Papers

Hierarchical Implicit Q-Learning (HIQL), an offline goal-conditioned RL method, selects subgoals by value-function advantages alone. This rule has two coupled failure modes. Optimistic bias treats lucky stochastic outcomes as skillful choices, and mode collapse reduces a multi-modal subgoal distribution to a single Gaussian mean that often falls in unreachable regions. We propose NFTR (Normalizing Flow subgoal policies with Triangle-slack Reweighting). A conditional Normalizing Flow replaces the Gaussian policy. A closed-form mode-averaging result identifies the Gaussian limitation, while conditional flows support multi-modal weighted maximum likelihood and direct sampling. A triangle slack score, computed from a jointly trained MRN distance head whose triangle inequality is guaranteed architecturally, corrects the AWR weight multiplicatively and measures a detour inside the learned geometry without requiring exact distance recovery. Triangle-slack vanishes on geodesics in deterministic MDPs and remains a conservative upper bound on composability violation under stochastic dynamics. The RWDR objective preserves AWR's population-level monotonic improvement and admits a three-term suboptimality decomposition. On OGBench the flow carries the larger share of the gain, while the full co-trained configuration adds task-dependent gains. The combined method avoids Gaussian mode averaging and performs well on stochastic tasks. GitHub page: https://github.com/erdemtbao/NFTR

Automated segmentation of cervical-spine MRI is increasingly used in clinical workflows, yet no fairness audit exists for this anatomy. We show that auditing these segmentation tasks is complicated by a common property of modern segmentation datasets: expert-annotated gold labels are expensive, so abundant machine-generated (silver) labels are added to limit annotation cost. This matters because the reference used to judge a model can itself be biased. In this study, we present the first fairness audit of cervical-spine MRI segmentation across sex, age, and race using the CSpineSeg dataset. We observe that the deployed model is demographically fair, but the choice of reference label, however, is not neutral. Because a dataset's silver labels are generated by a model trained on its gold labels, any new model trained on those same gold labels agrees more with the silver labels than with expert truth: scoring identical predictions against silver rather than gold overestimates performance by ~8 Dice points and turns the fairness verdict for age from non-significant to significant - not by the gap inflation Parikh et al. report (which we term false magnitude) but by collapsing within-group variance (which we term false confidence). Reference-label provenance is thus a first-order confounder in segmentation evaluation: performance and fairness should be reported against expert labels, and any fairness claim stated together with the provenance of its reference.

As large language models (LLMs) become increasingly capable, the next question is how can we enable models to continually learn? Today, the field largely frames this as a problem of context management and mitigating forgetting. We argue this framing is incomplete: continual learning is fundamentally about increasing model competence as the world changes. We disentangle this change along two axes – space, where the model encounters new domains, and time, where the underlying data drifts under a fixed task. This framing lets us study continual learning under realistic conditions: new domains arrive over time, facts drift past their training cutoff, and agentic interactions accumulate state across episodes. To evaluate methods under this setting, we recast widely used LLM benchmarks as sequential problems and introduce a single mechanism-agnostic protocol that compares prompt-based methods (GEPA, ACE), supervised learning (SFT, SDFT), reinforcement learning (GRPO, SDPO), and context compression (Cartridges, In-place TTT). Prompt-based methods fit each new stage quickly but degrade on future tasks. Distillation-based methods accumulate knowledge stably but struggle to update outdated facts. Context compression improves efficiency without substantially improving the ability to learn new tasks. Online reinforcement learning adapts most effectively to knowledge updates but remains sensitive to noisy reward signals. Overall, our results suggest that continual learning is not a single capability: different patterns of environmental change require fundamentally different update behaviors, determining when adaptation must be learned inside model weights and when it can be achieved through external scaffolding. We hope that understanding where each method succeeds and fails will guide the design of stronger continual learning systems.

The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive. We argue that the bulk consists of the weakly lifted pseudo-Goldstone modes of the continuous symmetries of the network parametrization. In deep linear networks these symmetries are exact: they generate flat directions and hence exact zero modes, whose eigenvectors we construct explicitly. Introducing a ReLU nonlinearity as a perturbation, we show that it breaks these symmetries weakly and explicitly. Resolving the spectrum at the level of eigenvectors, we find that the high-curvature directions are orthogonal to the symmetry subspace, while the bulk lies almost entirely within it. We demonstrate the mechanism in a two-layer ReLU student–teacher model and in a network trained on CIFAR-10. A convolutional example demonstrates that the same diagnostic extends beyond fully connected layers. Together, these results link the Hessian bulk to weakly broken symmetries and clarify the origin of near-zero modes.

While closed-loop motion planners trained on large-scale, object-level datasets, e.g., nuPlan, demonstrate strong in-distribution (ID) performance, their generalization to novel urban topologies and recovery mechanisms following execution perturbations remain under-explored. To address this, we present Shift & Drift, a novel dual-track benchmark designed to rigorously stress-test motion planners across two critical axes of distribution shift: (1) The Semantic Shift Track leverages a novel conversion pipeline that transforms the aerial, DeepScenario Open 3D dataset into the nuPlan simulation framework. This enables zero-shot evaluation of planners trained on North American and Singaporean data against 1,182 scenarios spanning four German cities and the US city of San Francisco featuring dense pedestrian-cyclist interactions. (2) The State-Distribution Drift Track injects stochastic perturbations into the ego vehicle's dynamics to quantify robustness against compounding execution errors. Based on this, we systematically evaluate the failure modes of diverse planning paradigms under semantic and state-distribution shifts. While imitation learning methods achieve high scores in ID benchmarks, they exhibit significant failures under semantic shift, particularly in pedestrian-dense environments, and suffer from persistent drift when subjected to temporally correlated actuation noise. In contrast, the evaluated reinforcement-learning-based planner demonstrates more graceful degradation, maintaining higher safety and progress metrics across both tracks. Our findings reveal an empirical trade-off between imitation fidelity and closed-loop resilience, providing the community with a rigorous benchmark to evaluate progress toward reliable deployment.

Gradient estimation – the task of computing the gradient of the expected value of a probabilistic program – has diverse applications in scientific computing, but is notoriously difficult because of issues such as high-dimensional integration, discrete random choices, and complex stochastic dependencies. This article introduces gradient inference, a new approach to developing sound and efficient gradient estimators for probabilistic programs. Gradient inference rests on a formal reduction from a gradient estimation problem to a closely related probabilistic inference problem, whose solution can be differentiated to obtain a gradient estimator. This inference problem is obtained by applying two powerful statistical operations – coupling and factorization – to the input probabilistic program. Our reduction lets us leverage the rich toolkit of probabilistic inference algorithms to design novel gradient estimators that extend and improve upon existing methods. We introduce GradInf, a probabilistic programming system that facilitates the sound and automated implementation of gradient inference. GradInf is centered around programmable source-to-source transformations for coupling and factorizing higher-order probabilistic programs, whose soundness is proven in terms of a denotational semantics. Key to our development is the use of information-flow typing to allow random choices in a probabilistic program to be factored out and partially evaluated, which improves our ability to deploy sophisticated probabilistic inference algorithms. The resulting system offers practitioners a principled framework for designing gradient estimators. We apply GradInf to several challenging case studies, showing that it can express prominent gradient estimators from the literature and enables the construction of new state-of-the-art estimators that outperform the best existing baselines.

Pseudo-nitzschia diatoms pose recurrent risks to coastal ecosystems and shellfish harvesting along the Portuguese Atlantic coast. Here we develop and evaluate a spatio-temporal machine-learning framework to predict harmful algal bloom (HAB) occurrence using exclusively satellite-derived predictors under realistic forecasting constraints. We characterised environmental and biological variability across shellfish production zones (L1-L9) using 5,882 observations, providing system-wide context. Predictive models were developed for zones L1-L2, a hotspot for Pseudo-nitzschia and domoic acid events, using a decade-long dataset (2013-2023; 1,440 observations; more than 1,000 satellite-based predictors including sea surface temperature, an upwelling index, chlorophyll-a, and plankton functional types). Sampling locations were partitioned into ecologically meaningful sub-regions using a river-aware spatial clustering scheme. A stringent spatio-temporal cross-validation strategy that simultaneously withholds entire years and spatial clusters prevents leakage and closely mimics real-world forecasting conditions. HAB occurrence proved moderately predictable across model classes and feature configurations. Ensemble tree-based methods achieved the strongest discrimination: Random Forest reached 0.74 +/- 0.05 with environmental predictors; Extra Trees reached 0.77 +/- 0.06 with biological variables added. Feature-importance analyses revealed that seasonal structure, spatial context, and lagged environmental conditions dominate model decisions, while biological indicators refine bloom likelihood within physically favourable periods. The framework demonstrates operationally relevant skill for satellite-supported HAB early-warning systems along eastern boundary upwelling coasts.

Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with $m$ neurons that fits $n$ noisy labels must have Lipschitz constant at least of order $\sqrt{n/m}$, with no restriction on the size of the weights. Bubeck and Sellke proved a universal version of this law for Lipschitz-parameterized classes, but under a polynomial bound on the parameters; at depth three that boundedness hypothesis is genuinely necessary. The two-layer unbounded-weight case requires a different argument. We prove the conjectured law, up to one logarithmic factor, for every continuous piecewise-linear activation, in particular for ReLU networks. For data drawn uniformly from $\mathbb{S}^{d-1}$, $d\ge3$, or from $N(0,I_d/d)$, labels in $[-1,1]$ with noise level $\sigma^2>0$, and any width-$m$ two-layer network with arbitrary real weights, biases and affine skip connection, fitting the data $\varepsilon$ below the noise floor forces $\mathrm{Lip}(f)\ge c\,\varepsilon\sqrt{n/(\bar m\log(C\bar m nd/\varepsilon))}$, $\bar m=(K-1)m+1$, with high probability. A realized-kink-count version holds on the same event: every realized two-layer piecewise-linear function with $k(f)\le n$ distinct kink hyperplanes obeys the bound with $\bar m$ replaced by $k(f)+1$, irrespective of how many redundant hidden units parameterize it. The proof replaces parameter-space covering, impossible for unbounded weights, by a function-space covering. The central deterministic ingredient is a rigidity lemma: on $B_2$, and on $\mathbb{S}^{d-1}$ for $d\ge3$, the coefficient of each canonical kink is controlled by the Lipschitz constant of the realized function, because kinks on distinct hyperplanes cannot cancel at generic points. Rigidity genuinely fails at $d=2$, and an explicit two-layer ReLU interpolant with $O(1)$ Lipschitz constant at width $2n$ matches the law at the overparameterized endpoint.

EEG-based emotion recognition is critical for mental health monitoring and affective brain-computer interfaces, yet existing deep learning approaches often treat emotion classes as isolated labels, ignoring their psychological interdependencies. We propose a graph-regularized learning framework that conceptualizes emotions as nodes in a graph where edges encode proximity based on dimensional emotion theories. We adapt three complementary regularization strategies–Graph Label Smoothing (intuitive soft labeling), Commuting distance on graph via Graph Laplacian (spectral graph theory), and Sliced Wasserstein Distance (optimal transport on graph)–ordered by increasing computational complexity. These strategies penalize model predictions that deviate from the established emotion topology. Our framework is evaluated across three representative backbone architectures: AudioTransformer (pure transformer), Conformer (CNN-transformer hybrid), and DCGNN (causal graph neural network), demonstrating architecture-agnostic benefits. Experiments on SEED-IV (4 classes) and SEED-V (5 classes) datasets show consistent improvements: best case up to +5.42% accuracy and 39% reduction in psychologically implausible misclassifications. Ultimately, our framework help raise the upper bound of performance achievable with standard approaches. Code will be released.

Starting from the utilization of deep neural networks to approximate the state-action value function that led to winning one of the most challenging games, to algorithmic advancements that allowed solving problems without even explicitly stating the rules of the challenge at hand, reinforcement learning research has been the center of remarkable scientific progress for the past decade. In this paper, we focus on the key ingredients of this research progress and we analyze the canonical evaluation and design paradigms in reinforcement learning. We introduce the theoretical foundations of scaling laws in reinforcement learning and show that the asymptotic performance of reinforcement learning algorithms does not have a monotone relationship between performance rankings and data-regimes. We conduct large-scale experiments and our results demonstrate that a line of reinforcement learning research under the canonical design and evaluation paradigms resulted in incorrect conclusions. Our analysis and results provide a core analysis on scaling, capacity and complexity of deep reinforcement learning.

Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the joint data distribution. We recast imputation under missing completely at random (MCAR) as density estimation from masked observations: estimate a distribution whose observed marginals exactly match those in the data. Leveraging positive semidefinite (PSD) kernel densities we obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method. We further introduce a non convex extension that supports adaptive hyperparameter selection through alternating minimization. The resulting PSD-Impute model yields both single and multiple imputations from the same fitted density, enjoys statistical consistency, beating the curse of dimensionality for very regular probabilities. Experiments indicate competitive distributional accuracy compared with popular imputation baselines, suggesting strong practical promise.

World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that must query the same dynamics at multiple timescales. Hamiltonian Generative Networks (HGN) offer a principled path forward, grounding predictions in a continuous-time energy function that is, in principle, independent of the observation frame rate. In practice, however, their temporal generalization breaks down in non-conservative settings. We show that in externally forced, dissipative environments, HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes, including latent magnitude growth driven by an unconstrained action-force map, and global truncation error accumulation from an under-resolved integrator. We identify a targeted fix for each mechanism and demonstrate stable dynamics prediction at temporal resolutions well outside the training distribution. In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.

Modern machine learning (ML) increasingly relies on complex models whose behavior is difficult to characterize beyond empirical performance metrics. Across a wide range of tasks, including prediction, generation, and decision-making, models with similar empirical performance can exhibit markedly different properties in terms of their transparency, interpretability, robustness, fairness, privacy, and certifiability. This survey highlights how optimization- and certification-oriented reasoning can provide a useful framework for reasoning about such differences, supporting tasks ranging from model training and selection to auditing and certification. We review and synthesize recent advances at the intersection of combinatorial optimization (CO) and trustworthy ML, covering both training and post-training tasks, including interpretable model learning, explanation generation, robustness analysis, fairness auditing, model compression, and privacy attacks and protections. Across these domains, CO formulations offer additional capabilities over purely heuristic approaches, e.g., gradient-based ones, notably global guarantees, formal certificates, and explicit treatment of trade-offs. While scalability remains an important challenge, continued progress in solvers and hybrid algorithms suggests a growing role for CO in the design and deployment of trustworthy ML systems.

Foundation models (FMs) have transformed machine learning from isolated task-specific model development toward general-purpose models pretrained on broad data and adapted to multiple downstream tasks. Earth observation (EO) is an important domain for this paradigm because satellite and airborne archives are large, high-revisit, and increasingly multimodal, while reliable field labels are often sparse. Remote sensing foundation models (RSFMs) cannot be transferred reliably/optimally without domain-specific adaptation. This is because EO data are governed by measurement physics and operational decision constraints. This chapter reviews the design principles arising from these domain-specific constraints. It first defines the FMs paradigm in remote sensing (RS), then synthesizes the current model landscape, pretraining objectives, architecture designs, downstream adaptation and trustworthiness requirements. The chapter also incorporates recent benchmark evidence showing that no single geospatial foundation model is universally best and that inconsistent evaluation remains a major issue to fair comparison and reliable deployment. In addition, two brief environmental monitoring case studies; physics-informed spectral targeted masking for harmful algal bloom prediction and reinforcement learning for adaptive environmental monitoring station selection to illustrate the FMs domain-guided principles in practice. This chapter posits that next-generation RSFMs should be evaluated not only by benchmark accuracy, but also by modality-aware transfer and physically plausible representations for trustworthy EO decisions.

Multimodal learning usually requires a dedicated encoder per modality. When a tabular modality is involved, prior work has been mostly using a plain MLP as the encoder. Yet if it were a strong encoder, the tabular domain would not be “the last unconquered castle for deep learning”. This study evaluates state-of-the-art tabular models as encoders in the image-tabular setting for the first time. An obstacle stands out. In-Context Learning models, among the best performing methods in the tabular domain, require labels to process instances, making it non-trivial to embed training and test instances the same way. We addressed this problem across multiple models of this family. With this study, we would like to highlight the importance of encoder factor in the multimodal learning.

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

Modelling psychological disorders in artificial agents offers a testbed for computational psychiatry and a lens on affective-control failure modes. Prior work induces one or two disorders by hand-tuned reward shaping, labels the behaviour post hoc, and reports single runs. We recast disorder modelling as dose-controllable manipulation of cognitive appraisal signals in an appraisal-guided PPO agent, expressing seven disorders (anxiety, mania, obsessive-compulsive checking, depression, impulsivity, addiction, and post-traumatic stress) each as a single knob grounded in a computational psychiatry account, with each symptom measured by a preregistered assay. Across more than a thousand runs (10 seeds, four controls, 95% confidence intervals) every disorder shows a graded, monotone dose-response that no control reproduces. Beyond these induced effects, three findings emerge that were not written into the reward: disorders self-organise into a two-dimensional affective space in which mania mirrors anxiety; removing a knob remits reward-distortion disorders (mania, checking, addiction) but not avoidance disorders (anxiety, PTSD), which recover under a graded exposure curriculum; and two simultaneous knobs interact nonadditively, yielding testable comorbidity predictions. The depression and addiction knobs further reproduce their double dissociation in a 3D pixel environment (MiniWorld) with a standard convolutional agent and no appraisal critic, showing the framework generalises beyond grid worlds.

Large Language Models achieve strong code generation for high resource languages like Python and Java but suffer sharp performance drops on Low-Resource Programming Languages~(LRPLs) such as Julia. Improving Small Language Models~(SLMs) for these languages faces a trilemma: Supervised Fine-Tuning~(SFT) is bottlenecked by data scarcity, inference-time scaling is too expensive for deployment, and Reinforcement Learning from scratch yields near zero advantages. We propose a three-phase pipeline that resolves this trilemma by decoupling syntax acquisition from algorithmic reasoning. First, we left-shift inference-time compute to an offline data synthesis engine that uses iterative compiler and test feedback to generate verified training examples. Second, we fine-tune an SLM on this synthetic, verified data to embed strong syntactic priors. Third, we apply Reinforcement Learning with Verifiable Reward~(RLVR) grounded by language-agnostic Input/Output tests, where the SFT prior constrains exploration away from syntax errors. Applied to Qwen3-8B, our pipeline improves pass@1 by up to +7.6 points on MultiPL-E and +14.2 points on the Agnostics LiveCodeBench for Julia compared to SOTA results. Furthermore, the pipeline only used $\frac{1}{3}$ data and $\frac{1}{6}$ cost over the previous state-of-the-art. We further demonstrate that the pipeline generalizes to Ballerina achieving 49.7% MultiPL-E Pass@1, a language with near-zero pretraining representation. Ablations confirm that both the SFT phase and execution-grounded rewards are necessary for stable training.

While accuracy, robustness, and calibration are all essential for reliable neural networks, they are often studied separately; developing models that satisfy all three simultaneously remains a central challenge. Lipschitz-constrained models guarantee robustness by design, yet the manual selection of the Lipschitz constraint L governs the resulting accuracy-robustness trade-off, and their calibration properties remain largely underexplored. In this work, we highlight a theoretical and empirical link between the enforced Lipschitz constraint and Temperature Scaling, a state-of-the-art calibration method. Specifically, we find that for a given training scheme, there exists a non-trivial value L* that yields an out-of-the-box calibrated network, and that calibration acts as a principled criterion to select a well-defined operating point on the accuracy-robustness Pareto front. Leveraging these insights, we introduce Lipschitz Scaling Training (LiST), a novel training paradigm that iteratively adjusts the global Lipschitz constant to reach this operating point. Through a margin parameter in the training loss, LiST further enables the construction of a fully calibrated Pareto front, allowing users to navigate the accuracy-robustness trade-off while remaining calibrated throughout. At convergence, LiST also enables the reintegration of calibration data into training, improving sample efficiency without sacrificing calibration. We validate LiST on CIFAR-10/100 and Tiny-ImageNet, demonstrating competitive accuracy and robustness against constrained and unconstrained baselines, while remaining calibrated out of the box. Code is available at GitHub.

Self-organization is an emergent property of life, driven by the collective behavior of individual components acting on local information. Biological neurons, through local interactions transmitted through synapses, are able to learn efficiently and can adapt their connections over an organism's lifespan. Motivated by these desirable properties of adaptability and local interaction, neural cellular automata (NCA) models have been successful at learning morphogenesis solely through local update rules, demonstrating stability over many updates and robustness to perturbations. In this work, we introduce Meta Neural Cellular Automata (MetaNCA), a framework that learns local rules which self-organize the weights of artificial neural networks. A learned rule network iteratively updates the weights of a task network using only local interactions on the computation graph. We propose a novel Weight Transformer architecture for the local rule network, which uses linear attention to aggregate signals from neighboring weights and hidden states. Once trained, the rule network generates task networks of diverse architectures without backpropagation. We show that MetaNCA generates weights for feedforward MLPs, CNNs, and ResNets on MNIST and CIFAR-100, scaling to networks of 2 million parameters. We further show that MetaNCA generalizes to architectures not seen during meta-training, and that architectural diversity in the training phase strengthens this generalization.

Modern LLMs are increasingly deployed in long-context applications such as retrieval-augmented generation, repository-level coding, and agentic workflows whose accumulated reasoning and tool traces routinely push the input an order of magnitude past the pretraining window, making zero-shot context extension the dominant deployment path for open-weight checkpoints. The dominant zero-shot methods (YaRN, Self-Extend, DCA) fix a single rescaling factor up front, so an aggressive factor sacrifices short-context fidelity while a conservative one breaks down at long contexts; recent length-aware variants adapt the mapping, but with a fitted or distance-dependent schedule. We propose Jet-Long, a tuning-free zero-shot method that pairs a local RoPE-faithful window with a long-range window whose rescaling factor adapts dynamically to the current sequence length via a parameter-free analytic schedule, recovering the base model exactly at short inputs while extrapolating cleanly at long ones. An inclusion-exclusion attention merge and on-the-fly RoPE correction enable a fused CuTe implementation. On H100 at 64K-128K, prefill retains 83-88% of FlashAttention-3 throughput across the evaluated Qwen3 sizes and 88-93% of a matched CuTe control; Qwen3-8B single-batch generation reaches 1.04-1.08 times FlashAttention-3 throughput. On Qwen3-1.7B/4B/8B up to 128K context, Jet-Long leads RULER by +4.79/+2.18/+2.03 percentage points over the strongest baseline at 1.7B/4B/8B, achieves the best overall accuracy on HELMET-RAG (a benchmark identified by HELMET as the most efficient predictor of downstream long-context performance) and attains the lowest PG-19 perplexity. Additional evaluations cover Meta-Llama-3-8B, post-trained Qwen3 checkpoints, and the hybrid Jet-Nemotron architecture, supporting broader applicability without retraining. The local-window hyperparameter remains robust across the tested settings.

Structure-property relationships are foundational to biology, chemistry and materials science, where function, reactivity and physical response emerge from spatial, chemical and periodic organization. Mechanistically explaining these relationships requires interpreting structural evidence through scientific principles and physical constraints, from stereochemistry and bonding to symmetry, energetics and periodic order. However, applying artificial intelligence to this process presents a joint challenge of representation and reasoning: models must preserve domain-native structural information while showing how specific evidence supports predictions under these constraints. Here we introduce SciReasoner, a multimodal scientific foundation model for native structural reasoning across proteins, small molecules and inorganic crystals. SciReasoner discretizes coordinates, topologies and periodic connectivities into a unified structure-aware vocabulary, treating structural tokens as addressable evidence units during reasoning. In homology-controlled Gene Ontology prediction, SciReasoner improves Cellular Component annotation for low-homology and orphan-like proteins, increasing $F_{\max}$ from 0.42 to 0.55. In chemistry, it raises single-step retrosynthesis accuracy from 0.63 to 0.72 while generating fragment-level disconnection and precursor-verification traces. In materials science, its representations separate elemental and compound phases and resolve high- and low-band-gap regimes. Across 86 benchmarks, SciReasoner achieves state-of-the-art performance on 67 tasks. Double-blind expert evaluation rates its reasoning traces as preferred or at least comparable to those of a frontier large language model in 98% of cases. By making structure an inspectable substrate for reasoning under scientific constraints, SciReasoner connects accurate prediction with interpretable scientific inference.

Externalizing knowledge in LLM pre-training is a promising avenue to achieve higher performance at smaller scales, control knowledge use, and overall increase model transparency. We propose continuous-query limited memory language models (Co-LMLM), an LLM that interleaves flexible vector retrieval queries with next-token predictions, and is pre-trained to copy knowledge returned from the KB, rather than memorize it. Co-LMLM is pre-trained with a scalable approach that jointly trains a knowledge-externalizing LLM, induces its knowledge base, and learns an expressive continuous retrieval mechanism. Across pre-training at multiple model scales, Co-LMLM outperforms prior knowledge-externalizing and vanilla LLMs in both perplexity and factual precision. At 360M scale, this includes lower perplexity than models pre-trained on 40$\times$ more data, and SimpleQA-verified performance that is in line with gpt-4o-mini and higher than Claude Sonnet 4.5.

The quadratic cost of causal self-attention severely bottlenecks long-context transformer inference. While numerous post hoc linearization pipelines exist, it is difficult to identify which components preserve model quality. This work isolates the effect of state update design in a strict frozen-backbone regime. We show that softmax relies on key-dependent, rank-1 orthogonal projections, elucidating why delta-style networks outperform purely gated accumulation. We identify a potential source of approximation errors and introduce structural interventions, specifically sink tokens, short convolutions, and fixed-budget cache routing, which reduces the remaining gap. We scale this linearization approach across LLaMA and Qwen models up to 32B parameters, outperforming prior post hoc baselines on MMLU and matching the long-context retrieval of complex adaptive-caching frameworks.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful paradigm for aligning generative models with human preferences. However, applying RLHF to diffusion models remains highly feedback inefficient, as existing approaches typically require large amounts of human or reward model evaluations. This limitation reduces the practicality of diffusion RLHF in realworld settings where feedback is the primary bottleneck. In this paper, we propose two complementary strategies that substantially improve the feedback efficiency of diffusion RLHF while preserving generalization to unseen prompts. Our key observation is that reward information in diffusion trajectories is unevenly distributed: not all denoising timesteps or trajectories contribute equally to learning from a reward signal. By emphasizing informative timesteps and trajectories during optimization, we obtain more effective gradient updates. First, we introduce a per-timestep weighting scheme that reweights denoising steps during policy optimization. We theoretically connect this weighting to the optimal convergence properties of proximal policy optimization (PPO) and approximate the resulting weighting trend empirically. Second, we introduce a replay mechanism that prioritizes informative trajectories, enabling the model to reuse past samples instead of repeatedly querying new rewards. Together, these strategies significantly improve the feedback efficiency of diffusion RLHF. Under identical hyperparameter settings, our approach achieves up to a 6$\times$ improvement in sample efficiency compared to widely used diffusion RLHF baselines.

Reinforcement learning from verifiable rewards (e.g. GRPO) is the engine behind today's reasoning models, yet it grades only the final answer. On hard problems this trains models to write more rather than to think better, since the trace itself is never graded and no label for good thinking exists. We introduce Agon, which makes two competing models each other's graders. Both attempt the same problem; in alternating roles, one drafts a solution and the other reads it while solving, and each is rewarded for out-solving the other. To win, a model must out-reason a rival that has seen its work, so reasoning is judged implicitly during training, with no process labels and no reward model. Because both models are optimized, each faces a progressively stronger rival, which single-model RL cannot provide. The two need only be comparably strong and behaviorally different. At inference the pair deploys as it trains, a two-stage cascade in which one model drafts and the other answers after reading the draft. On the hard split of DeepMath with Qwen3, this doubles GRPO's pass@1, roughly eight times the gain of an untrained Mixture-of-Agents pass over the same base. The ordering replicates on competitive-programming code and across model families (Qwen3.5, Gemma 4). For now the models talk in text; the next step is to let them reason together in latent space.

Electrocardiography (ECG) is one of the most widely used tests for diagnosing cardiovascular disease. Yet several remote clinics still utilize paper ECG printouts for their analysis due to limited connectivity and computational capacity. As a result, vast numbers of physical ECGs obtained in remote areas still remain incapable of being accessed by contemporary artificial-intelligence (AI)-based decision support as they require high computational resources or strong high-speed internet connectivity. This causes several cases where conditions like acute coronary occlusion (ACS) is overlooked and reperfusion therapy delayed. Although prior work has tackled digitization and diagnosis separately, and utilized advanced AI models for them, there still remains a lack of a compute-light, on-device framework that reconstructs paper ECGs at high fidelity, while accurately supporting multiple clinically relevant endpoints. We address this need with an end-to-end lightweight on-device digitization-to-diagnosis pipeline that converts a smartphone photo or scan of a paper ECG into a calibrated 12-lead signal and screens for Myocardial Infarction (MI) pathologies, with SHapley Additive exPlanations (SHAP) to support interpretability. Trained and evaluated on 21,799 ECGs from the PTB-XL dataset and further validated on hospital-acquired ECG-Matrix dataset, the complete system runs in <30 s per ECG on CPU-only resources, achieving 95.51% accuracy (F1 = 0.9519) for MI detection on PTB-XL and 88.89% accuracy (F1 = 0.8862) for OMI detection on ECG-Matrix. This work showcases that legacy paper records can be reliably democratized in any part of the world, providing a scalable decision support when digital ECG export, connectivity, or high-end compute are unavailable. Github: https://github.com/nshreyasvi/ECGLight

The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.

Many machine learning models are defined for inputs of different sizes, such as point clouds containing different numbers of points, sequences of tokens of different lengths, and graphs on different numbers of nodes. Such models are trained on finitely many examples of necessarily limited sizes. How well do these models generalize from inputs of small size to larger inputs of size not seen during training? Furthermore, evaluating such models on large inputs is often expensive. How can we sketch large inputs to obtain smaller ones on which the model takes similar values? At the heart of both questions is the need to compare inputs of different sizes and to approximate large inputs by small ones. We present a unified approach to address these questions by using random sampling maps to compare inputs of different sizes. The sampling maps we consider are generalizations of sampling with replacement, random binning, and species sampling. We characterize the application domains in which each type of sampling is appropriate in terms of the symmetries and relations between problem instances of different sizes in the domain. Our framework yields explicit generalization and sketching rates for function classes continuous with respect to a chosen notion of sampling, encompassing large families of functions defined on sequences, graphs, and tensors of different sizes. Specific examples include moment polynomials on measures, homomorphism densities and numbers of graphs, permutation-invariant transformers, and graph neural networks.

Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width $W$, the optimal frequency scales as $1/W$. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.