Papers

Prior information for real-world physical quantities is most elegantly expressed via partial differential equations (PDEs). In this paper, we propose a novel way to solve PDEs using probabilistic inference on a factor graph. In general, factor graphs provide a natural way to encode prior knowledge into a model as explicit factors; here, this knowledge is provided by a governing PDE, which narrows the solution space, while observed data further shape the posterior over the parameters. The approximate parameter posterior is inferred using message passing based on moment matching, without posterior sampling or global gradient-based optimization. We demonstrate our approach on the first-order advection and the second-order semi-linear Fisher-KPP equations, where it achieves predictive accuracy comparable to a standard baseline while providing structured predictive uncertainty. Moreover, the inferred posterior marginal means and uncertainty structure match more closely those obtained using Hamiltonian Monte Carlo than the evaluated mean-field variational inference baseline, while requiring up to 10x less training time in our experiments, with inference speed comparable to variational inference.

Online safe reinforcement learning (RL) seeks policies that maximize reward while satisfying safety constraints. Reward and safety can induce multimodal action distributions, challenging the prevailing primal-dual methods: Gaussian actors may collapse onto a single suboptimal mode, and optimization over the nonconvex Lagrangian landscape can be unstable. Diffusion and flow policies can represent such distributions, but recent work with a diffusion actor relies on estimating and matching the score of an augmented-Lagrangian target policy. Instead, we differentiate the augmented objective directly through the generation path of a flow policy, so no score needs to be estimated. Because a flow policy lacks a readily available action log-density for entropy regularization, we build on the density-free kinetic-energy regularizer of FLAC, a recent reward-only method, and propose Reparameterized Augmented-Lagrangian Flow Actor with Least Energy (RAFALE), an off-policy actor-critic method for safe RL. We formulate its update as a constrained one-ended generalized Schrödinger bridge and show that, for each source draw, this path-space problem is exactly an entropy-regularized problem in action space. At positive noise, its solution reweights the reward-only action distribution only where the estimated cost exceeds a threshold set by the Lagrange multiplier. As the noise vanishes, the optimal value converges to that of a least-energy map objective that the flow policy optimizes directly. Across seven Safety-Gymnasium tasks, RAFALE achieves competitive reward with mean final cost within budget on every task, whereas strong baselines trade one for the other; ablations support the necessity of both its augmented objective and its flow actor.

We study online dynamic pricing with censored demand, where an arbitrary inventory level is revealed before pricing and may adapt to past observations, while demand follows an unknown, price-dependent distribution that is stationary over time. For a horizon of $T$ rounds, Xu et al. [2026] achieved $\widetilde{\mathcal{O}}(\sqrt{T})$ regret under restrictive structural assumptions including linear demand, price-independent additive noise, and conditions relating inventory levels to the noise support. Our first contribution is to extend this framework to a substantially more general and statistically harder nonparametric setting, requiring only the natural assumption that expected sales are nonincreasing in price and allowing nonlinear demand curves and price-dependent noise. For this model, we first propose a simple baseline, Double-Grid-UCB, which discretizes both price and inventory and achieves $\widetilde{\mathcal{O}}(T^{3/4})$ expected regret using separate revenue estimates for each price-inventory grid pair. Then, we develop Threshold-UCB, which improves the expected regret to $\widetilde{\mathcal{O}}(T^{2/3})$. Unlike Double-Grid-UCB, Threshold-UCB reuses sales observations across inventory levels through shared estimates of demand-tail probabilities, allowing the same data to support revenue upper bounds for multiple inventories rather than a single inventory bin. We also complement this upper bound with an $\Omega(T^{2/3})$ lower bound via a reduction from stochastic posted pricing, establishing its minimax optimality. Finally, extensive experiments across inventory processes, demand functions, and noise models demonstrate consistently superior performance of Threshold-UCB over benchmark algorithms.

A two-hop question makes a language model retrieve twice: once to produce a bridge entity, and once to retrieve with it. Transformers resolve that entity in their early layers. Hybrid models replace most of the attention with a recurrent state, so where the key becomes usable, and where it is spent on an answer, is not known. Answering "Where is the ball?" from "the ball belongs to Alice" and "Alice is in the garden" turns on Alice, a name the question does not mention. A model could reach garden through Alice, the key it computed, or through where the fact sits in the prompt. Across twelve models, dense and hybrid, we move a hidden state from one story into another where the two routes lead to different places, and read off which place the model gives. An attention layer converts the key in every model we tested, and crossing that layer removes its usable effect, all of it where no attention follows. In sequential hybrids this makes the answer a handoff: recurrent layers carry the key forward, and attention spends it. Retrieval does not always stop there. Writing a different fact into the memory of the recurrent layers that follow the last attention layer can move the answer toward that fact, multiplying its odds by 1.3 to 2.7, and which hybrids do this is not settled by their architecture or training. That read is addressed by the key, not by position: recurrent state in a hybrid is not only a carrier, but a memory that later layers can query.

Inferring quantities of interest (QoI) from data is a central task in Science and Engineering. In such contexts, we often have access to both quantitative data and qualitative data. Quantitative data may be represented by noisy sensor measurements, simulation data, re-analysis data; qualitative data may be in the form of text descriptions of experimental setups, expected experiment outcomes, and human-perceived system behaviours. The task we address in this paper is the following. Given a training set of paired qualitative text and quantitative QoI data, we learn to exploit the inherent correlation between the two modalities to learn a highly informative data-driven natural-language-conditional Bayesian prior, such that when presented with a new physical system, we can coherently combine (i) the training dataset, (ii) qualitative text describing the new system, and (iii) a small number of noisy sensor readings from that new system, to perform inference and uncertainty quantification (UQ) over the QoI. To achieve this task, we develop two parallel approaches, one uses conditional diffusion and the other conditional autoencoders, and compare both against classical Bayesian methodology, unconditional generative models and deterministic supervised methods. Each approach has specific strengths and tradeoffs; conditional autoencoder offers theoretical tractability, allows for fast posterior sampling, and provides better-calibrated UQ, whereas conditional diffusion is explored for greater expressiveness and capturing complex posteriors with irregular QoI fields. The approach is tested on the steady-state heat equation, damped Helmholtz equation, and UK weather reanalysis data.

Graph convolutional networks propagate information by repeated local aggregation through a graph shift operator; i.e., a $K$-layer network reaches $K$ hops neighborhood. On the one hand, such spreading can lead to oversmoothing. On the other hand, long-range dependencies demand the depth. Transporting information on long distances and without attenuation requires the shift to distinguish a direction of flow, which a symmetric operator cannot perform but a directed one can fulfill. A natural way to extract pure-directionality is to take the skew-symmetric part of the shift operator through the Cartesian split, which, however, generally does not commute with the shift itself, meaning that the filters built on it are not shift-invariant. We instead use the spectral conjugate; i.e., the image of the operator under $\tau:z\mapsto \bar{z}$, which commutes with the shift and splits it into a dissipative and a non-dissipative part. Two filter families follow: a sum filter, whose non-dissipative component transports signal without energy loss, and a ratio filter, ratio in the pair of components rather than polynomial in the shift. Both arise from non-holomorphic kernels, placing them outside the holomorphic class underlying classical spectral convolution. On the directed cycle, the ratio filter becomes an IIR filter with global impulse response, for which we prove a long-range reach gap against every degree-$K$ polynomial filter. Chebyshev reparameterization gives stable vertex-domain layers with real coefficients, yielding TwinS-GCN, which solves graph transfer tasks at reduced depth and is competitive with state-of-the-art graph convolutional networks on node classification benchmarks.

Multi-agent systems built on large language models (LLMs) are largely homogeneous, as their agents behave alike even across distinct LLMs. We show that when such agents act concurrently without communication, they collide on targets they must split and diverge on targets they must take together, a double failure we term the symmetry trap. Theory of Mind (ToM), widely used for coordination without communication, cannot escape this trap, since homogeneous agents form the same prediction of one another and respond to it in the same way. We propose Theory of Scene (ToS), a training-free reasoning schema in which each agent reads its public role, the only difference between the agents, and the task context they all observe. Homogeneous agents thereby derive one division of labor, each taking the part its role fixes, which turns homogeneity from the cause of the trap into the cure. ToS reads the role together with the scene through role gating, which determines whether ownership overlaps or is already divided, and the task context through task coupling, which infers whether the team must converge on each target, divide it, or take its stages in turn. We evaluate on DivvyBench, a controlled environment we introduce, whose target types make an episode Competitive, Cooperative, or Mixed across Tabletop, Airspace, and Household scenarios, and on two established agentic benchmarks, GovSim and Overcooked. ToS outperforms all six baselines on every benchmark, and each baseline falls far behind it in at least one setting. Against ToM given the same inputs, ToS raises the DivvyBench success rate from 71.1% to 99.6%, the GovSim total gain from 207 to 400, and the Overcooked level-normalized throughput from 1.41 to 1.67.

Neural network training is inherently stochastic, with factors such as weight initialization leading to distinct models despite comparable predictive performance. This phenomenon is commonly associated with the Rashomon effect, which describes the existence of multiple near-optimal models for the same task. Although the Rashomon effect has received increasing attention, it remains unclear whether different sources of training stochasticity contribute similarly or differently to its manifestations. In this work, we present an empirical study of the Rashomon phenomenon along three complementary dimensions: solution-space multiplicity, predictive multiplicity, and decision-basis multiplicity. These dimensions are quantified through the size of the empirical Rashomon set, predictive ambiguity, and agreement between XAI attribution maps, respectively. By independently controlling three standard sources of stochasticity, namely weight initialization, mini-batch data ordering, and dropout, we isolate their respective contributions to each dimension of the Rashomon phenomenon. Experiments on tabular and image classification benchmarks reveal that these sources affect the three dimensions in different ways. In particular, larger empirical Rashomon sets do not necessarily correspond to greater predictive disagreement or lower explanation agreement, indicating that solution-space, predictive, and decision-basis multiplicity capture complementary rather than interchangeable aspects of the Rashomon effect. Overall, our results show that training stochasticity influences not only predictive performance but also the stability of predictions and explanations, highlighting the importance of identifying the specific sources of stochasticity responsible for different manifestations of the Rashomon phenomenon when assessing the reliability, reproducibility, and interpretability of neural network models.

In safety-critical applications, deployment uses a single policy, whose performance and constraint satisfaction should hold directly rather than only for an average or mixture of training policies. This motivates last-iterate guarantees in constrained reinforcement learning. Recent progress has established such guarantees in exact-gradient or tabular online settings, yet scalable results for structured large-state problems remain open. We develop a general, statistically efficient framework for last-iterate convergence in structured Constrained MDPs (CMDPs). Our analysis separates contraction of the regularised primal-dual dynamics from actor approximation and statistical errors in policy evaluation under online exploration. This enables model-free on- and off-policy learning with structured function approximation: optimistic policy evaluation avoids explicit transition-model construction, while a compact parametric actor avoids maintaining mixtures or histories of past policies. We instantiate the framework for linear CMDPs and general function approximation, obtaining representation-dependent complexity and improved target-accuracy dependence over prior optimistic regularised primal-dual analyses. We further validate the stabilising effect predicted by our theory on a synthetic linear CMDP: the regularised method exhibits stable last-iterate behaviour, whereas its unregularised counterpart shows larger oscillations.

Finite computational resources force a tradeoff between automatic System 1 processes and costly System 2 thinking. Large language models (LLMs) can spend extra computation on hard problems, yet direct answers struggle even with counting, an elementary operation humans and animals perform automatically. We ask why this requires thinking in LLMs. Evidence integration has long been used in psychology and neuroscience to probe decision-making. Our evidence-integration task presents one letter per conversational turn and asks which of two target letters appeared more often. A running count difference solves the task optimally by weighting every letter equally; tokens at each turn could represent and update this difference. Direct responses instead weighted evidence unevenly, with strong recency effects, and assigned less probability to the correct answer as difficulty increased. Thinking improved performance and made integration weights nearly uniform, yet final-query attention remained concentrated on the sequence ends in both modes. Reasoning trajectories showed models revisiting input, recounting letters, and checking intermediate counts that informed the answer, suggesting that thinking constructs the accumulated count that direct responses lack rather than reading out one already formed. Reasoning-token costs grew with the number of letters far more than with coherence. Outcome feedback did not bring this computation into direct responses: under in-context reinforcement learning (ICRL), performance deteriorated over repeated games and recency effects strengthened, yet models grew more confident. Humans and animals amortize such computations into automatic processes, whereas current LLMs still pay for them with thinking on every trial. Which operations learning can make directly available remains central to how future models allocate computation.

Brain-computer interfaces (BCIs) have emerged as transformative technologies that enable direct communication between the brain and external devices. Among various BCI paradigms, EEG-based motor imagery (MI) has gained prominence due to its simplicity, non-invasiveness, and potential to restore motor function and facilitate rehabilitation for patients with motor impairments. This paper presents a comprehensive review of the most practical processing algorithms developed over the past decade for decoding brain sensorimotor cortex signals. Specifically, this paper discusses the integration of artificial intelligence (AI)-based algorithms, particularly machine learning and deep learning techniques, and their contributions to improving the performance and efficiency of MI-BCI systems in detail. Furthermore, the paper reviews state-of-the-art hardware platforms and emerging converging technologies, including system-on-chip (SoC) architectures, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), wearable devices, the Internet of Things (IoT), and augmented/virtual reality (AR/VR), and discusses their integration with advanced signal processing algorithms to enable next-generation MI-BCI systems. By highlighting current achievements of EEG-based MI-BCI technology and predicting future research directions that could further enhance real-time capabilities, this paper aims to provide valuable insights for researchers and practitioners, fostering innovation in high-performance EEG-based MI-BCI systems.

Graph Neural Networks (GNNs) are widely used for representation learning on graphs, but most methods assume static topologies, making them inefficient on evolving networks where edges change over time. Existing dynamic approaches either model graph evolution through temporal GNN architectures without focusing on efficient dynamic maintenance, or are restricted to linear propagation models based on Personalized PageRank. In this work, we study how to efficiently maintain node representations for non-linear GNN propagation under edge insertions and deletions. The propagation has no learned parameters, and only a classifier applied afterward is trained. For a broad class of standard activation functions, we develop a residual-based dynamic algorithm that selectively propagates local errors via push operations, maintaining an approximation to the evolving fixed point without full recomputation. We prove that our method achieves amortized $O(1/\epsilon)$ update time per graph change under a degree-normalized error guarantee. Our approach uses a potential-based analysis in a degree-scaled norm and, in contrast to prior work on the linear case, requires no randomness assumptions on either the update sequence or the input vector. For the linear special case, we additionally provide an exact dynamic algorithm via low-rank matrix inverse updates. Experiments on benchmark datasets show that incorporating non-linearity improves accuracy while preserving efficient update performance, yielding a scalable and theoretically grounded method for maintaining this propagation on dynamic graphs.

Millimeter-wave (mmWave) radar and RGB-D cameras can record cardiac and respiratory waveforms continuously and without contact, but labeled recordings remain scarce because every label requires a supervised acquisition session. Self-supervised pretraining can exploit the unlabeled signals, yet contrastive methods depend on signal transformations and negative pairs whose validity is uncertain for cardiorespiratory data, where time warping changes breathing rate and distant windows can share the same physiological state. We present Phenomenon-Graph JEPA, a joint-embedding predictive architecture that learns from four processed one-dimensional streams without negative pairs or synthetic augmentation in its base configuration. Each stream is encoded by a temporal convolutional branch and a band-limited spectral branch. During pretraining, the model predicts stopped target embeddings along typed edges, which connect streams assigned to the same physiological phenomenon, and forward in time within a state episode. We treat this physiological typing as a testable hypothesis and compare it with wrong-edge and all-pairs prediction graphs. In the OMuSense-23 dataset, pretraining improves label-efficiency area over matched supervised training by 3.91 percentage points (95% interval 2.08 to 5.80, Holm-adjusted p = 0.006), and by 3.74 points under a second configuration evaluated on the same test participants. However, the wrong-edge and all-pairs controls do not establish a benefit from physiological typing. Optional Takens-inspired delay coordinates improve a validation comparison with learned history, whereas two wrist-only WESAD protocols do not establish a pretraining advantage. The study therefore separates the measured benefit of predictive representations from the physiological prior used to organize their training.

Transformer-based language models perform well on symbolic tasks, yet it remains unclear whether they learn generalizable rules or rely on statistical shortcuts. Mechanistic studies link algorithmic behavior to structured internal representations, motivating the hypothesis that robust reasoning benefits from separating values from the types that control their manipulation. Can making this separation an architectural primitive improve the learnability and generalization of logical mechanisms? We introduce STRAT (STratified Registers And Types), which partitions the residual stream into orthogonal Data and Type subspaces and uses Type-based attention and gating to govern Data transformations. Controlled arithmetic ablations identify three failure modes associated with data-control interference: the Linear Trap, Gradient Wall, and Open Gate Trap. Mechanistic analysis reveals interpretable logical structure, and in arithmetic, STRAT reduces median OOD error 35-fold relative to a Transformer baseline. On each of 11 datasets spanning 10 tasks, STRAT outperforms the Transformer baseline in mean accuracy, by 26 percentage points on average, with both models trained from 10 base examples per dataset using identical task-specific augmentation where applicable. Under distribution shift, STRAT's mean accuracy drops by only 2.39 percentage points, compared with 11.75 for the Transformer.

We introduce Adaptive LeWorldModel (ALeWM), a world model based on a joint-embedding predictive architecture (JEPA) that learns to concentrate predictive information in compact prefixes of a wide latent representation. To encourage this ordering, ALeWM learns a sequence-conditioned distribution over prefix lengths and trains the predictor to estimate the full next embedding from a sampled input prefix. As standard anti-collapse objectives encourage variation across latent coordinates and do not organize them by predictive importance, we also introduce MixSIGReg. MixSIGReg regularizes the masked embeddings against a prior-weighted mixture with Gaussian active prefixes and zeros in the remaining coordinates. As a result, the ALeWM objective encourages early coordinates to retain information useful for prediction and recursive planning. Our analysis shows that the mixture distribution used by MixSIGReg assigns higher variance to earlier coordinate blocks and lower variance to later ones. In addition, we show that, under specified assumptions, prediction error is minimized by placing the information most useful for prediction in earlier blocks. Empirically, we study the behavior of ALeWM in a controlled dynamical system with known state variables and in goal-conditioned visual control. We show that ALeWM consistently achieves higher mean success rates than tuned fixed-width LeWM, with lower planning capacity on average.

Recent progress in frontier models has renewed interest in large-scale reinforcement learning (RL), but the cost of generating large-model rollouts makes even testing RL recipes expensive. We ask whether reasoning improvements learned by a small, weak model can benefit a larger, stronger model without using the strong model's rollouts during training. We introduce Allspark, a training and inference framework for weak-to-strong transfer through alternating chains of thought. A weak teacher is trained alongside a frozen copy of the same model; the two alternate reasoning segments, and the frozen model produces the final answer. At inference time, a stronger student replaces the frozen training partner, while both models remain fixed. Because they communicate through text, the teacher can steer students from different model families and with different tokenizers. We study Allspark at two scales: controlled Qwen experiments across math and reasoning, and larger-scale Inkling experiments on ARC-AGI-2. The Inkling experiments show accuracy gains in within-family and cross-family settings, including transfer to Kimi and Nemotron, with benefits that vary across inference settings. These findings motivate reusing a trained weak teacher across strong students and examining the resulting accuracy–token tradeoff.

Neural theorem provers must both propose tactics and decide which valid successor states to explore. We study whether one-step Lean transitions provide a self-supervised signal for branch ordering. A JEPA-style model predicts latent successor representations and scores only kernel-validated, nonterminal successors generated by a fixed pretrained ByT5 proposer. JEPA achieves higher Top-1 than matched InfoNCE on a same-theorem ranking diagnostic(50.18% versus 31.55%), but averages 282.3 of 987 solved theorems across three seeds versus 308 for proposer ordering, while requiring more tactic checks. In this setting, accurate one-step transition ranking is therefore insufficient as a long-horizon search value. The controlled evaluation separates representation from proposal quality and treats kernel-checked proof completion as the primary endpoint.

Pretrained tabular foundation models process every dataset at a fixed depth, with inference costs growing with dataset size. To address this, we present the first study of depth-adaptive early-exit for pretrained outlier detection models. While early-exit is typically motivated by efficiency, we uncover a surprising benefit: exiting at the optimal intermediate layer can also improve detection performance on diverse real-world benchmarks by 4.7-7.3% on average, consistent across three distinct foundation models. First, we investigate the factors driving these gains, and identify a key mechanism: context pollution, i.e., the presence of outliers among in-context samples. Our analysis reveals that nearby in-context samples exert increasing influence on query predictions at greater depths, consistent with a retrieval-based view of these models. In effect, early-exit alleviates the adverse effects of retrieving accurate-yet-polluted neighbors, with gains of 13-21% when context pollution matches the natural outlier rate. Motivated by these findings, we pretrain a plug-in router to select a dataset-specific exit layer, using query outlier labels as privileged information available only during router training. The router operates post hoc, leaving the base model parameters and prediction head unchanged. Experiments on three large real-world benchmarks show that, on clean context, the router recovers up to 45% of the oracle gain with up to 1.8x speedup across three pretrained backbones, with larger gains as context pollution increases.

Sampling-based motion planners guided by diffusion models produce high-quality trajectories in a single run, yet the stochastic diversity available at inference time is left largely unexploited. We present two inference-time diversification strategies for a fixed, pretrained DiTree model, combined via H-Graph hybridization, and evaluate them on a holonomic AntMaze robot across 15 maze scenarios. The first, factorial diversity, sweeps the random seed and Diffusion Goal Bias (DGB) parameter, the second, refinement-only diversity, sweeps the diffusion refinement strength (RS) that controls how much an RRT-generated trajectory is edited. Because a single-run baseline only partially succeeds, we additionally compare H-Graph results with pool-based statistics. H-Graph improves the mean pool length of the factorial and refinement-only diversities by 18.8% and 14.5%, respectively. In addition, it also improves the best individual candidate's lengths by 9.7% and 6.8%, respectively. And last, compared with the successful baseline's trajectory length, it improves the results by 18.2% and 19.9%, respectively. These results show that inference-time parameter variation is a reliable, training-free source of path diversity, and that H-Graph hybridization reliably converts this diversity into shorter, higher quality trajectories.

Language models are increasingly evaluated as vulnerability detectors, and scores reported for similar models differ widely between papers. We measured how much of that difference evaluation protocol accounts for, with model outputs held fixed. In a paired test, a model must flag a vulnerable function and clear its version after a fixing commit. Three choices that published evaluations make differently were varied one at a time: metric, verdict extraction and output budget. Seven frontier and large open models were evaluated on five released pair benchmarks and a set pooled for this work under one protocol, and 61 open models of 1.5B to 36B parameters on the pooled set. Function-level F1 follows how often a model flags both functions of a pair (Spearman $+0.86$ over 42 combinations) and is nearly unrelated to pair-level correctness ($+0.16$). On the pair score, extraction changes a model's number by $+0.001$ at the median and budget by $+0.02$ with an interval through zero, whereas the model changes a benchmark's number by up to 0.18 and the benchmark a model's by up to 0.16; a function-level score therefore measures flag rate more than model. For 37 of 68 models the difference between correct and reversed pairs is within its 95% interval of zero, the value for a null model that flags each function at a fixed rate, while both-flagged and both-cleared rates exceed that null by 0.055 on median, and for 64 of 68 both functions of a pair receive one answer more often than independence predicts: verdicts are determined by the text common to both functions. On length-matched pairs a linear probe on activations separates 0.78 by within-pair ranking, against 0.64 for a tf-idf baseline and 0.5 for length; the generated verdict is near chance for three of six models and at 0.55 to 0.57 for the other three, and a prompted logit is at chance for all six.

Frozen EEG representations retain acquisition signatures as well as neural activity. Source predictability alone does not identify what should be removed: it can reflect measurement effects or genuine biological and population differences, which should not be erased. We propose Measurement-Gated Provenance Attenuation (MGPA), built on one principle: measurement evidence determines where correction may act, and preserved information determines what it should aim for. Paired measurement contrasts define a gate outside which nothing changes; inside it, the source score is moved to the value the preserved coordinates already predict: for a fixed affine score, this keeps the same information as any target set by those coordinates and needs the least expected squared movement. Closed-form and critic-guided iterative constructions apply it without source identity or encoder retraining. Three studies test the principle at increasing distance from its assumptions. Under controlled reference changes, where the source-task association is known, MGPA brings source to near chance with task performance unchanged, whereas erasing what predicts source (LEACE) lowers frozen-task AUROC from .753 to .656 while barely touching source; ablations attribute the attenuation to the gate's directions and 2.7x less movement to the conditional target. Across recordings from different devices and electrodes, iterative correction lowers source accessibility while preserving or improving task performance. Finally, one iterative map selected on one task and reused unchanged on existing heads for two others raises their worst-association AUROC (lowest over device-label shifts) by .057 and .019 over LEACE, at a cost to those heads while the training association holds. A reusable correction shows its value in how an existing predictor behaves once acquisition cues stop being reliable, not only in what a probe can read.

Gradient-based data selection methods such as LESS score each candidate by the alignment between its gradient and a target validation gradient, and recomputing per-example gradient features at every new checkpoint dominates their cost. Across three selection seeds, two model families, two candidate pools, and two target tasks, features cached at a post-warmup checkpoint and paired with fresh validation gradients preserve the ranking 40 optimizer steps later with Spearman correlation from 0.952 to 0.991, while the top-10% subset they induce misses 10 to 22% of the examples that full recomputation selects. We therefore propose Cached Diverse Influence Selection (CDIS), which recomputes gradient features for the top-ranked fraction $p$ of candidates under the stale scores, fits an affine calibration on the recomputed examples, and selects the final subset under source and length quotas. A refresh fraction at or above the selection fraction recovers the exact top-$k$ subset whenever the calibrated stale scores have bounded error, and the budget curves follow this rule: at $p=0.3$ the recovered top-$k$ subset coincides with full recomputation in every setting, allocating the same budget per stratum recovers the stratified subset at 0.92 to 1.00, and gradient-stage wall-clock drops 3.5 to 3.6 times. Iterating the cache over four checkpoints keeps top-$k$ overlap at 0.98 or higher at 1.9 gradient features per example against 4 for full recomputation, and stale-to-recomputed agreement on the refreshed examples provides a free check for unsafe reuse. Downstream, unconstrained top-$k$ selection collapses to a single data source and scores 13 points below random selection on GSM8K. CDIS scores 12 points above random selection with paired confidence intervals that exclude zero and trails full recomputation by 4.3 points, one training-run standard deviation, at 3.4 times lower selection cost.

A clear link is established between conventional numerical methods and neural network approximations for solving one-dimensional scalar conservation laws. The focus is on the construction of an appropriate flux term in the case of convex flux functions for improving the classical schemes. The first neural network developed here is able to rediscover Godunov's method, while the second one emulates the behavior of a second-order slope-limiter function. In this way, by merging them, second-order reconstruction-based schemes can be developed. The networks presented here employ a minimal number of parameters, significantly reducing the complexity compared to previous approaches. These networks can also be linked consecutively to get a deep one corresponding to multiple time steps. Training them with an appropriate loss leads to stable schemes, improving even the classical methods without increasing their complexity.

State-of-the-art pathology foundation models, trained on millions of histology tiles, can fail to preserve tissue similarity when comparisons cross slide or institution boundaries. We show that general-purpose multimodal LLMs, without being trained as pathology foundation models, consistently outperform these specialized models in cross-domain histological similarity judgments. Using a relative similarity framework that we release as the MOSAIC (Model Similarity Assessment across Institutions and Cohorts) benchmark, we evaluate 17 models across 6 datasets and find that pathology encoders often rank same-institution, different-disease tiles as more similar than same-disease, different-institution tiles, a clinically dangerous failure mode invisible to standard within-domain evaluations. LLMs appear less susceptible to this failure, likely because they perform semantic visual comparison of morphology and tissue architecture rather than relying on shortcut features tied to acquisition context. Scaling training data does not resolve the problem for pathology encoders, implicating the learning objective rather than data coverage. Our results expose a fundamental robustness gap in current pathology foundation models and establish multimodal LLMs as a viable alternative for cross-institutional retrieval, dataset harmonization, and multi-site quality control. Code and data will be released upon acceptance.

The first sentence of this abstract–and the introduction to these proceedings–was authored by a human, but the bulk of this document was generated by an agentic AI system. In this talk, I take stock of machine learning (ML) for the LHC physics program over the twelve months from May 2025 to May 2026. The corpus is the HEPML Living Review, split at May 2025 into 1,756 earlier papers and 569 later ones. An AI pipeline surveyed the 569 abstracts, ranked them by citations, recency, theme, and collaboration involvement, and read 103 papers in full (95 from after the split, plus 8 earlier baseline papers), producing a structured note for each. The notes were then synthesized into six claims about the state of the field, checked by independent reviewer agents, and re-verified against the source papers. The headline claim is that (1) ML for high-energy physics (HEPML) stopped being a research area that builds tools and became infrastructure that the LHC physics program depends on: ATLAS and CMS now publish physics results that depend on neural networks, and the archived ALEPH data have re-entered production. The other five claims are: (2) simulation-based inference and foundation models are two revolutions starting to merge; (3) AI agents are the genuinely new front, with 47 papers in twelve months and no adopted measurement yet; (4) "do we trust it?" is the fastest-growing agenda, with one recent paper in five about uncertainty, calibration, or interpretability; (5) what is slowing down is informative, since equivariance was absorbed into a tool and model-specific phenomenology ceded ground to model-agnostic searches; and (6) theory ML crossed a capability threshold in multiple research areas. I close with what is settled, what is incoming, and what is open, and briefly discuss the concerns raised by this way of working with AI.

Self-play proposer–solver methods improve reasoning by generating tasks and learning from verified solutions. However, for evidence-identifiable tasks, where case-specific evidence and domain knowledge determine a checkable answer, self-play requires generating plausible cases whose answers can be independently verified. We introduce counterfactual self-evolution, which generates counterfactual context for reconsidering the original case. A trainable Proposer constructs targeted evidence edits and describes potential outcome changes with causal explanations. We handcraft an expert-verified counterfactual instruction-tuning dataset to teach the Proposer to generate high-quality counterfactuals across a broad range of action–outcome scenarios. Each counterfactual instruction-tuning example specifies an edit within a defined category and explains its hypothesized causal effect on the decision, teaching the Proposer to reason systematically about what changes and why. We instruction-tune the Proposer on these examples, then formulate a fine-tuning reward that integrates feedback from the Solver and Verifier. Across diverse counterfactual scenarios, this reward favors high-quality counterfactuals and warranted revisions, while penalizing changes that overturn correct decisions. The counterfactual context aims to correct errors and strengthen confidence in correct decisions. Accepted counterfactuals accumulate in memory that supplies in-context evidence to the frozen Solver; the Solver adapts through evolving context rather than weight updates. We apply the framework to clinical reasoning, fact verification, and business reasoning. Our evaluation tracks performance over successive rounds as counterfactual memory grows, including transfer to harder cases. Our method achieves superior results across diverse frontier models.

Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate alone, and DNS relabeling is performed offline once per selected state. Experiments on $128^3$ turbulence show that OAS increases the median time to failure from 21 to 721 steps. The compared baselines achieve medians of at most 110 steps, and the advantage holds across training seeds. OAS also achieves the lowest pointwise error at step 15 and the best long-horizon statistics among the compared methods. OAS integrates physical models into neural simulation by extending supervision from fixed reference trajectories to states where the surrogate is likely to fail. This principle can guide the development of more reliable scientific surrogates when deployment takes models beyond the coverage of their training data.

Muon replaces the momentum buffer of each weight matrix by its orthogonal polar factor. We ask what this orthogonalization does near an optimum, where minibatch noise dominates the gradient. Under a Gaussian noise model, the expected Muon update becomes a scaled gradient step, so a linear method with a suitably matched learning rate reproduces Muon's first-order mean response. The stochastic update is a different matter: after the response is matched, Muon retains a nonlinear residual that is uncorrelated with the input noise and contributes additional covariance. A Hermite expansion shows how momentum acts on this residual. Its higher-order components decorrelate faster than the linear component, so momentum suppresses the residual's accumulated covariance relative to the linear part, but never eliminates it. In a local quadratic surrogate that evaluates the residual on the stationary noise buffer, the residual adds stationary covariance and raises the stationary loss floor at every stable step size, while leaving the contraction dynamics unchanged. Simulations of the full nonlinear recursion on quadratics and measurements on frozen transformer gradients support each step of this picture. Together, the results make a theoretical case for replacing orthogonalization by response-matched momentum SGD once optimization becomes noise-dominated.

Predicting spatial gene expression from routine H&E histology offers a scalable route toward spatial molecular profiling. Recent work has pursued increasingly sophisticated architectures to capture spatial context and richer expression structure. At the same time, simple estimators have shown strong performance in several studies, but what they already solve and where additional complexity is needed remain unclear. We study this behavior through the structure of prediction error under the mean-squared error (MSE) objective. Differences in average expression across genes can account for a substantial part of aggregate prediction performance, while a key unresolved error lies in recovering variation within each slide. Decomposing MSE into slide-level and within-slide components, we find that the within-slide component has lower residual-normalized parameter sensitivity in controlled neural experiments. This motivates Component-Guided Loss (CGL), which increases supervision of the within-slide component. CGL-Linear is a closed-form affine instantiation that achieves overall state-of-the-art performance across HEST-1k cohorts and gene-panel sizes. The same within-slide supervision improves existing neural models. These results suggest that substantial gains can come from aligning the training objective with prediction-error structure rather than increasing model complexity.

Deep Differentiable Logic Gate Networks (LGNs) and Lookup Table Networks (LUTNs) offer a promising approach for very low power inference due to their use of simple binary logic operations instead of arithmetic. In this work, we generalize the logic gates of LGNs to more than two input pins, naturally arriving at networks consisting of $N$-input LUTs. To obtain a differentiable expression for training the $N$-LUT entries, we adopt the Boolean equation of a $2^N$:1 multiplexer (MUX) and optimize its input parameters during training. We investigate the applicability of LGNs and LUTNs to inter-patient ECG arrhythmia classification using the MIT-BIH data set. The proposed models achieve up to 94.41% accuracy and a $j\kappa$ index of 0.683 on a four-class task, showing a competitive performance compared to existing CNN-, SVM- and SNN-based methods. Our LGNs and LUTNs only require an estimated 2.89k to 6.17k FLOPs, including preprocessing and readout, which is three to six orders of magnitude less than state-of-the-art methods. We verified our design, which consists of the preprocessing pipeline and a 6-LUTN classifier, by implementing it on a Xilinx Zynq-7000 ZedBoard. The complete system consumes a dynamic energy of 8.25 $\mu$J/inference, of which only 0.46 nJ is utilized by the LUTN classifier. These results show that both LGNs and LUTNs can be employed as lightweight hardware-based classifiers for inter-patient ECG arrhythmia classification.