Papers

Recurrent neural networks (RNNs) are widely used for sequence learning, yet their application is commonly associated with temporal data, although recurrent computation fundamentally operates on ordered sequences rather than on time itself. Building on this observation, we introduce the Ordered Structural Dependency Hypothesis (OSDH), which proposes that multiple admissible orderings of the same observations may reveal complementary structural dependencies inaccessible through a single sequential organization. To operationalize this hypothesis, we propose the Independent Structural Expert Principle (ISEP), whereby projection-specific sequence models are trained independently before their learned representations are integrated through a dedicated fusion model. As a concrete realization, we present Structural Evolution RNNs (SE-RNNs), which employ conventional RNNs as projection-specific structural experts while preserving the underlying recurrent computation unchanged. Proof-of-concept experiments on three synthetic datasets with substantially different levels of structural complexity demonstrate that the proposed architecture consistently benefits from multiple ordered projections when hidden structural dependencies are present, while remaining competitive on simpler datasets. Since OSDH is independent of the underlying sequence-processing model, the proposed framework naturally extends beyond recurrent networks and may be instantiated using alternative architectures. The results suggest a general computational perspective for exploiting complementary ordered representations across diverse structured learning problems.

Adversarial training under long tailed distributions suffers from a dual imbalance: the class imbalance skews the training objective toward head classes, and the adversarial inner maximization may further amplify this bias. Existing methods mitigate this issue by correcting class priors or adapting class wise robust supervision, yet they treat each class in isolation and fail to identify which boundaries drive long tailed collapse. We propose a Confusion Geometry Rebalancing method (CGRm) for long tail adversarial training, a plug in framework that leverages directed robust errors as training signals. CGRm leverages periodic robust evaluations to derive source class loss weights, class wise robust coefficients, and a directed confusion geometry graph. The method then couples feedback weighted robust optimization with graph guided margin correction, thereby boosting the robustness of vulnerable classes and sharpening the critical boundaries that drive long tailed performance degradation. Experiments on long tailed benchmarks show that CGRm achieves consistent robust performance gains over existing methods, with ablations validating the contribution of each component. We provide the code in the supplement.

Federated learning (FL) in Low Earth Orbit (LEO) satellite constellations is affected by non-IID data and irregular ground-station visibility, both driven by orbital geometry. Global aggregation performs poorly when orbit-level class distributions are disjoint, while strong personalisation can be excessive when these distributions overlap. We present FedOrbit, which combines continuous orbit-level training over inter-satellite links, class-aware hierarchical aggregation, quality-weighted feature aggregation with return-rate dampening, and adaptive feature decomposition based on inter-orbit class similarity. Across three remote-sensing benchmarks and two non-IID partitions, FedOrbit achieves the highest accuracy in five of six settings and is within $0.9$ percentage points of the best result in the sixth. The gains over the strongest baseline reach $16.1$ percentage points under Dirichlet partitioning and $8.6$ under pathological partitioning, with the smallest per-orbit accuracy spread in five of six settings.

Probabilistic coastal hazard assessments require accurate characterization of tropical cyclone (TC) parameters, yet datasets often contain missing records for the radius of maximum winds (Rmax), a key variable in Joint Probability Method analyses. This study evaluates data-driven approaches for Rmax imputation, including one-dimensional Convolutional Neural Networks (1DCNNs), Long Short-Term Memory (LSTM) networks, and conventional machine learning models. We examine physics-informed input augmentation, temporal modeling, and transfer learning using synthetic RAFT and STORM datasets for pre-training and observational IBTrACS data for fine-tuning. Including the radius of 34-knot winds (R34) substantially improves performance across all model types. Temporal models achieve higher average correlations than non-temporal models despite using approximately an order of magnitude fewer samples, indicating better preservation of relative Rmax variability across storms. This advantage is more pronounced when R34 is unavailable, suggesting temporal information can partially compensate for missing storm-size predictors. Transfer learning does not improve performance, likely because synthetic datasets have lower and less variable Rmax distributions than IBTrACS. These findings demonstrate the potential of temporal deep learning for reconstructing incomplete TC records and highlight the importance of physics-informed inputs, observational data availability, and distributional consistency in coastal hazard assessment.

AI coding agents now write a growing share of production code, and human security review does not scale at the rate code is generated. The agents in widest use are closed-weight, so a deploying team cannot read their internals. It can instead run an open-weight model as a reviewer over the agent's output. That reviewer's activations are readable. We ask whether reading those activations recovers a security signal that simply asking the same reviewer misses. We fit a single linear probe per model on a corpus of paired vulnerable-and-fixed Python functions, then test it without retraining on real disclosed vulnerabilities whose weakness type the probe never saw in training, across five open-weight reviewer models. On the vulnerabilities fixed by changing a single function, the probe scores the vulnerable function above its fix on 61-67% of cases for every model, beating the 50% chance line. It also beats the same model's prompted YES/NO win-rate read from its logits, under every prompt we try. Asking the model for a written verdict, even with chain-of-thought, returns the same answer on the vulnerable and fixed function most of the time and so cannot tell them apart. Model activations carry a code-security signal that prompting the same model misses.

Face presentation attack detection (PAD) aims to reliably detect a wide range of presentation attacks. While PAD methods achieve strong performance within individual datasets, their performance degrades under cross-dataset evaluation. Variations in sensors or lighting conditions can reduce the effectiveness of detectors from near-perfect to nearly random. Foundation models (FMs) have emerged as a promising alternative because typical PAD datasets, such as the MCIO benchmarks (MSU-MFSD, CASIA-FASD, Replay-Attack, and OULU-NPU), are small relative to the scale used for web-based pretraining. However, existing PAD systems primarily focus on CLIP-based foundation models, while overlooking other FMs with different architectures and training procedures. This study addresses this question by systematically evaluating 32 FMs. Zero-shot prompting achieves performance near chance across model families and scales. The vision encoders, when low-rankadapted (LoRA) with fewer than 1% trainable weights, achieve below 2% intra-dataset ACER in most cases, while cross-dataset ACER is substantially higher. LoRA primarily refines the decision boundary within a dataset, suggesting that pretrained representations and the adaptation dataset play a larger role in cross-dataset generalization than the evaluated lightweight adaptation strategy.

Collision avoidance systems are commonly used to avoid fragmentation events occurring in Low-Earth Orbit (LEO) and Geosynchronous Equatorial Orbit (GEO). However, these events have been growing in frequency as orbital congestion worsens with the launch of megaconstellations. Consequently, conjunction alerts and collision risks are becoming increasingly common. Current practices, which are commonly manual or rule-based, have difficulty scaling to these worsening dynamic environments. To address this intensifying situation, we propose a reinforcement-learning policy for autonomous collision avoidance, trained via Proximal Policy Optimization (PPO) along with an open-source, high-fidelity astrodynamics simulator for training and evaluation. In 1,000 deterministic GEO episodes, our agent achieves a 97.5% collision avoidance success rate, outperforming traditional controllers such as a rule-based baseline (20.7% success) and an impulsive delta-v planner baseline (27.5% success). To achieve these results, we designed a simulator to train and evaluate our agent, using real-world and simulated debris. We simulate Newtonian two-body dynamics using Sun/Moon third-body perturbations, fuel-dependent thrust, and configurable debris fields. The agent is trained with curriculum learning and shaped rewards oriented toward encouraging survival, adequate projected miss distance, and delta-v conservation. Finally, our evaluation consisted of a fully deterministic pipeline, including shared seeds, per-episode logs, and telemetry exports. Our work is a publicly available framework at https://purl.org/sat-trajectory-avoidance

Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs. Unlike forms of regression that fit parameters assuming a fixed model structure, symbolic regression is a search problem over the space of expressions, represented, for example, as abstract syntax trees using a library of operators. Symbolic regression is typically used in settings with limited, noisy data in the natural sciences. However, searching for a single best-fitting expression fails to capture the epistemic uncertainty about the expression, which motivates a Bayesian perspective that enables uncertainty quantification and specification of natural priors to constrain the search space. In this work, we propose ERRLESS (Entropy-Regularized Reinforcement Learning for Expression Structure Sampling), a scalable approach for sampling from the posterior distribution over expressions given data using maximum-entropy reinforcement learning. ERRLESS learns a neural policy that constructs expressions sequentially by building up their abstract syntax trees. At convergence, the policy samples expressions from the posterior. At test time, expressions can be sampled by rollouts of this policy. We demonstrate that ERRLESS achieves competitive results on the Feynman benchmark while producing short and interpretable expressions. Additionally, we demonstrate that the mean of the posterior predictive approximated by ERRLESS achieves a high coefficient of determination ($R^2$) compared to an SMC baseline, highlighting the benefits of the Bayesian perspective in symbolic regression.

Lane detection requires recovering thin, elongated, and frequently occluded lane structures under challenging driving conditions. While anchor-based detectors provide efficient candidate generation, their performance is limited by two coupled issues: backbone features often lose structural continuity along partially visible lanes, and classification confidence may decouple from line-level localization quality, allowing inaccurate anchors to persist before non-maximum suppression (NMS). We propose a structure-enhanced and quality-aware framework that improves lane representation and dynamic-anchor scoring while preserving the inference pipeline of the Anchor Decomposition Network (ADNet). Specifically, a Gated Horizontal-Vertical Token (GHVT) module enhances mid- and high-level backbone features via lightweight directional token interactions with a learnable residual gate. In parallel, Line-Quality-Aware Dynamic Anchor Scoring (LQAS) calibrates existing classification logits using quality supervision, hard-negative suppression, and pairwise ranking without adding inference branches. On the VIL-100 dataset, our method improves ADNet-R34 from 89.97 to 91.28 in F1 score at the 0.5 intersection-over-union threshold (F1@50), reducing both false positives and false negatives. Additional experiments on CULane and TuSimple datasets, extensive ablations, score-distribution diagnostics, and runtime analysis confirm complementary structural and ranking improvements with minimal computational overhead.

Graph Neural Networks (GNNs) suffer from two fundamental limitations: over-smoothing, where node representations become indistinguishable with depth, and over-squashing, where long-range information is compressed through limited message-passing channels. Existing metrics such as Dirichlet energy provide global characterizations of over-smoothing but lack the resolution to analyze node-level behavior and guide architectural improvements. In this paper, we propose LEED (Local Embedding Evolution Distance), a novel local metric that quantifies over-smoothing by tracking the evolution of individual node embeddings across layers. By operating at the node level, LEED enables fine-grained analysis of representation dynamics during training, revealing heterogeneous over-smoothing patterns that are invisible to global energy-based measures. This locality induces informative node importance scores, interpreted as embedding-driven centrality measures. We leverage LEED to design a more efficient strategy for virtual node selection. Unlike existing approaches that depend on multiple heuristic centrality measures, our method uses LEED as a unique criterion to guide the construction of Local Virtual Nodes to mitigate over-squashing. Experiments show that LEED provides more informative diagnostics than Dirichlet energy while preserving global evaluation, and enables more effective virtual node integration, improving GNN performance across datasets.

Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities. Despite this progress, how such representations behave under continual learning poses fundamentally different challenges that remain underexplored. This work provides a geometric perspective on this problem and establishes a theoretical foundation for representation preservation in hyperbolic space, showing that preventing forgetting requires cross-modal invariance under a shared hyperbolic isometry. We further show that forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion, motivating preservation of both cross-modal relational structure and hierarchical geometry. Guided by these insights, a principled continual learning framework is derived that preserves essential geometric structure while allowing effective adaptation to new tasks. Experiments on continual multimodal benchmarks corroborate the effectiveness of the proposed approach.

Optimization theory is a widely used tool for intelligent decision-making. While classical optimization deals with fixed, time-invariant objective functions, many modern applications operate in dynamic environments where data arrive sequentially, and the learning objective evolves over time, often under decentralized data and communication constraints. Motivated by these trends, we study decentralized optimization from streaming data through a structured time-varying formulation in which the global objective is a temporally weighted average of losses observed across the network. We analyze multi-iteration decentralized first-order methods, including decentralized gradient descent. For strongly convex and smooth losses, we develop guarantees for the Euclidean-norm tracking error through a contraction-mapping viewpoint. The resulting bounds decompose the tracking error into a fixed-point tracking component and a bias term induced by decentralization and data heterogeneity. We specialize our analysis to uniform and exponentially discounted weights, as well as their finite-memory windowed counterparts. The bounds explicitly characterize the roles of the temporal weighting rule, per-step iteration budget, step size, and network connectivity. Uniform weighting yields a vanishing fixed-point tracking contribution of order $\mathcal O(1/t)$, whereas discounted and windowed strategies generally induce non-vanishing tracking floors governed by the discount factor and effective memory, respectively. In all cases, decentralization induces an additional non-zero bias floor under a constant step size. Numerical experiments illustrate the predicted trends.

How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for determining whether task-specific behavior must be stored in model weights or can instead be induced at inference time through the prompt. We show, in an approximation-theoretic sense, that pretraining is optional: a single-layer softmax attention network with random, untrained weights can approximate any Hölder function on a compact manifold when steered by an appropriate soft prompt. Guided by the connection between softmax attention and kernel methods, we construct explicit soft prompts (a prompt per target function, independent of the query) as solutions to linear systems matching attention logits to Gaussian kernel exponents, under which the frozen transformer emulates the classical Nadaraya-Watson kernel estimator. The construction requires only a mild rank condition on the weights, which we show holds almost surely under Gaussian initialization. The prompted network inherits the theoretical guarantees of kernel regression, leading to universal approximation theorems with minimax-optimal rates that depend on the intrinsic dimension. We further quantify the cost of prompting, exposing a tradeoff between the norm of the constructed soft prompt tokens, prompt length, and hidden dimension. Numerical experiments corroborate the constructions and predicted rates.

Large reasoning models (LRMs) achieve remarkable success on complex tasks but remain vulnerable to harmful prompts that induce unsafe outputs. Recent methods align LRMs using direct refusals or safety rationales, yet often focus on prompt patterns rather than intrinsic attack mechanisms. As a result, these pattern-centric alignments struggle to generalize across diverse jailbreaks, compromising adversarial robustness and reasoning utility. We propose AdvSafe, a dual-adversarial framework that enables LRMs to internalize unsafety knowledge by explicitly deconstructing adversarial mechanisms. This moves beyond pattern-dependent traces, fostering robust cognitive defense without compromising reasoning utility. Our pipeline operates via a two-phase adversarial game. First, in adversarial synthesis, an autonomous agent dynamically crafts deceptive jailbreak prompts, adapting its strategies to breach a strong teacher model. Second, in adversarial extraction, the breached teacher executes a cognitive counter-attack. For every successful jailbreak, the teacher unmasks the camouflage, explaining why the attack succeeds and how such prompts can be identified and mitigated. This dual-adversarial process yields a compact reasoning dataset capturing rich, generalizable unsafety knowledge. Student models trained on this dataset implicitly acquire safety alignment through intrinsic threat comprehension. Experiments show that with only 1K synthesized samples, AdvSafe-aligned LRMs achieve significantly stronger jailbreak robustness than existing baselines, with almost no utility degradation. Furthermore, AdvSafe improves robustness against out-of-distribution prompts, demonstrating that learning unsafety knowledge enables a superior robustness-utility trade-off and generalizes beyond seen attack patterns.

Stochastic gradient descent (SGD) and its variants train deep neural networks (DNNs) effectively in practice, yet classical optimization theory does not fully explain this success: conventional analyses rest on differentiability, convexity, and smoothness, assumptions that DNN objectives routinely violate. We close this gap by generalizing convexity and smoothness, through Legendre functions and convex conjugation, into a unified optimization framework for DNN training. We introduce \(\mathcal{H}(\psi)\)-convexity and \(\mathcal{H}(\Psi)\)-smoothness, a single formalism that encompasses convex and non-convex as well as smooth and non-smooth objectives and reveals a natural duality between generalized convexity and smoothness. Building on these notions, we derive generalized gradient descent (GD) and generalized SGD via convex conjugation. We prove that generalized GD attains an optimal learning rate of exactly \(1\), and we establish rigorous gradient-energy-based convergence rates for both optimizers. We further recast DNN training as a composite optimization problem and show that its convergence hinges on jointly reducing the gradient energy and controlling the extreme eigenvalues of the structure matrix; a model capacity risk quantifies the residual error that no optimizer can remove. Experiments on six datasets (MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100, TREC, and SST-2) and on convolutional, residual, and Transformer architectures, with five loss functions, are consistent with the predicted training dynamics.

We present a reproducibility study of XFeat, a lightweight local feature extractor and matcher designed to identify corresponding points across images efficiently on resource-constrained hardware. We re-implement the architecture based on the paper and supplementary material, re-evaluate the authors' released checkpoint alongside our re-implementation, and conduct additional architectural ablations to examine design choices that were not fully justified in the original work. This distinction between re-evaluation and reproduction is important, as the paper, supplement, and public code differ in several implementation details, including the backbone layout, fusion block, and training losses. Empirically, our reproduced models closely match and, in some cases, outperform the re-evaluated original checkpoint on MegaDepth-1500 and ScanNet-1500, supporting the main claim that XFeat provides a strong accuracy-efficiency trade-off for standard image-matching benchmarks. Our ablations provide a more nuanced view of two architectural arguments from the original paper. In particular, the parallel keypoint branch is important for semi-dense matching, but its benefit is less pronounced than originally claimed, while the evidence for the specific placement of the single skip-connection remains inconclusive. Finally, we reproduce the original downstream evaluations and find close agreement for homography estimation, while Aachen visual localization remains below the reported results, even for the released checkpoint, suggesting sensitivity to underspecified evaluation details. We then extend the analysis to zero-shot out-of-distribution and cross-modal matching across retinal, thermal-visible, and multimodal remote-sensing imagery, where XFeat remains effective in some settings but degrades sharply under severe modality shifts.

We consider the extensive-form bandit problem where on each trial the learner plays an extensive-form game against an oblivious adversary. We focus on the notion of switching regret, which measures the expected performance of the learner against that of any switching sequence of mixed strategies in retrospect. Our algorithm takes a parameter $\rho>0$ and achieves a switching regret of $\tilde{\mathcal{O}}((1/\rho+\rho K)\sqrt{H A T})$ where $K$ is the number of switches in the comparator sequence, $H$ is the maximum number of the learner's information sets that can be traversed during a play of the game and $A$ is the number of actions that the learner can possibly take. Our algorithm is extremely efficient, taking a per trial time of only $\mathcal{O}(H B)$ where $B$ is the maximum number of actions available to the learner at any of its information sets.

In this paper we provide Monte Carlo and deep neural network approximations for stochastic representations of solutions to linear elliptic partial differential equations with constant diffusion, drift and killing. Building on the modified Walk-on-Spheres algorithm of Beznea et al. (arXiv:2209.01432), we introduce Monte Carlo estimators that explicitly incorporate sampled random times arising in the analyzed stochastic representations. We establish uniform error bounds for these estimators and show that, under suitable assumptions, a prescribed approximation accuracy is achieved with sample complexities growing at most polynomially in both the inverse accuracy and the problem dimension. Furthermore, we prove a deep neural network approximation result for the stochastic representations. Assuming suitable neural network representations of the boundary data and the distance function to the boundary, we use the constructed Monte Carlo to design deep neural networks that approximate the representation uniformly with a number of parameters growing at most polynomially in the inverse accuracy and the problem dimension. These results extend previous complexity analyses to a broader class of elliptic equations involving drift and killing.

Task arithmetic composes skills by adding weight displacements, and merged models are then judged on benchmark suites. We measure when that composition is functionally additive, and find that the answer depends as much on how the model is prompted as on which tasks are merged. Across two-dimensional composition surfaces – five model settings from 0.5B to 8B, two families, LoRA and full fine-tuning – pairwise non-additivity is real, seed-stable, and transfers in coarse order to unseen task pairs: all eight preregistered sign predictions held. But it is input-conditioned everywhere we measured: the same merged model that shows a six-point interaction contrast on code prompts shows none on math prompts, and wrapping the identical code prompts in the instruction template the adapters were trained on collapses the contrast twenty-fold, from +6.9 to +0.3 points – while re-serializing them in an untrained chat template leaves it intact (+12.5), falsifying our own preregistered prediction. Execution benchmarks (pass@1) inherit the training-format wrapper's blindness. Weight-space composition therefore supports coarse, input- and format-conditioned functional statements – not a universal merging-performance predictor, and not one that training-format evaluations can see.

Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention. However, existing T-PINNs still face a fundamental challenge: they mainly rely on pre-specified low-rank tensor decompositions with manually tuned ranks, which limits their ability to capture the underlying structures of multivariate solution functions and hinders their practical deployment. To address this challenge, we propose a hierarchical rank-evolving (abbreviated as HRE) representation for multivariate functions, which endows us to faithfully capture the underlying structure of the targeted multivariate function accompanying with automatic rank determination. Concretely, in the hierarchical design of HRE representation, the target multivariate function is decomposed as a small-scale inner tensor with a set of univariate functions along each mode, where a customized tensor network decomposition can be readily deployed to capture the underlying structure of the small-scale inner tensor. In HRE representation, the crucial hyperparameters, ranks, can be adaptively revealed during the decomposition, freeing us from manual rank tuning and making HRE practically applicable to real-world problems. Besides, we build the HRE-PINNs correspondingly. Extensive numerical experiments, including high-dimensional static problems (Helmholtz equation and Poisson equation), nonlinear time-dependent problems (Klein-Gordon equation), and complex fluid-dynamics problems (flow mixing equation and Navier-Stokes equation), demonstrate that HRE-PINNs consistently outperform existing state-of-the-art approaches in terms of accuracy.

State Space Models (SSMs), as a mainstream research direction of linear Transformers, aim to achieve higher efficiency than standard Transformers in long-context modeling. However, existing SSMs suffer from limited input adaptivity and constrained memory capacity, leading to information loss when modeling ultra-long sequences. To address these limitations, we propose MixFormer, a novel linear Transformer that integrates a Mixture-of-Memory-Experts (MoE) mechanism. Specifically, the model maintains differentiated memory states through multiple collaborating memory experts and employs a novel Time-Aware Linear Attention (TALA) mechanism, which leverages learnable exponential decay functions and positional biases to dynamically update memory. This design enables the model to selectively reinforce important historical information while effectively mitigating memory dilution, substantially improving long-range dependency modeling. Experiments on long-sequence text and image generation tasks demonstrate that MixFormer not only achieves significant performance gains but also provides a more sustainable computational backbone for the next generation of web infrastructure.

Cardiac digital twin research is moving from subject-specific anatomical replicas toward virtual cohorts that represent clinically relevant population subgroups. Yet access to representative imaging-derived anatomy datasets remains limited by cohort size, subgroup sparsity, and data-sharing constraints. Conditional generative models could help address this gap, but virtual cohorts are useful only if they preserve realistic, metadata-dependent anatomical variability. Existing cardiac anatomy generators largely rely on conditional variational autoencoders (cVAEs), which couple representation learning and metadata conditioning through a shared regularized latent prior. We introduce CAN-FLOW, a two-step Conditional ANatomy generation framework based on normalizing FLOWs that first learns geometry-only latent representations of diffeomorphic cardiac shape momenta and then models their sex-, age-, and body-mass-index-dependent distribution with a conditional normalizing flow. We trained CAN-FLOW on 2,208 healthy UK Biobank subjects and compared it with cVAEs across regularization strengths. CAN-FLOW generated plausible stochastic biventricular anatomies that better reproduced clinical phenotype distributions, metadata-dependent trends, subgroup variability, point-cloud coverage, and high-dimensional shape variability. Together, these results establish CAN-FLOW as a shareable framework for generating realistic, stochastically varying, metadata-conditioned biventricular anatomies for virtual cohort construction and in silico clinical trial workflows.

On–off cycling is the main cause of compressor wear in residential heat pumps, yet reinforcement learning (RL) controllers for buildings typically optimise only energy cost and thermal comfort, ignoring how much the learned policy cycles. We add a levelised compressor-wear term to the control reward and study how the resulting behaviour depends on the RL algorithm. Training Soft Actor—Critic (SAC) and Proximal Policy Optimisation (PPO) on an identical Markov decision process for the BOPTEST bestest hydronic heat pump case, we find that SAC learns a continuous modulation policy that keeps the compressor permanently engaged—the operating principle of an inverter-driven heat pump—achieving zero start-ups per day, whereas PPO collapses to bang-bang control that cycles more than the baseline. On the BOPTEST emulator the SAC policy cuts thermal discomfort by up to 90.7% for an 11.5% cost increase, while eliminating all baseline cycling.

Betting-based sequential tests and Blackwell approachability are linked by a rate-explicit reduction through support-function residuals. For a compact convex target $S$ and vector observations $r_t$, an OCO learner selects a predictable normal $w_t$ and produces $q_t=\langle w_t,r_t\rangle-h_S(w_t)$. We prove the exact pathwise identity $$ \dist(\bar r_T,S) =\frac1T\sum_{t=1}^Tq_t+\frac{\Reg_T}{T}. $$ When $|q_t|\leq B$, composing this identity with one-sided betting yields a finite-time transfer: if the OCO and log-wealth regrets are at most $a_T$ and $\ell_T$, respectively, then a target gap exceeding \[ \frac{a_T}{T} +2B\sqrt{\frac{\log(1/\alpha)+\ell_T}{T}} \] forces rejection by time $T$, while non-rejection certifies the converse radius. We then formulate a controlled stochastic experiment in which an action selected after $w_t$ satisfies Blackwell's supporting-halfspace condition for every null mean payoff. The resulting wealth is an e-process under adaptive nulls; sublinear OCO regret gives stochastic approachability, whereas persistent mean separation under an alternative gives exponential wealth at rate at least $\delta^2/(4B^2)$. Deterministic Blackwell games and passive tests are, respectively, the noise-free and singleton-action cases of this protocol. Bounded two-sample means, kernel MMD, and active heterogeneous data sources instantiate the reduction. The resulting connection is exact algebraically, quantitative at finite time, and operational when experiments are controlled.

On-policy distillation (OPD) aligns a student with a teacher on trajectories sampled from the student itself, reducing the train-test state mismatch of offline distillation. The same feedback loop can nevertheless be unstable: each update changes both the policy and the states on which the next update is computed. We introduce WDL-OPD, a mixture-constrained co-training method with two trainable policies. An anchor policy generates every rollout, an auxiliary policy evaluates the same visited states, and a geometric mixture of their token distributions is matched to a frozen teacher by reverse KL. Both policies receive gradient. We show that freezing the auxiliary recovers an anchor-plus-contrast proxy target closely related to OPD$^2$ and W2S-OPD, whereas joint training creates branch-level degrees of freedom that a static delta cannot express. In recorded Qwen3 experiments at 1.7B and 4B scale, WDL-OPD produces the strongest student checkpoint in each of four scale-domain settings. It raises MATH500 accuracy from 0.630 to 0.685 at 4B and from 0.521 to 0.585 at 1.7B. In code generation, seven single-policy OPD configurations exhibit entropy growth or trajectory degradation, while co-training reaches independently re-evaluated development scores of 0.637 and 0.375. Because several comparisons differ in curriculum or initialization, these results support a stabilization hypothesis rather than a universal causal claim. We provide the exact training algorithm, failure evidence, and the controlled comparison matrix needed to test that hypothesis.

A main promise of looped language models is depth-adaptive inference. By looping a block of shared layers a variable number of times, the model can use less compute for "easy" tokens and more for "hard" ones. However, tokens with different numbers of loops cannot share a uniform forward pass and therefore cannot be handled by standard batching systems such as vLLM. The practical value of depth-adaptive inference thus hinges on whether batching can be made efficient. We introduce the first efficient method for depth-adaptive looped LMs via continuous depth batching (CDB), which forms new batches between loop steps. Our method dynamically schedules looped and non-looped parts of the architecture, manages looped KV-caching, and predicts which tokens will exit the loop in advance so it can prepare batches asynchronously. Experiments on Ouro 1.4B and Huginn 3.5B show that fully looped architectures are best suited to depth-adaptive inference, as large non-looped layers outside the recurrent core (e.g., token embedding, LM head, and unshared transformer blocks) slow down and complicate scheduling. Overall, CDB realizes up to 99% of the estimated maximum speedup available, leaving further gains primarily dependent on model architecture and exit behavior.

In regulated domains such as finance, a model that cannot be explained cannot be deployed, yet many interpretable classifiers defeat their own purpose by producing formulas with dozens of features that no regulator could read. We take the reverse direction. Starting from an interpretable classifier expressed as a single equation over the input features, we progressively simplify it into more readable forms, including a pruned monomial, a directional if–then rule, and the integer scorecards and tallies that finance already deploys. Because the equation is itself the predictive model rather than a post-hoc explanation we can directly quantify what is lost under each simplification. Across four financial datasets, we find that pruning is nearly free and that fidelity can erode faster than predictive performance, allowing simpler rules to remain effective classifiers without faithfully reproducing the original model. A human assessment shows that simplification improves perceived readability, while preferences for different representations vary by professional background. Beyond measuring these losses empirically, we show that some can be anticipated from the original model: we derive a bound on the change caused by pruning and predict how faithfully a rule retaining only the direction of each feature's effect preserves the original ranking.

Wearable human activity recognition (HAR) remains challenging due to the computational and energy constraints of deep learning models on resource-limited devices. Existing lightweight approaches often rely on recurrent architectures (e.g., GRU and LSTM), limiting parallelism and increasing inference latency. We propose LITEWAY, a modality-agnostic, fully convolutional framework for multichannel sensor time series that replaces recurrent temporal modeling with structured convolutional decomposition. LITEWAY combines lightweight convolutional blocks, strided temporal processing, and convolution-attention pooling to efficiently capture temporal dependencies while reducing computational complexity. We evaluate LITEWAY on 16 HAR datasets against TinyHAR, TinierHAR, and MLP-HAR. LITEWAY achieves competitive macro F1 while reducing model size by 4.06x-9.52x (Light) and 3.87x-9.07x (Full) compared with TinyHAR and TinierHAR. Deployment experiments further show energy reductions of 2.29x-3.14x (Light) and 1.46x-2.01x (Full) compared with TinierHAR and MLP-HAR, highlighting efficient fully convolutional temporal modeling for wearable HAR. The source code is publicly available at https://github.com/dominique-nshimyimana/liteway.

Deep decoder-only Transformers often replace the original Post-Norm architecture with Pre-Norm variants because Post-Norm training is highly sensitive to warmup and learning rate under conventional initialization schemes. Although prior work has identified rank collapse and gradient vanishing as related symptoms, it remains poorly understood how causal attention creates high-similarity representations and why training dynamics fail to repair them. We give a two-stage analysis of Post-Norm rank collapse using token similarity as a scalar state variable. First, at initialization, causal attention acts approximately as a prefix-averaging operator that increases token similarity across depth, while the SwiGLU branch contributes only a smaller damping effect. Second, once training enters a high-similarity regime, growth of pre-normalization residual norms makes the RMSNorm backward factor contractive; under mild conditions, gradients to earlier layers decay geometrically. As a complementary result, we characterize the properties of a collapsed network: its best predictor is frequency distribution with relatively high loss floor, and gradients in collapsed layers vanish at frequency distribution. Experiments on 48-layer decoder-only Transformers trained on C4 dataset match the predicted initialization-time similarity growth and collapse-time gradient contraction, and show that collapsed runs stay near the predicted frequency loss. Together, these results distinguish the forward similarity amplification and backward repair incapacity in Post-Norm collapse, while also characterizing the behavior of collapsed networks.

Invariant-learning objectives pursue similar goals yet produce qualitatively different regularization paths, leaving unclear when shortcuts can be suppressed without damaging stable modes. Our starting point is simple: in the desired shortcut-suppressed regime, shortcut loading is small, so the objective's low-order expansion governs local stability and residual amplitude. This brings the problem into the domain of Landau phase-transition theory. We establish a mathematical isomorphism between the near-critical normal form of predictive-mode learning and Landau theory, identifying the learning objective as an effective free energy and critical-mode amplitude as an order parameter. The resulting low-order objective signatures predict distinct regularization phenotypes: quadratic $R_2$ terms shift phase boundaries and enable finite-strength elimination, whereas quartic $R_4$ terms continuously attenuate acquired modes while leaving nonzero residual loading at finite strengths. Higher-order terms may further shape nonlinear tails. In a canonical bilinear model, we derive exact phase boundaries and equilibrium loadings, identifying conditions for a selective-retention window in which shortcut suppression preserves stable structure. Controlled bilinear and ReLU experiments, including an MNIST construction, support the predicted signature-phenotype relation, while coupled-feature experiments validate its extension to collective modes. The framework connects the mathematical structure of invariant-learning objectives to what models learn as regularization varies.