Papers

Large foundation models have been introduced with the promise of efficient adaptation to downstream tasks. Yet, under limited supervision, MLLMs, an important class of large foundation models, remain challenging to adapt to various downstream tasks. Adaptation typically relies either on MLLM parameter fine-tuning or on training neural-based decoders. Both approaches struggle under limited supervision, while fine-tuning additionally requires access to model parameters, which is often unavailable for closed-source models. We introduce AdaKerNet, a novel learnable task-adaptive neural kernel decoder. AdaKerNet is fully agnostic to the parameters of the underlying MLLM and operates solely on its (frozen) rich representations obtained from the diverse available modalities. AdaKerNet relies on (i) a set of learnable, Lipschitz-controlled multimodal features derived from these MLLM representations; (ii) a reference kernel that provides a soft structural prior on those features; and (iii) a lightweight nonlinear neural predictor that adaptively deforms that structure. Learning the kernel representation and the neural predictor jointly within a unified optimization framework allows AdaKerNet to capture features and geometric relationships relevant to the downstream task. Numerical tests across four MLLMs: BLIP-2, LLaVA-1.5, Qwen2.5-VL, and Gemini Embedding 2, and multimodal inputs spanning text, audio, images, and tabular measurements demonstrate significant and consistent improvements over direct MLP, attention-, autoencoder- and kernel-based decoders, across a range of scarce-label budgets, with average error reduction of up to 41% across baselines. These results establish AdaKerNet as an effective approach for prediction from frozen multimodal representations in the scarce label regime. Additional structural ablations highlight the complementary contributions of AdaKerNet's components.

Understanding how the brain parses actions and events from time-varying natural inputs is a central challenge in neuroscience. Recent work has used deep neural network (DNN) models to build stimulus-computable fMRI encoding models that predict single-voxel responses to complex natural videos. However, the majority of video-computable encoding models predict responses using simple linear mappings from model tokens, overlooking the spatiotemporal structure shared by video representations and neural responses. Recent cross-attention encoding models address this limitation for static images, enabling flexible stimulus-dependent weighting of image content across space. Here, we extend this framework to naturalistic video, using per-parcel cross-attention to dynamically route features from a self-supervised video model (V-JEPA-2) across both space and time, fitting this model to fMRI responses to short video clips. We compare joint spatiotemporal attention with factorized and selectively constrained alternatives, and find that joint routing improves predictions of brain responses to held-out videos across higher visual regions, most consistently in lateral and dorsal visual areas associated with dynamic motion perception. Moreover, our method provides interpretable, stimulus-specific attention maps that dynamically follow moving objects, revealing which locations and temporal moments contribute to each neural response. We further show that attention maps from parcels in different category-selective networks (face-, body-, scene-selective) differentially weight content in accordance with expected semantic selectivity. Together, this work provides a new computational framework for understanding how visual information is adaptively weighted by cortical populations during dynamic visual perception.

Standard video generators do not natively compact historical context into reusable memory tokens. As generation continues, the growing history makes it increasingly difficult to retain information from earlier frames due to long-context degradation. Key-frame-based approaches address this challenge by retaining selected past frames, but can discard information needed for future generation. Rather than relying on frame selection alone, we study whether a frozen video generator can supply the supervision needed to learn a compact representation of the history. We propose Prediction-Aligned Context Compaction (PACC), which uses a learned compressor to aggregate information across past frames into compact memory tokens. We train the compressor through on-policy distillation, using the same frozen generator both as a student when conditioned on compressed memory and as a teacher when conditioned on the full history. The student generates continuations, while the teacher provides targets for the same noisy inputs at each denoising step. Only the compressor is updated to align the student's predictions with these targets. We evaluate PACC on MBench, which jointly measures memory-event coverage and consistency. PACC outperforms the strongest baseline by 6.63 points on Causal-rCM and 3.19 points on Causal Forcing. Evaluation on VBench-Long using MovieGen prompts further shows that PACC produces minute-long videos with generation quality competitive with baselines. Together, these results show that learning to compact historical context can improve long-video memory without modifying the underlying generator.

Deep learning models have achieved strong performance in artificial intelligence for science, yet their black-box nature limits our understanding of how they learn scientific tasks. Existing methods for interpretability provide limited insight into how models organize evidence and evolve during learning. We introduce explainability from training (EFT), a model-agnostic paradigm that traces model interpretation during training to explain why models rely on specific features and how they organize these features as predictive evidence. We apply EFT to four state-of-the-art T cell receptor (TCR)-epitope prediction models, TCR-SRIM, TULIP, MixTCRpred, and NetTCR-2.2, spanning post-hoc and interpret-by-design approaches as well as transformers and CNNs. To investigate how structural information affects model explanations, we introduce a benchmark, TCR-XAI2, containing 388 unique experimentally resolved TCR-epitope structures, complemented by structures predicted using AlphaFold3, Boltz-2, TCRModel2, tFold-TCR, and OpenFold3. Using EFT with TCR-XAI2, we demonstrate that (1) CNN and transformer models exhibit distinct learning trajectories; (2) TCR $\alpha$ and $\beta$ evidence can conflict during learning, limiting the benefits of jointly modeling both chains, while MHC information mitigates this; and (3) real versus predicted structural data for TCR-epitope prediction exhibits distinct TCR and peptide feature preferences as well as differing trajectories of model certainty.

Vision-language-action (VLA) models perform well on shorter-horizon manipulation tasks but still struggle with long-horizon tasks that require multiple dependent manipulations from a single command. Online reinforcement learning (RL) can improve these policies through environment interaction, yet many existing methods provide reward only after the complete task succeeds. However, such terminal supervision is sparse and does not distinguish early failures from rollouts that make substantial partial progress. We propose StructRL, an online RL framework that constructs structured intermediate supervision from verifiable subtask completions. StructRL decomposes each task into verifiable subtasks, grants intermediate rewards only after the prerequisite subtasks have been completed, and scales each reward according to completion pace. Across RoboCasa365 and LIBERO-Long with GR00T-N1.5 and pi 0.5, StructRL consistently outperforms evaluated online RL baselines. These results show that verifiable, structured intermediate rewards improve long-horizon VLA post-training. Code is available at https://github.com/amazon-science/StructRL.

Generative and representation learning remain asymmetrically connected: semantic representations are used to improve diffusion generation, whereas the models' own representations are often treated as a by-product of synthesis. We ask whether diffusion models can instead be trained to learn substantially stronger semantic representations without sacrificing generation quality. SelfFlow takes a step in this direction by introducing self-supervised patch alignment into flow matching, but its main gains remain in faster convergence and improved generation. Inspired by DINO and iBOT, we extend this framework with cross-view class-token alignment to further strengthen semantic representations. Specifically, we form two independently noised, dual-timestep observations of each image and align each student class-token representation with the stop-gradient EMA-teacher target from the other observation. This objective is optimized jointly with the inherited flow-matching and local patch objectives. Notably, although the additional objective acts only on the class token, it strengthens both class-token and patch representations. Compared with a matched two-view baseline, ImageNet linear-probing accuracy improves by 9.4% using the class token and 10.1% using mean-pooled patch tokens, while frozen-backbone VOC2012 segmentation improves by 3.6 mIoU. These representation gains are achieved while maintaining comparable ImageNet generation FID. In text-to-image training, the same objective also improves generation FID, reducing it from 2.52 to 2.37 at matched checkpoints. Our results show that representation need not remain a by-product of generation or merely a tool for improving it: it can be directly optimized as a first-class capability of diffusion pretraining alongside generation.

Tabular foundation models achieve strong performance by conditioning on labelled examples in context, but softmax attention limits their use on large datasets. Existing linear-time alternatives, however, are mostly causal, and their potential for tabular in-context learning (ICL) remains underexplored. To address this, we (1) revisit causal training setups, (2) compare linear sequence mixers, and (3) investigate their ICL generalisation beyond the pretraining context length. First, we show that the best training setup for causal models resembles next-token prediction. Then, perhaps surprisingly, the most promising linear sequence mixer is causal: DeltaNet outperforms even non-causal linear attention. However, it degrades beyond $2$-$4\times$ the pretraining context length, and existing mitigation strategies such as bidirectionality defer the problem at best. A hidden-state oracle shows that this is not a capacity problem. Instead, our analysis points to an instability in the recurrent state, which drifts in deeper layers of causal models. Since DeltaNet's learned write rates overfit to the pretraining regime, we modulate them with a time-dependent decay schedule intervention to stabilise length generalisation. Finally, re-introducing non-causality by reading out from the final state allows us to closely match a controlled softmax attention baseline on OpenML-CC18 and TabArena.

The state-of-the-art Membership Inference (MI) methods calibrate their signal separately for each example using reference models, auxiliary models trained to exclude the target. This paradigm scales poorly to modern large models, however, whose training is too expensive to replicate. This has motivated one-round settings, where only a single trained model is available; but without reference models the per-example calibration that drives the strongest attacks can no longer be estimated, leaving the membership signal weak. We ask whether neighbors of the target point can recover this calibration without training any additional model. Our key observation is that reference models serve only to reveal how an example behaves under models not trained on it, and that querying the target model on nearby samples yields the same information. We propose two complementary ways to obtain such neighbors, and show that querying them against an early training checkpoint further sharpens the signal. We evaluate across three image classification datasets and three training setups, showing that neighbors yield strong membership signals and competitive attack performance at no additional training cost.

Parameter-efficient fine-tuning (PEFT) determines not only how many parameters are trained, but also which local directions a model can move in, so similar adapters can affect subgroup losses differently. Since curvature matrices are infeasible to form at adapter scale, scalar summaries such as the Fisher trace are often used instead. We study what the trace reveals and what it loses through the reachable Fisher: each subgroup's full-model Fisher pulled back through the adapter Jacobian. Under likelihood losses, it represents the Gauss-Newton curvature accessible to the adapter, and its trace can be computed from score-gradient norms without forming the full matrix. Under matched subgroup gradients, a positive-definite reachable-Fisher difference, with a margin exceeding the Hessian-Fisher defect, implies that every sufficiently small nonzero model-changing update increases the signed gap. In contrast, the restricted operator norm determines worst-case quadratic change, while a matrix-free Frobenius discrepancy bounds its reachable-Fisher component. Trace alone cannot certify definiteness or control matrix mismatch. Equal traces rule out a positive-definite difference but can still hide large operator discrepancies. Across 306 single-seed models, higher trace accompanies greater subgroup difficulty in 75.7 percent of 1,218 eligible evaluations, while trace matching reduces the best-worst subgroup gap in all 30 dataset-encoder-adapter combinations. However, held-out audits show that operator discrepancy decreases in 23 of 30 combinations, while the unbiased squared-Frobenius statistic decreases in only 16 of 30. Fisher trace is therefore a scalable diagnostic and training heuristic, but not a certificate of local gap behavior or matrix alignment.

Flow-matching text-to-speech (TTS) models achieve high synthesis quality but require many neural function evaluations (NFEs) to integrate their generative trajectories. Recent few-step flow-map distillation approaches for TTS construct targets from numerically integrated teacher trajectories, creating a trade-off between target accuracy and training cost. We propose Local Flow-Map Distillation (LFMD), which adapts Eulerian Map Distillation to conditional TTS and avoids teacher trajectory integration during target construction. For inference, we derive a sampling schedule (TD-DP) from teacher dynamics and consistency of the learned maps, with a single cost graph supporting multiple NFE budgets without external audio-metric evaluation. Because scheduling offers no flexibility at one NFE, we refine this regime with alignment-aware temporal self-distillation using soft-DTW. Across Seed-TTS and LibriSpeech-PC, LFMD improves low-NFE synthesis over a matched integral-distillation baseline. On Seed-TTS, the refined student reaches 1.80% WER with 1-NFE, compared with 1.76% for its 32-NFE teacher.

Chunked KV-cache compression reduces the memory and attention costs of long-context inference by compressing windows of consecutive tokens into fewer cache entries at a fixed stride. Such compression also introduces a new positional coordinate: a token's phase, or its position relative to compression-window boundaries. We uncover a systematic asymmetry in models using such compression: the same information can be easy to retrieve at one phase and difficult at another. We call this periodic variation in retrieval performance phase sensitivity. In large open-weight models with such compression, long-context retrieval accuracy can differ by up to 40 percentage points across phases, revealing periodic weak spots that average benchmark scores can conceal. To investigate this behavior, we pretrain a family of transformers from scratch across multiple KV-compression designs, reproducing phase sensitivity across the variants. Mechanistic analysis using causal interventions in these models reveals phase specialization: different attention components contribute asymmetrically to retrieving information at different source phases. We further analyze idealized retrieval models, showing how gradient flow dynamics may favor sharp phase specialization. Evaluating models with chunked KV-cache compression thus requires measuring across compression phases: high average accuracy can coexist with systematic positional failures.

Evaluation awareness (EA) can cause large language models (LLMs) to behave differently during audits than in deployment, yet measuring and accounting for EA remains challenging. We introduce verbalization training (VT), a method for making LLMs less reticent about verbalizing evaluation awareness while avoiding to supervise the latent belief itself. VT uses a model's spontaneous verbalizations as evidence that awareness is present and truncates each rollout immediately before the verbalization, producing training prefixes at which the model is presumed to be aware. The model is then trained with an RL objective designed to increase verbalization in a calibrated way. Across Qwen3.6-35B-A3B, Kimi K2.6, and Inkling, VT increases verbalized EA by 2.4-2.9 times and transfers to held-out agentic settings, while measured latent EA and behavior remain largely stable. In a causal experiment, we independently implant meta-knowledge about evaluations through synthetic-document fine-tuning and show that VT-induced verbalizations reflect the richer knowledge acquired by the model.

Wildfires are an increasing hazard to ecosystems, air quality, and human systems, creating a growing need for datasets that support systematic development and evaluation of models for predicting fire spread across diverse landscapes. Effective prediction requires integrating meteorological conditions, fuels, vegetation, and topography at spatial and temporal resolutions suitable for both physical simulation and data-driven approaches. However, existing datasets often lack the resolution and coverage needed to capture these interacting controls. The PyroStack dataset addresses this gap by providing a harmonized, event-based collection of wildfire and environmental data across the contiguous United States and Alaska. It integrates satellite-derived fire observations with atmospheric reanalysis, vegetation, fuel characteristics, and topographic information into a unified framework spanning 6994 wildfires that occurred between 2012 and 2024 across a wide range of ecosystems and climate conditions. PyroStack offers spatial resolutions ranging from 30 m to 9 km and hourly temporal resolution, along with fire progression data at 12-hour intervals to support model initialization and evaluation. By combining broad spatial coverage with fine spatial and temporal detail, the dataset enables systematic analysis of wildfire dynamics and supports both physics-based and machine learning approaches, providing a foundation for benchmarking and improving fire spread models, with future extensions aimed at incorporating additional regions and fire suppression data streams to further advance wildfire prediction.

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.

Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the dual domain, these pointwise constraints give rise to functional dual variables. In this work, we propose to learn these dual variables, motivated by the fact that their values encode useful information about the underlying constrained problem. By representing the dual variable as a parametric function of each sample, we enable the learned multiplier to be evaluated on new, unseen samples. This contrasts with standard empirical dual formulations, which assign an independent multiplier to each training sample. We characterize the error in the recovered primal solution induced by restricting the dual variable to a parametric function class and show that it is controlled by how well this class approximates the optimal statistical multiplier. Moreover, we show that the learned parametric multiplier retains the sensitivity interpretation of the optimal statistical multiplier, yielding approximate sensitivity guarantees that extend beyond the samples used for training. We empirically validate our theory across a variety of everywhere learning tasks, showing that the resulting constrained problems can be solved efficiently and that the learned dual variables provide meaningful representations of sample-level sensitivity.

Partial Least Squares (PLS) regression extracts a few outcome-aligned directions in a high-dimensional X and is widely used across applied science, but inference on the resulting fit is either expensive, biased and discouraged, or absent. We reduce inference to held-out OLS refits of the supervised subspace, a primitive shared by PLS, supervised PCA, and linear probes, and supply two tests using held-out correlations: a Nadeau-Bengio corrected asymptotic t-test as a fast approximation, and a permutation test with comparable power, finite-sample valid under outcome-predictor independence and iid rows. Held-out predictions are unchanged under any orthogonal rebasing of the supervised span, so an interpretable basis such as varimax inherits the joint claim but not a per-axis p-value; per-component claims come from a fixed-sequence test on the PLS extraction order. We validate on synthetic geometries, two NIR chemometric datasets, and cross-lingual word-embedding regressions; the exact test also transfers to supervised PCA and a ridge probe. The proposed tests have more power than CV-permutation-Q^2, at a fraction of its cost. A pre-run check on n and the spectrum of X says when the approximation is safe. We release a Rust library with Python, R, and Julia bindings, plus a Python text pipeline.

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan–code–component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

While foundation models have revolutionized natural language processing and computer vision by leveraging universal vocabularies, Graph Machine Learning (GML) remains fractured due to the absence of a unified feature and structural representation across diverse domains. Existing works claiming to be Graph Foundation Models (GFMs) are typically restricted to node-level predictions or require fixed feature dimensions, failing to provide a truly task-agnostic backbone for the full spectrum of graph learning applications. In this paper, we introduce the Universal Classifier (UC), which supports arbitrary feature and class cardinalities, unifying node-, edge-, and graph-level objectives under a single similarity-based classification objective. The UC reformulates all node-, edge-, and graph-level prediction tasks as maximizing similarity in the latent space: by lifting heterogeneous features and labels into 3D latent tensors, the model learns transferable features independent of specific input schemas. This architecture allows a single pre-trained model to generalize to node classification, node regression, and link prediction across unseen graphs with varying feature semantics. Experiments show strong zero-shot transfer performance across node-, link-, and graph-level tasks.

Mixture-of-Experts (MoE) layers are central to frontier language models, and recent architectures push toward more and smaller experts. In this regime, the standard linear router becomes a bottleneck: with $M$ experts and hidden dimension $h$, its per-token cost $\Theta(Mh)$ dominates the MoE layer once $M$ is large. We introduce MoRE (Mixture of Rank-reduced-routed Experts), which factorizes the router weight matrix at rank $r$ and reduces the routing cost to $O((h + M)r)$. We prove that rank logarithmic in $M$ suffices for routing expressivity when the number of active experts is fixed, and is necessary up to precision factors. We also prove that logarithmic rank preserves load balance in a Gaussian memorization model, and training on a synthetic phonebook task shows that low rank does not hurt memorization. At matched active FLOPs, the factorization allows a factor of $\Theta(h/r)$ more experts. To realize this gain in wall-clock time, we design a fused Triton kernel at inference that avoids expensive memory operations on HBM. Empirically, MoRE improves memorization on the phonebook task and performance on knowledge-intensive Q&A benchmarks after pretraining, while matching reasoning ability. Code available at https://github.com/Matheart/MoRE_code.

Sparse autoencoders (SAEs) expose interpretable features in large language model activations, yet existing structured SAEs impose single-parent trees or forests, while post-hoc graphs permit multiple parents but neither guide feature learning nor ensure reliable relation recovery. We introduce the Adaptive Graph Sparse Autoencoder (AG-SAE), a structure-guided training paradigm that treats each feature's complete parent set as an atomic structural hypothesis and lets evidence select zero, one, or multiple parents. By competing complete parent sets against null, subset, and alternative explanations, AG-SAE identifies jointly necessary multi-parent relations while rejecting redundant or spurious alternatives and verifying that each child contributes beyond its parents. The induced topology over SAE features then defines a differentiable structural loss that guides SAE training, while topology-guided refinement mitigates feature absorption and uses persistent reconstruction gaps exposed by the learned structure to initialize new features. The entire graph is then induced again from the revised dictionary by reassessing every feature's complete parent set, closing the dictionary-graph self-consistency cycle. Experiments demonstrate exact mixed-topology recovery in a controlled toy model, greater relational reliability and semantic validity than structured and post-hoc baselines on real LLM activations, and stronger feature-level causal interventions than conventional SAE features. AG-SAE thereby turns recovered mixed-topology feature structure into an unsupervised training signal that improves the dictionary, enables reliable feature organization beyond the topological limitations of trees, and exhibits stronger causal control beyond reconstruction.

EEG foundation models (EEG-FMs) are intended to generalize across different datasets by learning representations that, ideally, are invariant to dataset-specific EEG configurations such as electrode montages. However, EEG-FMs that accept different montages as input do not guarantee that representations and predictions remain stable across different electrode configurations, especially outside the training setting. In this work, we investigate the effects of different electrode montages through a joint functional and representational analysis of four EEG foundation models selected to span distinct montage-handling designs. We evaluate embeddings on cross-subject resting-state eyes-open/closed and within-subject motor-imagery classification under spatially informed channel reduction. Functional robustness is tested through the generalizability of linear probes across channel counts, while representational robustness is assessed through within-subject similarity and preservation of between-subject geometry. The four models show distinct robustness profiles, and the two axes dissociate: large changes in embedding similarity need not come with comparable probe degradation, and stable embeddings can still lose downstream performance. Comparing two readouts of the same encoder further shows that aggregation, not the encoder alone, determines functional robustness: pooling into anatomically aligned regions degrades less than a learned global readout, despite being montage-invariant by construction. Montage robustness is therefore a joint property of the encoder and its aggregation, and characterizing it requires both a representational and a functional axis. Input compatibility alone is evidence for neither.

Deep forecasters predict from a fixed-length lookback window, and lengthening it gives diminishing returns at a growing cost. Retrieval augmentation instead shows the model how similar past situations continued. Retrieving a whole past window gives every variate the continuation of the same past moment. In multivariate series, however, the best past match differs from variate to variate. We present GNA (Granular Neighbor Assembly), a retrieval layer for forecasting backbones that assembles neighbors at two granularities: whole past windows, which keep the variates coherent, and per-variate neighbors, in which each variate takes its future from its own best-matching past. A learned gate decides, per forecast step and variate, how much to trust these futures against a persistence forecast, next to the backbone's own forecast. Candidates come from an embedding trained to predict each window's future, and retrieval is strictly causal: a past window is used only once its future has been observed. With the same lookback for every model and the same retrieval constants for all datasets, GNA improves two Transformer backbones in 85 of 96 dataset-horizon settings, gives the lowest MSE on 8 of 12 standard benchmarks and beats its backbone in every seed on 10 of them. Both granularities are needed, and neighbors of mismatched queries are worse than none. Retrieval helps most where the lookback says least: the gate shifts trust to retrieved futures further ahead. Where it fails, on hourly non-stationary series at long horizons, the loss is consistent with a drifting level of the retrieved futures.

Recent work has established that power-law spectral conditions on data enable tight convergence bounds for deterministic gradient descent, resolving the conflict between classical exponential bounds and observed power-law learning curves. In this work, we extend this result to the stochastic regime of high-dimensional machine learning. We provide two main contributions: (1) We generalize the power-law spectral theory to Stochastic Gradient Descent (SGD), showing that the same spectral exponents govern stochastic dynamics; (2) For the fundamental case of isotropic Gaussian data, we provide a precise analysis of data shuffling, deriving exact constants that prove Single Shuffle is strictly superior to Flip-Flop and IID sampling. Our results bridge the gap between abstract spectral theory and practical stochastic training choices, offering a unified picture of how data geometry drives optimization speed.

Large language models can learn abstract rules from just a few in-context examples, but how their internal mechanisms activate as examples accumulate is not well understood. We trace a three-stage symbolic reasoning circuit (abstraction, induction, retrieval) across shot counts in three model families and find it is detectable and functional well before the model achieves high accuracy. Per-head causal contribution grows up to 8x from 1- to 10-shot, and cross-shot activation patching raises accuracy from 1% to 56% at 0-shot and 17% to 88% at 1-shot. Function vectors scaled and injected at 0-shot rescue accuracy up to 86%, largely substituting for the induction stage but depending critically on an intact downstream retrieval stage. The infrastructure for abstract rule-following is present in the weights before any demonstrations; in-context examples, function vectors, and related interventions appear to supply input to the same latent circuit.

Existing multimodal scaling laws fit multimodality terms empirically after testing and never vary how much data is multimodally paired at fixed data budgets. We investigate how, under the same total data per modality, changing the number of paired data affects loss curves in multimodal classification tasks. We train models in three different environments and run experiment sweeps varying data sizes and pairing budget. Pairing ratios have a dramatic impact on loss and this impact is directly tied to how much information synergy the task contains. Only paired data is able to reduce synergistic loss, while unpaired data can reduce redundant or unimodal information up until unimodal floors. Unlike traditional scaling laws where loss drops immediately in power law decay, synergy acquisition is gated, requiring a critical threshold of paired data before synergistic loss falls at all. We introduce a new family of multimodal scaling laws where total data-attributable loss is the sum of four individual power laws corresponding to the four different information channels of redundancy, a unique channel per modality, and synergy, and show how this law is both more theoretically sound and empirically valid across our experiments. This law predicts multimodal loss in our experiments more accurately than existing laws, with 3.2% error on fit tests versus 10.4% error for the best pairing extension of published laws.

Recent studies have observed that parameter changes during language-model post-training can be concentrated in a small subset of coordinates. This phenomenon has been reported in reinforcement learning, on-policy distillation, and supervised fine-tuning on near-policy data. Its recurrence across different post-training paradigms suggests shared structure in training dynamics. In this paper, we examine this pattern through the diagonal model Fisher, which measures the sensitivity of the model's output distribution to individual parameters and is independent of any particular reward or teacher signal. Theoretically, we show that small diagonal Fisher leads to small expected gradients across a range of training objectives, providing a common explanation for sparse gradient updates. Empirically, we test this connection in RL and OPD. We find that Fisher identifies where gradients are concentrated, and fixed sparse masks selected from the initial Fisher retain a large proportion of the improvement from full training. Finally, we investigate the mechanisms underlying low Fisher in on-policy training. Our results show that high-probability next tokens tend to have similar parameter sensitivities, contributing to low Fisher. Together, these results establish the diagonal model Fisher as a unifying perspective linking update sparsity to on-policy training dynamics in LLM post-training.

Linear RNNs offer linear-time sequence processing and constant-memory decoding, but their fixed-size recurrent states must accommodate all past key–value associations. Existing forgetting mechanisms and Delta Rule updates reduce interference by selectively clearing or correcting the state, yet earlier associations can still become difficult to retrieve. We introduce CyFA (Cyclic Flow Attention), a Linear RNN with relative-time-partitioned memory. At each step, a learned clock controls the cyclic transport applied jointly to the key and value states before the current key–value pair enters the age-zero slot, thereby organizing stored associations across relative-time slots. We further derive an exact change to absolute-clock coordinates that expresses CyFA as two scalar-decay linear attention recurrences and enables efficient chunk-wise training. Across 400M–1.4B pretraining experiments with matched recurrent-state sizes, CyFA improves recall-intensive performance while maintaining competitive language modeling and high computational efficiency. At 400M, CyFA outperforms KDA on FDA (42.60 vs. 26.07) while requiring only 46.7% and 48.3% of KDA's forward and backward core-operator execution times, respectively. Our code is publicly available at \href{https://github.com/Chyxx/CyclicFlowAttention}{this https URL}.

Closed-form recourse moves a rejected user along the unit gradient $\hat g$ of the classifier score $f$ by the promised distance $d_p=|f(x)|/\|\nabla f(x)\|$, at which the linearized score reaches zero. We ask when this one-shot step succeeds and what additional model queries change. To leading order the step ends on the favorable side exactly when the path curvature $\kappa=\hat g^\top\nabla^2 f(x)\,\hat g$ is nonnegative. Across 80 shallow models, the fraction of rejected users whose step ends there and the fraction with $\kappa\ge0$ correlate at $r=0.985$, although on Fashion-MNIST the first falls below the second by 8.2 points on average. No rule that uses only the score value and gradient can be valid for every score with path curvature bounded by $K$ without overshooting some by order $Kd_p^2/\|\nabla f(x)\|$. When the curvature is also Lipschitz and the step is short, one evaluation of $f$ at the promised point attains the minimax rate among deterministic one-query rules that know the curvature bound and its Lipschitz constant, and split-conformal calibration makes such a rule reach the first crossing or abstain with probability at least $1-\delta$. Training with an asymmetric curvature penalty lets 99-100% of paths cross within the promised step on undershoot-prone shallow data, at about 4-22 times the overshoot of symmetric penalties (Fashion-MNIST, COMPAS). Because $\kappa$ and $d_p$ depend on how the score is scaled, part of this gain can be a longer promised step, and at matched validity a smaller audit of briefly trained models finds no uniform advantage over tuned inflation. Where a per-user line search along the ray is affordable, it is exact to grid resolution and preferable.

Action chunking provides temporal abstraction in reinforcement learning by selecting short action sequences instead of individual actions, but many existing approaches face two limitations in high-dimensional robotic control. First, many rely on value functions over action chunks, which can be difficult to learn as action dimensionality and chunk length grow. Second, executing chunks open-loop removes within-chunk feedback, limiting reactivity in contact-rich tasks. We present Action Chunking PPO (ACPPO), a PPO extension that uses a chunked actor while retaining a standard state-value critic, thereby avoiding chunked Q-functions. We further propose ACPPO-Corr, which augments the chunk planner with a stepwise feedback corrector that adjusts planned actions online within each chunk. Across 25 simulated robotics tasks from IsaacGym and Bi-DexHands, spanning locomotion, arm manipulation, and dexterous hand-object interaction, ACPPO-Corr achieves the strongest aggregate performance among evaluated methods and performs best on both decision-frequency-sensitive and decision-frequency-neutral task subsets. Ablations show that moderate chunk lengths work best and that corrector regularization is important for balancing chunk-level planning with local feedback. These results suggest that action chunking can be effective in online PPO when chunk-level planning is paired with closed-loop correction. The code is available at: https://github.com/hshhahn/ACPPO.

Full-page blind restoration of historical Manchu manuscripts is challenging due to scarce annotations, unknown degradation regions, and fragile connected strokes. Generic restoration models may improve visual quality but often modify intact content, leading to over-restoration. We propose SAGE-Restore (Stroke-Aware Gated rEstoration), a selective restoration framework that first assesses where restoration is needed and then uses this assessment to guide restoration candidate generation and pixel-level selection. Its encoder predicts patch-level repair probabilities from complementary appearance and stroke-structural cues to condition restoration candidate generation, while the corresponding repair logits are refined into a pixel-level soft gate that selectively controls where the restoration candidate is applied. We further introduce a fidelity-aware evaluation protocol that jointly measures degraded-region recovery, intact-content preservation, and their balance. SAGE-Restore achieves the highest R-Recovery (0.463) and RFS (0.626), while maintaining high U-Fidelity (0.968), demonstrating an effective balance between restoration and content preservation.