Papers

Group Relative Policy Optimization (GRPO) stalls on a model's hardest problems: when no rollout in a group succeeds, the group-relative advantages vanish and the problem contributes no gradient, wasting the frontier examples we most want to learn from. Prepending a correct prefix of a reference solution raises the success rate, making prefix length a continuous knob on difficulty. Concurrent methods set the knob once; AdaPrefix-GRPO turns it into a feedback controller: throughout training it adjusts how much of the solution each problem gets, holding its success rate near 50%, where GRPO's gradient signal is largest, then withdraws the assistance entirely, so the deployed model solves problems unaided. On hard math, at matched training FLOPs, it more than doubles GRPO's accuracy on held-out problems from the training distribution for a 0.6B model (2.1x), with 1.6x on Qwen3-1.7B and 1.7x on AIME, while roughly halving trace length. The method is implemented in data preparation plus a loss mask on prefix tokens; the trainer is otherwise stock. The smaller the model, the larger the gain.

Medicine is inherently multimodal, requiring clinicians to synthesize information across diverse data streams. Yet the development of multimodal foundation models is constrained by limited access to large-scale, high-quality clinical data. Although PubMed Central (PMC) offers a complementary source of expert-authored image-text data, existing PMC-derived resources remain limited in fidelity, reproducibility, and clinical validation. We introduce MedPMC, an automated, continuously updatable framework that transforms permissively licensed literature into high-fidelity infrastructure for medical multimodal models. Applied to 6.1 million PMC articles, MedPMC curated 11 million medical image-text pairs. Component evaluations showed strong performance for initial screening (F1 = 93.2), multi-panel figure detection (F1 = 96.5), figure separation (mAP = 89.8), caption separation and alignment (F1 = 81.4; ROUGE-L = 85.3), and medical figure classification (F1 = 96.5). Manual review by five annotators, three with medical training, found 95.3% of MedPMC images medically relevant, versus 19.7% in a prior PMC-derived dataset. Across 26 benchmarks spanning 11 specialties, a MedPMC-trained CLIP-style model improved average zero-shot AUC by 7.1 percentage points over the strongest architecture-matched biomedical CLIP baseline despite using fewer than half as many image-text pairs. As the vision encoder in a multimodal large language model, it improved medical visual question-answering by 1.9 and 16.9 percentage points across two benchmarks. In 10,524 Yale New Haven Health System dermatology photographs, it improved morphology-to-image retrieval Recall@5 by 11.7 percentage points. These findings show that high-fidelity literature curation strengthens medical multimodal foundation models across benchmark and clinical settings. We publicly release the framework, corpus, benchmarks, and pretrained models.

Probabilistic circuits (PCs) can model complex joint distributions while supporting exact and efficient computation of many inference queries. However, standard likelihood-based PC learning is vulnerable to overfitting and fragile generalization when confronted with data noise, small sample sizes, or distribution shifts. This can be mitigated using distributionally-robust optimization which consider worst-case distributions within a Wasserstein ball of the empirical distribution, but current methods are limited to training a model from scratch in this framework. Instead, we propose PeTeR: a novel, data-free post-training framework designed to robustify pre-trained PCs against distribution shifts without retraining from scratch. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR effectively robustifies baseline models against both random and adversarial perturbations, achieving competitive or superior performance to data-dependent robust learning baselines.

Large language models hallucinate most about entities they have never seen. We ask whether a model's activations betray entity familiarity before a single answer token is generated, and whether that signal predicts the factual reliability of the answers. On four Polish Bielik models (1.5B-11B parameters), we probe four entity domains (athletes, cities, writers, musicians), each with 42 well-known, 42 obscure-but-real, and 42 fabricated entities addressed by a one-sentence question (504 prompts per model). Two unsupervised, single-forward-pass dispersion measures over post-SwiGLU MLP activations, inverse participation ratio and spectral entropy, separate known from fabricated entities at AUROC 0.95-1.00 across all domains and scales; a supervised linear probe reaches 0.99-1.00. Both clear selection-aware permutation floors of about 0.70-0.74 (empirical p<=1e-3), survive held-out layer selection (0.93-0.99), and persist on real names (known vs. obscure-but-real: 0.96-1.00). The signal transfers across entity types (mean off-diagonal AUROC 0.92-0.99); a matched-template counterfactual shows the only large drops are template-caused, not entity-type effects, and the signal is diffuse across heads. This representational signal is already at ceiling at 1.5B, whereas behavioral factual reliability scales sharply: 0, 2, 10, and 19 of 42 known athletes are answered fully correctly by the 1.5B, 4.5B, 7B, and 11B models under a strict judge. Within known entities, separating correct from hallucinated answers is much harder (probe 0.93; dispersion no better than a first-token-entropy baseline). A five-sample semantic-entropy baseline reaches only 0.71-0.83 at 5x the inference cost. Despite this internal awareness, the models almost never abstain: an audit of 2,520 answers finds 2 refusals and 1 hedge. Entity familiarity and factual reliability are distinct phenomena on different scaling curves.

Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules. We analyze CFG through an asymptotic-preserving, numerical-analysis lens. Building on a recent result that the deterministic DDIM step is the unique fitted operator for the unguided terminal layer, exact on the final small-sigma stretch of sampling, we show that guidance re-stiffens exactly the discriminative subspace to an anomalous exponent 1+w. DDIM is therefore no longer fitted there, and on coarse meshes its guided residual diverges as sigma_min goes to zero. We prove a guided clock barrier with three ordered step-size thresholds, and read one-step oversaturation as its endpoint: a solver artifact on the calibration model rather than the continuous guided law. The same analysis yields a one-coefficient, zero-extra-NFE repair: replace CFG's w(r-1) by r^(1+w)-r on the guidance direction. On the calibration model's discriminative crossover, this removes CFG's sigma_min-divergent blow-up and is first-order accurate against the exact guided flow as sigma_min goes to zero. On learned CIFAR-10 checkpoints, and as a cross-domain smoke test on Stable Diffusion 1.5 DDIM, it acts as a high-guidance stabilizer at no extra cost rather than a universal quality knob: it cuts residual amplification and saturation, gives 9/9 point-FID wins over CFG on the tested grid, and preserves classifier-proxy target accuracy in the hard-cell blocks. We report the limits alongside: it is not a universal image-quality win, and against a dense vanilla-CFG reference it is not a uniformly better integrator of that field.

Deep learning has significantly advanced time series imputation, yet most existing architectures primarily rely on localized temporal context within the corrupted input sequence. This reliance can be limiting in real-world scenarios, where time series often exhibit non-stationary dynamics, weak temporal correlations, and infrequent patterns that are difficult to reconstruct from nearby observations alone. In this paper, we propose ALER-TI, Aligned Latent Embedding Retrieval for Time Series Imputation, a retrieval-augmented framework that explicitly leverages historical patterns to supplement degraded local context for more reliable missing-value reconstruction. The core of ALER-TI is Latent Embedding Alignment (LEA), which mitigates the representation mismatch between corrupted queries and complete historical candidates. By applying post-hoc masking in the latent space, LEA aligns candidates with the query's missingness pattern while allowing historical embeddings to be pre-computed and cached for efficient retrieval. ALER-TI is model-agnostic and can be integrated with various imputation backbones through a lightweight adaptation module. Extensive experiments on six real-world datasets under different missing rates demonstrate that ALER-TI consistently improves strong baseline models and enhances robustness across diverse imputation settings.

This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a continuous-time optimal control problem, we derive rigorous error estimates that quantify how approximation error distributes across network layers. This error decomposition enables a principled depth adaptation strategy: new layers are inserted at locations of maximum estimated error, allowing the network to efficiently capture complex, nonlinear variations in the underlying problem. Our framework introduces a novel network architecture that treats weights and biases as piecewise linear functions varying across layers, with the error estimator bounding the discrepancy between this discrete representation and the true continuous optimal control solution. The approach leverages dual weighted residual methodology from finite element analysis to derive computable upper bounds on the functional error. A key theoretical contribution is the derivation of explicit error bounds that decompose the total approximation error into interval-wise contributions, providing a rigorous basis for targeted architecture refinement. We demonstrate the effectiveness of our method on scientific datasets, including learning the observable-to-parameter map for the Navier-Stokes equation. Numerical results reveal that our approach consistently outperforms existing architecture adaptation methods in terms of generalization performance.

Nonlinear least-squares objectives form the foundation of scientific machine-learning tasks, yet even curvature-aware optimizers remain geometrically inconsistent at finite step sizes: Levenberg-Marquardt (LM) derives its direction from local Riemannian metrics but realizes it as a straight parameter update. Here we introduce RNC-LM, which carries the LM direction along a locally constructed curved trajectory in Riemann normal coordinates. A recursive reformulation of the geodesic equation generates arbitrary finite-order corrections while reusing the same damped Gauss-Newton matrix factorization, and curve length is controlled separately from damping. On a reaction-diffusion physics-informed neural network benchmark, RNC-LM reduces relative $L^2$ errors below $8\times10^{-3}$, whereas L-BFGS, LM and LM with geodesic acceleration remain near one. On a large-scale machine-learning potential fitting task with 985,160 configurations, fourth-order RNC-LM reaches a fixed training-error target with a $34\times$ wall-clock speedup over LM. These results establish finite-step geometric realization as a distinct optimizer design principle.

Background: Graph neural networks improve computational prediction of polypharmacy side effects, but standard binary cross-entropy training allocates equal capacity to well-classified and difficult examples, potentially missing clinically significant interactions. We evaluated whether an asymmetric focal objective could improve multi-relational drug-drug interaction (DDI) prediction by emphasizing difficult positive interactions. Methods: ClinicalFocal loss was integrated into a relation-aware graph convolutional network using molecular fingerprints, physicochemical descriptors, and learned embeddings. The model was evaluated on TWOSIDES using five-fold cross-validation with identical experimental conditions (architecture, features, data partitions, hyperparameters, and random seeds) for ClinicalFocal loss and binary cross-entropy baseline. Results: ClinicalFocal loss increased accuracy from 0.699 to 0.892 (+19.3 percentage points) and F1 score from 0.700 to 0.894 (+19.4 percentage points). AUROC increased from 0.766 to 0.914, and AUCPR increased from 0.714 to 0.860. The false-negative rate decreased from 29.8% to 9.1%, while specificity increased from 69.6% to 87.5%. Overall classification error decreased from 30.1% to 10.8%, corresponding to a 64.1% relative reduction. Improvements were consistent across all five folds. Conclusions: Asymmetric focal optimization improved classification and ranking performance while achieving 90.9% recall for observed interaction triples, without modifying the underlying architecture. Loss-function design is a direct, tunable lever for improving graph-based DDI prediction.

Assigning Common Weakness Enumeration (CWE) categories to Common Vulnerabilities and Exposures (CVE) records remains an important but largely manual step in vulnerability analysis. We study this task as a text classification problem and compare two modelling choices: a multi-class formulation that predicts a single CWE per CVE and a multi-label formulation that allows multiple assignments. Three transformer encoders (BERT Base, SecureBERT, and CySecBERT) are evaluated on three nested label spaces (83, 47, and 25 classes). Multi-class training achieves higher macro-F1 across all settings, although the gap to multi-label narrows from 21 to 2 percentage points as the label space shrinks. Post-hoc threshold optimisation on the multi-label side closes this gap on the 25-class setting. Confusion analysis shows that the dominant misclassification patterns follow the CWE hierarchy and are shared across all three encoders (Pearson $r > 0.92$), which suggests that the error structure is driven more by taxonomy design than by encoder choice. A hierarchy-relaxed evaluation that forgives within-family confusions raises macro-F1 from ${\sim}$81% to ${\sim}$90%, indicating that strict metrics understate branch-level classifier quality. CySecBERT achieves the strongest results overall, with statistically significant gains concentrated in the multi-label setting.

One-shot federated learning (OSFL) addresses the communication overhead of federated learning by limiting training to a single round, but doing so without sacrificing model quality is non-trivial, particularly when client data distributions diverge. Recent work has addressed this challenge by aggregating client knowledge on the server through the construction of transferable synthetic datasets or distillates. However, most of these methods lack formal privacy guarantees, leaving a gap in jointly achieving low communication, robustness to heterogeneity, and rigorous privacy. We propose FedKT-CSD (Federated Knowledge Transfer via Collaborative Synthetic Data), a framework inspired by neural image compression that closes this gap by leveraging publicly pretrained autoencoders as a shared latent space. Each client encodes its private data in a single forward pass, computes class-conditional latent statistics, and transmits these to the server. The server aggregates these statistics via secure aggregation, adds calibrated differential privacy noise, and decodes a synthetic dataset for training a global model and further downstream tasks. This design provides formal $(\varepsilon,\delta)$-differential privacy by construction, while keeping client-side computation and communication lightweight. Despite operating under privacy constraints, FedKT-CSD is competitive with and even outperforms non-private baselines across diverse datasets and heterogeneity settings, and scales to a large number of clients. Our code is available at: https://github.com/an7123/FedKT-CSD

One-shot pruning methods like Wanda and SparseGPT apply the same sparsity ratio to every layer of a transformer, ignoring known variation in layer importance. We propose PALS (Percentile-Aware Layerwise Sparsity), which adjusts per-layer sparsity based on the 99th percentile of activation magnitudes, bounded to $\pm 5\%$ around the target ratio. On LLaMA-2-7B at 50% sparsity, PALS achieves 10.96 WikiText-2 perplexity versus 12.92 for uniform Wanda (mean over 9 runs, $p < 0.001$). The benefit is architecture-dependent: LLaMA-3-8B shows marginal gains and Mistral-7B shows none. We also find that gradient-based allocation – the seemingly more principled approach – produces results worse than random, suggesting that gradient magnitude does not predict the impact of discrete weight removal. PALS adds negligible cost to the pruning pipeline and requires no fine-tuning.

Training a model with noisy gradient descent can be idealized as overdamped Langevin dynamics, and a natural safety question is to bound the probability $\nu_t(\mathcal{A}_H) = \mathbb{P}(Q_t \in \mathcal{A}_H)$ that the trajectory lies in a designated failure region $\mathcal{A}_H$. We study this for a smooth, strongly convex loss in $d$ dimensions, with $\mathcal{A}_H$ separated from the minimizer by an energy gap. At the end of training, the equilibrium mass $\pi(\mathcal{A}_H)$ is exponentially small in $d$, with a complementary energy-barrier rate when the noise is small. Along the trajectory, a shape-free bound $\nu_t(\mathcal{A}_H) \le \pi(\mathcal{A}_H)(1 + \sqrt{\chi_0^2/\pi(\mathcal{A}_H)}\,e^{-mt})$ shows the in-set probability relaxes to (twice) the static value after a burn-in of order $d$, using only the global spectral gap $m$. A worked Ornstein-Uhlenbeck example shows this burn-in is necessary: an angular slice of the equilibrium shell can transiently swell by a factor exponential in $d$, though its equilibrium mass is tiny. To rule this out we introduce a local relaxation rate, defined through the spectral measure of the region's centered indicator rather than a Dirichlet-form Rayleigh quotient. For geometrically isolated regions this rate exceeds the global one, shrinking the burn-in, and with a maximum-principle ceiling it caps the trajectory probability uniformly in time. Strong convexity sets how fast training relaxes, but the shape of the unsafe set decides whether the trajectory bulges through it on the way to equilibrium.

Artificial intelligence (AI) is a double-edged sword: while it has achieved remarkable success across a wide range of domains, its deployment also calls for effective oversight and regulation, for which the detection of AI-related content and artifacts is perhaps the most direct and cost-effective approach. To this end, we propose a unified detection framework based on Mahalanobis distance scores (MDS), applicable to several important settings, including the detection of large language model (LLM) generated text, hallucination, watermark, and adversarial examples. A key component of the proposed method is to accurately characterize the positive class–such as human-generated text, factual statements, unwatermarked text, or non-adversarial samples–which requires an efficient and robust estimator of the covariance matrix of deep representations of positive samples before computing the MDS. Since the positive samples typically consist of multiple classes, and these classes may exhibit both homogeneity and heterogeneity, we develop joint estimation methods for both the casewise and cellwise minimum covariance determinant (MCD) estimators. We provide efficient optimization algorithms for both estimators and prove their convergence. We provide a reasonable definition of the breakdown point for the joint estimators and prove their corresponding high breakdown point properties. Empirical evaluations confirm the effectiveness of the proposed detection framework.

We address the problem of efficiently sampling multimodal probability distributions, where standard Markov Chain Monte Carlo methods often suffer from poor mixing and mode trapping. To mitigate these issues, we propose Gradient-free Riemannian Langevin Sampler (GRiLS), a novel proposal that improves exploration without requiring gradient evaluations of the target density. Our approach introduces a Riemannian metric which reshapes the local geometry in order to facilitate transitions across modes. The resulting gradient-free MCMC algorithm is particularly suitable for complex, computationally expensive targets where derivatives are unavailable or impractical. The GRiLS proposal requires knowing the mean and covariance of the target density, which we estimate using an ensemble of interacting particles. Empirical results on multimodal benchmarks demonstrate that GRiLS achieves improved mixing compared to existing gradient-based and gradient-free MCMC approaches.

Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation. We provide one. Data augmentation induces a similarity graph on the unlabeled data, so downstream learning on that graph is graph-Laplacian-regularized learning. We prove a fast transductive rate, $O(1/n_L)$ in the number of labels, in place of the supervised $O(1/\sqrt{n_L})$, by carrying the leave-one-out stability apparatus of Johnson and Zhang (JMLR 2007) over to the augmentation graph, and without the unrealistic assumptions of limit-based analyses (exact kernel, generalizing features). The bound makes augmentation quality explicit: the expected error is at most $C/n_L + R_{\mathrm{DA}}(y)$, where the data-augmentation alignment error $R_{\mathrm{DA}}(y)$ is proportional to the graph-cut mass of augmentations that cross a label boundary, so good augmentations let few labels suffice. The analysis uses a streamlined loss that drops the projector, negative-sample, and orthogonality overhead of standard objectives yet still recovers the top-$K$ ideal features in the infinite-data limit, the augmentation-kernel eigenspace studied by Zhai et al. The bound gives a mechanistic account of the accuracy-versus-label-count curve through augmentation quality, verified in a controlled model where the constants are known.

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.

Reinforcement learning (RL) is becoming increasingly important for post-training large language models (LLMs). Previous RL pipelines for LLMs were mostly synchronous and batch-interleaved, which is inefficient for long-horizon agentic tasks. Recently, asynchronous RL has emerged as a more efficient alternative by updating the model as rollouts arrive. However, existing asynchronous RL systems often emphasize throughput, while leaving training stability and task effectiveness largely underexplored. For example, a key challenge is that group-wise sampling in the widely-used GRPO framework does not naturally fit asynchronous agentic training. In this paper, we present Single-rollout Asynchronous Optimization (SAO) to address the stability and off-policy challenges in asynchronous RL. To reduce off-policy effects and improve generalization, we replace group-wise sampling with single-rollout sampling, that is, using one rollout per prompt. We further improve this single-rollout strategy with practical value-model training designs. To improve optimization stability, we introduce a strict double-side token-level clipping strategy. SAO is able to train stably for one thousand steps and consistently outperform GRPO and its variants on agentic coding and reasoning benchmarks, such as SWE-Bench Verified, BeyondAIME, and IMOAnswerBench. We also demonstrate that single-rollout RL is particularly effective in a simulated online learning setting, where the model must adapt to changing evolving environments. To this end, SAO is successfully deployed in the agentic RL pipeline for training the open GLM-5.2 model (750B-A40B).

Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder – either from scratch on the target dataset or via pretraining on large corpora – and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.

Testing is a major effort for the gaming industry, requiring a significant part of development budget and people power. We present a case study on a development version of the ice hockey game EA SPORTS NHL 26, for which human playtesters test the goalie AI for behavioral exploits. To reduce the effort of re-testing the goalie AI after every game or behavior modification in the development phase, we propose Reward-Adaptive Iterative Discovery (RAID), a novel approach to automatically find exploits using an iterative Reinforcement Learning (RL) approach that trains a population of goal scoring agents. While previous approaches can already successfully find exploits, RL algorithms tend to overfit to a single solution. We introduce a simple extension on top of existing RL algorithms, such that they find multiple diverse high-quality solutions. For our first deployment of this approach, within a single experiment we were able to find six hockey scoring exploit strategies that were qualitatively similar to those that playtesters had found in hours-long manual testing sessions.

Gradient communication is a primary scaling bottleneck in large language model (LLM) pretraining. Communicating gradients in low-precision formats, such as FP8 and NVFP4, can significantly reduce the communication volume. Existing methods quantize gradients via linear or nonlinear mappings in Euclidean space, often degrading model performance because highly anisotropic gradients incur direction-dependent distortion. We present GeoFP8, a geometry-informed gradient scaling method that performs low-precision communication in geometry-aware coordinates. By transforming gradients into a near-isotropic space before quantization, GeoFP8 makes low-precision representations substantially more faithful to their high-precision counterparts. GeoFP8 only changes the coordinate system used for low-precision gradient communication and does not change the optimizer, training recipe, communication collective, or low-precision format. We also develop a simplified geometry-aware transformation algorithm with low-rank approximation and selective application to balance the computation overhead and communication reduction. We examine the empirical convergence of GeoFP8 using Llama-300M and Llama-600M models. Our results show that GeoFP8 reduces the end-to-end pretraining time of Llama-600M by 7.6% on 64 NVIDIA GH200 Superchips, while improving the downstream task preservation profile over direct Euclidean FP8 communication under the same optimizer and communication path.

FFT-based spectral preprocessing of learned query-key (Q/K) projections substantially improves transformer attention on character-level language modelling. On TinyShakespeare: a fixed random spectral filter achieves val=1.031 (Delta=+0.443); a single learned frequency at paragraph scale achieves val=0.608 (Delta=+0.867); and four learned frequencies spanning paragraph to word scale achieve val=0.309 (Delta=+1.166), a 79% reduction over standard dot-product attention. The single-frequency result is confirmed across three random seeds (mean val=0.236, std=0.019). The four frequencies converge to a near-geometric multi-scale ordering (49, 27, 10, 6 tokens/cycle) corresponding to paragraph, sub-paragraph, phrase, and word scales. The gain is specific to spectral preprocessing: random orthogonal and non-orthogonal projections of Q/K produce no measurable improvement, suggesting the benefit comes from global frequency-domain mixing rather than metric distortion. All results are verified by a shuffled-validation diagnostic against positional leakage. Causal filters (Gaussian, Mexican Hat, Morlet) do not improve over standard attention at character-level tokenisation: the bilateral FFT kernel is structurally non-causal, coupling every position to future tokens. This defines an architectural boundary between bilateral spectral attention (this paper) and genuinely causal spectral attention at word-scale tokenisation (companion paper MorletQK). This work is architecturally distinct from FNet (Lee-Thorp et al., 2021), which replaces attention with Fourier mixing of token embeddings. Here, spectral preprocessing applies only to Q/K projections while the full attention score structure is preserved.

Machine learning models are increasingly deployed in high-stakes domains, raising concerns about both privacy and fairness. Differential Privacy (DP) has become a gold standard for privacy-preserving data analysis, while fairness-aware mechanisms aim to mitigate discrimination against underrepresented groups. However, these objectives can conflict: DP often amplifies disparities across demographic groups, and little is known about whether established fairness interventions remain effective under DP constraints. In this work, we present, to our knowledge, the first systematic evaluation of fairness interventions on differentially private synthetic tabular data. Our benchmark centers on the Adaptive Iterative Mechanism (AIM), identified as the state-of-the-art marginal-based DP synthesizer (Cormode et al. 2025). We thus evaluate fairness interventions across four datasets, multiple group fairness metrics, and three categories of mitigation strategies (pre-processing, in-processing, and post-processing) under a wide range of privacy budgets. We compare four pipeline configurations: (Baseline) training on original data; (DP-only) training on DP synthetic data; (Fair-only) applying fairness mechanisms on original data; and (DP+Fair) combining fairness mechanisms with DP synthetic data. Our results demonstrate that while DP alone can degrade both utility and fairness, applying fairness interventions can partially restore equitable outcomes. Among them, post-processing methods tend to provide more stable fairness-utility trade-offs across privacy budgets and synthesizers, achieving strong fairness improvements while preserving competitive utility relative to other intervention stages. We release all code, data, and experimental artifacts in an open-source repository to ensure full reproducibility and to support future research on the privacy-fairness-utility trade-off.

We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\ell^1$, and observations are generated through a possibly nonlinear forward operator $A:\ell^1\to H$, where $H$ is a vector-valued reproducing kernel Hilbert space. We propose an $\ell^1$-regularized empirical risk minimizer and develop a theoretical analysis of its statistical properties. Under mild assumptions, we establish almost-sure consistency and derive non-asymptotic high-probability convergence rates in both the prediction and $\ell^1$ reconstruction norms. The rates depend on the source smoothness parameter $r$, characterized by a variational source condition, and the effective dimension exponent $b$, describing the polynomial spectral decay of the covariance operator. We further prove matching minimax lower bounds, showing that the obtained convergence rates are optimal. To relate the theory to practical sparsity models, we consider finitely smoothing operators of the form $A=G\circ S$, where $S$ is a synthesis operator, and show that approximation-space assumptions imply the required variational source conditions. In particular, we prove that membership in the approximation space $k_t$ is equivalent to polynomial decay of the best $n$-term approximation error. Finally, we verify the assumptions for two representative inverse problems: reaction coefficient identification in elliptic PDEs and sparse computed tomography. For filtered Radon transforms, we derive explicit effective-dimension asymptotics, yielding concrete convergence rates for standard image models and sparsifying systems.

Agents acting on our behalf in the real world (e.g. placing phone calls) must learn online from costly, often irreversible interactions rather than cheap simulator steps. Two things follow. First, deployability depends on the path, not only the outcome. An agent must respect outcome-neutral constraints such as not repeatedly calling an unresponsive user, respecting business hours, or completing required authentication constraints that outcome-based rewards cannot express, since violating them frequently improves apparent success. Second, because each interaction is expensive, the agent must learn efficiently from very few examples. Reinforcement learning from verifiable rewards (RLVR) is blind to both challenges: it optimizes solely on the outcome and wastes expensive rollouts on all-fail groups where group-relative advantage collapses to zero. Attempts to densify supervision by rewarding progress target the hard-to-verify direction. In contrast, real agentic environments can cheaply detect bad moves. Since group-relative advantage is equivalent to within-group variance, a dense signal helps only when it supplies variance the outcome lacks. A verifiable penalty on the path meets this condition reliably, while a progress potential helps only where partial progress is reachable. The resulting recipe "penalize the path, reward the outcome" achieves high task success with near-zero violations, where outcome-only training violates constraints on nearly every episode. We provide four design rules for effective penalties, including avoidance of the inaction trap that arises when a penalty is used in isolation.

Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding differential equations into neural network training, enabling constitutive operators to be recovered directly from sparse and noisy observations. However, the extent to which operator recovery depends on architectural design, optimisation strategy and the information within the data is not yet well understood. We present an empirical study of how these factors influence mechanistic inference using BINNs applied to one-dimensional advection-diffusion-reaction partial differential equations. Across a suite of problems, we investigate how network expressivity, learning rate, loss weighting and batch size influence optimisation behaviour, reconstruction accuracy and operator recovery. We show that mechanistic inference is governed by balancing competing objectives rather than maximising any single aspect. Moderately expressive architectures outperform complex networks, intermediate learning rates balance efficient exploration with optimisation stability, accurate operator recovery requires a balance between data-fitting and PDE residual losses and intermediate batch sizes provide the best compromise between efficient parameter space exploration, computational efficiency and reproducibility. We further identify practical diagnostics for recognising common failure modes, including over-fitting, unstable optimisation and poor mechanistic recovery. These findings establish guidelines for deploying BINNs as credible tools for biological model discovery and demonstrate that reliable mechanistic inference is achieved by appropriately balancing model expressivity, optimisation, physical consistency and data informativeness.

We prove that, in the realizable PAC setting, the sample complexity of exact-trace learning for full autoregressive Chain-of-Thought traces is upper bounded by the standard multiclass rate of the local next-token class, where this rate is governed by the Daniely–Shalev-Shwartz dimension. Under exact-trace loss, one wrong action makes the whole trace incorrect; nevertheless, for every stopping rule $\mathtt{halt}$ and every pointwise $\mathtt{halt}$-halting local class $\mathrm{H}$, $n_{\mathrm{PAC}}^{\varepsilon,\delta}(\operatorname{Roll}_{\mathtt{halt}}(\mathrm{H}))=O((\operatorname{DSdim}(\mathrm{H})+\log(1/\delta))/\varepsilon)$, with no dependence on rollout length. The dependence on $\operatorname{DSdim}(\mathrm{H})$ is worst-case optimal, since one-step stopping recovers ordinary multiclass learning of $\mathrm{H}$. The proof introduces parity dimension, a rollout-stable refinement of DS dimension based on even pseudo-cubes. It controls one-inclusion density via a low-coordinate spanning theorem on finite restrictions and, unlike DS dimension itself, does not increase under autoregressive rollout. We also show why this detour is necessary: DS dimension can increase under rollout.

While whole-body multimodal medical imaging scanners have been increasingly recognized for more effective medical applications, the excessive long acquisition time in PET-MR scanning is a major obstacle in more efficient clinical practice. Deep learning-based MRI translation provides a potential solution to reduce scan duration. However, current models often focus on specific anatomical regions and face challenges for whole-body scans that consists of highly heterogeneous feature distributions mainly due to (1) different anatomical regions across whole-body, and (2) lesions or pathological tissues. This paper tackles the challenges through a novel Heterogeneity-Adaptive Diffusion Schrodinger Bridge (HA-DSB) framework. By explicitly modeling translation as stochastic transport between source and target distributions, HA-DSB incorporates region context embeddings derived from a vision-language model (VLM) to enable region-specific modeling. To enhance fidelity of the pathological tissue, lesion-aware metabolic prior from PET is integrated directly into the bridge dynamics through a dual-stage guidance mechanism. Specifically, a PET-guided noise modulation module adaptively scales spatial diffusion perturbations during the forward process, while PET features are leveraged during the reverse process to selectively amplify lesion-relevant structures via an attention mechanism. Experiments demonstrate the superiority of our method across different body regions in whole-body MRI translation and show improved translation quality in lesion areas under PET guidance. Our code is available at Github.

Reliable confidence estimation remains a key limitation of test-time adaptation in vision-language models (VLMs), where prompt tuning improves zero-shot accuracy but often degrades calibration due to entropy-driven overconfidence. Prior approaches mitigate this using LLM-derived class attributes and contrastive regularization, yet treat attributes independently, ignoring their relational structure. We propose ARGTCA, which represents (class, attribute) pairs as nodes in a Symbolic Attribute Graph and trains a Graph Attention Network (GAT) using contrastive objectives to produce structurally informed embeddings that capture inter-attribute dependencies. We introduce two attribute selection strategies: ARGTCA-DIV for intra-class diversity and ARGTCA-DISC for inter-class discrimination. Experiments across nine benchmarks show that ARGTCA-DIV reduces average Expected Calibration Error (ECE) by approximately ~37% over baselines, while ARGTCA-DISC consistently performs as the second-best variant, reducing average ECE by approximately ~17% over baselines. These results suggest that modeling symbolic attribute interactions provides a principled approach for reliable test-time adaptation in VLMs.

Large Language Models (LLMs) store factual knowledge and domain-specific patterns implicitly in dense Transformer parameters, making knowledge expansion costly through pretraining, fine-tuning, retrieval augmentation, or longer contexts. Engram-style memory offers a compact hidden-state injection pathway, but existing GPU-resident designs often rely on hash-based compression, causing unrelated phrases to collide in shared slots and weakening phrase-level semantic fidelity. We present TF-Engram, a train-free Engram system that constructs phrase-specific semantic memory offline from external corpora, stores large memory tables across a GPU–DRAM–SSD hierarchy, and uses Early-Exit Guided Predictive Prefetching to hide external-memory latency during autoregressive decoding. On Qwen3-0.6B, TF-Engram improves the average downstream score from 57.6 to 59.4, outperforming both the frozen backbone and a parameter-matched LoRA baseline. System evaluation shows that large TF-Engram tables can be built with moderate offline cost, SSD-backed storage substantially reduces GPU memory demand, and predictive prefetching recovers much of the throughput loss caused by external memory access. These results demonstrate that static phrase memory can be integrated into LLM inference as a scalable, train-free, and low-overhead system component.