Papers

The Platonic Representation Hypothesis (PRH) holds that increasingly capable models converge toward a common representation. However, recent studies have shown different views on aligning representations via their neighborhoods, spanning trees, and distances. We show that these views can differ because the alignment criteria behind them sit at different points of one lattice, and we formalize this explanation as the Lattice Representation Hypothesis (LRH). Under the LRH, the convergence claimed by the PRH is agreement at the top of the lattice, whereas its evidence comes from neighbor overlap, a criterion near the bottom. The Aristotelian Representation Hypothesis (ARH) restricts convergence to local neighborhoods because calibration keeps the growth of neighbor overlap with model size but largely removes that of centered kernel alignment. We show that this removal can come from calibrating a maximum over layers, so global convergence remains open. Back into Plato's Cave (BPC) infers coarse shared structure from the collapse of neighbor overlap on larger evaluation sets, whereas we trace it at least partly to a fixed number of neighbors covering shorter distances. We show that the spanning-tree overlap used by Structure over Geometry (SOG) mostly repeats one-nearest-neighbor overlap. The LRH also extends to independently trained models, whose training procedure and objective decide the criteria met reliably across runs. We prove this claim for the training procedure in a linear autoencoder and for the objective in a finite contrastive Gibbs model. Experiments on dozens of pretrained vision and language models and thousands of runs of both theoretical models support these conclusions. We hope this work paves the way toward a general theory of representation hypotheses, with a framework to analyze them and compare their evidence. Project page: https://eethanshi.github.io/LRH

Designing RNA sequences that satisfy target tertiary-structure objectives is an important problem in RNA engineering, with broad applications in synthetic biology and therapeutics. Existing 3D RNA design methods have made substantial progress, but they largely treat the target fold as a geometry-only objective. This is incomplete for RNA, whose functional folds are specified not only by tertiary geometry but also by secondary base-pairing topology. We therefore formulate RNA inverse design as a topology-and-geometry co-design problem and propose TANGO, a multi-objective multi-agent reinforcement learning framework for this task. TANGO adopts a staged curriculum: it first learns a topology-aware policy from secondary-structure targets, then transfers this policy to tertiary-structure targets to train a general co-design model, and finally applies frontier-guided fine-tuning to refine target-specific trade-offs among secondary-structure fidelity, tertiary-structure fidelity, and sequence diversity. Experiments show that TANGO generates diverse and novel designs, improving tertiary- and secondary-structure performance by 18.3% and 52.7%, respectively, over the strongest baseline.

Learnable downsampling and spectral-domain filter parameterizations have each made convolutional networks more flexible, but their interaction has not been systematically examined. We bridge this gap by examining convolutional kernels learned in the spatial and spectral domains, together with learned downsampling ratios under a cropped resizing implementation. We find that spectral and spatial kernels respond differently to learned resolution allocation, with larger gains for the spectral kernel. We observe this consistently on three datasets (EuroSAT, CIFAR-10 and STL-10) and at two model sizes (differences in accuracy gain of +0.013 to +0.028 on held-out test sets). Part of this difference reflects the greater gain of the spectral kernel from retaining more spatial area, but the difference remains positive when total retained area is matched. This pattern is observed across datasets and model sizes, although its magnitude and dependence on the complexity budget vary with model size and the resizing implementation.

Single-channel radio-frequency (RF) signal separation is important for interference mitigation when a signal of interest overlaps with a co-channel interferer in time and frequency. Classical matched filtering and LMMSE receivers are limited under structured non-Gaussian interference, while diffusion and score-based methods often require iterative sampling or optimization. We propose FlowSep-RF, a rectified flow matching framework that learns a clean-endpoint transport from the received mixture to the signal of interest. The model combines time-domain IQ samples with frequency-domain features and recovers the separated waveform using one endpoint velocity evaluation. We evaluate FlowSep-RF on QPSK mixtures with OFDM-BPSK, OFDM-QPSK, and RFChallenge CommSignal2 interference against classical, discriminative, and generative baselines. FlowSep-RF achieves the lowest average BER and MSE among evaluated baselines across all three settings with one-step inference.

Client-level fair federated learning, in the form of $q$-fair federated learning ($q$-FFL), agnostic federated learning, or tilted empirical risk minimization, has emerged as an attractive solution to equalize utility across heterogeneous clients. This paradigm grants high-loss clients greater relative influence, while a central server aggregates their loss-weighted updates into a single shared model. Yet, the Byzantine robustness of $q$-fair federated learning has been largely neglected, leaving the server unable to tell legitimate fairness-induced amplification from malicious update scaling. To address this critical gap, we formalize the problem of Byzantine-robust $q$-fair federated learning under an update-only interface, in which the server observes nothing but the fairness-scaled client updates. Our analysis under shared class-conditional label skew shows that fairness scaling preserves the nonnegative class-mixture structure of honest updates, while replacing their unit-sum constraint by a client-dependent radial scale. Moving beyond magnitude-based screening, we show that this warped geometry supplies two complementary tests, one radial and one structural, that a single norm cannot provide. We then introduce FUSE, a structure-aware robust aggregator that uses a small trusted labeled dataset for coefficient recovery, scale and cone-consistency screening, and post-screening step-size control. Across four benchmarks and seven Byzantine attacks, FUSE improves seed-wise worst-attack accuracy over the strongest baseline on each benchmark by 3.9–30.1 percentage points, while largely preserving the influence of the high-loss honest clients that fairness is meant to protect.

Deploying a general-purpose model as an agent means running it inside a product-specific runtime harness that decides which actions are executable, how state advances, and when the loop may terminate. Ordinary trajectory supervision shows which action was taken but leaves the runtime semantics behind that action implicit. We introduce Harness Policy Distillation (HPD), which makes these runtime control semantics an explicit training target alongside actions to align the harness policy. HPD replays reference trajectories through the harness to recover the runtime semantics that are implicit in ordinary trajectory data, and represents them as control documents at each model-call boundary. These documents provide privileged information for a teacher to generate actions, while harness verification ensures that the resulting targets are executable under the runtime contract. We jointly train a shared model on the runtime semantics recovered from control-state privileged information and native history, thereby internalizing these semantics into the model policy. At deployment, the trained model uses the original harness interface without requiring the control document or any additional supplement. On TRAJECT-Bench with the Pi harness, Qwen3-8B trained with HPD reaches 22.98% autonomous task success and 49.23% runtime compliance, against 3.09% and 19.90% for the unadapted model. Harness-verified teacher actions substantially improve the native deployment policy, while joint control-state supervision provides further gains in task completion and runtime compliance. HPD turns executable runtime semantics into dense supervision for learning harness-compatible actions at each decision boundary.

Long-horizon agents must coordinate reasoning, tool use, and environment feedback over extended interactions. Learning from sparse outcome rewards requires weighting trajectories of different lengths and updating the policy while rollouts are still being collected. We examine a single-rollout asynchronous recipe combining Muon, token-averaged loss, truncated importance sampling, and auxiliary length and tool-error penalties. Single-rollout sampling allows asynchronous learning without waiting for multiple trajectories for the same issue. We study optimizer choices and recipe components for repository-level issue resolution across two model families. The evaluated training runs show higher training success with the full recipe than with the baselines.

Deep reinforcement learning (DRL) policies for planetary landing and other aerospace guidance, navigation, and control tasks are commonly trained under randomized disturbances to improve robustness. However, typical stochastic perturbation sampling assumes independent variations, whereas real mission disturbances often exhibit spatial and temporal correlation and cannot be reproduced through independent random draws. This work investigates adversarial reinforcement learning to discover challenging off-nominal conditions. A secondary agent generates physically constrained perturbations that degrade the performance of a landing controller, forming an asymmetric sequential zero-sum game. Training proceeds in three stages: baseline controller learning, robustness enhancement with stochastic perturbations, and an iterative adversarial phase in which the controller and disturbance generator are alternately optimized. Preliminary experiments in a three-degree-of-freedom landing environment show that adversarial disturbances reveal vulnerabilities missed by conventional randomization and provide early indications that, with a more extensive training campaign, the approach can yield improved robustness and stronger generalization under previously unseen perturbation regimes.

Boundary delineation of anatomical structures in prostate MRI is often compromised by regional ambiguity. Automated segmentation methods relying on global overlap loss functions tend to be insensitive to surface deviations, leading to significant errors in ambiguous regions. Most existing uncertainty-aware methods treat uncertainty as a post-hoc quality indicator or prediction filter. We propose Contrastive Uncertainty Learning (CUL), a supervised framework that uses predictive uncertainty to directly guide representation learning. Using Monte Carlo Dropout, CUL identifies voxel-wise uncertainty and structures the embedding geometry accordingly: low-uncertainty, correctly predicted features form stable voxels while high-uncertainty or misclassified features are actively repelled, preventing feature collapse at difficult boundaries. We evaluate CUL on a 589-scan 3D prostate MRI multi-structure segmentation task (8 anatomical structures) using a ViT with UperNet decoder architecture. Average Dice ($83.38\%$) remains comparable to the baseline ($83.35\%$), while surface distance decreases significantly ($p<0.001$) across 6 of 8 anatomical structures. A hard-case analysis reveals a $22{\times}$ asymmetry between significantly improved and degraded cases ($18.8\%$ vs $0.9\%$). Ablation studies show that removing uncertainty-guided sample selection eliminates improvements for the transition zone, while replacing the contrastive objective with a boundary loss additionally removes bladder improvements, demonstrating that both uncertainty-guided sampling and the contrastive objective are essential for the observed gains. These findings demonstrate that the proposed uncertainty-guided representation learning is a useful mechanism for reducing the risk of extreme errors in safety-critical medical segmentation

Multilingual models share capacity across languages, so adding languages can hurt performance on existing ones. Mixture-of-experts models expand this capacity with little additional per-token computation. Given this extra capacity, does adding experts reduce what each additional language costs? To answer this question, we propose a repetition-aware joint scaling law relating number of active parameters, training tokens per language, number of experts, and language coverage. Fitted on 26,300 per-language loss observations from 64 pretrained configurations, our law reduces prediction error on held-out configurations by 28% relative to the strongest evaluated baseline. At matched number of active parameters and training tokens per language, 32 experts reduce the loss penalty of expanding from 12 to 200 languages by 83% compared with a dense model. Our law further shows that broader language coverage favors more experts across a wider range of compute budgets, guiding capacity allocation as multilingual models scale.

Anomaly detection is a fundamental task for time-series analytics, with important implications for the downstream performance of many applications. Despite the large number of anomaly detection methods proposed in the literature, recent benchmark studies have shown that no single detector performs best across highly heterogeneous time series. Therefore, a practical and scalable solution is to develop a model-selection method that, for a given time series, selects the anomaly detector most likely to perform well. Nevertheless, the model selection approaches proposed in the literature suffer from a significant drop in accuracy when applied in Out-of-Distribution (OOD) settings. In this paper, we tackle the aforementioned limitation and propose RAMSAD, a retrieval-based framework for model selection in time-series anomaly detection. Given a new time series, our method queries a knowledge base of previously observed instances, retrieves the top-k most similar series, and transfers detector recommendations from their performance profiles. The framework can operate with standard similarity measures as well as embedding-based representations. Our results show that RAMSAD outperforms existing baselines in In-Distribution (ID) settings and is the most robust selector in OOD, where, when selecting a small subset of detectors, it matches or exceeds ensembles that run the entire detector pool, at a fraction of their cost. Overall, we demonstrate that similarity-based retrieval constitutes a strong and efficient foundation for model selection in time-series anomaly detection.

Graph Neural Networks (GNNs) excel on graph-structured data but suffer catastrophic forgetting when classes arrive sequentially. In class-incremental graph learning, predictions are often dominated by recently learned classes, causing severe recency bias. Dynamic expansion can isolate knowledge across sessions, but many methods assume task-incremental settings and require task identities at test time to select branches or heads—information unavailable in class-incremental learning. Learnable routers offer an alternative, yet continual fine-tuning the router on new data can bias routing toward recent components. We propose MAEM, a replay-free, capacity-controlled dynamic mixture-of-experts framework for class-incremental graph learning. MAEM builds representations with Simplified Graph Convolution (SGC) and trains a dedicated expert for each new session, then freezes it to protect prior knowledge. For routing without task IDs or a shared trainable router, each expert uses a masked autoencoder (MAE); test nodes are assigned to the expert with the lowest reconstruction error, reducing routing-level recency bias. When the expert pool reaches a fixed capacity, MAEM merges the least-used experts via Git Re-Basin alignment and further distills them into a fused expert using topology-aware pseudo data synthesized from MAE distributions (DeepInversion-style), without storing or revisiting historical graph data. On four class-incremental graph benchmarks, MAEM mitigates recency bias, outperforms strong continual graph learning baselines, and keeps model capacity bounded under strict replay-free learning.

We investigate the minimal width of deep neural networks that can approximate all continuous functions from $\mathbb{R}^n$ to $\mathbb{R}^m$ in the topology of uniform convergence on compact subsets. We show that whenever the real projective space $\mathbb{RP}^{n-1}$ admits a smooth immersion into $\mathbb{R}^n$, the minimal width is at least $n+\min\{n,m\}$, assuming that the activation function is continuous and monotone. As a consequence, the minimal width of ReLU networks is $n+m$ whenever $n$ is equal to 2, 3, 4, 7 or 8 and $1\le m \le n$, extending results of Hanin-Sellke and Hwang. This suggests an intriguing connection between the approximation theory of neural networks and differential topology.

Diffusion models are a powerful framework for learning complex probability distributions. While widely used diffusion models for continuous data rely on Gaussian noising processes, we instead develop diffusion models based on Poisson noise. More precisely, we introduce and study a new mathematical framework, called Mixed Poisson Diffusion Models (MPDM), with noising dynamics driven by multivariate counting processes. Our methodology is motivated by Poisson inverse problems. The success of Gaussian diffusion models has led to their use as prior models in a growing number of posterior sampling methods for inverse problems. However, most of these approaches focus on Gaussian inverse problems, in which observations are generated through a deterministic forward operator corrupted by additive Gaussian noise. By contrast, Poisson inverse problems, where observations are discrete and Poisson distributed, remain comparatively underexplored in this literature. Building on our Poisson generative dynamics, we develop a natural framework for posterior sampling in Poisson inverse problems and derive several posterior sampling algorithms based on the proposed model. We evaluate our approach on realistic Poisson inverse problems and show that the resulting framework is well suited to this class of problems.

Building foundation models for MRI has emerged as a promising direction for advancing medical image analysis and improving accessibility of task specific models. Existing approaches primarily focus on effective pretraining strategies and evaluating their performance across diverse downstream tasks. While these methods show performance gains, limited attention has been given to understanding task alignment between pretraining and downstream objectives. Unlike language models, where the two stages are naturally aligned, such alignment is less evident in vision based applications. Motivated by this gap, we explore continual pretraining. Specifically, continually pretraining a pretrained ViT encoder using Low-Rank Adaptation (LoRA) on a prostate segmentation task to enhance task alignment and downstream performance. We further perform layer-wise representational analysis using Centered Kernel Alignment (CKA) to assess representational shifts and their correlation with task outcomes. Our experiments show improved performance in 3 of 6 downstream tasks and comparable results in the others. Our Feature analysis reveals that, for segmentation tasks, continually pretrained encoder features exhibit greater similarity to those of the finetuned encoder than the original pretrained encoder, correlating with observed performance gains.

Routability prediction enables rapid evaluation of placement quality without routing, providing effective feedback for routability-driven placement optimization. Recent machine learning methods have achieved efficient routability prediction through data-driven approach. However, their prediction performance highly depends on the capability of input representations to capture essential circuit information. To address the limitations of existing circuit representations in simultaneously preserving logical topology, physical layout and routing resource information, this paper proposes HGRP, a heterogeneous graph neural network for routability prediction. HGRP models the cells, nets, and routing grids as distinct types of nodes and explicitly represents topological connectivity, spatial mapping, and grid adjacency, thereby constructing a heterogeneous graph representation that preserves multi-level circuit semantics. Based on the representation, a heterogeneous message passing mechanism is developed to enable information interaction and feature fusion among distinct types of nodes, effectively learning the complex correlations between circuit structures and routing behaviors. Experimental results on the CircuitNet dataset show that HGRP improves F1-score by 18.69% relative improvements compared with the state-of-the-art in the congestion prediction task. The source code is publicly available at https://github.com/ShenShan123/HGPR.

This paper investigates the use of Behavior Cloning (BC) for autonomous driving from a bird's-eye view (BEV) perspective in simulated urban environments. BC uses supervised learning to mimic expert driving behaviors. Previous works have applied BC in the CARLA simulator but did not fully address the challenges of traffic light compliance. Our approach enhances BC by integrating a kernel density estimator to adjust training sample weights based on action density, thereby improving the learning of rare but critical actions such as stopping at red lights and accelerating at green lights, specially in scenarios of scarce number of expert demonstrations. Using BEV inputs, which provide an abstract top-down view of the driving environment, our method simplifies the policy learning process. The trained convolutional neural network (CNN) outputs steering and acceleration actions based on these BEV inputs and additional state variables. Experimental results in the CARLA simulator demonstrate that our weighted BC method significantly improves driving performance, achieving higher route completion compared to standard BC. This weighted approach proved to be crucial in learning correct driving behaviors, particularly in test environments not encountered during training, highlighting its potential for enhancing autonomous vehicle navigation.

Tracking changing comparators is a central problem in online learning. For exp-concave losses, previous work established the $T^{1/3}P_T^{2/3}$ dependence on the horizon $T$ and Euclidean path length $P_T$ for fixed dimension, while the optimal cost of dimension remained unresolved. We resolve this question by establishing a sharp $d^{1/3}$ curved dimension factor, improving the $d^{2/3}$ factor of recent switching and interval reductions [1, 2]. To achieve this improvement, we develop a proper, full-information learner on compact convex subsets of $\mathbb{R}^d$ that adapts to the unknown path length and, under fixed dimension-independent diameter, gradient, and curvature parameters, guarantees $$\operatorname{Reg}_T(u_{1:T}) \le \widetilde{O}\left(d+\min\left\{d^{1/3}T^{1/3}P_T^{2/3},\sqrt{TP_T},T\right\}\right).$$ A matching lower bound on a diameter-one Euclidean ball establishes the minimax frontier up to logarithmic factors when $T\gtrsim d^2$, including the transition from the curved rate to larger path budgets. The lower bound already holds for losses that depend on only one coordinate per round, isolating an unavoidable cost of learning across directions. Our upper bound follows from square-root Gaussian KL control of comparator movement and a cancellation argument that pays for history restarts. The curved learner maintains $O(\log^2 T)$ Gaussian states, uses one gradient per round, and runs in time near-linear in $T$ under a Mahalanobis-projection oracle.

Probes on activation vectors are widely used to detect misbehavior in language models, but their success relies on the assumption that models cannot control what their activations encode. Humans can learn, through neurofeedback, to control the firing of even single neurons, and recent studies investigated whether this ability extends to language models, reaching conflicting conclusions. No experimental design so far disentangles competence at the task from genuine access to one's own activations. We fill this gap with in-context neurofeedback sessions, in which a "subject" model is asked to maximize (or minimize) a score derived from its activations, shown back to it at every turn. In our first experiment, the sentences are generated either by the subject or by a second "writer" model, while the score always derives from the activations of the subject. We test ten open-weight models from five families, with sizes from 9B to 32B. Some models move their own scores considerably, but no more than a writer of comparable competence moves them. Is this because the task requires no privileged access, or because the subject controls its activations while processing the sentences, whoever wrote them? To answer this, we prefill a fixed sentence as the subject's reply at every turn and ask it to increase or decrease the score. Three out of ten models show small but consistent control effects. We further ask whether models can control their activations to the point of fooling an activation monitor. We make models repeat sentences a monitor would flag, such as a deceptive answer for a deception monitor, and ask them to raise or lower the monitor's score. No model learns to lower it, but one model can raise it. In-context control of a model's own activations might not yet be a threat to activation monitors, but it exists in a few models and needs to be tracked as models evolve.

Reinforcement Learning on Mixed-domain preference data (Mix-RL) has become the mainstream approach for training general-purpose Generative Reward Models (GRMs). However, Mix-RL suffers from two critical bottlenecks: the reward sparsity induced by outcome rewards, and the cross-domain interference arising from jointly optimizing heterogeneous capabilities, which together give rise to imbalanced capability acquisition and pervasive reward hacking. Inspired by the success of On-Policy Distillation (OPD) in multi-domain capability integration, we introduce RM-OPD (Reward Modeling via On-Policy Distillation), a two-stage framework that separates specialist acquisition from capability integration. First, we cultivate domain-specialized teacher models via single-domain GRPO fine-tuning, allowing each expert to reach its performance ceiling in isolation; then we consolidate these teachers into one student model through (i) routed on-policy distillation, which provides dense signed token-level supervision on student-generated critiques; (ii) domain contribution reweighting, which reweights token guidance toward target domain shares, preventing specific domains from dominating optimization; and (iii) optional criteria context distillation, which conditions teachers on domain-specific evaluation criteria to sharpen token-level supervision. Across multiple RM benchmarks and two base models, RM-OPD consistently outperforms vanilla Mix-RL and other strong baselines, achieving overall superior performance and exhibiting an emergent "teacher-surpassing" effect. These results establish RM-OPD as a promising paradigm for building generalist GRMs.

We study the problem of learning accurate and cognitively simple binary classifiers that are directly interpretable as Boolean rules. We propose mixed integer linear programming (MILP) formulations for training sparse disjunctive normal form (DNF) networks, viewed as small networks with a conjunctive hidden layer and a disjunctive output layer. Contrary to previous work that uses MILP for inductive rule learning, we start with a fixed network structure, for which we then find optimal weights. A regularized objective explicitly trades off misclassification costs against sparsity, yielding globally optimized rule sets. Our main technical contribution is an enhanced formulation that substantially reduces the number of integer decision variables and eliminates redundant constraints, while preserving exact Boolean semantics for all feasible solutions. Furthermore, we develop a combined approach based on initialization and dropout to break symmetries in the weights between rules, mitigating redundancy, and encouraging more diverse and stable rule representations. Experiments on synthetic benchmarks and UCI datasets show that the advanced formulation improves computational efficiency and achieves competitive or superior accuracy compared to established interpretable baselines, including SAT-based DNF learning and well-known rule- and tree-based learners. Overall, our approach provides a principled optimization framework for learning compact Boolean rule sets with explicit control over accuracy and sparsity trade-offs.

Language models often produce semantically similar answers to open-ended questions, even when many plausible alternatives exist. Generating useful alternatives requires identifying both what the query calls for and what existing responses already cover. We introduce Gap Detection, a framework that searches for relevant but unoccupied directions in a shared text embedding space. Its objective, GapScore, combines query relevance (Demand) with dissimilarity to the nearest existing item (Defensibility). The framework optimizes this product on the unit sphere, maps candidate directions to concept words with a language model, and uses task-specific filtering and constrained prompting to turn those concepts into text. On five curated topics and 90 INFINITY-CHAT queries, the reported mean relative reductions in output Collision are 12.8% and 10.8%, respectively. We also instantiate the framework for generative engine optimization over four product markets and for iterative synthetic-data augmentation. In the latter setting, with 100 training examples per method, Gap Detection reduces Collision from 0.324 to 0.298 relative to undirected accumulation and increases the Vendi Score from 27.16 to 29.20; the accuracy difference is one example on a 40-example test set. Component ablations expose the trade-off between semantic separation and relevance, while also showing that better direction scores do not uniformly yield better downstream metrics. These results support explicit gap search as a practical mechanism for diversifying content, with task validity checked separately from geometric novelty.

Batch black-box optimization is important for expensive systems where many candidates can be evaluated in parallel, yet only a few rounds of evaluation are affordable. In this regime, effective batch construction must identify multiple promising regions while avoiding redundant evaluations, and conventional Bayesian optimization can require increasingly difficult batch-selection procedures as the batch size grows. We introduce Flow Matching for Thompson-Sampling Refinement (FMTR), an amortized approach that learns offline a continuous, history-conditioned proposal distribution from which variable-size batches can be sampled. FMTR is trained offline by conditional flow matching on Thompson-sampling argmaxes refined toward high-value regions via a horizon-dependent Langevin pushforward map, adapting the exploration-exploitation tradeoff over the optimization horizon. At test time, the model parameters remain fixed and batch generation requires neither task-specific surrogate refitting nor numerical acquisition optimization. FMTR achieves strong performance against batch BO and in-context baselines on synthetic and real-world benchmarks, while substantially reducing the computational cost of batch selection.

Vision-language models (VLMs) are moving onto edge devices, but little is known about how much energy they draw on single-board computers with NPU or GPU accelerators, or where that energy goes. We measure total-system energy, latency, and thermal behavior of Qwen2-VL-2B-Instruct and its text-only sibling on a Raspberry Pi 5 with a Hailo-10H NPU and on a Jetson Orin Nano Super, on both CPU and accelerator, and separate the fixed energy of each request from the energy that grows with output length. Because the accelerators use different quantization and serving software, we compare deployment stacks rather than silicon. Three findings stand out. First, NPU offloading makes the Pi a much more efficient VLM platform: it cuts energy per generated token by about two-thirds, leaves the host CPU largely free, and avoids the thermal throttling that the CPU backend reaches in sustained use. Second, an image adds both fixed and per-token energy, but at typical response lengths generating the answer costs far more than processing the image. Third, the Jetson GPU favors short responses through its lower fixed cost per request, whereas the Pi NPU favors longer ones through its lower cost per output token; their energy curves cross near 40 output tokens.

We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal space. This novel viewpoint is general enough to recover classical neural operators as well as a new variant, coined Bregman neural operators, which includes the inverse activation operator and features the same expressivity of standard neural operators. Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models.

KANLab is a browser-based visualization tool designed to interactively teach the core concepts of Kolmogorov-Arnold Networks (KAN), forked from the widely successful TensorFlow Playground. To maximize educational clarity, KANLab omits residual connections and learnable scaling parameters found in modern KAN implementations, ensuring that displayed B-spline activation curves directly correspond to their underlying trainable control points. Users can inspect and modify activation functions, initialization schemes and observe gradient descent correcting manual disruptions. Furthermore, user can explore phenomena such as activation variance, interactive pruning, and re\-/training within a compact 2D machine learning setting. KANLab is open-source and available at https://kanlab.app/

Prior work on implicit bias shows that gradient descent selects the Frobenius max-margin direction on linearly separable problems, whereas Fan et al. (2025) established spectral max-margin behavior for spectral-norm steepest descent methods, including idealized Muon with exact orthogonalization. In practice, however, Muon approximates orthogonalization using finite Newton-Schulz iterations and a positive stabilization constant. We prove that these implementation choices cause Muon to select the Frobenius rather than the spectral max-margin direction in linear classification with separable data. We also establish this behavior for both exponential moving average and Nesterov-style momentum. The key technical ingredient is a summable perturbation argument showing that the resulting parameter trajectories remain at bounded distance from those of gradient descent. We then disentangle the roles of Newton-Schulz iteration count, the stabilization constant, and the Newton-Schulz polynomial, revealing distinct asymptotic behaviors, including directions that achieve neither Frobenius nor spectral max-margin. Finally, we show that Muon can recover its spectral max-margin bias with Newton-Schulz iterations growing logarithmically over training.

Neural symbolic regression (SR) models require diverse datasets of mathematical expressions for robust training. However, existing datasets rely predominantly on stochastic sampling methods, which suffer from high structural redundancy and incomplete functional coverage. To address this, we introduce an exhaustive dataset of univariate canonical skeletons generated via a deterministic constrained context-free grammar. A canonical skeleton acts as a generic structural representation that subsumes more specific functional forms, eliminating redundant expressions and avoiding repeated computational efforts. Although our dataset consists of univariate skeletons, it is designed to support the decomposable SR paradigm to solve multivariate SR problems without assuming linear separability. Furthermore, we pair this dataset with a sampling strategy that generates clean numerical data without triggering numerical instabilities or relying on artificial protected operators. Canonicalizing two existing neural SR datasets reveals that our dataset is substantially more compact, eliminates structural repetitions, and achieves a uniform operator distribution free of simplicity bias. Finally, we establish a benchmark of 150 SR problems across three tiers, on which state-of-the-art SR methods are shown to struggle significantly.

Autoregressive transformers trained on limit order book (LOB) message streams are increasingly proposed as foundation models for market microstructure. Because the generative process of real markets is unknown, these models can be judged only by the realism of their output, leaving open what they actually learn. We make the question answerable by inverting the setup: we train GPT-style models on order flow from simulators whose latent parameters are known, so that the Bayes-optimal predictor, the generating state, and the exact data entropy serve as references. Measured against them, next-token pretraining on order flow implements amortized Bayesian inference over market regimes. The learned predictive matches the exact Bayes optimum to within a millinat per token and approaches the oracle floor even on a nonstationary family whose latent state drifts within an episode, a regime that requires filtering. The latent regime is linearly decodable from frozen activations, well above baselines, so a frozen-model read-out calibrates simulator parameters more accurately than windowed maximum likelihood at a fraction of the cost. In our experiments these capabilities are not produced by scale: capacity and token volume saturate early, and it is the diversity of training regimes, not the token count, that determines generalization to unseen markets. On real NASDAQ data, zero-shot transfer is set by how well the simulator prior covers real flow: an enriched mixture nearly closes the gap to an in-domain baseline, and pretraining beats from-scratch training at every budget across held-out tickers. Known ground truth turns average next-token loss, which is uninformative near the entropy floor, into an exact comparison against the Bayes-optimal and oracle predictors.

Federated learning over decentralized networks inherently trades off the suppression of local finite-sample noise through collaboration against the bias that collaboration introduces between heterogeneous nodes. We study this tension by performing a large-dimensional analysis of Generalized Total Variation Minimization with least-squares models. Using tools from random matrix theory, we show that Lipschitz observations of the global GTVMin solution concentrate in large dimensions, universally for any underlying network structure. We provide exact analytic expressions for the asymptotically precise performance under both i.i.d. and non-i.i.d. Gaussian mixture distributions on a fixed network. For the latter, these expressions quantify how regularization balances local adaptation against collaboration. Our theoretical results are confirmed by experiments on synthetic and real-world data.