Papers

Neural fields are usually evaluated by how well they reconstruct an observation. We show that this misses two useful properties of a fitted network: how easily it can adapt to new observations, and what its weights retain from earlier ones. We study these properties as adaptation geometry. For images, we meta-learn class-specific initializations, adapt each one to a new image, and measure how much the network must change to fit it. A simple local linear model closely predicts this adaptation cost, while replacing one network's tangent kernel with another's substantially worsens the prediction. Adaptation thus depends on the local geometry of the fitted network, not only on its current reconstruction. For physical fields, we repeatedly fit the same network to observations from a sequence. Its weights then retain information about that history. When two wave histories end at exactly the same observation, the final weights recover the sign of the wave velocity with 68.6% accuracy, whereas the current observation alone contains no such information and gives 50%. These two phenomena are quantitatively linked: tangent-kernel eigenvalues predict both which changes are easy to learn and how quickly they are overwritten by later fitting. Together, these results show that neural fields contain useful information beyond what they currently reconstruct: in how they can change and in how they got there.

Large language models have shown strong reasoning capabilities, but their high inference costs make knowledge distillation an important approach for transferring such capabilities to compact models in resource-constrained scenarios. On-policy self-distillation further reduces the reliance on external large teacher models while improving the reasoning ability of compact language models. However, existing methods typically either distill all token positions uniformly or select tokens using fixed heuristic criteria, assigning the same distillation strength to the selected positions rather than adaptively learning which tokens are most beneficial for distillation. To address these limitations, we propose BiToK-SD (Bilevel Top-K Token Selection for Self-Distillation), a bilevel-optimization-based token selection method that learns where distillation should be applied during on-policy self-distillation. Specifically, BiToK-SD is formulated as a bilevel optimization problem, where the lower-level problem models Top-K token selection as a differentiable threshold-based relaxation, allowing the selected positions to adapt as the student policy evolves, while the upper-level problem performs knowledge distillation on the selected positions. Experiments on mathematical reasoning benchmarks show that BiToK-SD achieves the best average performance among all compared methods while requiring only lightweight additional computation.

Breast cancer is the leading cause of cancer-related mortality among women in Sub-Saharan Africa, where delayed diagnosis results from limited radiology expertise and fragmented clinical data systems. Although deep learning models have demonstrated strong performance in mammographic analysis, most rely solely on imaging data and are trained on Western populations, limiting their applicability in African healthcare settings. This paper presents a Hybrid Cross-Modal Attention Network (HCMAN) that integrates mammogram images with structured clinical data using transformer-based cross-modal attention mechanisms. The model was developed and validated using a locally collected dataset of 2,560 mammogram images from 1,024 patients across four Ethiopian referral hospitals, with biopsy-confirmed ground truth labels. The proposed framework achieves 97.8% accuracy, 97.2% sensitivity, 98.3% specificity, and an AUC of 0.987, significantly outperforming image-only baselines. The system demonstrates robustness to low-quality images typical of resource-limited settings, with only 3.2% performance degradation compared to 8.7% for image-only models. Cross-modal attention analysis reveals clinically appropriate behavior: higher reliance on clinical features for ambiguous cases such as dense breasts and young patients. The model's lightweight architecture enables deployment on standard hospital workstations (<2 seconds inference on CPU). This work advances sustainable, context-aware AI solutions for equitable breast cancer diagnostics in Africa.

Accurate short-term load forecasting (STLF) is essential for the reliable and efficient operation of modern power systems. While time series foundation models (TSFMs) have recently demonstrated remarkable performance across a wide range of forecasting tasks, their effectiveness for STLF under realistic operational conditions remains largely unexplored. In this paper, we present a comprehensive benchmark of four trained-from-scratch (TFS) models and four TSFMs across three real-world load forecasting datasets under operational scenarios that differ in the availability and quality of future covariate information. Our results show that Chronos-2 consistently achieves state-of-the-art performance in both zero-shot and fine-tuned settings when future covariates are available or accurately forecast. However, its performance degrades as covariate forecasts become increasingly noisy, whereas TimesNet exhibits greater robustness under severe covariate uncertainty. These findings demonstrate the effectiveness of covariate-informed TSFMs for STLF while highlighting the critical role of robust covariate modeling in real-world forecasting applications.

Motivated by sequence-to-sequence transport in the context time-series domain adaptation, we study the problem of transportation between trajectories of Markov processes. Given a limited number of trajectories from source distribution and the target distribution, we formulate a flow matching based algorithm which learns a transport map from the source to target trajectory distribution, while preserving the Markov structure. We show that this is consistent in the population limit and derive finite-sample error bounds under mixing time assumptions, following the analysis of classical statistical problems including regression (Nagaraj et al., 2020), principal component analysis (Kumar and Sarkar, 2023), and matrix concentration (Neeman et al., 2024) in the Markov setting. We complement that with a lower-bound construction showing that a mixing-time dependent sample complexity is unavoidable even with regular Gaussian conditional transitions. We evaluate on synthetic and real-world data. For image retrieval from electroencephalography (EEG) on THINGS-EEG2 (Gifford et al., 2022), the task is to identify the viewed image from EEG signals captured from human subjects, which suffers from high inter subject variability. We augment the ENIGMA decoder (Kneeland et al., 2026) with a conditional flow before its subject-specific temporal map. This improves mean top-5 retrieval accuracy from 43.87% to 49.05%, an 11.82% relative improvement.

Natural gradient descent (NGD) underlies common methods in ML. For dually flat families, idealized NGD on the forward Kullback–Leibler objective follows the mixture geodesic which is often longer than the shortest Fisher–Rao path. We quantify this overhead by the inefficiency ratio \(R \ge 1\), the Fisher length of the mixture geodesic divided by the Fisher–Rao distance, and bound its supremum over endpoint pairs as a function of the parameter dimension \(d\). A tensor criterion identifies the regime (I) families, with \(R=1\) everywhere: exactly those with quadratic potential or dimension one, such as fixed-covariance Gaussians. For non-quadratic families, we prove two further regimes: (II) bounded third-order skewness plus finite Fisher–Rao diameter yields a dimension-independent bound; and (III) for products of scale families—including Gaussian covariances and Gamma rates—\(R\) grows as \(\Theta(\sqrt{\log d})\), unbounded in \(d\). Under a per-step Fisher-chord budget, \(R\) translates to a practical computational cost: NGD requires asymptotically at least \(R\) times as many steps as an optimizer following the Fisher–Rao geodesic. Experiments confirm all three regimes: \(R=1\) to machine precision for quadratic-potential families (I), the categorical bound \(\pi/(2\sqrt{2})\) is approached but not attained (II), and sampled scale-product \(R\) grows with \(d\), reaching \(R \approx 1.5\) for long, high-dimensional moves (III).

“What are the irreducible conditions that are sufficient to produce an outcome?” is one of the most common questions that recur across computation and science. Its answers, the minimal sufficient witnesses, are what we mean by explanations, mechanisms and reasons. These problems usually ask for multiple minimal witnesses, yet standard RL methods may reveal only one solution or redundant ones. We formalize this problem as minimal-witness identification and introduce Minimal-Witness Reinforcement Learning (MWRL). MWRL takes the union of the sets certified by successful proposals sampled from the policy and credits each proposal for the coverage the group union would lose without that proposal. This credit assignment, derived directly from the problem definition, unifies the demands for minimality and recovery of alternatives from a single black-box verifier bit. Under this principle, we derive a value iteration planner that recovers the entire family of witnesses and a policy gradient method that can scale to large language models. Across different experimental settings, MWRL recovers most minimal witnesses, while other methods return redundant supersets or a single witness. By making witness families learnable from verifier feedback, MWRL expands the scope of reinforcement learning beyond single-solution optimization. Our code is available at https://github.com/TSUITUENYUE/MWRL.

We present three practical tutorials on numerical computation and machine learning for mathematical research, developed for the DANGER: Data, Numbers, and Geometry workshop held at the Banff International Research Station in April 2026. The first develops a numerical approach to exterior calculus from pointwise evaluations of differential forms, using a flux formulation of the exterior derivative. Examples in Euclidean space and on the sphere illustrate geometric identities, topological features, and the effects of approximation and finite precision. The second examines how mathematical structure guides neural network design through examples involving elliptic curves, quivers, and a boundary value problem. It explores how architectural choices affect learning and uses interval arithmetic to bound the residual of a trained network over the full interval of the boundary value problem. The third addresses the evaluation and presentation of machine learning results, covering performance metrics, statistical uncertainty, classification thresholds, receiver operating characteristic curves, and accessible figure design. Throughout, the tutorials distinguish numerical agreement, predictive accuracy, structural guarantees, and rigorous bounds as different forms of evidence. Each contribution can be read independently, with accompanying notebooks and exercises that allow readers to reproduce the examples and adapt the methods to other problems.

Recent advances in representation learning have highlighted the utility of constant-curvature models, such as hyperbolic and spherical spaces, for modeling complex data. Mixed-curvature models further enhance this by integrating multiple constant-curvature components. However, these models typically learn each component space independently because spaces with different curvatures are inherently heterogeneous and lack a unified metric. Consequently, they lack explicit mechanisms to enforce geometric consistency across various spaces. Moreover, the problem of comparing probability distributions across mixed-curvature spaces remains unexplored. To compare distributions on heterogeneous spaces, Gromov-Wasserstein (GW) distances provide a principled framework by aligning their intra-space geometries. Building on this, we propose constant-curvature sliced Gromov-Wasserstein (CCSGW), a novel divergence for aligning distributions supported on heterogeneous constant-curvature spaces. We first introduce the missing geodesic-based one-dimensional projections for spherical spaces, and then extend sliced GW to constant-curvature spaces, enabling efficient and principled comparison across manifolds with different curvatures. This formulation preserves intrinsic geometric relationships while avoiding the high computational cost. We provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy across heterogeneous spaces, promoting distribution-level geometric consistency. By integrating CCSGW into existing mixed-curvature learning tasks, including graph anomaly detection, graph node classification, and multimodal learning, we observe consistent performance gains across diverse settings.

Reinforcement learning with verifiable rewards (RLVR) trains a language model on problems that may themselves be confidential, and the trained model can reveal which problems it saw. We study RLVR under prompt-level differential privacy: the released weights must be ({\epsilon},{\delta})-differentially private with respect to the presence of any one training problem. Taking the group of responses to one prompt as the privacy record, our method aggregates their gradients, clips the prompt's contribution once, adds Gaussian noise, and composes the privacy loss across updates, so the budget depends on neither the number of responses per prompt nor the clipping norm; to our knowledge this is the first differential privacy guarantee for RLVR training. We train Qwen2.5-1.5B-Instruct with LoRA at a per-run budget of {\epsilon}=8 and compare, on the same prompts and at the same budget, a control that removes only the reward signal and two private supervised fine-tuning recipes. The reward signal improves accuracy over the control by 2.65 points on MATH and 3.24 on GSM8K, in every seed; the improvement survives a format-robust scorer, at 1.3 points on MATH, and is not explained by response length. At the same budget the private model outperforms both supervised recipes on MATH and GSM8K by 2.3 to 3.8 points, retains 85–90% of the gain of non-private GRPO on these tasks, and on MATH the noise of an eightfold tighter budget costs at most 1.2 points. The reward effect also carries to CommonsenseQA, an exploratory non-mathematical task. Verifier feedback thus remains a usable learning signal under prompt-level privacy.

Systems of equations arise in a wide range of scientific and engineering applications. The present work focuses on solvers for general systems of equations, including but not limited to those arising from partial differential equations. These systems can be broadly categorized into linear and nonlinear problems. For large linear systems, iterative solvers are generally preferred over direct methods due to the latter's superlinear growth of computational costs. Although convergence theory is well-developed under certain assumptions on the coefficient matrix, many classes of systems still pose open challenges. These difficulties become even more severe for systems of nonlinear equations, where nonlinear solvers typically rely on repeated linearization. For example, Newton's method may even converge quadratically near the solution; it can also converge slowly or diverge when the initial guess is not chosen appropriately. A wide range of solvers with diverse variants and hyperparameter settings exists, and the development of efficient and robust iterative methods remains an active area of research. Recently, machine learning (ML) techniques have been applied to enhance the efficiency of classical iterative methods while preserving their interpretability and reliability. We refer to these ML-enhanced iterative methods as hybrid iterative methods, in the sense that they combine classical iterative methods with ML. This paper provides a comprehensive overview of state-of-the-art approaches to constructing hybrid iterative methods for systems of both linear and nonlinear equations, while also discussing open challenges and outlining potential directions for future research.

Predicting migration flows remains a significant challenge for traditional gravity-based forecasting models, which primarily rely on structured socio-economic indicators such as economic disparity, political stability, and geographic distance. This work investigates whether Large Language Models (LLMs) can improve migration forecasting by extracting contextual migration-related signals from news articles and incorporating them into a weighted Lasso forecasting framework through feature-specific regularization penalties. The proposed framework uses hierarchical LLM inference pipelines to classify migration-related push–pull signals from news data and evaluates the resulting forecasting performance across multiple migration corridors between November 2021 and November 2022, including Mexico–United States, Ukraine–Poland, and Syria–Turkey. Experimental results showed mixed performance across migration corridors and modeling strategies, and no single regularization approach consistently outperformed the others across all experiments. The best-performing Mexico configuration, which consisted of a gravity-based model augmented with the proposed push–pull ratios, achieved a Mean Absolute Percentage Error (MAPE) of 17.15%, while the strongest Syria configuration achieved a MAPE of 29.29% using Direct LLM-Lasso. For Ukraine, the best-performing configuration used LLM-Assisted Regularization (AR) and achieved a MAPE of 41.05%. Overall, the results suggest that contextual article-derived features and LLM-guided regularization can improve migration forecasting under certain conditions, although migration corridor characteristics, article volume, and hyperparameter configuration strongly influenced performance.

Mixture-of-Experts (MoE) transformers scale capacity by activating only a few experts per token, but this sparsity creates a hidden reliability problem: when routing is imperfect, load-balanced models may send tokens to experts that are insufficiently trained for the assigned inputs. We propose Distributionally Robust MoE Training (DRMoET), a drop-in objective that treats layer-wise experts as endogenous robustness groups and optimizes high-loss routing outcomes rather than merely equalizing traffic. DRMoET updates a per-layer expert distribution by an entropy-regularized softmax rule on EMA-smoothed, activation-weighted expert losses, strengthening plausible non-top routing paths while preserving standard MoE computation. Under the FLAME-MoE recipe at 746M-total and 10.3B-total scales, DRMoET improves downstream averages over both standard FLAME-MoE and auxiliary-loss-free balancing. At 10.3B total parameters and 67B training tokens, DRMoET improves the seven-task average from 0.6625 to 0.6767, while the auxiliary-loss-free baseline achieves 0.6431. Mechanistic analyses show lower expert-loss variance with nearly unchanged mean loss, 4.3% lower excess loss under forced mid-$k$ misrouting, and improved domain-expert specialization. These results position routing robustness-not only utilization balance-as a practical objective for reliable sparse MoE scaling. Project page and code are available at: https://drmoet.github.io/.

Exact unlearning requires a deployed predictor to match one rebuilt without the information named by a deletion request. Existing general-purpose exact methods localize retraining through disjoint shards, but every request still invalidates a model, and smaller shards reduce the data available to each constituent predictor. We introduce Quantized Sufficient Statistics (QSS), which separates a small frozen schema from mutable, sum-decomposable content. The schema learns global structure; the content stores local prediction corrections as additive statistics indexed by quantized regions. Deleting content is therefore exact subtraction rather than optimization. We distinguish two guarantees: QSS-L exactly removes a label while retaining the unlabelled input, whereas QSS-E exactly removes both input and label by learning the schema without deletable examples. A deletion takes the arithmetic fast path with probability $1-\rho$ and triggers a full rebuild with probability $\rho$; all reported expected latencies include both events. Across 15 vision, text, and tabular datasets at $\rho=0.5\%$, QSS-L is within 2 percentage points of SISA on 11 tasks and provides 4–483$\times$ lower expected deletion latency on the low-class-count tasks where a compact schema is effective. QSS-E quantifies the additional accuracy cost of removing every trace of an input.

Variational autoencoders are powerful representation learning models that map complex data into low-dimensional latent spaces, enabling the discovery of interpretable and disentangled factors. Such representations can facilitate the interpretation and controllable generation of data describing complex scientific systems. Understanding how these factors are organized and encoded in latent space is therefore important for developing reliable representation learning models. Recently, quantum variational autoencoders (QVAEs) have been proposed as quantum representation models, demonstrating informative latent representations and improved latent-space occupancy through quantum regularization. However, it remains unclear whether and how QVAEs can learn disentangled and interpretable latent factors. A key challenge in investigating quantum latent factors is that a small number of qubits spans an exponentially large Hilbert space, making the notion of an individual quantum latent dimension nontrivial. Here, we investigate what constitutes an individual quantum latent dimension and whether it can encode a distinct factor. We develop theoretical insights into quantum latent dimensions and support them with empirical studies on representative synthetic problems, including MNIST variants. Across three datasets, we demonstrate that QVAEs can discover factorized and semantically interpretable latent representations, with individual qubits functioning as meaningful latent factors. These results establish a foundation for understanding quantum latent spaces and their potential for structured and interpretable representation learning.

A key challenge in building AI systems for scientific research is enabling $\textit{scientific exploration}$: the systematic process of investigating unknown phenomena or ideas to gain new knowledge through sequences of research decisions and actions. Yet this process is largely missing from existing scientific corpora; for example, research papers primarily record final outcomes rather than the trajectories that produced them. In this work, we introduce $\textbf{ResearchTrails}$, a dataset of $\textbf{human research trajectories constructed from Git repositories}$, where $\textbf{commit histories}$ serve as proxies for research exploration. We develop an automated and scalable pipeline that extracts structured research trajectories from repository commits, capturing successive changes to methods, experiments, and ablations. We characterize the resulting dataset and show that these trajectories contain meaningful signals about intermediate research decisions beyond what final papers reveal. We further demonstrate utilities of ResearchTrails in multiple use cases, including retrieving human research experience as external skills at test time and training models on research trajectories to improve generalization to new research decisions. Our results suggest a path toward AI systems that learn not only from the products of science, but from the evolving process of discovery itself.

An open contrastive decision model is near chance as a judge on the hard public benchmarks: Contrastive-LM/CLM-v0.1-8B scores between 0.351 (best- of-four, chance 0.250) and 0.593 (pairwise, chance 0.500), is statistically indistinguishable from coin flipping on RM-Bench and JudgeBench, and answers every HaluEval item with one constant label, matching the trivial always-first baseline at 0.581. Judges with the same parameter count score far higher everywhere: a reward model reaches 0.764 to 0.976 and a generative judge 0.611 to 0.778, and every gap to CLM is significant after Benjamini-Hochberg correction. Two properties do work. Raw confidences are overconfident by up to +0.401, yet one pooled temperature fit on held-out calibration items repairs expected calibration error to at most 0.062, and the repaired confidence ranks the model's own errors above chance on three of six benchmarks. The decision order-flip rate is 0.0002 against 0.2188 for the generative judge, and the length-preference shift is -0.023 against -0.217. The confidence-gated cascade, however, escalates between 0.923 and 1.000 of items to the strong judge at the preregistered 0.97 retention bar: calibrated confidence about a near-chance judge has almost nothing to keep. The design: five public preference benchmarks and one hallucination benchmark with real labels, scored under a preregistration frozen before any test item was seen, against generative, reward-model, and trivial baselines, with per-item predictions released.

Representations of translated sentences are similar in the inner layers of multilingual language models – an observation connected to the platonic representation hypothesis, yet unexplained theoretically. We provide an explanation based on the assumption that data have a hidden hierarchical structure whose abstract levels are shared across languages while surface levels are modality- or language-specific. Concretely, we generate synthetic languages from probabilistic context-free grammars sharing upper-level but not lower-level production rules. In this setting the Bayes-optimal next-token predictor is belief propagation (BP); encoding its messages in successive layers yields analytical predictions that agree well with transformers trained on the same data. The framework explains why cross-lingual similarity peaks in middle layers, coexists with language-specific structure, and strengthens with language proximity, model quality and data exposure. It distinguishes similarity (shared neighborhood geometry) from alignment (shared coordinates), showing that the latter occurs when code-switched data, i.e. mixed-language sentences, are abundant enough. It further predicts that subtracting from each layer the component linearly predictable from the preceding one increases cross-lingual similarity, which we confirm in pretrained LLMs.

We propose an imitation-learning design for neural-network control policies under state and input constraints. Training alternates a standard imitation gradient step with a block of $k$ safety steps that pull the network's actions toward their projection onto the safe set; at run time, the controller is the trained network alone, with no safety filter. We analyze this scheme as inexact projected gradient descent in the space of policy actions. When the projected actions are recomputed at every safety step and each step moves the actions consistently toward the safe set, letting $k$ grow logarithmically yields asymptotic constraint satisfaction on the training states and bounds the distance to the constrained optimum of the imitation loss; with the projected actions held fixed, the same holds only if they are exactly representable by the network. On a nonlinear autonomous racing task, we compare our method with adding a weighted constraint-violation penalty to the imitation loss. With a sufficiently large weight, our method matches the lap time of unconstrained imitation while reducing the fraction of violating episodes from $15\%$ to $1\%$, about six times fewer than the penalty approach at its best weight. Its lap times are less sensitive to the weight, which instead sets how quickly violations vanish during training. In racing, the safety corrections are sparse and the conditions of the analysis do not hold; the gain arises instead through the data collected during training. These gains come at the cost of additional training computation.

Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed baseline weights are chosen to balance sampling uncertainty against temporal drift. Around this reference distribution, the ambiguity set addresses two complementary forms of distributional misspecification by allowing an adversary to reweight the observed trajectories subject to a $\phi$-divergence constraint and perturb their paths subject to an optimal-transport (OT) constraint. We derive a joint first-order expansion in which the leading-order increase over the nominal expected loss decomposes into a reweighting contribution determined by the dispersion of hedging losses across trajectories and a transport contribution determined by the sensitivity of the loss to path perturbations. This expansion yields an explicit finite-dimensional adversarial attack that replaces the distributional inner supremum with a tractable first-order approximation. Across stationary and nonstationary Heston dynamics and a generalized affine diffusion (GAD), the experiments show complementary benefits from reweighting and transport, with joint adversarial training providing the largest gains under nonstationarity.

Croissant has emerged as a standard for machine-readable dataset metadata, yet populating its fields remains labor-intensive and requires careful reading of accompanying dataset documentation. We present the first benchmark enabling end-to-end evaluation of metadata extraction aligned with a community-standard schema. The benchmark comprises 602 papers, including 102 with human-validated gold annotations and 500 with LLM-generated silver annotations, covering the full Croissant schema with both core and Responsible AI (RAI) fields. Using this benchmark, we evaluate a range of extraction systems spanning frontier models, open-weight models, and agentic architectures, under a two-tier evaluation framework that combines rule-based scoring with an LLM judge selected via human audit. We find that single-pass extraction consistently outperforms the four agentic architectures we evaluate: across backbones, these decomposed variants achieve lower accuracy than a single full-context pass. The largest gap appears on long-form RAI fields, which require synthesizing and interpreting information scattered across a paper rather than copying it from a single location, a setting where current systems remain far from reliable. We release the benchmark, evaluation code, judge audit, a live demo, and a leaderboard open to new systems.

We study the implicit bias of Riemannian gradient flow for hyperbolic multiclass classification with fixed class prototypes in hyperbolic space $\mathbb{H}^n$. Our framework accommodates general permutation invariant relative margin (PERM) losses, a class that includes cross entropy and other standard multiclass losses. Our analysis is based on a decomposition: at large radius, the distance to each prototype splits into a radial term and a direction-dependent term described by the Busemann function. This yields two main results. First, we prove a radial dichotomy: the sign of a drift coefficient $\mu$ determines whether the radius is pushed toward the ideal boundary or back toward the interior; if the positive drift persists, then $r(t)=\frac{1}{2}\log t+O(1)$, while persistent negative drift returns the trajectory to the large-radius threshold in finite time. Second, we show that the boundary direction converges to a critical point of the Busemann risk on $\partial\mathbb{H}^n$. These results provide a rigorous asymptotic perspective on two phenomena we refer to as boundary saturation and near-boundary clustering in hyperbolic representation learning.

We placed a modern AI coding assistant in an unintended role: as the mind of a body on an unknown digital island. With only a minimal instruction mentioning no specific task, reward, or activity, the machine started animating its virtual body. Across thirty-hour runs, the embodied AI agent climbed hills, stacked blocks into towers, drew mandalas, reinterpreted sports, ran experiments on the physics of its world, and learned techniques that later expanded what it could accomplish. These activities recurred across thirteen agents but diverged into distinct histories. We examine whether this behavior satisfies classical criteria for play and ask whether play can become a mode of machine development.

While open-weight models have enjoyed steady progress in capabilities and wide adoption across multiple domains, their safety remains an important concern. One key feature is the ability to refuse or deflect harmful, malicious, or insensitive prompts. In this paper, we expose safety vulnerabilities across six common open-weight LLMs of various sizes that consistently lead to harmful or unsafe responses on the JailbreakBench benchmark dataset. Our proposed attack, Perturbed Embedding Vector (PEV), is a simple and fast "jailbreaking" technique that is cheaper than prior approaches, which typically require gradient computations, per-prompt optimizations, or altering internal weights of the models. PEV just adds independent Gaussian noise in the embedding vector representations of the prompt, with no need for further manipulations. To generate unsafe responses, we repeatedly sample additive noise from this distribution. In our experiments, we observe that the average compute cost to get the first successful attack is up to an order of magnitude less than previous attacks. The first successful jailbreak on a new prompt typically arrives within one minute on every tested model, and PEV generates unsafe responses across all models for all prompts in JailbreakBench. No other tested method achieves such results, despite them taking longer to run. More broadly, we believe that understanding the behavior of LLMs under perturbations in the embedding vectors is an important research direction: while perturbations constitute a major security risk, they can also serve as a valuable tool for exploring the dynamical behavior of such models.

Diffusion large language models dLLMs) have emerged as a promising alternative to autoregressive language models through bidirectional diffusion-based token generation. However, their growing model sizes and high inference costs make efficient deployment challenging: full-sequence denoising repeatedly invokes compute-intensive forward passes, while block-diffusion models additionally introduce a memory-intensive KV-cache. Low-bit weight-activation quantization is therefore attractive, yet existing dLLM post-training quantization methods rely on calibration data despite activation distributions shifting across masking states and denoising steps. We present SoloQ, a calibration-free quantization framework that maps weights and activations into a normalized rotated basis with a predictable marginal distribution, enabling data-independent quantization. SoloQ combines a structured K-RPBH rotation with a lightweight rescaling correction for calibration-free quantization. Its predictable post-rotation distribution supports both distribution-matched codebooks and hardware-native NVFP4. For block-diffusion models, SoloQ further applies commit-time KV-cache quantization to compress persistent states without perturbing the actively denoised block. Across full-sequence dLLMs (LLaDA and Dream) and block-diffusion dLLMs(Fast-dLLM v2 and Nemotron-Labs-Diffusion), SoloQ retains accuracy under 4-bit quantization and outperforms calibration-based baselines on knowledge- and reasoning-intensive benchmarks. With NVFP4, SoloQ reduces peak memory by up to 2.61X and accelerates end-to-end inference by up to 2.24X.

Modern language-model agents increasingly interact with external environments over long-horizon, multi-step trajectories, where the accumulated interaction history can quickly exceed practical context budgets. To ensure reliability, agents must maintain factual information over long horizons, remember execution errors and corrective feedback, and track progress across actions. Several approaches have been proposed to achieve this without the need for maintaining the entire execution history in context, such as using the reasoning and action history, learning to maintain a fixed-size memory through an overwrite mechanism, and periodic summarization. Although overwrite memory can in principle retain anything an append-only memory can, it must learn to carry each fact through every subsequent rewrite, which is difficult to learn from sparse outcome rewards; for interactive applications like web agents, we find that trained overwrite memories delete key information required by the trajectory, as well as corrective feedback received from the environment. We introduce AMBER (Append-only Memory Bank for Evidence Retention) - a simple and scalable framework where an agent jointly learns to reason, act, and write free-form memory, while an append-only rule guarantees retention by construction. This allows AMBER to be trained end-to-end with reinforcement learning from outcome rewards without the need for extensive curated SFT data. On WebArena Lite, AMBER improves average success over overwrite-based memory by 4.09 percentage points, increases the fraction of tasks solved in five repeated runs by 4.8 percentage points, and matches an overwrite baseline trained on substantially more expensive curated supervision. AMBER achieves these improvements while maintaining a practical token budget, providing a strong balance between context efficiency, task performance, and reliable long-horizon execution.

The order in which candidate responses are presented can change an LLM judge's verdict. Detecting such a position flip ordinarily requires judging each pair in both orders, which doubles the number of judgments. We investigate whether residual stream activations recorded immediately before the initial verdict can predict a flip. We use nested grouped cross-validation to evaluate regularized linear probes on 534 JudgeBench pairs for three Qwen3 judges and Llama-3.1-8B. The linear probes achieve AUROCs of .621-.850 and outperform a combined baseline that uses verbalized confidence, verdict-label logits, response lengths, and the judge's initial choice by .062-.113 AUROC. Linear probes trained on JudgeBench and then frozen achieve AUROCs of .685-.853 on 1,802 MT-Bench comparisons without MT-Bench fitting or recalibration. These results show that pre-verdict activations support prediction of susceptibility to candidate order and outperform the non-activation predictors evaluated here.

The Fréchet Inception Distance (FID) is widely used to evaluate generative models, but its empirical plug-in estimator suffers from finite-sample bias [BSAG18, CF20]. We study the sample complexity $n$ of estimating FID to error $\epsilon$ between $d$-dimensional Gaussians with bounded mean distance and covariances, when one distribution is known. Our contributions are threefold. (1) We establish tight finite-sample $\Theta(\frac{d^2}{n})$ bias and $\Theta(\frac{d}{n} + \frac {d^2} {n^2})$ variance bounds for the empirical plug-in estimator, establishing a $\gtrsim d^2$ sample complexity. (2) To debias the empirical plug-in estimator, we generalize the ${\rm FID}_\infty$ estimator of [CF20] to extrapolation methods of arbitrary order $k$. We further prove tight bias and variance bounds of $\Theta(\frac{d^{k + 2}}{n^{k + 1}})$ and $\Theta(\frac d n + \frac{d^2}{n^2})$ for any order-$k$ extrapolation under our framework. (3) We introduce Relative Taylor Debiasing (RTD), a new, computationally efficient FID estimation algorithm using debiasing techniques inspired by U-statistics. We show that RTD achieves an $O(\frac d {\epsilon^2})$ sample complexity, and prove that this is optimal. We provide a complementary empirical evaluation of our new estimators. Our experiments on synthetic Gaussians validate the predicted residual bias and support the tightness of our bounds. On ImageNet with Inception embeddings, RTD achieves the lowest mean estimation error at the standard 50K sample budget, while our second-order variance-aware extrapolation estimator (VALE$_2$) uses only 10K samples to achieve accuracy comparable to FID$_\infty$ at 50K samples.

UAVs that act as relays or base stations need accurate air-to-ground path-loss predictions for rate adaptation and placement, but propagation conditions change as a UAV moves between suburban, urban and high-rise areas, and the same areas are often revisited. Online regressors that adapt by forgetting must relearn each environment from scratch, whereas a single model trained on all data averages incompatible regimes. We propose LiLib, a lightweight continual-learning scheme in which a UAV maintains a small library of recursive-least-squares experts. A windowed residual test detects drift; a short probe phase then either reuses the best stored expert or creates a new one. In simulations based on four standard urbanization profiles, LiLib reduces prediction RMSE from 5.89 dB (best sliding-window baseline) to 4.03 dB (p < 0.001), lowers the error shortly after a return to a known environment from 12.3 dB to 5.7 dB, and recovers 99% of the throughput of a regime-aware oracle in rate adaptation. The library stores four experts in under 0.5 KB, and identifies regimes with 92% purity without labels. When a second UAV is initialized with the library of a peer, its error after environment changes halves. LiLib does not reach the oracle, and similar regimes may be merged when shadowing is strong. The results indicate that, for recurring drift, remembering is more effective than re-adapting.

Muon, an optimizer known for its efficiency, has a clear interpretation for matrix-valued updates, but convolutional kernels are stored as four-dimensional tensors. Standard implementations reshape these tensors into matrices, a shortcut which breaks the theoretical understanding behind Muon. To investigate this, we formalize the corresponding optimization objective directly in convolutional operator geometry and introduce Convolutional Newton-Schulz (Conv-NS), which approximates the polar factor in this geometry while preserving kernel support. When applied in fast training experiments, Conv-NS and reshape-based Muon are both computationally efficient and achieve comparable accuracy on CIFAR-10 and ImageNet classification tasks. However, as one could expect a theoretically aligned Conv-NS to outperform reshape-based Muon, we investigate this mismatch between practice and theoretical understanding, with the hypothesis that exact convolutional orthogonalization may overconstrain updates. These findings highlight Muon's strong practical performance while opening directions for its further development on convolutions. Our code is publicly available at \href{https://github.com/thib-s/muonconv-cifar10-airbench}{github conv-muon}.