Papers

Neural representations can encode more features than they have dimensions, a phenomenon known as superposition. We study the dimension needed to compute Boolean gates from such representations. For a single threshold layer with a Gaussian random dictionary and uniformly random sparse Boolean inputs, we derive sharp dimension thresholds under two error criteria. A vanishing expected error count can require more dimensions than correctness of every output with high probability. Shared reads explain the gap: rare realizations can produce many errors at once. The expected-count threshold has ball geometry, while joint reliability has box geometry when a gate is evaluated on every feature tuple. Optimizing shared readout weights and biases gives explicit thresholds for conjunction, disjunction, and majority. For pairwise conjunction, the analysis also describes the transition near the threshold, in agreement with exact simulations.

We present TraceRelay, an attention-aligned recurrent architecture that distributes persistent representations over a rolling sequence of low-dimensional traces. Local right looking attention forms increments from lower-layer representations; delivery is delayed until all attended inputs are in the causal past. A fixed additive phase recurrence accumulates the delayed increments, and left-looking attention reads the resulting residual augmented stream. A stride-wise prefix sum supports parallel prefill and bounded-buffer continuation. We study 36 small-model runs on Equal Repeats, bounded Dyck closing-type prediction, and causal Most-Freq generation, using three seeds per setting. At trained length 256, Equal Repeats models with recurrent phase inheritance reach 98.81-99.69% accuracy versus 50.73-51.63% for separately trained variants without inheritance, despite the latter receiving more updates. Accuracy drops sharply at lengths beyond the training range. At the longest evaluated lengths, models with more dimensions in the middle layer's recurrent traces perform better on Dyck (76.34% versus 55.49% close accuracy at length 4096), whereas models with fewer trace dimensions perform better on five-symbol Most-Freq (70.74% versus 55.60% exact generation at length 1024). These contrasting cases motivate further study of how the size of recurrent representations should be chosen for different tasks, without establishing a general rule across tasks or model configurations.

Neural networks are typically trained using first-order methods and back-propagation. It is unclear whether this approach is optimal for morphological layers whose weight Jacobians are sparse and whose resulting parameter gradients can be poor. In this work, we propose a novel weight update method for morphological neural networks inspired from the Multiplicative Weights Update (MWU) scheme. We view each morphological perceptron as an instance of the learning from experts' advice problem in logarithmic space, and use a correlation-based reward that favors inputs aligned with the desired output change, regardless of whether a strong gradient signal has reached their weight. We empirically evaluate our approach by training fully connected layers both as stand-alone models and as parts of larger transformer networks. Across nine benchmarks, correlational training yields improvements on eight, by up to 32.84 percentage points, while substantially reducing run-to-run variability.

Bayesian physics-informed neural networks (B-PINNs) are a popular framework for parameter and state inference from sparse or noisy observations. They are commonly formulated via a collider structure, in which physical and trajectory parameters are assumed to be a priori independent and become coupled through virtual likelihoods on differential-equation residuals that enforce physical consistency. We show that this modeling choice can induce severe systematic bias in the posterior over physical parameters: even when the prior is favorably centered on the ground-truth parameters, the resulting posterior can drift away and concentrate far from them. As a remedy, we advocate a hierarchical chain model in which physics generates trajectories, which in turn generate observations. The chain model does not suffer from this posterior bias, but it poses a harder, so-called doubly intractable, inference problem due to a physics-dependent normalization constant. This challenge can be resolved by discretizing the underlying stochastic dynamics, after which the chain posterior can be sampled exactly with particle MCMC. We identify two distinct mechanisms characterizing the collider bias, derive analytical approximations of their magnitudes, and establish diagnostic criteria for predicting when standard B-PINNs remain reliable. Experiments confirm the predicted bias and show that the chain formulation successfully avoids it.

We introduce Timer-M1, a pretrained multivariate time series foundation model that learns with primitives for zero-shot forecasting. Across domains, time series share elementary temporal and relational patterns, termed primitives, yet differ in how these primitives manifest and evolve across different contexts. Despite progress in zero-shot and task-general forecasting, existing foundation models may still struggle to generalize to complex real-world scenarios. To this end, we develop a primitive-based data synthesis and pretraining pipeline. The synthesis pipeline generates series with temporal primitives shared across domains and then assembles real and generated series into multivariate samples using relational primitives. Afterwards, samples are organized into episodes by assigning distinct channel roles as target variates, past-only covariates, and known-future covariates, ensuring that the model is optimized on predictable variates using available exogenous information. Technically, Timer-M1 further adapts gated two-dimensional Transformer blocks that dynamically allocate cross-variate attention across layers. Across three large-scale forecasting benchmarks, Timer-M1 ranks first on both FEV and TIME and second on GIFT-Eval among most recent time series foundation models. These results support effective primitive-based pretraining as a route to robust general forecasting technique across domains and task settings.

Standard weight decay treats each weight matrix as a vector and ignores its spectral structure. We introduce spectral weight decay, a post-step decoupled nuclear-norm update that applies additive rather than multiplicative spectral shrinkage. We connect the update to approximate proximal descent and show that its sensitivity to update order can exceed that of conventional $\ell_2$ weight decay near rank deficiency. Across LLaMA models with $124$M to $500$M parameters, spectral weight decay lowers effective rank and improves SVD-LLM compression at matched validation loss. At $500$M and a $4\%$ distortion budget, it reaches $1.89\times$ compression and $1.18\times$ GPU inference speedup, compared with $1.14\times$ and $1.01\times$ after standard weight decay. Under fixed-horizon training with $60\%$ label noise, it also improves final mean clean-test accuracy over matched $\ell_2$ regularization by up to $17.8$ points on MNIST and $4.6$ points across four BERT-base tasks. Code is available at https://github.com/brain-lab-research/SpectralWD.

Multimodal meme understanding is increasingly used to analyze socially sensitive content, yet existing models often exhibit biased behavior when interpreting economic dependence and social roles under ambiguity. Many memes express economic relationships through sparse text or symbolic visual cues, providing insufficient evidence for gendered attribution. In such underspecified settings, models tend to rely on pretraining correlations, leading to hallucinated and stereotypical economic role assignments. In this work, we study gendered economic dependence in image-text memes through the lens of contextual sufficiency and identify epistemic overcommitment-inferring roles without adequate evidence-as a primary source of bias. We propose CGER-Net, a context-grounded multimodal framework that estimates whether the input provides sufficient evidence for gendered economic reasoning and applies evidence-gated inference to enable confident attribution when cues are explicit while favoring principled abstention otherwise. We evaluate CGER-Net on EconMeme-GE, a curated dataset of image-text memes annotated as Men, Women, Neutral, or Ambiguous. Across strong contemporary multimodal baselines, CGER-Net reduces Gender Overcommitment Rate by up to 44% on ambiguous instances while maintaining comparable accuracy on unambiguous cases. Human evaluation further shows that 79% of generated rationales are judged as epistemically aligned with the available evidence. These results highlight the importance of modeling when not to infer for reliable and responsible multimodal analysis.

We describe a 4-tensor attention model that predicts the next semantic state of a scene, for video generation and robot planning. A window of states has positions (x, t) and two fibers, a semantic fiber and a temporal-context fiber, and one softmax normalizes attention jointly over the window. Frames and an agent's situation are written as those states; the encoder, the renderer, and the planner remain outside the update. To test the update on its own, we train on ROCStories, where each window poses the same next-sentence task at the semantic layer. On the validation split, with one seed per setting, the last-sentence cross-entropy on the three matched settings is lower for the 4-tensor model than for a free-running one-dimensional transformer by 5.3% at H=2, L=2, by 2.6% at H=4, L=2, and by 2.4% at H=4, L=3. At H=4, L=2 the parameter counts are nearly the same, 172.5M and 175.9M. On the same two GPUs that 4-tensor run finished in 2.4 hours and the baseline run in 45.2 hours; the baseline is trained by free-running decoding, one sequential forward pass per target token.

Hypernetworks that map a context directly to a LoRA adapter let a large language model carry that context in its weights, but prior work has demonstrated them only on base models of up to 14 billion parameters. We present the Internalizer, a state-of-the-art, portable Context-to-Parameter Mapping hypernetwork that generates document-specific LoRA adapters for the frozen 284B-parameter DeepSeek v4 Flash, a target two orders of magnitude larger than in any previous work. Most of its parameters live in a model-agnostic trunk with only thin entry and exit layers per base model, so it trains cheaply against small models before being ported to the large one. On unseen documents of up to 4096 tokens, the generated adapters reach 84.9% top-1 and 97.8% top-5 teacher-forced accuracy against 63.4% and 83.5% for the base model, with nothing in the context window but a three-word instruction. Once the hypernetwork is trained, a single forward pass turns any document into an adapter for such a model, which could be served alone for speed or alongside the document in the window to raise accuracy further.

Self-blended images are widely used to train face-swap detectors, but primarily capture blending artifacts. We investigate whether adding illumination inconsistencies improves detection. Temporal Self-Blended Images (T-SBI) transfer lighting statistics between frames of the same video, with the mismatch controlled by luminance difference ({\Delta}L). Using five training regimes and a three-seed comparison of high- and low-{\Delta}L training, we find no evidence of illumination-specific improvements. AUC differences remain within seed variability across four datasets, and an analysis of 506,328 attribute-binned samples shows no preferential reduction in errors under harsh lighting. Instead, T-SBI shifts prediction scores, changing optimal thresholds by approximately 0.34 on FaceForensics++ and 0.30 on Celeb-DF, making comparisons at a fixed threshold misleading. However, T-SBI improves robustness to heavy JPEG compression on DFDC (AUC 0.780 versus 0.696), potentially reflecting greater reliance on low-frequency cues. These findings highlight the importance of evaluating training methods against their intended targets and accounting for threshold effects.

Unsupervised learning is one of the main branches of machine learning. Here I argue that unlike the other branches of machine learning (supervised and reinforcement learning), unsupervised learning is a rather heterogenous field that can serve several different goals. It seems futile to try to define one single goal for unsupervised learning. I identify four different goals for unsupervised learning: 1) Estimating the distribution, 2) Generating new data points, 3) Extracting features for downstream tasks, and 4) Understanding the data.

Foundation models supply reinforcement learning (RL) with priors that mitigate its longstanding weaknesses in sample efficiency and transfer, but their token-by-token generation makes queries sequential and costly. Jev, a recently released decision model, generates nothing and returns calibrated, typed answers in a single forward pass. Existing work studies foundation models in RL either as models to be trained or as generators to be prompted, and Jev belongs to neither category, having so far served only as a black box in single domains. How well such a model decides on its own in RL environments, and how it can improve RL as a component of training, therefore remain unaddressed. To this end, in this paper we first examine the requirements that the objects of an RL system place on the answers they consume, and establish that Jev can fulfill all of them except the cardinal use of a value function. The remaining objects form positions that admit several roles each. We then construct algorithms that employ Jev at three of these positions, as a reference policy, an exploration judge, and a replay rater, to improve sample efficiency, exploration, and learning performance. Across nine MiniGrid tasks and three Atari games, training with Jev outperforms a standard RL learner, including where the learner makes no progress alone, while the model itself remains untrained. To our knowledge, we present the first use of Jev within the RL learning process and establish a frozen decision model as a usable component of RL training, inviting further exploration of how Jev and other advanced decision models can improve RL.

Fusing a learned camera-noise fingerprint with an RGB appearance backbone is an appealing route to generator-independent deepfake detection, because the noise residual is grounded in image-formation physics rather than in the texture statistics of a particular generator. We test, on FaceForensics++, whether a Noiseprint++ residual channel carries information complementary to an RGB Xception backbone for face-swap detection. A three-model ablation (RGB-only, residual-only, late-fusion) shows that fusion does not improve over RGB alone and that the residual branch alone is near chance. A seven-level bottleneck diagnostic localizes the cause: the noise maps do carry a discriminative signal, but it is statistical—carried by the per-sample first and second moments (mean, variance, energy) of the residual—and the per-sample InstanceNorm layer placed at the noise-branch input, following the TruFor template, standardizes exactly those moments away (five-fold cross-validated AUC drops from $0.747$ to $0.554$). A context-crop control rules out cropping geometry, and two fixed-fusion variants that remove the bottleneck recover the statistical signal yet still fail to beat RGB on every dataset. We conclude that, on this manipulation distribution, the noise residual is redundant with RGB rather than complementary, and we give concrete guidance for practitioners adopting noise-residual fusion for face-swap detection.

Diffusion models generalize early in training and later reproduce individual training samples. Standard tests detect memorization only once one-shot generation produces near-copies, leaving a released model unaudited until its outputs fail. We show that memorization is encoded in the geometry of the learned energy landscape before it appears in generated samples, a state we call latent memorization. Using score divergence and basin volume, we find that localized basins form around training samples and separate them from held-out samples before the first memorized sample appears, with an onset that follows the same $O(n)$ scaling as the memorization time. We probe these basins with cyclic denoising, which repeatedly applies partial noising and denoising. Under the exact empirical score, we prove that cycling started near an isolated training sample recovers it and returns to it over any finite number of cycles with high probability. In trained models, cycling recovers training images from CelebA and CIFAR-10 checkpoints whose one-shot samples contain no copies, and at a CelebA checkpoint with 0.1% one-shot copies, 500 cycles raise the memorized fraction above 30%. Cycling also reveals degenerate attractors that match no single training image and fade as training proceeds, so residence in a basin does not by itself imply memorization. These findings hold on a Gaussian mixture, CelebA, and CIFAR-10 across optimizers, architectures, noise schedules, and training-set sizes, and extend to off-the-shelf Stable Diffusion v1.4, where the cycled conditional-unconditional divergence gap separates memorized from non-memorized prompts with an AUC of 0.944 and a TPR of 0.866 at 1% FPR. More broadly, what a diffusion model has memorized is a property of the geometry and stability of its learned distribution, and assessing it requires examining this structure rather than generated outputs alone.

Reliable predictive uncertainty in Laplace approximations depends critically on the prior precision, yet selecting it requires a posterior sweep that is prohibitively expensive for neural networks with billions of parameters. Under the Maximal Update Parametrization ($\mu\mathrm{P}$), we derive a rescaling of the prior covariance that makes the selected precision stable as model width grows. This leads to $\sigma\mathrm{Transfer}$: we select the precision on a smaller model and zero-shot transfer it to the much larger model, i.e., without searching for the precision on the larger model at all. We show convergence of the prior kernel, posterior covariance, selected precision, and posterior-derived decisions under explicit conditions, and verify $\sigma\mathrm{Transfer}$ across regression, image classification, and Transformer readouts. For example, measured precision-sweep speedups reach $\sim 5000\times$ when transferring from width 128 to 4096 on MNIST, at a target-NLL degradation of $0.002$; transferring from a public 1B to 7B model gives a median search speedup of $\sim 2.3\times$ (up to $\sim 330\times$), with a mean measured target-NLL increase below $10^{-4}$ across ten tasks. The same posterior stability also enables transfer of acquisition, OOD-detection, and abstention decisions without constructing a target posterior.

Online platforms contain growing numbers of bots, deceptive reviewers, and scam accounts that imitate legitimate users. Such camouflage blurs graph neighborhoods and behavioral attributes, making it difficult for graph neural networks (GNNs) to distinguish both well-disguised fraudsters and legitimate users. Across diverse GNNs, we observe overlapping errors on a shared hard region, suggesting the presence of latent fraud evidence that graph topologies and standard features fail to capture. Fraud-specific GNNs can mitigate particular graph pathologies, yet they still make limited use of heterogeneous evidence such as structured records, text, images, and audio; uniform multimodal fusion may also disturb nodes already handled reliably by the graph. We propose Evi-VN to learn and correct these shared blind spots rather than build another fraud detector. To our knowledge, Evi-VN is the first graph fraud detection framework to use feature isolated evidence chains to correct hard regions shared across GNNs. Its evidence chains connect behavior, content, and context across structured, textual, visual, and acoustic sources, helping expose camouflage that graph neighborhoods may miss. Crucially, Evi-VN selectively applies this evidence only to likely hard samples via virtual class nodes, preserving both the reliable predictions and the input design of existing GNNs. Shared hard regions also let Evi-VN enhance generic, fraud-specific, and unseen GNNs even with imperfect evidence models. Experiments across bot, fake-review, refund-evidence, and telecom-fraud tasks validate these advantages.

Improving a long-horizon LLM agent means evolving the harness around a frozen model or training its weights. We let a self-evolving harness make the system stronger first, then cross seed and evolved harnesses with base and trained weights to learn which gains the trained model keeps and which still need the runtime. We show that the right lever can be read off the agent's failure composition: labelling failed trajectories by the first signal that fires separates process failures (blocked calls, loops, exhausted step budgets) from content failures (a delivered plan that is poor). Harness evolution repairs the former, the behaviour it instils can be trained into the weights, and content failures are what weight training is for. On DeepPlanning, a self-evolving harness loop lifts the held-out score of Qwen3.5-4B from 0.16 to 0.30 and of Qwen3.5-9B from 0.32 to 0.44; for 4B, held-out delivery rises from 55% to 90% while content failures are left for the weights. LoRA adapters trained on evolved-harness trajectories internalise the gain: under the original harness they add +0.13 on held-out tasks for both sizes; on 4B they stack with the harness to more than double the held-out score, and on 9B the adapter alone matches the full evolution line, cutting content failures from a quarter of trajectories to one in twenty. A placebo adapter trained on answer-shuffled trajectories falls below the base model. The loop transfers to WebArena-Lite (+0.09 on 117 unseen tasks), where the gain lives in what the model sees and adapters do not add to it. The result is a diagnose-then-intervene rule applied twice: read the failure composition to choose between harness and weights, then read what the accepted edits changed to decide which gains to train in. Scores are four-rollout means against fresh anchors, same-night except where marked, across eight models from six families and two benchmarks.

German is a morphologically rich language whose syllable structure is exceptionally well-predicted by the Knuth–Liang hyphenation algorithm. We ask whether phonologically informed tokenization can serve as a competitive target for end-to-end speech recognition. We compare three tokenizer families on the Omnilingual ASR wav2vec 2.0 backbone fine-tuned with CTC: the pretrained multilingual character inventory, a data-driven Byte-Pair Encoding (BPE) over orthography, and phonologically informed units from Pyphen syllabification and grapheme-to-phoneme conversion. Across 40 fine-tunes, we evaluate on three German test sets spanning orthogonal shifts: in-domain read speech, dialectal spontaneous speech, and standard-German spontaneous speech. In-domain, all phonologically informed tokenizers match BPE and the multilingual character baseline on both WER and CER. Under domain shift the picture splits along vocabulary size rather than the linguistic axis of variation: at small vocabularies, syllable-aware tokenization improves on dialectal speech, where phonetic surface forms vary but syllable structure is preserved, and stays ahead on spontaneous speech, where new word-forms violate vocabulary closure. A phoneme-level confusion analysis further shows that all tokenizers commit the same canonical function-word errors, indicating that the acoustic encoder, not the tokenizer, dominates the error topology. Our findings suggest that tokenizer choice may depend on the vocabulary budget as much as on the distribution shift expected at deployment rather than reducing to a single universal optimum.

Machine unlearning updates a trained model after records are deleted, aiming to match exact retraining without repeating the full training procedure. We develop Gaussian mechanisms for Newton updates under sequential deletion requests. Using Gaussian differential privacy (GDP) and its adaptive composition rule, we show that the full sequence of released models is statistically difficult to distinguish from matched exact retraining. To calibrate these mechanisms for empirical risk minimization, we derive upper bounds on the error of the Newton approximation relative to exact retraining and on how this error changes after each deletion batch. Independent Gaussian noise is calibrated using bounds on the full residual at each release, whereas Gaussian random walk noise uses smaller bounds on residual increments. These bounds yield allocations minimizing the worst-case maximum noise variance across releases under the resulting GDP certification constraints. With count-based bounds, the random walk asymptotically matches the worst-case variance of a single release at deletion cap $M$, while independent noise incurs an additional factor of order $M$. Set-based bounds can reduce the noise variances by using gradients and Hessians of the deleted records. For singleton deletion, we further show that count-based independent noise, count-based random walk noise, and set-based independent noise are minimax among fixed Gaussian covariances under their respective residual or increment bounds. With set-based bounds, allowing variances to adapt to deleted records can improve on every fixed covariance by a factor of order $(\log M)^2$ on some data sequences. The residual and noise bounds also yield parameter and predictive consistency relative to exact retraining, uniformly over deletion policies. Simulations and a credit default data analysis evaluate bounds, noise variances, and estimation errors.

Repairing scientific models from functional observations differs fundamentally from supervised prediction: feedback may certify a solution without revealing which structural correction is responsible. We study this setting for genome-scale metabolic model (GEM) repair, where multiple reaction edits can explain the same phenotypes and many apparently distinct edits correspond to the same biological mechanism. This many-to-one structure creates a hidden failure mode for conventional exploration: diversity in the output space need not translate into diversity of scientific hypotheses. We introduce QuotientPO, which collapses equivalent repairs into canonical mechanisms and optimizes exploration directly over the resulting quotient space. To make quotient exploration informative under finite rollouts, we derive a kernelized Rényi estimator that resolves graded crowding among distinct repair cores beyond coarse exact-match counts. On 2,212 held-out GEMs, QuotientPO improves Success@32 from 17.93% to 20.10% (+12.1% relative) while consistently increasing distinct successful-core discovery under the same sampling budget. These results establish quotient-space exploration as a principled approach to mechanism-level discovery under verifier-induced equivalence.

Consensus can make pseudo-label learning more reliable, but only when its predictors contribute genuinely different evidence. Multiple models that repeat the same boundary provide additional votes without additional information. We address this problem by con structing decision sources through controlled changes to within-class structure. Starting from a shared graph representation, we vary center granularity and neighborhood mixing, reproduce each resulting source to test its stability, and select a complementary subset using node pair coassignment. Unanimous predictions from the selected sources are then ranked for student training. On the public fixed splits of Cora, CiteSeer, and PubMed, evaluated with five random seeds, the constructed sources improve fixed-budget training pseudo-label precision by 1.19 to 4.39 percentage points over three conventionally initialized GCN sources. Under matched structural filters, three-source consensus is more precise than each constituent source in all 45 dataset slot eed comparisons. The gains are strongest in pseudo-label quality: downstream accuracy remains competitive but does not lead on every dataset. These results identify source construction rather than model count alone as an important design problem for consensus-based pseudo-label learning.

We develop a model-free policy gradient method for discrete-time mean-field control (MFC). In MFC, the policy affects the objective both through the controlled dynamics and through the population distribution. Standard REINFORCE estimators capture the first effect but not the second. We introduce Transport REINFORCE, a transport map-based approach that perturbs a suitable transformation of the population distribution to estimate this missing mean-field contribution. The method applies to both finite and continuous state spaces. In finite state spaces, we perturb the population distribution directly on the probability simplex through a convex combination of the current population weights and random weights. In continuous state spaces, we project the population distribution onto the manifold of Gaussian mixtures, and then randomize it via a transport map that ensures the perturbed law remains within this manifold. We prove consistency of the perturbed objective and gradient as the perturbation vanishes, and derive bias and mean-square error bounds for the resulting sample-based gradient estimator. Numerical experiments on several MFC benchmarks show that Transport REINFORCE improves over standard REINFORCE.

We introduce NanoProof, to our knowledge the first factorized execution-guided theorem prover in Lean 4 whose training data, extraction tooling, training pipeline, and weights are all released, making it end-to-end reproducible using open-source resources. To this end, we build and release a dataset of structured proof trees, as well as a tool for programmatic interaction and data extraction within the Lean 4 formal verifier. To support sustainable research, we focus on compute efficiency to facilitate accessible training and evaluation. NanoProof achieves 50.8% pass@16 on MiniF2F-Test, exceeding the two closest systems of its class, HyperTree Proof Search and ABEL, at roughly 90x and 7x less compute, and using more than four orders of magnitude less compute than AlphaProof. Stronger open-weight provers exist, but they are fine-tuned from large pretrained language models and release neither training data nor pipeline; NanoProof shows that the factorized execution-guided class of provers can be rebuilt from scratch with modest resources.

To test conditional independence of $X$ and $Y$ given a text or an image $Z$, one conditions on an embedding $\psi(Z)$ in place of $Z$. The embedded test is valid if $Z$ is independent of $X$ or of $Y$ given $\psi(Z)$, which cannot be confirmed from data, and when this fails, the rejection probability under the null hypothesis can tend to one. We study this failure, and show that focusing on a specific form of dependence relaxes what the embedding must retain. For a residual correlation test inspired by the Generalised Covariance Measure, validity only requires that the parts of $\mathbb{E}[X \mid Z]$ and $\mathbb{E}[Y \mid Z]$ missed by $\mathbb{E}[X \mid \psi(Z)]$ and $\mathbb{E}[Y \mid \psi(Z)]$ are uncorrelated. Otherwise, we treat the discarded information as an omitted variable. Under the null hypothesis, the bias equals the absolute correlation of the missed parts times the geometric mean of two partial $R^2$ values. This identity yields a robust test valid under a declared tolerance for the geometric mean, which, like a sensitivity parameter, is not identified from the data. On synthetic data and text embeddings, the robust test holds its level approximately. On text generated by a language model, under an exact null hypothesis, every embedding, even the generator's own states, biases the embedded test.

Accurate trajectory forecasting and well-defined predictive uncertainty are crucial for reliable, safety-critical applications such as autonomous driving. Most trajectory prediction approaches provide point estimates only, while uncertainty-aware approaches typically quantify uncertainty only in the trajectory space. In physics-aware approaches, uncertainty in the predicted motion variables should be explicitly modeled and propagated through the vehicle dynamics. Otherwise, the resulting trajectory-space uncertainty may not fully reflect the variability introduced by the underlying motion prediction. Therefore, in this work, uncertainty-aware extensions of X-TRACK (X-TRACK-DE and X-TRACK-MCD), a physics-aware trajectory prediction framework, are proposed. The proposed framework predicts future vehicle motion variables and models both aleatoric and epistemic uncertainties by propagating motion space uncertainty to trajectory space. Additionally, conformal prediction is applied to the trajectory space predictive covariance to construct uncertainty regions targeting a desired marginal coverage level. Evaluation on the highD dataset shows that X-TRACK-DE improves trajectory prediction accuracy over the deterministic baseline, while both uncertainty-aware variants provide predictive uncertainty that can be conformally calibrated to the desired marginal coverage level.

Sparse Mixture-of-Experts models scale parameter capacity efficiently while maintaining a fixed compute budget per token. However, traditional training paradigms enforce a static choice of top-$k$ experts, which converts a continuous routing distribution into a rigid step function. This constraint introduces a brittle boundary where highly competitive experts are arbitrarily separated into full-supervision and zero-feedback zones based on minor score fluctuations. To address this issue, we propose Elastic Expert Routing, which stochastically samples the active expert budget from a localized discrete distribution centered at $k$. Over multiple training iterations, this mechanism softens the sharp threshold into a gradual probability distribution. Because the sampling neighborhood remains symmetric, this approach matches the expected computational cost of deterministic training, while preserving the inference budget. During supervised fine-tuning, elastic routing improves downstream macro-averages on OLMoE-1B-7B and Qwen3-30B-A3B by $+0.84$ and $+2.02$ points, respectively. In addition, in from-scratch pretraining, it reduces validation LM loss by up to $0.04$ and outperforms the static top-$k$ baseline by $1.6$ points on average across downstream tasks. Comparisons on Qwen3 fine-tuning and from-scratch pretraining further show higher average scores than Noisy top-$k$, expert FFN dropout, and DefaultMoE.

Battery state of health (SoH) forecasting is important for battery management, but remains challenging due to nonlinear degradation and heterogeneity across batteries. Existing data-driven approaches primarily use temporal models to learn from numerical battery time series, and higher-level degradation characteristics are often not explicitly represented. These characteristics, however, can provide degradation guidance to support reliable forecasting and make the influence of degradation more interpretable. In this paper, we propose Sera, a semantic representation aggregation framework that complements temporal modelling with degradation semantics. Guided by battery domain expertise, Sera extracts degradation semantics from time series and constructs two complementary representations using rule-based knowledge and LLM-based interpretation. The representations are independently encoded and integrated with the representation learned by temporal models through gated aggregations. Experiments on the mainstream benchmark across multiple prediction horizons and different temporal models show that Sera consistently improves forecasting performance, achieving up to a 37.3% reduction in prediction error over the temporal baseline and enhanced generalizability. Counterfactual analysis examines how forecasts respond to changes in degradation semantics to assess interpretability. The results show that prediction responses are consistent with the meanings of key degradation descriptors across tested horizons. Together, these findings demonstrate that structured degradation semantics and effective aggregation can improve forecasting accuracy and support reliable and interpretable battery health forecasting for advanced battery management.

We study personalized federated linear stochastic approximation (LSA), a framework which notably encompass personalized temporal difference learning. In this setting, heterogeneous agents collaborate to solve distinct linear fixed-point equations, each corresponding to an agent-specific learning problem. A central open question in personalized learning is whether a single method can adapt to an unknown level of heterogeneity by converging to each agent's personalized solution in all regimes while achieving a linear speedup in the number of agents when their learning problems are sufficiently similar. We answer this question affirmatively by introducing PF-LSA, a minimalist algorithm that mixes each agent's local stochastic update with the average update across agents, at no additional computational cost relative to standard federated methods. We prove that PF-LSA, achieves best-of-both-worlds guarantees without any prior knowledge on the level of heterogeneity. Our analysis is based on a sharp decomposition of the error into consensus and disagreement components. The consensus error decays rapidly, whereas the disagreement error decays more slowly but becomes negligible in low-heterogeneity regimes.

We study online sparse linear regression (OSLR) where any algorithm is restricted to accessing only $b$ out of $d$ attributes per instance for prediction and $b_0\geq 0$ additional attributes after prediction, which was proved to be NP-hard. Previous work focused on designing computationally efficient algorithms under regularity assumptions, but did not characterize its information theoretic complexity. In this work, we give the first lower bound on the minimax regret of OSLR and design algorithms with better upper bounds without regularity assumptions. We characterize how minimax regret scales with problem-dependent parameters, capturing the information theoretic complexity of OSLR.

Acquiring realistic microstructure data through Electron Backscatter Diffraction (EBSD) is costly and time consuming, often relying on specialised equipment. As microstructures strongly influence material properties, generating realistic samples is essential for modelling the behaviour of polycrystalline materials. We introduce a generative model for synthesising realistic polycrystalline microstructures using flow matching and graph neural networks. By representing microstructures as anisotropic power diagrams, our model learns a compact geometric parametrisation and can render generated samples at arbitrary pixel resolution. A $C_4$-equivariant architecture incorporates rotational symmetry directly into the model, ensuring that rotations of the input noise produce corresponding rotations of the generated microstructure. We also demonstrate how training-free guidance can be used to generate complex microstructures, based on user defined objective function. In particular, we generate microstructures resembling a copper weld, cast metal slab, 3D-printed stainless steel and heterogeneous lamella titanium.