Papers

Tabular foundation models (TFMs) achieve state-of-the-art performance on IID benchmarks, but how do they respond to repeated measurements at the same inputs? Across six TFMs, synthetic and semi-synthetic experiments show that additional measurements can improve predictions at measured inputs while degrading them elsewhere. Harm is most frequent at low noise, and irrelevant features amplify it in several models; real repeated-measurement datasets show similar patterns. Statistically, the IID rule targeted by PFN pretraining treats each repeated input as fresh evidence about the input distribution. When the prior links this distribution to the response function, the resulting protocol mismatch can outweigh the benefit of additional measurements, even under exact inference. Computationally, interventions identify row-count dependence in TabPFN-v3's attention scaling as a contributor to harm. Resetting the count largely reverses distortion in a noiseless linear diagnostic and attenuates amplification by irrelevant features. Finally, we evaluate ways to retain the benefits of repeated measurements while limiting their harm. Averaging measurements usually outperforms supplying them separately at larger repetition counts, whereas count reset can suppress both harm and useful gains. Code, saved results and reproduction instructions are available at https://github.com/drizmiz/PFN-Repeated-Measurement-Supp

Chain-of-Thought (CoT) enables transformers to solve complex reasoning tasks by generating intermediate reasoning steps. Despite strong empirical success, the mechanisms by which such reasoning abilities emerge during training remain poorly understood, particularly from a theoretical perspective. In this work, we study this question in a stylized yet fully analyzable setting: in-context $\mathrm{K}$-nearest-neighbor ($\mathrm{K}$-NN) prediction with a one-layer transformer. Earlier work has demonstrated that one-layer transformers can be trained to perform $1$-NN without CoT (Li et al., 2024a) by having the softmax attention attend to the nearest neighbor in context. However, this result on $1$-NN cannot be extended to $\mathrm{K}$-NN for $K>1$, as softmax attention is much less naturally suited to attending to the 2nd through $K$-th nearest neighbors. We first give a rigorous negative result showing that this limitation already appears on a well-separated class of binary classification tasks for odd $K>1$. We then give an explicit construction of a one-layer transformer, and show that it can solve $\mathrm{K}$-NN via CoT reasoning. We further prove that, under a stylized training setup, gradient descent can recover this construction, thereby showing that transformers can acquire the capability to solve $\mathrm{K}$-NN through training. In addition, we show that the resulting trained model applies to a broader test class than that assumed in the training analysis. Our results shed light on how CoT expands the ability of transformers to learn and solve tasks that are otherwise hard to solve.

Proximal Policy Optimization (PPO) is widely used in reinforcement learning with verifiable rewards for language-model reasoning. While value evolution along trajectory characterizes relative token-level credit, yet standard critics often fail to track it under sparse terminal rewards. To model this evolution, we analyze the relation between successive prefix values and show that they admit a Bayesian decomposition with additive updates in log-odds space. We use this additive structure to construct Tracking-Value PPO (\method), a cumulative value parameterization that sums position-wise scalar outputs into value logits. These outputs are learned through terminal-outcome supervision on the reconstructed values. \method improves aggregate mathematical reasoning scores over PPO by 7.0 and 8.4 points on Qwen3-4B-Base and Qwen3-8B-Base, respectively, while improving out-of-distribution generalization. Gains extend to Qwen3-4B, Qwen2.5-Math-1.5B, Qwen3.5-9B and to countdown, and scientific coding tasks. Further analysis shows more accurate tracking of value evolution and more reliable advantage estimates. Our code is publicly available in https://github.com/LINs-lab/TPPO.

Adaptive optimization methods have received considerable attention in recent years due to their strong empirical performance. However, they generally require maintaining a preconditioning matrix, which incurs prohibitive computational overhead in large-scale applications. To address these limitations, we investigate the acceleration of preconditioned optimization methods through frequent directions (FD), a widely used matrix sketching technique. We first propose FTSL by integrating FD with adaptive subgradient methods under the primal-dual framework and adding back the cumulative information discarded by FD. FTSL obtains a tighter regret bound than existing state-of-the-art results. We then apply a doubling trick that further reduces the time complexity of FTSL, while maintaining the same regret guarantee. We also consider optimization over matrix-valued decision variables and exploit their structural properties to construct sketched preconditioners. We develop FTSL-Shampoo by adapting FD to Shampoo and give a novel analysis under the primal-dual framework. To further mitigate its computational complexity, we design one-sided variants of FTSL-Shampoo under both mirror descent and primal-dual frameworks. Our algorithms not only reduce the computational cost of FTSL-Shampoo, but also achieve tighter regret bounds. We extend our methods to offline stochastic convex optimization and exploit smoothness to achieve faster convergence rates. Finally, we introduce practical variants of our algorithms and empirically demonstrate their efficiency and effectiveness across a broad range of tasks.

Generating and editing presentation slides requires models to combine accurate text rendering, instruction following, visual grounding, aesthetic design, and precise editing within one canvas. Existing work covers only subsets of these capabilities and lacks large-scale slide-native supervision and diagnostic evaluation. We formulate four slide-centric tasks and build a scalable data engine with over 13M continual-pretraining records and 1.9M supervised fine-tuning records. We also introduce VisSlideBench, a benchmark of 1,527 manually screened instances that covers all four tasks with task-specific, multidimensional evaluation. Its automatic rankings agree with blinded, dimension-wise human rankings. Using these resources, we train InfoVis, a unified 9B slide generation and editing model. On VisSlideBench, InfoVis leads every evaluated open-source model on all eleven metrics and scores 7.94 overall against 7.99 for Nano-Banana-2. Starting from FLUX.2-klein-base-9B, slide-specific post-training adds 1.6 points overall, with the largest generation gains in content faithfulness; the remaining gap to proprietary models is smallest in content faithfulness and largest in aesthetic quality. Built on InfoVis, our document-to-slide workflow achieves the second-highest Aesthetics score on the external SlidesGen-Bench. We will release the model, code, data, and benchmark.

Parallel token proposals need a joint law, not merely accurate token marginals. We construct coordinate-Bethe-ansatz laws from the periodic XXZ chain and compare them with their maximum-entropy pairwise projections at identical one- and two-site moments. In an eight-site, three-excitation sector, symmetry makes the full probability-law difference one-dimensional, determined by a contiguous three-site moment $\delta$. Along the Bethe branch, this gap changes sign and vanishes exactly at $\Delta=(3+\sqrt3)/2$, where the eigenstate law becomes pairwise. A nonlinear two-token readout preserves separate token marginals yet exposes a distance $2|\delta|$; a direct three-token readout preserves all one- and two-token marginals yet exposes $4|\delta|$. At $\Delta=1.5$ these deterministic binary distances are $0.02654573$ and $0.05309145$. We give an exact target-alignment formula and prove a strict speculative accepted-prefix advantage throughout an unrestricted open neighborhood of a constructed target. These are finite-law existence results, not measured language-model or wall-clock gains.

Relational learning typically predicts from a database state, but decision making asks a different question: how will that state change under an action? In operational systems, the answer depends on system-specific dynamics that may not be visible in the database itself. We view each such system as a relational "world" and ask whether a model can infer how it behaves from observed executions. We introduce TabWM (Tabular World Model) and WorldRel, a generator of executable relational worlds for pretraining. Given executions from an unseen world, TabWM uses them as context to predict the sparse structured edits caused by a new action without parameter updates. Across 512 held-out worlds, complete-edit F1 rises from 0.016 with no observed executions to 0.685 with 64, where a correct edit must match its operation, relational location, and value. Because these predictions are explicit relational edits, they can be applied recursively to imagine candidate futures and compare actions before they are taken. Broader search over these predicted futures improves the realized return of selected action sequences. Together, these results suggest that relational dynamics can be learned in context, broadening relational learning from modeling system state to modeling how that state changes under action.

LLM-based information systems need safety guardrails. Most guardrails classify the prompt alone. If the prompt looks harmful, the system rejects it before any answer is generated. This is costly. Many rejected prompts would have received a safe response. Users lose help they should have received from the information system. This cost grows as conversational and generative search becomes common. Prompt-level labels treat harm as a property of the query. But harm depends on what the model actually writes. Existing input-output guards do look at responses. But they judge a finished response, so the decision comes after full generation. However, we observe that safety of model interaction with the input prompt can be inferred early with only partial output. So the system can start generating, watch the partial response, and stop only if it turns harmful. We test this idea in three steps. First, we build a dataset of 41,944 prompt-response pairs with seven open weights LLMs from three families: Llama, Gemma, and Qwen. Second, we show that prompt harmfulness and interaction safety differ. Prompt labels and response labels agree on only 50.46% of items (Cohen's $\kappa$ = 0.06). Of the prompts that make any model respond harmfully, only 3.5% do so for all seven LLMs. Third, we show that partial responses carry most of the signal. Fine-tuned classifiers predict response-level harm well (best AUPRC 0.885, F1 0.807). About one third of the response tokens recover almost full-response AUPRC.

Comparing machine-labelled sentiment across social media platforms is now routine: differences in classifier scores between platforms are read as differences in public opinion. These comparisons rest on an assumption that the classifier measures the same construct, on the same scale, on every platform. Some studies check a classifier's validity platform by platform, but to our knowledge none has modelled the platform as a facet of the classifier's measurement. We adapt the psychometric equivalence toolkit (generalizability theory, measurement invariance and differential item functioning, and score linking) to machine-labelled policy sentiment, treating the platform as a survey mode, and specify a six-step protocol with anchor events fixed in advance, an anchor-density audit, and a two-classifier convergence control. A simulation with known ground truth illustrates what the assumption can cost in one generating configuration fixed in advance: across 500 replications, because the platforms measure through different functions, a pooled index that takes platform scores at face value reports the wrong sign of aggregate sentiment on nearly a quarter of days, whereas an index adjusted with each platform's known measurement function does so on under one day in sixty on average. A case study of the instrument from the first author's MSc dissertation, a fine-tuned BERT classifier over 255,446 UK economic-policy comments from Twitter/X, Reddit, YouTube, and Quora, motivates the design and illustrates the instrument-dependence the protocol addresses. The full four-platform application, under fresh collection with the pre-specified design, is the designated follow-up study. The protocol lets a researcher test whether pooling platforms is defensible in a given corpus, or whether platform scores must be linked before any average is taken.

We present NFMap, a dimensionality reduction method for 2D visualisation that extends Generative Topographic Mapping (GTM) with a bijective normalizing flow. Like GTM, NFMap places a fixed mixture grid prior over a 2D latent map, giving a parametric embedding, an explicit likelihood, and the ability to project new points onto an existing map; the likelihood is an effective out-of-distribution signal on chemical datasets. Unlike GTM, whose latent-to-data mapping is an RBF network of bounded flexibility, NFMap's mapping is a normalizing flow, and is therefore fully invertible: any location on the map can be carried back to data space. To alleviate map crowding on large datasets, NFMap additionally supports heavy-tailed Student-t mixture components. NFMap maps data to a latent space of the same dimension, split into a 2-dimensional navigable map and an off-manifold residual. Because the flow is bijective and its objective penalises volume contraction, variance squeezed out of the residual must reappear in the navigable map. The residual scale is the main control between local neighbourhood fidelity and global distance fidelity; its effect depends on the dimensionality of the data and is coupled to the extent of the latent grid.

Attention sinks are usually studied after they have formed. We ask whether a measurable hidden-state change appears beforehand and whether changing that geometry alters what happens later. To remove network depth as a shortcut, we compare prompts in the same model and at the same layer. When sink timing varies across prompts, simple spectral summaries of the hidden states add information beyond current attention, with the clearest prompt-specific signal in a short window about two to three layers before sink formation. The predictive strength varies across cohorts, so we treat the spectrum as a readout of a pre-sink state change rather than a universal warning statistic. The signal is broader than one measured extreme activation. We then modify only the singular values of the post-layer hidden states after current attention has already been computed. These interventions change later sink behavior in Qwen2.5, GLM-Z1, and GPT-OSS relative to norm-matched random spectral perturbations. In Qwen2.5, the immediate suppressive effect is accompanied by a reduction in next-layer query–key preference for position~0, and the learned spectral directions remain stable when estimated from substantially less training data. Together, the results show that attention sinks are preceded by a short spectral reorganization of hidden states, and directly perturbing this geometry can causally alter subsequent sink formation.

Video-to-robot pipelines for quadrupedal imitation insert a learned lifting stage, either a monocular depth model or a per-clip 3D reconstruction, to recover the one axis a side-view camera cannot see. We present CopyQuad, which omits that stage and pins the missing axis to the robot's own stance width instead. The setting is side-view footage of sagittally dominated motion, where limb motion is almost entirely in the image plane. A frozen 2D keypoint detector and a fixed analytic retargeting then turn a single uncalibrated clip into a robot reference whose foot targets are reachable by construction, so no per-clip trajectory optimization is needed. One phase-indexed reward structure, whose only per-behavior freedom is three scalars from a shared sweep, learns a dog walk, a horse walk, a horse trot and two non-periodic gestures, all deployed zero-shot on hardware. We then measure what omitting the axis costs. In a training-free rigidity test, a video depth model varies the distance between the animal's hips by $40$ to $107\%$ of its own mean and a single-image metric model by $22$ to $58\%$, though that distance cannot move. Motion capture puts the true lateral paw travel of a dog walk at $4.5$ cm peak to peak, a mean deviation near $1.4$ cm against the $3.5$ cm of lateral foot error our policies already leave, so the discarded axis sits below the pipeline's resolution. Depth repaired to feasibility never beats the constant, and the unrepaired estimates put the robot on the ground.

Monte Carlo sampling algorithms aim to produce samples from a target distribution with a given unnormalised probability density function. The high cost of running Monte Carlo algorithms, with many simulation steps or particles needed to obtain a good empirical approximation to the target, can be reduced by introducing learnable components into the sampler – a form of amortisation. Once these components are trained, amortised samplers can produce high-quality samples with less computation at sampling time than training-free algorithms would require. We propose an amortised sampler built upon the framework of adaptive importance sampling – a hierarchical importance sampling procedure where the proposal is iteratively adapted. Our amortised adaptive importance sampling algorithm fits a lightweight neural network that adapts the proposal using information obtained over the course of sampling. By training our sampler over many different targets taken from the same family of distributions, we obtain a sampler that can adapt to a specific target at sampling time without a priori access to the target's parameters. We show that our procedure can efficiently sample from targets within the family the sampler was trained on, giving improvements over target-specific amortised samplers and training-free adaptive importance sampling algorithms. We also explore the potential for generalisation, where the trained sampler is used to sample from targets outwith its training family.

Existing benchmarks for GUI agents primarily focus on increasing task difficulty by extending task horizons. Besides, enabling agents to explore unfamiliar environments and successfully complete tasks within them is also a critical yet challenging problem. We introduce LatentGUIWorld, a benchmark of six tasks in three matched pairs organized by the evidence needed for control: $I_0$ uses prior knowledge and available observations, $I_1$ requires interaction that directly reveals hidden semantics, and $I_2$ identifies dynamics from action-response relationships. Frontier models struggle especially on $I_2$ tasks. We introduce MOVE, which separates movement from button events and exposes intermediate visual feedback, together with demonstrations of iterative exploration and control. Ablations show that both action granularity and multi-step demonstrations improve performance. After SFT, LatentLearner-9B achieves 50.0% overall success on LatentGUIWorld, comparable to several frontier models. Joint RL further raises egocentric Drag and Ten-Choice success to 92.0% and 75.3%. Behavioral analysis reveals multi-step exploration. In egocentric Drag, RL increases Pearson correlation between error-normalized commands and ideal gain compensation from 0.610 to 0.803. Together, these behaviors show that models learn to explore through interaction and adapt their control to environment dynamics. The same format improves GUI grounding after RL, reaching 67.37% mean accuracy across five benchmarks versus 66.72% for conventional RL.

Language models have recently solved open Erdős problems and achieved gold-medal level performance on International Mathematical Olympiad problems. But their solutions, written in natural language, cannot yet be verified by proof assistants. An erroneous reasoning step can invalidate every step that comes after, so it is advantageous to detect errors early. Several methods have been proposed to detect erroneous reasoning quickly based on the features of the forward pass of the language model that performs reasoning. In this work, we study whether the directed Forman curvature of that model's attention graph, a local quantity computed at an edge from the attention weights around it, carries information about a step's correctness. To do so, we evaluate four per-step verifiers on ProcessBench with and without the curvature appended to their input. Appending curvature values improves the overall mean performance of all four verifiers. ReProbe, the verifier that takes every token of a step as input, shows the largest improvement. Adding the curvature increases the time of the language model's forward pass by 18% on average.

This paper considers a distributed estimation system where edge nodes transmit averaged features to a center node for parameter estimation. A key challenge arises when the center node possesses auxiliary side information: how to design local extractors that are universally optimal for any downstream task, while avoiding redundancy with the side information. To tackle this problem, we orthogonally decompose the joint function space and demonstrate in the weak-dependence regime that the modal decomposition of the canonical dependence kernel's conditional-additive component yields optimal, task-independent features. We construct a distributed nested H-score to learn this decomposition and show that, under a limited feature budget, the mean-squared error (MSE) gap to the best task-specific features is determined solely by the task's alignment with the discarded, least informative modes, and vanishes to leading order for every square-integrable task once the budget is sufficient.

Adversarial detection on evolving attributed graphs faces two challenges: fraud labels arrive late or not at all, and natural distributional drift erodes any trained decision boundary. Modern detectors can reach strong detection rates when labels are available and the distribution is stationary; sustaining that quality without labels and under drift is the open problem. We identify feature-context consistency – the alignment between a node's attributes and its aggregated neighborhood attributes – as a single structural signal that addresses both. We formalize it as the Context Boost (CB) score within a Restricted Boltzmann Machine framework (CB-RBM) and prove two complementary worst-case guarantees: a strict separation between the expected CB of legitimate and adversarial nodes, with gap growing linearly in model capacity, whenever the adversary's context stays far enough from legitimate neighborhood context; and a Wasserstein-Lipschitz bound on how far the CB distribution moves under natural drift. We validate on XBlock Ethereum phishing (~153K nodes) and Reddit banned-user detection (~11K nodes), with two further datasets in the appendix spanning diverse domains. With zero labels, CB-RBM achieves AUROC >= 0.96 on four adversarial attacks and keeps FPR close to its calibrated 5% target under drift – outperforming supervised GNNs (hundreds of labels), unsupervised graph-anomaly baselines, and a standard RBM whose FPR collapses to 89-100%. What typically requires separate mechanisms – label-free operation and drift stability – here follows from a single structural regularity of the data. Code: https://github.com/serval-uni-lu/CB-RBM.

Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood. We study a single resampling step for a d-dimensional ensemble of N particles with d/N -> c. For any unbiased scheme, the resampled empirical second-moment matrix dominates its pre-resampling counterpart in conditional convex order, while the conditional mean is preserved; the excess second spectral moment equals the Frobenius energy of the resampling perturbation. For multinomial resampling, the empirical count law converges to the mixed-Poisson law determined by the limiting weight law. For residual resampling, the count law is determined by the joint limit of floor-fraction pairs: we classify all residual limits of weight sequences converging to delta_1 in law as a one-parameter family between the deterministic identity and the full multinomial count law. Each count law feeds a common covariance-side spectral map, yielding exact consequences: a closed-form zero-eigenvalue mass, a rank-and-spectral-gap transition with a universal lower edge benchmark, computable regular edges, unbounded right support, and scheme-specific second-moment costs. The effective sample size determines one bulk statistic but cannot determine the limiting spectrum. Pre-registered numerical experiments confirm the theory at every level.

Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We propose a neural-network-based amortized variational framework that learns a reusable inference rule mapping a variable number of replicated point patterns to a distribution over their shared latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule without ground-truth intensity supervision. At test time, it performs inference of the latent distribution in a forward pass. On synthetic data, additional realizations improve intensity recovery and yield narrower credible intervals with broadly stable coverage. Our method is tested on bicycle-sharing data and achieves the highest mean held-out log likelihood among the evaluated methods while requiring substantially less inference time than the Log-Gaussian Cox Process baseline.

There is growing interest in applying Parameter-Efficient Fine-Tuning (PEFT) to Continual Learning, as it enables faster training, mitigates catastrophic forgetting, and facilitates better adaptation to new tasks. Prior approaches have explored a range of strategies, including extending new LoRA branches for each incoming task, training under orthogonal loss objectives across all task-specific LoRA modules, and employing gating mechanisms to integrate new and existing LoRA modules. However, these methods incur memory costs that grow linearly with the number of tasks, limiting their scalability. More recent approaches investigate training a single LoRA by leveraging asymmetries in its parameterization; however, they often suffer from insufficient representational alignment across the LoRA parameter space. To address these limitations, we propose Stiefel Optimization and Aligned Rotation (SOAR), a two-stage framework for continual LoRA learning. First, we constrain the A matrix to lie on the Stiefel manifold, thereby reducing coordinate misalignment to the space of orthogonal rotation matrices. Second, we introduce an Orthogonal Procrustes alignment procedure for the B matrix to estimate the optimal rotation, coupled with a per-rank retention merging strategy that quantifies directional agreement between representations of new and previously learned tasks. We conduct extensive experiments across multiple models and benchmarks, demonstrating that SOAR achieves strong continual learning performance without incurring additional memory overhead.

Information-theoretic and geometric compression have been widely studied as possible explanations for generalization. Yet their temporal dynamics in recurrent networks remain largely unexplored. Using discretized LSTMs, whose finite embedding space enables direct estimates of information quantities, we observe pronounced compression across the final timesteps of many datasets. We explain this effect through three competing mechanisms: (i) class separability permits stronger compression at the final timestep; (ii) shared recurrent dynamics propagate this pressure across timesteps with similar activation states, making its extent depend on temporal stationarity; and (iii) limited representational capacity opposes prolonged compression because it restricts information available for subsequent computation. We systematically test these mechanisms through controlled synthetic interventions and real-world sequence tasks. Our results identify class separability, temporal stationarity, and network capacity as key determinants of temporal compression, and suggest that compression acts as a regularizer-potentially beneficial when excess capacity is available, but harmful to generalization when it consumes memory needed for the task.

Wireless propagation modeling is foundational to the evaluation and design of modern communication systems. To achieve accurate wireless propagation prediction, recent learning-based approaches leverage scene geometry and materials, demonstrating promising generalization across transceiver locations and unseen scenes. However, these approaches remain largely confined to a fixed configuration of array size, receiver orientation, and transmit beam. In this work, we introduce RFWeave, a learned wireless propagation model designed to generalize across scenes, transceiver locations, and transceiver configurations. To accommodate varying array structures, RFWeave incorporates variable-length transceiver tokens that represent antenna elements individually. Furthermore, to capture the geometry between transmit and receive antenna elements, RFWeave aggregates their pairwise spatial relations into propagation tokens. A configuration-conditioned decoder predicts the spatial spectrum and received power. RFWeave is trained on a large-scale simulated dataset spanning 10,000 indoor scenes and more than 5 million channel records under diverse transceiver configurations. Extensive evaluations show that RFWeave achieves state-of-the-art performance across all evaluated generalization settings, improving spatial spectrum structural similarity (SSIM) by up to 15.7% and reducing received power mean absolute error (MAE) by up to 35.4% over the strongest baselines on unseen scenes. Additional experiments on measured DICHASUS data and in beam management further demonstrate RFWeave's broader applicability to real-world channels and downstream wireless tasks.

Flow matching models are typically trained to transport a Gaussian source to the data distribution, with source and target samples paired independently. We replace the source with a fitted Gaussian mixture and couple each data point to a mixture component through an entropic optimal transport problem. We show that the resulting transport reduces to the standard Gaussian-source problem up to a guidance-like correction, which enables the reuse of a pretrained velocity field. This correction is a closed-form function of the fitted mixture plus a term that we learn with a small correction network. We test our model on published checkpoints for CIFAR-10 and CelebA-HQ. It improves FID at every step count, and on CelebA-HQ it reaches the quality of the baseline with about half the steps. The closed-form term alone, with no training, already delivers most of this improvement; the small correction network accounts for the rest.

Counting is a simple task on which transformers can nevertheless fail at long sequence lengths. We study the cost of counting in a single attention layer, up to a maximum length $L$, focusing on how softmax attention and layer normalization shape the representation from which the count is recovered. We mainly focus on regression read-out but also consider classification read-out. For regression, we show unnormalized linear attention counts exactly at parameter norms independent of $L$. For softmax attention, regression cannot count exactly with finite parameters; it recovers the count after rounding, but only when the vector parameter norms grow with $L$. We measure this cost by $B_{\min}$, the smallest bound that can be placed on every trainable vector to ensure exact counting after rounding, and derive tight rates. At fixed model dimension, $B_{\min}$ grows as $L$ without normalization, as $L^{3/2}$ under bare post-normalization, and as $L^{3/4}$ with learned post-normalization. The last rate is unexpected: post-normalization discards the magnitude that carries the count and might be expected to make counting harder, yet with a learnable gain it counts at a smaller norm than softmax without normalization. Bare pre-normalization is different: it bounds the attention scores, so beyond a finite length no parameter norm suffices. A classification read-out keeps every norm bounded under every placement, but a dense head stores one output vector per count and costs more in storage. Experiments on the post-normalized model reproduce this split between the two read-outs. Together, our theoretical and empirical findings characterize how self-attention, layer-normalization placement, and read-out choice shape the representation geometry and parameter cost of counting in the minimal single-head architecture studied here.

We introduce IND-Eval, a public benchmark that organizes industrial time series across domains into source-specific forecasting tasks. Relative to established benchmarks such as GIFT-Eval, it emphasizes finer sampling resolutions and a greater prevalence of multivariate forecasting. Evaluating Chronos-2, TiRex-2, and TimesFM-3, we find that TimesFM-3 achieves the lowest source-balanced aggregate nMASE and nCRPS and leads seven of nine sources under each metric; source-specific exceptions reinforce the need for domain-representative evaluation for model selection. These findings also motivate improving domain alignment during pretraining, where real industrial data are often too scarce to close domain-specific gaps directly; we therefore investigate whether a domain's statistical structure can guide simulator design. In a case study on two offshore well-monitoring regimes, we improve a general simulator's coverage using an oscillator-augmented simulation pipeline. This lowers forecasting error in the target domain but reduces performance on the subset of GIFT-Eval with natively univariate targets. A 50/50 mixture of the general and augmented simulation recipes achieves the lowest error among the three training recipes for all four event-metric pairs in the case study while recovering most of the lost GIFT-Eval performance. Together, these results illustrate how domain-representative evaluation can guide model selection and the composition of simulated data while revealing a trade-off between specialization and generality.

Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representations, and robustness to missing data. We introduce DFK-Former, a set-to-field transformer that reconstructs divergence-free velocity fields from sparse, noisy, and irregularly sampled 3D observations. The model is inherently invariant to the number and ordering of input samples and predicts the parameters of a divergence-free kernel representation, producing continuous, mesh-free velocity fields that satisfy incompressibility exactly by construction rather than approximately through soft constraints or projection operators. Unlike existing divergence-free kernel approaches, which estimate kernel coefficients via a separate optimization for each field, DFK-Former predicts these coefficients directly in a single forward pass. This eliminates costly iterative fitting while providing a learned prior that enables accurate reconstruction even when observations are insufficient to uniquely determine the field. To enhance representational power, we introduce adaptive and anisotropic divergence-free kernels that preserve exact incompressibility guarantees while capturing more complex flow structures. Extensive experiments across varying levels of sparsity, noise, and occlusion, including transfer to real Direct Numerical Simulation (DNS) turbulence data, demonstrate substantial gains in both accuracy and efficiency. DFK-Former reduces endpoint error by up to 4.6x compared to per-field divergence-free-kernel optimization, while reconstructing each field in 7.5 ms instead of 9.8 s, yielding a speedup of more than three orders of magnitude. These results establish direct, feed-forward prediction of divergence-free kernel parameters as a practical and effective paradigm for physically consistent velocity-field reconstruction from sparse observations.

Learning a response law for continuous decisions from observational time series is central to many real-world decision systems, yet temporal non-stationarity poses a fundamental challenge: as outcomes drift over time, naively pooled models can conflate action effects with shifting baselines and even reverse action rankings. Even when the one-step response is identifiable, unrestricted cross-time generalization remains fundamentally ill-posed. We therefore seek the part of the response that remains stable for decisions even when outcome levels do not. We propose deployable causal action geometry: the action-response shape that remains after anchoring away action-independent level shifts on a selected link scale and profiling out positive amplitude variation. Building on this target, we develop a two-stage orthogonal estimator that first obtains cross-fitted pilot estimates of anchored responses and then performs honest profiled selection over link, representation, and shape classes. The resulting estimator admits oracle guarantees for the restricted target and, under approximate persistence, produces decision rules that remain near optimal in future periods. Experiments on synthetic data and Dominick's support the proposed target and its transfer behavior. In a randomized Taobao A/B test, the deployed system improves GMV and purchase counts by \(1.16\%\) and \(1.70\%\).

Natural-language self-consistency and executable programs provide complementary test-time evidence for mathematical reasoning, yet either channel may support the same semantic error. Thus we propose ACED, a reference-anchored framework that treats the self-consistency answer as the default and executable outputs as supporting evidence rather than interchangeable votes. ACED converts source-specific answer counts into smoothed supports, combines them through a weighted logarithmic pool, and overrides the reference only when a calibrated relative-evidence margin is exceeded. The same rule supports both candidate selection and admission of executable-only answers. Across five math word-problem benchmarks, ACED matches or outperforms the corresponding baselines. On GSM8K, ACED-CANDIDATE recovers 89.7% of the attainable candidate-set gain with only three damaging overrides, while ACED-ALL reaches 86.9% accuracy versus 82.6% for direct Program-of-Thought aggregation. These results show that preserving evidence provenance enables more reliable integration of natural-language and executable reasoning.

Accurate long-term air quality forecasting is challenging due to long-range transport, meteorological variability, and nonlinear chemical reactions underlying secondary pollutant formation. Purely data-driven models often suffer from long-horizon drift and lack physical consistency, while existing physics-informed approaches commonly follow open-loop designs that fuse neural and physical components only at the output level. We propose AeroChem, a closed-loop physics-informed state space framework for chemically reactive air quality forecasting. AeroChem adopts a two-branch co-correction design: a UDE-based process branch provides a structured but imperfect physical prior, while a Mamba-based virtual measurement branch captures long-range temporal context and produces probabilistic virtual observations. Neural Kalman Fusion couples the two branches by correcting the latent physical state at each forecasting step and feeding the posterior state back into the simulator, reducing long-horizon drift. We further introduce HanoiAir, a real-world dataset integrating pollutant concentrations, meteorology, and emission inventories. Experiments on HanoiAir and a public benchmark show that AeroChem improves long-horizon stability and sudden-change forecasting.

Existing human-centred XAI research predominantly evaluates explanations after they have been generated. However, this fails to provide actionable insights into improving accessibility. This study incorporates human-based feature understandability into feature selection to improve the generation of human-centred explanations. Natural language explanations for machine learning models trained on tabular data often cite influential features in the input data to explain a given decision. As a consequence, users' ability to understand the produced explanation hinges on their understanding of the cited features. To quantify this natural-language feature understandability, Rossberg et al. proposed the Feature Understandability Scale, which assigns numerical `understandability scores' to features based on user feedback. To evaluate the degree to which these scores can improve machine learning explanation quality, this study collects understandability scores across two datasets, proposes an understandability-aware feature selection algorithm to select features that are both understandable and informative, and trains a random forest based on these feature subsets. The SHAP-based explanations generated by this model are evaluated using user feedback, and changes in explanation quality are assessed. The individual evaluation of the explanations showed that while the understandability-based explanations scored higher on average, the difference was not statistically significant. In contrast, the comparative evaluation found that participants preferred these explanations significantly more frequently than expected at the chance level. It is concluded that the integration of understandability can yield more understandable explanations at minimal cost to classification performance, although changes to quality require elucidation in larger cohorts.