大型扩散模型和科学模拟器中,因此必须高效利用采样预算。现有方法在每个输入处抽取相同数量的样本,导致在响应分布简单的地方浪费样本,而在分布复杂的地方采样不足,从而使集合膨胀,并导致这些输入的覆盖率不足。我们提出 CASA(保形自适应样本分配),通过刻画额外样本的边际价值,在满足边际覆盖率和平均采样预算约束的条件下,在各个输入之间分配样本,以最小化期望集合大小。理论分析表明,在相同预算下,自适应分配得到的集合小于固定数量分配得到的集合:遗漏一个模态会迫使半径跨越模态之间的间隔,即使是全知半径也无法弥补这一点。在合成任务和真实任务中,CASA 在相同预算下生成的集合显著更小,通常还能改善条件覆盖率,并且可以与现有的半径自适应方法互补。

arXiv cs.LG75

Deflating the Hessian: Rank-4 W4A4 Quantization for Multimodal Diffusion Transformers

arXiv:2610.11315v1 Announce Type: new Abstract: In diffusion transformers, low-rank branches can mitigate 4-bit weight--activation (W4A4) post-training quantization (PTQ) loss by decomposing each weight into a low-bit residual and a high-precision low-rank component. Existing low-rank PTQ approaches, however, either optimize low-rank compensation and residual quantization separately, often requiring higher ranks, or rely on second-order weight updates without explicitly modeling activation quantization error, which becomes particularly pronounced under 4-bit quantization. To address these limitations, we present \method{}, a unified framework modeling low-rank-assisted W4A4 PTQ as a coupled calibration problem and deriving optimization-based solvers from the joint objective. Eliminating the output-side low-rank factor yields a \emph{deflated Hessian} that discounts residual errors already captured by the low-rank component, while an activation-noise surrogate is incorporated to suppress activation quantization error. Across five diffusion backbones, rank-4 \method{} consistently outperforms rank-4 SVDQuant in PSNR and LPIPS. It further surpasses rank-32 SVDQuant on SANA-1.6B, FLUX.1-schnell, and FLUX.1-dev with an $8\times$ smaller rank and up to $6.25\times$ faster quantization. Furthermore, on the Qwen3-8B LLM, rank-4 \method{} improves MMLU accuracy from 61.50\% to 68.17\% over rank-32 SVDQuant. Overall, \method{} achieves better W4A4 performance with substantially lower rank and quantization cost.

arXiv cs.LG64

NP-Hardness of Minimizing Neurons in Two-Hidden-Layer ReLU Neural Networks

arXiv:2610.11313v1 Announce Type: new Abstract: A fundamental question in neural network architecture optimization is whether the minimum hidden-neuron count required to approximate a target function within a prescribed tolerance can be computed efficiently. This paper resolves this question for two-hidden-layer ReLU networks under an $L^p(\mathbb{R}^d,\mathbb{R}^m)$ approximation constraint. For every fixed $d \ge 1$, $m \ge 1$, and $1 \le p < \infty$, we prove that computing the optimum exactly is NP-hard. The result holds even when the target is represented by a rational ReLU network whose realization is nonzero, componentwise nonnegative, compactly supported, globally Lipschitz, and continuous piecewise affine. The polynomial-time reduction from 3-SAT produces an architecture gap in which unsatisfiable formulas yield an optimum of zero, whereas satisfiable formulas yield an optimum of at least $d+2$. The proof constructs compactly supported polyhedral frustum functions realized by two-hidden-layer ReLU networks and establishes the $L^p$-density of finite linear combinations of box-frustum functions. The results offer theoretical justification for employing heuristic approximation methods in the design of ReLU neural networks, illustrating that attaining a minimal configuration within polynomial time is computationally unachievable.

arXiv cs.LG74

From Geometry to Generalization: Why Row Normalization Can Beat Adam and Muon

arXiv:2610.11309v1 Announce Type: new Abstract: Different optimizers can fit the same training data while selecting classifiers with substantially different geometries, but whether this difference provably affects population performance remains unclear. We show that row-wise normalization can achieve strictly higher population accuracy than full-batch Adam, a proxy for random-reshuffling Adam, and exact-SVD Muon in high-dimensional multiclass classification. Under an isotropic Gaussian-cloud data model, this advantage arises because row normalization's class-wise Euclidean geometry asymptotically preserves the population decision-boundary directions, whereas Adam's coordinate-wise geometry and Muon's spectral geometry introduce nonvanishing distortions. Beyond isotropy, the advantage persists for full-batch training on class means with independently oriented class-mean and test-noise covariances. It holds for power-law spectra with class-mean exponent below one, even under heavily anisotropic test noise. When both covariances are diagonal and sufficiently close, the advantage over Adam can reverse, while applying the same random rotation to both restores it by changing only their alignment with Adam's coordinate axes. Synthetic and last-layer language-model experiments support the predicted advantage.

arXiv cs.LG71

Memorization and Malign Generalization in Conditional Diffusion Models with Random Features

arXiv:2610.11288v1 Announce Type: new Abstract: Conditional diffusion models generate diverse, novel, and high-quality samples under prescribed conditions. However, theoretical understanding of their memorization and generalization remains limited, while recent works have characterized these behaviors primarily in unconditional settings. In this work, we analyze a random-feature conditional score model in the high-dimensional proportional limit, deriving asymptotic expressions for training and test losses. By decomposing the test loss, we show that in the overparameterized regime, increasing model width improves prediction of the condition-dependent mean while reducing within-condition prediction variance, a phenomenon we term "malign generalization." Furthermore, analyzing the training loss reveals that more informative conditions lead to memorization of training samples at smaller widths. These theoretical findings are supported by experiments with U-Net architectures on realistic data.

arXiv cs.LG77

How to post-train on a surrogate: Envelope sampling mitigates reward hacking

arXiv:2610.11281v1 Announce Type: new Abstract: Large language models (LLMs) are commonly post-trained against LLM judges and other cheap surrogates because the true reward, such as human preference, is too expensive to query at scale. This practice often leads to reward hacking, where reinforcement learning against a miscalibrated surrogate leads to undesirable side effects. In this work, we study a setting in which a small number $n$ of model outputs are annotated with ground-truth labels (e.g., from expert review) and used to recalibrate the LLM judge before optimizing against it. Prior approaches to judge recalibration are costly or heuristic, and it is known that on-policy sampling fails when the surrogate is miscalibrated on a rare set of outputs. In this work, we propose envelope sampling, a theoretically-grounded method for judge recalibration that seeks to minimize an upper bound on the regret of the post-trained model under the assumption that the human reward and re-calibrated reward lie in an $L^2$ ball around the judge. We give practical algorithms to sample from the envelope by rejection or by fine-tuning against a modified reward, and experiments on clinical note generation and on a controlled sycophancy task show that recalibrating on envelope samples mitigates reward hacking where recalibrating on base-model samples does not.

arXiv cs.LG70

Residual spectral instabilities in representation learning

arXiv:2610.11257v1 Announce Type: new Abstract: Learned representations can lose latent degrees of freedom successively, suggesting a cascade of transitions whose underlying stability principle remains unclear. Here we formulate dimension-wise posterior collapse in variational autoencoder (VAE) as a fluctuation theory around partially collapsed states. Interpreting the negative evidence lower bound as an effective free energy, its quadratic expansion defines a Gaussian theory whose Hessian acts as a mass matrix for latent fluctuations. We show that the collapsed directions form an invariant fluctuation sector and derive its exact mass spectrum in terms of a conditional residual operator. A local reactivation direction lowers the free energy when the decoder variance falls below the residual spectral upper edge, with equality marking marginality. The criterion recovers principal component thresholds in the linear Gaussian VAE limit. Viewed in reverse along continuously connected branches, the reactivation boundary provides a local criterion for successive collapse. Numerical continuation experiments show successive loss of latent dimensions near these spectral marginalities. These results support a spectral cascade interpretation governed by residual information left unexplained by the surviving representation.

arXiv cs.LG71

Neuro-Memory Fuzzy Inference System for Mimicking Human-like Car Following Behavior

arXiv:2610.11252v1 Announce Type: new Abstract: This study presents the Neuro-Memory Fuzzy Inference System (NeMeFIS), a hierarchical machine learning architecture that asymmetrically models acceleration and deceleration in car following behavior by integrating five human memory types procedural, working, episodic, semantic, and declarative. By linking external variables to memory functions via metaheuristics and validating them through factor and p-value analyses, NeMeFIS uncovers latent cognitive influences across Arterial, Collector, and Rural Highway corridors for different types of vehicles. Results from 54 different trained models emphasize cognitive thresholds shaped by driver perception limits and cognitive load. The trained NeMeFIS models outperform traditional statistical and conventional machine learning models in replicating realistic driving behavior, including comparisons with Linear Regression, ANFIS, and LSTM architectures. Fuzzy rule analysis reveals that declarative memory demands the highest rule, especially during deceleration, indicating complex braking decisions. Procedural memory drives acceleration, while semantic and declarative memory guide deceleration. Risk perception also emerges as a key factor, particularly on urban roads. Validated on both heterogeneous and homogeneous datasets, NeMeFIS offers a robust framework for modeling driver cognition. The findings support psychotherapeutic applications and the development of adaptive, human-like decision systems in Connected and Autonomous Vehicles (CAVs) to enhance traffic safety.

arXiv cs.LG79

Why On-Policy Distillation Sometimes Fails: Vanishing Learning Signals

arXiv:2610.11247v1 Announce Type: new Abstract: On-policy distillation (OPD) enables effective capability transfer between language models, yet the mechanisms underlying its failures are not fully understood. Across code generation and mathematical reasoning, OPD with larger-scale teachers exhibits early loss plateaus, with an average final loss reduction of 25.1% after 200 updates, compared with 96.2% for self-RL teachers, obtained by further reinforcement learning (RL) training of the initial student. To understand this difference, we analyze OPD as an idealized continuous-time dynamical system in the small-learning-rate limit. Our training-log diagnostics associate these plateaus with an early decline in a gradient-based learning-signal proxy while substantial loss remains; these measurements do not establish why the underlying gradient weakens. We further prove a local recovery guarantee for teachers sufficiently close to the initial student in a shared parameterization under regularity conditions, offering a conditional explanation for the success of self-RL teachers in our experiments. Across runs with and without loss plateaus, we observe small relative parameter changes (0.025-0.098%) and high similarity between the student's representations before and after OPD (linear CKA $>0.98$ across layers). These observations suggest that limited representation adaptation may contribute to learning-signal collapse, a hypothesis that remains to be tested. Code is available at https://github.com/leizhao7/opd-learning-signals.

arXiv cs.LG80

Read What Matters: Query-Adaptive Quantization for KV Caches

arXiv:2610.11245v1 Announce Type: new Abstract: KV-cache entries are stored before their future queries are known, but each decoding query needs precision in different places. We study this mismatch using separate budgets for retained bits and bits fetched per query. ReadKV stores each key and value in a progressive code whose prefixes support different reconstruction precisions. For each query, it allocates key-channel prefixes using the query, computes attention from the reconstructed keys, and then allocates value-token prefixes using that attention. Stored entries remain unchanged. Each stage optimizes a calibrated distortion objective under a fixed budget; we prove exact allocation under diminishing refinement gains and relate these objectives to attention-output error. We also exhibit a finite-dimensional attention family where query-dependent access strictly outperforms every query-independent reader at the same read budget, even with unrestricted competing encoders and decoders. Across six base models, reading four bits on average from an eight-bit cache increases C4 perplexity by at most 0.66%, using about one quarter of the logical reads and half the retained capacity of a 16-bit cache. It is consistently more accurate than storing and fully reading four bits at the same payload-read budget. Retaining more bits than each query fetches is aimed at long-context decoding, where the cache bytes moved per step, rather than the weights, dominate cost. Long-context question answering and retrieval on two instruction-tuned models provide additional quality evidence. On the tested 8K-token, batch-one, single-layer workload on an NVIDIA A10G, a restricted eight-bit ReadKV reader with a two-bit mean payload-read budget has 39% lower latency than the tested TurboQuant codec.

arXiv cs.LG78

Low-Cost Sensor Calibration for Indoor Air Quality Monitoring: A Dataset, Evaluation Scenarios, and a Lightweight Model

arXiv:2610.11236v1 Announce Type: new Abstract: Low-cost sensors enable scalable indoor air quality monitoring but require calibration because of nonlinear distortions, noise, and temporal drift. The conventional strict pairwise calibration setting requires a co-located reference sensor at each deployment location and does not account for spatial and temporal heterogeneity. To address these limitations, we introduce a six-month dataset comprising multivariate indoor air-quality measurements from low-cost and reference sensors with contextual metadata collected at five locations. Using this dataset, we define four evaluation scenarios. The reference-efficient and location-transfer scenarios evaluate spatial generalization, whereas the long-term drift and event-conditioned scenarios assess robustness to gradual and abrupt distribution shifts. Based on these scenarios, we derive design requirements and propose a lightweight temporal model that combines input-window compression with residual temporal and feature fusion. Experiments show strong calibration performance across all four scenarios with low edge-inference cost.

arXiv cs.LG74

SteerCast:用于仅解码器时间序列预测的基于检索的潜在空间引导

arXiv:2610.11229v1 公告类型:new 摘要:时间序列预测旨在根据历史观测值和辅助特征预测未来值。我们提出了 SteerCast,这是一种基于检索的潜在空间引导方法,可在推理时改进仅解码器预测器,而无需更新其参数。SteerCast 通过存储每个历史窗口的表示以及在预测器潜在空间中计算得到的引导向量,从训练集构建数据库。该引导向量定义为:由真实后续序列诱导的表示与由模型自身预测诱导的表示之差。在测试时,SteerCast 为查询历史检索最近邻样本,聚合其引导向量,并在自回归生成的每一步将所得信号注入预测器的隐藏状态,从而引导预测结果趋向于与相似训练案例一致的轨迹。在涵盖多种多变量基准数据集和多个预测跨度的实验中,SteerCast 始终比微调后的骨干模型和基于检索的基线方法取得更高的预测精度,同时无需在原始微调之外进行额外训练,并且仅使用训练集作为检索语料库。

arXiv cs.LG70

Multimodal Graph Retrieval-Augmented Sequential Recommendation via Collaborative Filtering Paths

arXiv:2610.11228v1 Announce Type: new Abstract: Multimodal Large Language Models (MLLMs) have demonstrated strong potential for sequential recommendation through their ability to reason over complex multimodal data. However, existing approaches either rely solely on the target user's own interaction history, neglecting collaborative signals from neighboring users, or incur substantial computational overhead through repeated MLLM inference over long interaction histories. To address these challenges, we propose MGRASRec, a multimodal graph retrieval-augmented framework for sequential recommendation. MGRASRec injects collaborative filtering signals conditioned on the candidate item directly into the MLLM prompt by retrieving structured paths from a user-item interaction graph, extended via multimodal similarity to increase coverage beyond exact co-interaction overlap. This retrieval also surfaces the history items most relevant to the candidate at no additional cost, removing the need for recurrent summarization and keeping inference to a single forward pass per candidate. All components are unified into an augmented prompt for parameter-efficient fine-tuning of an MLLM. Extensive evaluations across three publicly available datasets validate the effectiveness of MGRASRec, achieving the best performance on all metrics with particularly strong gains in ranking quality.

arXiv cs.LG81

The Lattice of Transition Laws

arXiv:2610.11216v1 Announce Type: new Abstract: Diffusion and autoregression (AR) have long been seen as different categories of generative models, with diffusion specialising in continuous fields and AR specialising in discrete tokens. Recent work seeks to combine the advantages of the two models, and each hybrid fixes its decoding schedule by design. In this paper, we ask whether the performance of decoding schedules of one model can be predicted before decoding at a fixed number of steps. We describe diffusion, AR, and models in between as paths on one corruption lattice, and define the cost of a schedule as the dependence its parallel steps discard. The cost shows that the fewest steps of a zero-cost schedule are set by the geometry of the data, in the same way for tokens and for continuous fields. In particular, for data that are Markov on a graph and dependent along its paths, the fewest steps equal the graph's treedepth, which is logarithmic in the length of a sequence and linear in the side length of a grid. With fewer steps than the treedepth, every schedule pays a positive cost, whose ranking we predict before decoding with a kernel of pairwise dependence estimated from pretrained weights. Across text generation, image generation, and video generation, we verify most of the predictions about the rankings of different schedules under different metrics and benchmarks. This work therefore provides a design principle for decoding for future AR models, diffusion models, and anything in between. Our code is available at https://github.com/TSUITUENYUE/The-Lattice-of-Transition-Laws.

arXiv cs.LG82

架起 KV-Cache 量化与线性注意力之间的桥梁:从理论到预训练权重迁移

arXiv:2610.11214v1 公告类型:新 摘要:KV-cache 量化和线性注意力是应对 Transformer 存储与计算成本的两种代表性方法。KV-cache 量化将单个 KV 条目压缩为离散编码,但保留所有条目;而线性注意力则以递归方式聚合多个历史 KV 贡献,将其存入固定大小的连续状态中,但可能引入干扰。这一对比引出了一个问题:能否在单一机制中桥接逐 KV 压缩与多 KV 聚合,从而实现高效注意力?我们发现,RAM-Net 通过在离散地址空间上的软分配实现了这一桥梁。这些分配决定了与每个地址关联的连续槽状态的递归更新。在一种受限的 RAM-Net 构造下,我们证明,软地址分配能够将硬量化匹配扩展为可分离的读写重叠,在局部近似全注意力相似度的同时支持递归聚合。这些联系进一步支持通过一种基于软量化中间构造的新路径,实现从 Transformer 到 RAM-Net 的权重迁移。在 9 个参数量介于 0.3B 和 7B 之间的预训练 Transformer 模型上,仅使用每个模型 500M 个 token 的预算,RAM-Net 在 6 项常识与知识任务中,平均恢复了教师模型相对于随机猜测所获得准确率提升的 87.1%。

arXiv cs.LG76

Do Flatter Minima Drive Better Generalization? An Algorithmic Separation in Grokking

arXiv:2610.11206v1 Announce Type: new Abstract: Flat loss landscapes have long been linked to better generalization in neural networks. However, its role as a causal mechanism for generalization is less established. Grokking provides an unique testbed to understand this distinction: models are prone to fit observed data using non-generalizing structure and remain in that regime for prolonged periods, transitioning to generalization only under particular training conditions. In this work, we study whether flat loss landscapes can act as a driving mechanism in this transition. While recent work has argued for flatness as a necessary geometric condition for this transition, we find that biasing training toward flatter solutions using sharpness-aware minimization (SAM) is insufficient to reliably induce this transition, despite producing flatter solutions. However, when SAM is paired with mechanisms that drive generalization such as weight decay, an interesting property emerges: SAM can accelerate the transition to generalizing solutions by up to 4x at the epoch-level. We theoretically untangle this relationship between SAM and weight decay using a minimal interpolating two-layer ReLU model with both memorizing and generalizing solutions. We show that even in this simple setup, flatness alone cannot distinguish a memorizing solution from a generalizing one, while weight decay favors generalizing solutions. However, under a local stability analysis, there exists a window where a memorizing interpolant is locally stable under gradient descent but unstable under SAM in the low-norm regime, which can explain SAM's ability to accelerate this transition. Overall, our results provide a more interpretable account of the role of flatness in driving generalization, especially in settings where models are vulnerable to minimizing loss through learning non-generalizing structure.

arXiv cs.LG76

细胞命运指派中的预测多重性:无标签 Rashomon 集与逐细胞认证的局限

arXiv:2610.11185v1 公告类型:新论文 摘要:单细胞轨迹推断将转录组测量结果映射到发育连续谱上,但对数据拟合程度同样好的配置可能会指派出相互冲突的细胞命运。FateMultiplicity 是一个无标签框架,无需谱系标签即可构建统计上可接受的模型集合,即 Rashomon 集;其方法是在以随机种子变异校准的非劣效性检验下,利用交叉拟合的留出基因评估模型偏差。预测多重性很大,且更多地取决于模型空间的多样性,而非其规模:第二种算法的十二种配置揭示了 20.0% 的细胞存在多重性,而第一种算法的二十四种配置仅揭示了 3.8%。随后,我们检验逐细胞认证的命运间隔 FM 是否能比拟合模型本身提供更可靠的指派,结果表明不能。在具有真实值的模拟数据上,针对同一批细胞,FM 判别错误指派的 AUC 为 0.682,而基线配置自身决策间隔的 AUC 为 0.965(p = 0.003),基于随机种子离散程度的基线方法则为 0.854。信息量取决于可接受集合的广度,而非其基数:当基数为四时,更换随机种子重新拟合得到的集合对应 AUC 为 0.933,扰动超参数得到的集合则为 0.701。将下确界放宽为 q 分位数可恢复判别能力,但会趋近于单个模型自身的置信度;上确界达到 0.973,是因为 theta* 属于集合这一事实为其提供了下界,而下确界则缺乏锚定。轨迹推断中的多重性值得测量和报告,但在无标签 Rashomon 集上进行逐细胞认证,并不能带来更可靠的命运判定。两种构造仍然有效:间隔侵蚀比可在模拟中区分真实与虚假的分支点(AUC 为 0.890,尚未在真实数据上检验);以克隆观测到的命运为参照,未通过认证的细胞与其所属克隆结局不一致的比例,比通过认证的细胞高出 16.4 个百分点(p < 0.001)。

arXiv cs.LG70

SACQ: Structured Decoding with Memory-Conditioned Refinement for Long-Horizon Forecasting

arXiv:2610.11170v1 Announce Type: new Abstract: Long-term time series forecasting (LTSF) models predominantly employ patch-based encoders terminated by a flatten readout head that maps the entire encoded historical memory to all future steps through a single shared projection. This implicit coupling of future positions obscures position-specific historical-to-future alignment and amplifies sensitivity to corrupted inputs and extreme supervision noise. We present SACQ, a plug-in structured prediction head that replaces flatten readout while keeping the encoder unchanged. SACQ adopts a two-stage decoding pipeline: it first establishes a coarse patch-grid forecast scaffold, then refines each future position through cross-attention over historical memory and merges the attention-derived correction with the coarse scaffold via a learned per-patch gate. To stabilize optimization under long horizons and noisy labels, we further propose a batch-adaptive scaled log-cosh loss that automatically calibrates robustness to the current residual scale, suppressing outlier gradients while preserving MSE-like sensitivity for typical errors. SACQ attains top-tier test MSE/MAE across PatchTST, DLinear, and patch-Mamba backbones with only modest incremental overhead in parameters and latency. Under inference-time input corruption and training-set label-noise stress tests, SACQ substantially outperforms flatten readouts, with ablation studies validating each architectural component.

arXiv cs.LG63

PIVOT: Perplexity-Informed KD-to-RL Transition Scheduling for Vertical-Domain Few-Shot Distillation

arXiv:2610.11167v1 Announce Type: new Abstract: Vertical-domain few-shot classification remains challenging for small language models, as limited supervision makes it difficult to acquire domain-specific decision knowledge. On-Policy Distillation (OPD) can improve teacher-guided adaptation by supervising student-generated rollouts, while GRPO-based reinforcement learning can further refine downstream predictions. However, existing KD-to-RL pipelines typically rely on globally fixed transition schedules, ignoring that different samples may require different amounts of teacher-guided acquisition before reward-driven refinement. We propose PIVOT (Perplexity-Informed Transition Optimization), a dynamic transition framework that routes samples between OPD and GRPO according to teacher-evaluated sequence perplexity. PIVOT moves low-perplexity samples to GRPO for reward-driven refinement while keeping high-perplexity samples under OPD for continued domain knowledge acquisition. Experiments on Banking77 and HWU64 show that PIVOT consistently outperforms continued OPD and globally synchronized OPD$\rightarrow$GRPO baselines under the same number of post-warm-up student optimization steps, achieving stronger downstream performance and more stable training dynamics.

arXiv cs.LG75

CARE: A Lightweight Plug-in Gated Correction and Uncertainty-aware Module for Long-term Time Series Forecasting

arXiv:2610.11165v1 Announce Type: new Abstract: Multivariate long-horizon forecasting is critical to electricity load scheduling and traffic flow management, and to financial risk control. Existing deterministic backbones output a single trajectory, masking heterogeneous prediction difficulty across horizons and channels and providing no localized reliability signal. We present CARE (Corrective branch with Aligned context and Relative-error Estimation), a lightweight plug-in that enhances any deterministic forecaster without architectural redesign. Operating in parallel with the base model, CARE resamples historical context to match the forecast horizon, learns residual correction patterns from this aligned history, and applies scale-aware bounded updates modulated by per-coordinate sigmoid risk gates. A multi-objective loss jointly optimizes forecast accuracy, residual tracking, risk alignment, and base-model anchoring. Across eight benchmarks with three representative backbones, CARE improves accuracy with marginal parameter and latency overhead. Its risk gates reliably identify high-error regions: on Weather, the highest-gate tertile exhibits nearly four times the error of the lowest-gate tertile, offering planners an interpretable per-step trust signal. Code is available at https://github.com/CG-BNYC/CARE.

arXiv cs.LG81

RideBench:面向网约车时间序列预测的大规模外生信息感知基准

arXiv:2610.11164v1 公告类型:新发布 摘要:我们发布了 Ride-Hailing,这是一个基于 DiDi 平台覆盖 200 个空间区域的市场数据合成的大规模网约车时间序列数据集。Ride-Hailing 以半小时为时间粒度,涵盖连续四年的数据,并覆盖三种具有代表性的外生场景:天气扰动、节假日效应和大型活动影响。基于 Ride-Hailing,我们推出了 RideBench,这是一个面向外生信息感知网约车预测的综合基准,涵盖常规的未来一周预测,以及预测步数最多达 2,688 步的未来八周长跨度预测。RideBench 评估了 30 余种具有代表性的预测方法,包括仅使用内生信息的模型、外生信息感知模型和时间序列基础模型。结果表明,未来已知的外生变量能为常规的未来一周预测带来显著收益,尤其是在天气、节假日和大型活动(如重大体育赛事和演唱会)场景下。然而,在复杂外部环境中,当前的外生信息感知模型仍难以充分捕捉扰动引起的模式变化。对于长跨度预测,现有模型无法同时实现较低的逐点误差、准确的整体趋势预测和可靠的近期预测。这些发现揭示了现有预测模型与现实网约车需求之间的明显差距,凸显了开发以下模型的必要性:更好地利用未来已知的外生信息,能够扩展应用于异质区域,并支持长跨度规划。通过推出 Ride-Hailing 和 RideBench,我们希望鼓励研究社区探究现实网约车预测中的这些实际挑战。

arXiv cs.LG78

Do LLMs Learn from Rewards in Context? : Rethinking the role of reward in In-Context Reinforcement Learning

arXiv:2610.11152v1 Announce Type: new Abstract: LLM agents increasingly improve at inference time by accumulating experience in context rather than by updating parameters. This process is often described as in-context reinforcement learning (ICRL). Whether in-context learning (ICL) can actually play the role of RL, however, has not been tested. We study this question in its simplest form, direct ICRL, where the model conditions directly on raw trajectory-reward pairs, and ask whether the reward acts as a learning signal. Through controlled experiments on four benchmarks across six models, we find that the reward is read, but its effect is small: flipping, randomizing, or removing the reward leaves the improvement curve almost unchanged, and this holds even under meta-prompts that explicitly instruct the model to explore, exploit, or reason over rewards. Trajectories drive improvement, but not through their semantic content: shuffled or corrupted trajectories work as well as real ones. These patterns closely mirror those known in ICL, suggesting that direct ICRL is better understood as a special case of ICL than as inference-time RL. This reframing has implications for agent memory design: ICL factors such as input distribution and demonstrations may matter more than RL elements such as reward shaping and exploration.

arXiv cs.LG80

用于信用风险建模的 Ranking Prior Alignment:外部先验何时发挥作用?

arXiv:2610.11146v1 公告类型:新论文 摘要:冷启动信用评分——在标注数据稀缺、特征较弱或模型容量极小的条件下部署模型——是金融机器学习中反复出现的问题。当新的信贷产品上线时,带标注的违约数据稀缺,特征流水线尚不成熟,而模型必须以极小的容量部署,以避免过拟合。标准应对措施依赖的仍是同一批有限数据;真正需要的是一种以领域知识为基础的外部正则化来源。我们提出 Ranking Prior Alignment,这是一个模型无关框架,通过温度缩放的 KL 散度损失,将外部排序先验(来自领域专家、教师模型或 LLM)蒸馏到任意评分模型中。该框架通过统一公式 L = L_task + gamma(t) * KL(P_agent || P_model),将神经网络架构(MIL 注意力机制)与基于树的架构(XGBoost 自定义目标函数)统一起来,其中 gamma(t) 遵循指数衰减调度。该方法在推理时无需外部模型,其基于树的实现可容忍高达 eta = 0.5 的标注噪声。在一个包含超过 150 万商户的工业数据集上,MIL 对齐在使用 3,000 个包时,7/7 个评估项均取得正向提升(1 项 ID 指标 + 3 项 OOT 指标 + 3 项退化指标;在 OOT-1 上,Delta AUC 峰值为 +0.020),而 XGBoost 消融实验在使用 300 个包时,9/9 项指标均取得正向提升。在公开 Amex 数据集上进行的跨数据集验证显示,5/5 个交叉验证折均取得正向提升(平均 Delta AUC = +0.041)。四类模型(MIL、XGBoost、LightGBM、Logistic Regression)和四种教师架构的实验表明,该框架既不依赖特定模型,也不依赖特定先验来源。我们进一步观察到,对齐收益呈现逆向缩放规律:随着数据丰富度 N、模型容量 C 和特征质量 Q 的下降,收益反而增加,这有助于从业者判断何时值得投入先验标注。

arXiv cs.LG75

ActiveMedAgent:面向多模态医学诊断的成本感知轨迹学习

arXiv:2610.11140v1 公告类型:新投稿 摘要:临床诊断本质上是一个序贯过程:只有在预期新增证据能够消除诊断不确定性时,临床医生才会从低成本检查逐步转向高成本检查。我们提出 ActiveMedAgent,这是一个将这种成本感知的序贯逻辑引入多模态医学人工智能的框架。在使用参数冻结、通过 API 访问的视觉语言模型的情况下,ActiveMedAgent 跟踪候选诊断的概率分布,并以每一步的诊断效用减去成本,对每次信息获取进行评分。随后,基于这些已评分的轨迹离线训练一个轻量级 MLP 控制器,使其学习何时请求更多证据,以及何时作出最终诊断。在三个常用基准上,基于轨迹的策略学习始终优于无引导的信息获取方法和全模态基线。值得注意的是,我们发现了一种信息过载效应。在 175 个病例中,该智能体利用更少的信息通道得出了正确诊断,而全模态基线却未能正确诊断,这表明,学习省略哪些信息可能与学习获取哪些信息同样重要。

arXiv cs.LG81

QUILT:通过共享查询执行重新思考稀疏注意力预填充

arXiv:2610.11134v1 公告类型:新论文 摘要:稀疏注意力降低了长上下文注意力的开销,但现有内核通常独立处理各个查询,反复加载并反量化多个查询共享的 KV 条目。我们观察到,相邻查询所选的 KV 条目存在大量重叠,为跨查询复用创造了机会。我们提出 QUILT,一种工作负载感知的稀疏注意力执行机制,通过联合处理相邻查询并复用共享 KV 条目,减少冗余的内存流量和计算。QUILT 引入 Shift-and-Compare Set Decomposition(SCSD),将不规则的集合操作转化为适用于现代加速器的规则数据并行原语,并将 SCSD 与注意力计算以流水线方式执行,以隐藏其开销。级联共享在多个粒度上分层实现复用。一种分块感知的执行策略在共享粒度与硬件分块利用率之间取得平衡,并选择性地移除重要性较低的查询专属尾部,以消除利用不足的分块。我们使用 GLM-5.3 和 DeepSeek-3.2,在张量并行和序列并行两种设置下,基于 LongBench 评估 QUILT。与最先进的稀疏注意力内核相比,QUILT 将平均内核延迟最多降低 55.1%,将处理的 KV 数据量最多减少 55.9%,同时将首个词元生成时间(TTFT)延迟最多降低 36.8%,且准确率下降可忽略不计。

arXiv cs.LG60

Machine Learning Optimization for Enhanced OS Fingerprinting

arXiv:2610.11133v1 Announce Type: new Abstract: Operating System (OS) Fingerprinting is a technique that can be used to identify a network's operating systems by evaluating network traffic in the form of TCP/IP packets. This research will explore the effectiveness of passively identifying operating systems on the CIC-IDS2017 dataset, a collection of over 47 gigabytes of pcap files with their corresponding operating systems. This research also proposes a new command line interface, OsirisML, which uses nPrint to preprocess the data into tabular data and XGBoost to apply ML to the data to generate, retrain, and test ML models. When packets are split randomly between training and testing, OsirisML models reach an accuracy of 97.66% on a down-sampled subset of the Friday capture and 84.69% on the entire capture. On the entire Monday capture, which contains no attacks, OsirisML reaches an accuracy of 73.83% and an F-1 score of 79.38%.

arXiv cs.LG78

Dynamics as Code: On Model Compression via Dynamic System

arXiv:2610.11115v1 Announce Type: new Abstract: The escalating size of pretrained neural networks has rendered model compression a prerequisite for deployment under stringent memory and compute constraints. With the irrational winding as an example, earlier work introduced a dynamic system (DS) paradigm that reconceptualizes compression as compact weight representation: high-dimensional parameters are encoded by the index of a trajectory produced by a dynamic system, from which the vector is recovered during decompression. This mechanism is fundamentally distinct from pruning, quantization, knowledge distillation, and low-rank decomposition. Along this direction, we prove that under a Diophantine condition, a finite trajectory of \(M = O(\epsilon^{-(d+\nu)})\) states in the irrational winding constitutes an \(\epsilon\)-net over the \(d\)-dimensional weight space, thereby linking state resolution, decompression error, and compression ratio in a predictable manner. Furthermore, we propose a generalized DS-based model compression framework by unifying four DS families---space-filling curves (Hilbert, Peano, Morton/Z-order, Snake), chaotic systems (Lorenz), congruential and pseudo-random generators (LCG, PCG), and low-discrepancy sequences (Halton). Also, we introduce the KD-tree and coordinate-template acceleration to scale to large models as well as outlier identification to control the error. Experiments on ResNet-18 and Qwen2.5-1.5B/Qwen1.5-7B validate that DS-based compression achieves competitive compression ratios without post-hoc retraining, with controllable decompression error and flexible state-space design, establishing it as a principled and practical compression approach.

arXiv cs.LG77

Cova-PINN:用于复杂几何结构中流固共轭传热的跨域守恒物理信息神经网络

arXiv:2610.11108v1 公告类型:新投稿 摘要:多域物理信息神经网络(PINNs)能够灵活地构建针对不同介质的表征,以求解流固共轭传热(CHT)问题。然而,标准多域 PINNs 在各域分别采样的支撑点集上施加控制方程和界面条件约束,这可能产生看似合理的温度场,却导致端到端能量传递和出口温度不准确。我们提出 Cova-PINN,这是一种多域 PINN 框架,可使守恒约束的支撑与复杂几何结构中的热相互作用路径相匹配。Cova-PINN 联合优化局部尺度上的跨域复合控制体平衡与换热器全局尺度上的配对壁面闭合。我们采用统一方案,在四种三重周期极小曲面(TPMS)换热器和一种几何结构不同的 DualMS 设计上,将 Cova-PINN 与针对 CHT、面向优化以及适用于复杂几何结构的 PINN 基线方法进行比较评估。相较于最接近的基线 MUSA-PINN-CHT,Cova-PINN 在四种 TPMS 拓扑结构上的平均出口温度误差和设备级闭合误差分别降低了 $37.7\%$ 和 $60.2\%$,同时还提高了全场预测和换热量的准确性,并在 DualMS 上取得了一致的改进。

arXiv cs.LG68

DaCe-DT: Data-Centric Offline Multi-Task Reinforcement Learning via Adaptive Prompts and Trajectory Correction for Heterogeneous Tasks

arXiv:2610.11085v1 Announce Type: new Abstract: Offline multi-task reinforcement learning (Offline MTRL) heavily depends on the quality and distribution of pre-collected data. However, existing methods mainly focus on algorithmic optimization, with less emphasis on data-level improvements to enhance learning ability and generalization performance. This paper, from a data perspective, reveals three key bottlenecks that limit Offline MTRL performance:(i) ineffective utilization of prompts length under diverse task complexities, and (ii) semantic irrelevance of randomly sampled prompt segments, (iii) misleading supervision induced by fragmented and discontinuous trajectories. To address these challenges, we propose DaCe-DT, a robust offline MTRL framework designed to be insensitive to heterogeneous task complexities and data quality, featuring length-gated prompt masking (LGPM), retrieval-augmented prompt construction (RAPC), and value-adaptive return calibration (VARC). Together, these mechanisms enable DaCe-DT to deliver data-centric prompt adaptation and trajectory refinement, resulting in robust multi-task generalization and stable policy learning amid heterogeneous offline data and tasks. Experimental results on Meta-World show that DaCe-DT consistently outperforms state-of-the-art methods, achieving an average improvement of 11.73% on optimal datasets and an improvement of 13.34% on suboptimal datasets, demonstrating its effectiveness in learning stably from imperfect data and improving overall multi-task performance.

arXiv cs.LG75

Stability-Plasticity Balance via Singular-Vector Selection in LLM Continual Learning

arXiv:2610.11076v1 Announce Type: new Abstract: Domain-specific continual adaptation of LLMs risks catastrophic forgetting, creating a fundamental tension between acquiring new capabilities and preserving those learned during pretraining. PEFT mitigates this problem by restricting the number of trainable parameters, but existing methods lack a principled unit for deciding where plasticity should be allocated and stability should be preserved. We identify the singular-vector channel as a natural unit for managing this trade-off. Each channel represents an input-output transformation, which can be updated to acquire new knowledge or fixed to preserve pretrained capabilities. Based on this perspective, we introduce SVC, a parameter-efficient continual-learning method that selectively updates Singular-Vector Channels. Before fine-tuning, SVC uses domain-specific data to estimate each channel's adaptation benefit and a fixed public general-domain corpus only as a history activation proxy for estimating forgetting cost. It then adaptively selects trainable channels based on these scores via knee-based cost screening, Pareto-front filtering, and Otsu thresholding. Experimental results across four LLM families and eight downstream tasks show that SVC better preserves pretrained capabilities while achieving strong downstream performance relative to existing PEFT baselines. Further analysis of channel scoring and selection demonstrates that selective plasticity at the singular-vector-channel level enables effective continual LLM adaptation.

arXiv cs.LG73

Optimally Pacing Budget Spending and Learning

arXiv:2610.11074v1 Announce Type: new Abstract: We establish near-optimal regret bounds for budget-constrained online learning against arbitrary classes of budget-pacing experts in the adversarial setting. In particular, given any class of $F$ experts and a candidate budget pacing schedule, we provide a full-information algorithm which obtains regret $O(D \sqrt{\log F}+ \sqrt{T\log F})$ against all experts whose cumulative spending stays within distance $D$ of this schedule, matching lower bounds established by Braverman et al. (2025). We additionally show that our technique extends to various problems in online resource allocation, where the learner gets to see the rewards and costs of the current options available to them, and establish $O(D\sqrt{\log F})$ regret bounds when fractional allocation is allowed. This is the first algorithm we are aware of which can achieve $o(\sqrt{T})$ guarantees for such tasks.

arXiv cs.LG75

CityDeploy-Bench:面向多发射机网络部署的物理基础空间集合规划基准

arXiv:2610.11065v1 公告类型:new 摘要:在复杂的城市传播环境和全网干扰条件下,实现城市尺度的无线部署自动化仍然颇具挑战。我们提出 \textbf{CityDeploy-Bench},这是一个基准,将多发射机部署重新定义为统一射线追踪验证器下的\emph{物理基础空间集合规划}问题。该基准将效用表示与规划动态分离,从而能够在不同规划器之间,对直接标量奖励、关系模型和高阶交互结构进行受控比较。实验揭示了随着物理耦合增强,规划行为会发生明显转变。部署质量越来越取决于所学习的效用是否能够捕捉发射机之间的集体交互,而单纯增强搜索能力无法弥补关系结构的缺失。这表明,多发射机部署本质上是一个针对物理交互集合的协调问题,而不是一组相互独立的空间决策。我们发布了 CityDeploy-Data 和该基准框架,将其作为一个可复现的测试平台,用于开展决策学习与基于物理的无线网络设计相结合的研究。

arXiv cs.LG83

衡量并缓解 RLVR 中的解法模式坍缩

arXiv:2610.11064v1 公告类型:new 摘要:语言模型(LM)通常可以用不止一种方式回答同一个问题,但带可验证奖励的强化学习(RLVR)并不在意模型生成的是哪一种正确答案。无论一个解法是熟悉答案的第一千个副本,还是模型此前从未生成过的答案,它获得的奖励都相同。然而,在训练模型的过程中,让模型保留多个正确解法可能具有潜在价值。例如,多种模式可以为用户提供选择,并提供能够提升模型整体性能的问题求解策略。在本文中,我们介绍了 ModeBench,这是一个多解任务基准,其中验证器会同时返回答案是否正确以及所发现的模式。随后,我们使用 ModeBench 衡量 RLVR 后训练过程中解法多样性的变化。我们发现,即使准确率保持不变或有所提升,RLVR 后训练仍会将概率集中到更少的正确模式上;此外,前沿模型的概率分布本身也已经高度集中。接着,我们介绍了我们的方法 Re:Max:在重放缓冲区中为每个已发现的模式存储一个经过验证的示例,并对这些存储的模式进行均匀训练。因此,一个只被发现过一次的解法,与一个被反复发现的解法获得同等频率的训练。在三种模型规模、两种强化学习目标以及更具挑战性的任务构造中,重放机制既提升了策略成功的频率,也增加了策略能够成功采用的不同方式数量。

arXiv cs.LG71

Emergent Inverse-Depth Scaling From Nonlinearity In Attention

arXiv:2610.11063v1 Announce Type: new Abstract: Scaling laws describe power-law improvements in model performance with dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-attention models, this scaling is tied to a power-law data spectrum: unable to selectively attend to relevant tokens, these models learn according to global spectral strength, with stronger directions learned before weaker ones. Large language models, however, can be strongly nonlinear. Here, we show that nonlinear attention yields inverse-depth decay of loss across all tested data spectra. Nonlinearity enables attention to focus selectively on relevant tokens, allowing strong and weak spectral directions to be learned in parallel. Similar focusing across layers motivates a connection to the central limit theorem: shared error across layers sets the loss plateau, while aggregation turns layer-specific differences into continued gains with depth. Our findings suggest that depth scaling may arise from nonlinearity in attention, which allows large language models to focus locally and may make the global covariance structure less relevant.

arXiv cs.LG81

Low-rank tensor structure of precipitation and its application to satellite-reference merging

arXiv:2610.11000v1 Announce Type: new Abstract: The intermittent and variable nature of precipitation makes its accurate estimation over extended domains difficult, yet its spatiotemporal structure suggests that a low-rank representation may be possible. This work represents daily precipitation over the contiguous United States (CONUS) as spatiotemporal tensors and applies CANDECOMP/PARAFAC factorization, showing that preserving the native spatial and temporal modes yields more accurate reconstruction than factorizing independent daily fields or unfolded space--time matrices. Building on this finding, this work presents TMerge, a tensor-based framework that integrates satellite precipitation with sparse reference observations through shared low-rank spatial and temporal factors. TMerge was applied to correct the IMERG Final Run product with climate prediction center reference observations over CONUS. During 2019-2022, TMerge increased correlation from 0.53 to 0.85 and reduced root-mean-square error and mean absolute error by 48.2% and 29.3%, respectively. TMerge consistently outperformed linear bias correction, quantile mapping, and neural networks across seasons, precipitation-intensity regimes, and regions. Improvements were spatially coherent and largest in coastal regions where IMERG errors were greatest. These results demonstrate that low-rank tensor structure parsimoniously approximates the dominant spatiotemporal variability of precipitation and provides a practical mechanism for improving satellite estimates under limited reference observations over extended domains.

arXiv cs.LG74

F$^3$NO:具有跨尺度条件调控的频率分解有限时间流映射神经算子

arXiv:2610.10998v1 公告类型:新 摘要:神经算子能够实现快速的PDE预测,但重复预测会累积误差,且细尺度结构仍然难以解析。我们提出一种频率分解有限时间流映射神经算子(F$^3$NO),利用更新后的低频特征引导高频信息的非线性细化。在每一层中,这种跨尺度条件调控将全局频谱处理与局部细节细化连接起来。该模型直接预测指定未来时刻的状态,并根据预测时间间隔调整两条分支的贡献。对于更长的轨迹,它将短时间片段内的并行预测与片段之间的递归传播相结合。在五个PDE基准测试上的实验表明,与自回归基线和直接预测基线相比,该方法提升了预测精度。消融实验显示,频率分解细化能够以更少的参数提高精度,而分段带来的收益取决于空间分辨率和动力学状态。

arXiv cs.LG63

Invariant-Measure Reasoners: Stable Representations for Latent Reasoning

arXiv:2610.10996v1 Announce Type: new Abstract: Latent reasoning models repeatedly update a latent state using the same recurrent block. As the recurrent depth increases, the sequence of latent states may converge to a compact subset of the state space without necessarily converging to a fixed point. Existing models typically predict by applying a prediction head to a single latent state. However, the latent state can continue to change even after many updates, potentially making predictions unstable across recurrent depths. To address this instability, we introduce invariant-measure reasoners (ImR), a framework that uses an invariant measure as a stable representation. This measure describes the long-run distribution of latent states on the compact subset and is invariant under updates by the recurrent block. ImR predicts from the expectation of the prediction head's output under this measure. We use ImR in two ways: fine-tuning only the prediction head of existing models and training models from scratch. Both approaches reduce prediction instability and improve accuracy in many settings on maze and Sudoku tasks. In some settings, models trained with ImR exhibit non-fixed-point behavior more frequently than existing models yet achieve high accuracy even with such behavior, unlike existing models. These results suggest that ImR can leverage otherwise destabilizing dynamics for latent reasoning.