Papers

Large language model (LLM) agents increasingly rely on reusable external skills to solve long-horizon interactive tasks. Existing training-free skill adaptation pipelines usually update skills from full trajectories or session-level feedback, which makes failure attribution coarse and often produces unstable or overly broad revisions. We propose SkillAdaptor, a training-free step-level skill adaptation framework with explicit failure attribution, and it can plug into OpenClaw-class agent harnesses. Given a failed trajectory, SkillAdaptor identifies a first actionable fault step, links responsibility to candidate skills, and applies targeted updates under explicit acceptance checks while keeping the backbone frozen. We evaluate on WebShop, PinchBench, and Claw-Eval with Kimi-K2.5, GLM-5, and GPT-5.2. SkillAdaptor improves over no-skill and skill-adaptation baselines on all three suites, with the largest single-metric improvements of +1.5 points on PinchBench Avg Score%, +1.8 on Claw-Eval Avg Score, and +1.7 on WebShop success rate. These results indicate that step-level attribution supports more stable and auditable training-free skill maintenance\footnote{The code will be released at https://github.com/zjunlp/SkillAdaptor.}.

While Transformer-based architectures have established themselves as a dominant paradigm in Multivariate Time Series Forecasting (MTSF), their core self-attention mechanism inherently functions as a low-pass filter, systematically smoothing out high-frequency signals vital for sharp local changes. Recent advancements have increasingly incorporated frequency-domain operations to address this bias, however, most existing designs rely on fixed spectral bases and apply sequence-wise (uniform) modulation, implicitly assuming a time-invariant frequency response. This overlooks a key property of real-world series that their spectral characteristics often evolve over time, making uniform modulation insufficient for capturing fine-grained temporal dynamics. To tackle these limitations, we propose FAiT, a Frequency-Aware inverted Transformer. Specifically, FAiT rectifies the spectral bias internally through Inverted Attention, which interprets the attention map as a learnable low-pass operator and constructs a dedicated complementary high-pass branch by inverting the attention matrix to recover attenuated transient signals. Furthermore, FAiT introduces Dynamic Temporal-Frequency Modulation (DTFM), which synthesizes instance-conditioned weights to adaptively re-calibrate the energy of spectral sub-bands, enabling fine-grained control over evolving multi-scale patterns. Extensive experiments on widely used benchmarks demonstrate that FAiT consistently outperforms state-of-the-art Transformer-based and frequency-enhanced baselines, while maintaining computational efficiency.

Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.

Modern large-scale deep learning exhibits two striking empirical phenomena: behavioural scaling laws (predictable performance gains with increasing scale) and emergent mechanisms (structured internal representations and circuits in deep neural networks). We hypothesise that these two phenomena are connected: that predictable changes in behaviour are the result of predictable changes in internal computational structure. In this paper, we report preliminary evidence of such a connection. We find a correlation between scaling patterns in performance and representations in small transformers trained to predict the outputs of a hidden Markov model, for which residual activations are known to linearly encode a belief distribution over latent states in a probability simplex.

Time series anomaly detection is a crucial task in various domains, including finance, healthcare, and industry. However, existing methods often struggle to generalize across different datasets, especially when anomalies are subtle or context-dependent. To solve this issue, we introduce ChronosAD, a novel architecture for anomaly detection that uses a time series foundation model as a feature extractor. Specifically, it employs a two-stage pipeline: first, it uses the foundation model to extract embeddings for each time series in a zero-shot manner. Then, a custom-developed Temporal Block, composed of Bidirectional Long Short-Term Memory (BiLSTM) and Multi-Head Attention, refines these embeddings to capture temporal dependencies and highlight salient patterns. Unlike previous approaches, our model requires minimal task-specific tuning and demonstrates robust generalization across a wide range of domains, including industrial, medical, cyber-physical, and automotive systems. Extensive experiments on 11 benchmarks show that ChronosAD outperforms existing methods by 4.72% in AUC and 6.60% in AP on average. The source code is available at https://github.com/intelligolabs/ChronosAD.

Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks. Existing remedies act on the write side of memory through gating, delta updates, or kernel feature maps, but the read step is left unchanged: every past key contributes additively to the output, so useful targets are diluted by the bulk of stored vectors. We borrow one specific piece of softmax's geometry to construct a cheap read-time contraction of the query. A second-order Taylor expansion of the softmax log-partition at the isotropic-attention point gives a local quadratic model whose curvature coincides with the running key covariance, a quantity that can be maintained with the same recurrent/chunkwise mechanism as the linear-attention state. The associated linear operator contracts the query along the high-variance directions of memory before it reads the state. We call this mechanism Curvature-Conditioned Query (CCQ). CCQ modifies only the read step and is composable with any linear-attention backbone. Attached to GLA and Gated DeltaNet, it improves perplexity, zero-shot downstream accuracy, S-NIAH retrieval at and beyond the training context, length-extrapolation perplexity from 4K to 20K, and LongBench accuracy.

Teacher-Student Knowledge Transfer (KT) is ubiquitous in modern machine learning, ranging from classical model compression via Knowledge Distillation (KD) to the emergent phenomenon of Weak-to-Strong (W2S) generalization. While existing studies offer isolated insights, a unified theoretical framework explaining the efficacy of KT across these disparate regimes remains lacking. In this work, we establish a unified spectral analysis of SGD dynamics in high-dimensional linear regression, elucidating the efficiency of KT across seemingly disparate regimes. We characterize KT efficiency through two distinct mechanisms: Spectral Horizon Expansion in KD, which enables the capture of statistically inaccessible high-frequency signals, and Spectral Denoising in W2S, where the student acts as a filter for optimization noise. Our framework unifies these phenomena, revealing that the efficacy of transfer is governed by the interplay between implicit regularization and heterogeneous spectral learning speeds over the spectrum.

Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution. While recent foundation models achieve strong in-domain performance through large-scale pretraining, their effectiveness often relies on broad data coverage and implicit pattern memorization, which can limit generalization when data are scarce or source and target domains are disjoint. In this work, we propose FSA, a feature-to-strategy framework for controlled zero-shot univariate forecasting. Instead of directly modeling raw sequences in the observation space, FSA learns a structured mapping from an interpretable feature space to an autoregressive strategy space. This design introduces explicit inductive biases that disentangle global trends, periodic components, and local temporal dynamics, enabling the model to capture transferable time-series structure with fewer data assumptions. Empirical results show that, under identical pretraining data, training protocol, and comparable parameter budgets, FSA outperforms Transformer-based architectures in our controlled zero-shot setting.

The rapid progress of frontier large language models has led to widespread benchmark saturation, limiting the ability of existing datasets to differentiate model capabilities or provide useful training signal. For instance, on LiveCodeBench, frontier models achieve over 99% Pass@1 on easy splits and exceed 90% Pass@1 on average across difficulty levels. Constructing new, challenging datasets typically requires substantial human effort, creating a bottleneck for progress. We introduce BenchEvolver, a solution-centric evolutionary framework that automatically transforms existing coding problems into harder variants. Rather than generating problems from scratch, BenchEvolver evolves reference solutions through structured transformations and derives corresponding statements and tests from the evolved solutions. This design grounds generation in executable semantics, enabling scalable construction of high-quality, diverse, and difficult tasks with verifiable correctness. Applying BenchEvolver to LiveCodeBench and SciCode, we obtain evolved tasks that are substantially harder while maintaining validity, reference correctness, and diversity. We further curate LiveCodeBench-Plus, a 91-problem benchmark combining evolved and difficult original LCB-v6 tasks, where frontier-model Pass@1 ranges from 27.5% to 62.6%, restoring clear discrimination among strong coding models. Importantly, evolved tasks remain challenging even for the model that generates them, enabling self-improvement. We further show that RL on evolved LCB tasks improves held-out coding performance: for gpt-oss-20b, seed+evolved training achieves +8.7 and +8.3 Pass@1 gains on LCB v6 Hard and LCB-Pro Easy, exceeding seed-only gains by 70.7% and 34.8%, respectively. Our results show that BenchEvolver can convert saturated benchmarks into frontier-level evaluation suites and reusable training signal.

Modeling spatial dependencies is central to spatiotemporal data analysis using Graph Neural Networks (GNNs). Traditional methods rely on distance-based kernels with predefined parameters, which restricts model capacity. Although generic adaptive mechanisms (e.g., Graph Attention Networks) offer flexibility, they often fail to capture the underlying geometric structure, performing worse than distance-based models in data-sparse scenarios. Addressing this, we revisit the kernel parameterization problem and theoretically prove that misspecified kernel parameters introduce unavoidable approximation errors in GNNs. To overcome this, we propose AdaKernel, a simple yet effective approach that learns adaptive kernel parameters within the neural network. Unlike methods that learn graph structures from scratch, AdaKernel adopts a structure-preserving strategy that optimizes the scale of physical interactions rather than discarding them. Extensive experiments on Kriging, Imputation, and Forecasting demonstrate that AdaKernel consistently improves various GNN architectures and outperforms model-agnostic adaptive baselines, validating that accurately learned kernel parameters are superior to both fixed priors and fully latent graph structures.

Text-to-Image (TTI) systems are now everyday infrastructure for journalism, education, advertising, and public communication, and the demographic and cultural stereotypes they inherit from training data (rendering women, people of colour, older adults, and non-Western cultures as under-represented or caricatured) become a population-level harm at deployment scale. Existing mitigations either require costly retraining, infeasible for the closed-source backbones that dominate consumer products, or rely on fixed demographic templates that ignore cultural context. We present KG-FairDiff, a model-agnostic, inference-time framework that formalises fairness-aware prompt refinement as a constrained optimisation problem and operationalises it as a closed-loop pipeline: a knowledge graph of ~1,200 culture- and bias-related triples retrieves structured context, an LLM rewriter proposes refinements, and a validator accepts only prompts that reduce a divergence-based fairness loss while preserving semantic fidelity to the user's original intent. We prove a finite-termination bound for the refinement loop, contribute a mathematically consistent evaluation suite linking Bias-P/Bias-W to divergence from target distributions and ENS to KL divergence, and audit eight widely-deployed backbone generators. KG-FairDiff substantially reduces gender, race, age, and intersectional disparities while preserving prompt semantics, offering a practical, deployment-ready route to more equitable generative AI.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.

Spatio-temporal point processes (STPPs) provide a principled framework for modeling asynchronous events in continuous time and space. Recent diffusion-based approaches offer a flexible alternative to deterministic prediction by modeling complex conditional distributions, but their application to STPPs remains challenging: reverse sampling from pure noise is costly, and weak structural constraints in sparse spatial domains can lead to poorly localized probability mass. We propose GLIDE (Graph-guided Leap Inference for Diffusion Estimation), a conditional diffusion framework for next-event modeling in STPPs. GLIDE organizes historical events into a multi-scale historical graph and encodes temporal evolution and spatial topology through a dual-stream architecture, yielding a structured conditioning context for a dual-branch diffusion denoiser. It further introduces a prior-guided leap inference mechanism, in which a lightweight mean predictor provides a deterministic anchor and the reverse process starts from an intermediate diffusion step instead of from pure Gaussian noise. Experiments on multiple real-world datasets show that GLIDE improves both distribution fitting and next-event prediction, with the largest gains appearing on the spatial side. The results also indicate that prior-guided leap inference substantially reduces reverse-sampling cost while preserving the stochastic generation capability of diffusion models.

This paper demonstrates the effectiveness of machine learning-driven optimization for designing application-specific GaN tri-gate FinFETs in vertical power delivery systems. Conventional TCAD-based approaches are computationally intensive and insufficient for navigating the high-dimensional, nonlinear design space of advanced GaN devices. To address this, a physics-informed active learning framework is used to intelligently guide simulations, accelerating convergence while preserving accuracy. This ML-guided approach enables the discovery of optimal configurations by efficiently exploring key structural parameters – most notably the GaN-to-AlGaN thickness ratio – a long-standing focus of debate in device design. By systematically exploring key structural parameters, two optimized devices with aggressively scaled gate-to-drain lengths are identified. Single-fin, multi-channel simulations show that device~D2, with a thinner GaN channel relative to the AlGaN barrier, achieves higher drive current. However, in a 300-fin configuration, device~D1 outperforms device~D2 by delivering 3.3\,A at 0.49~ohm on-resistance – approximately 2$\times$ better – despite slightly higher parasitics. Both devices operate in a normally-off mode. Based on an application-specific figure of merit, device~D1 achieves 5\,pC$\cdot$ohm, demonstrating 2$\times$ greater switching efficiency than device~D2, while both designs outperform industrial benchmarks from different performance standpoints.

Standard positional encodings for transformers - sinusoidal and rotary (RoPE) - treat every position as equally local: they encode where a token is, but not how far its positional influence should extend. We propose that the Morlet wavelet, which simultaneously minimises uncertainty in position and frequency, is the natural basis for positional encoding, and introduce Morlet Positional Encoding (MoPE): each embedding dimension learns its own frequency and locality bandwidth from data. The main theoretical result is a unification: sinusoidal PE and the RoPE correlation kernel both emerge as limiting cases of MoPE when locality is switched off (sigma_i -> infinity). The phase of MoPE recovers the RoPE rotation angle exactly; the amplitude adds a learned Gaussian locality kernel that standard encodings lack. Empirically, MoPE combined with Energy-Gated Attention achieves +0.119 improvement over standard attention on TinyShakespeare, outperforming either component alone. Analysis of the learned parameters reveals that all 128 frequency-bandwidth pairs converge to the wavelet admissibility boundary - an empirical observation consistent with a companion result on energy gating, suggesting a reproducible property of character-level language signals that warrants further investigation.

This paper introduces a distribution-free framework for constructing post-detection confidence sets for changepoints after stopping a sequential change detection procedure. It is well known that conformal test martingales can be used to sequentially detect changes in distribution, but by themselves provide no inference for the time at which a proclaimed change occurred. Past work on post-detection inference requires pre- and post-change classes of distributions to be known, but this paper accomplishes localization of the changepoint without any distributional assumptions. We establish finite-sample coverage guarantees (conditional on correct detection). We provide non-asymptotic bounds on the conditional expected size of the confidence sets. Under suitable asymptotic regimes, we prove that the conditional expected size of the confidence set remains uniformly bounded and demonstrate strong empirical performance on simulated and real data. To the best of our knowledge, this is the first general distribution-free framework for sequential changepoint localization with valid post-detection coverage.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

Inspired by the function-space theory of neural networks, we formulate and analyze a variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation. We characterize its unit ball as the closed convex hull of a vector-valued single-neuron dictionary in Bochner spaces. For the ReLU activation, the bounded linear operators in this space are precisely the Schatten-$1$ operators, with equivalent norms. For operators in this space, we establish encoder–decoder approximation bounds in the Bochner $L^q$-norm, where the error decomposes into input and output encoding errors and a finite-width term of order $N^{-1/2}$. Under sub-Gaussian assumptions on the input and noise, we further derive high-probability generalization bounds for empirical least squares over path-norm-constrained encoder–decoder networks; the finite-sample contribution to the squared prediction error is of order $K^{-1/2}$ up to logarithmic factors. The finite-width and finite-sample constants are independent of the encoding dimensions and bases, with the latter also independent of the network width. When the encoding errors decay algebraically, these bounds yield algebraic approximation and learning rates, in contrast to the complexity barriers for Lipschitz and Fréchet differentiable operator classes.

Latent reasoning enables Large Language Models (LLMs) to perform multi-step inference within continuous hidden states, offering efficiency gains over explicit Chain-of-Thought (CoT). However, the opacity of these continuous thought vectors hinders their reliability and controllability. This paper bridges the gap between mechanistic interpretability and actionable control. We first present a systematic analysis using structural, causal, and geometric probes, revealing that latent vectors encode compressed, faithful representations of reasoning steps, with early vectors acting as critical causal hubs. Building on this, we operationalize these interpretability insights into a suite of training-free, decode-time interventions that refine the latent reasoning process by imposing the identified geometric and semantic priors. Extensive experiments across multiple model scales and diverse task domains demonstrate that our approaches consistently improve reasoning accuracy. Our interpretability-guided interventions consistently unlock latent capabilities and improve reasoning accuracy without any parameter updates.

While diffusion-based policies have impressive performance and expressivity, their long offline training slows down the data collection and policy deployment loop. We introduce Closed-Form Diffusion Policies, a class of training-free diffusion-based policies for imitation learning using the closed-form score derived from the demonstration dataset. We deploy CFDP with real-time inference with a mobile CPU in hardware experiments, showing it can successfully perform imitation directly from the dataset in milliseconds and with faster inference than neural diffusion policies. In experiments on imitation learning benchmarks, we show that CFDP is competitive against neural baselines that require hours of training, providing a favorable tradeoff between training time and performance. Finally, we show how closed-form diffusion policies act as a composable primitive that enables data-driven inference-time editing of pre-trained neural diffusion policies, including policy guidance and novel demonstration augmentation.

The GDP of a country is modelled as the relative interaction between two agents - working hours, reflecting the social choice of a population, and Total Factor Productivity, reflecting the collective investment in productivity enhancers. It is shown that a Random Forest model can accu- rately predict the GDP from these two factors. The differences in the choices made by Germany and USA are analysed though Gini importance, SHAP plots and partial dependency. It is shown that the differences in the social structure of the countries are reflected in the relative contribution of working hours and productivity to the GDP.

Many networks not only support but also rely on transient non-normal amplification, an orders-of-magnitude increase in the activity of an otherwise stable system. Constructing such networks under hard sign/sparsity/diagonal constraints – the regime relevant for biological connectomes and structured RNN initializations – has so far required either gradient-based local search with thousands of inner-loop eigendecompositions or Schur-form direct construction in an abstract basis that breaks the constraints under projection. Here we introduce DAGGER (Directed Acyclic Graph Guided Edge Reweighting), a gradient-free single-pass algorithm. Given a stable signed sparse matrix, DAGGER produces an output with the same sign, sparsity, and diagonal. A single scalar $\beta$ controls a Wasserstein-2 budget that smoothly trades exact multiset preservation ($\beta = 0$) for amplification; peak amplification grows essentially without bound with $\beta$, empirically reaching $10^{10}$ before numerical overflow. DAGGER matches or exceeds gradient-based methods at multiset preservation in a single forward pass – 30-100$\times$ fewer eigendecompositions than a typical gradient inner loop – and at moderate $\beta$ beats them by orders of magnitude with connectivity exactly preserved. We develop the algorithm, compare it to the existing methods and on a downstream signal-detection task, and examine the diagnostics that show why DAGGER is structurally different from other amplifying networks.

Imbalanced learning is a critical challenge in machine learning, where underrepresented target values can bias models and degrade prediction performance on rare but important cases. Although extensively studied in classification, imbalanced regression remains relatively underexplored. Existing methods mainly focus on either data-level balancing, which may introduce noise and overfitting, or algorithm-level balancing, which often struggles with highly complex target distributions. To address these limitations, we propose a unified hybrid framework that integrates both data- and algorithm-level balancing strategies into a regressor-agnostic pipeline. The proposed framework consists of five stages: (1) adaptive bin partitioning to dynamically segment the target space based on local linear coherence; (2) target-conditioned representation learning using a Conditional Variational Autoencoder; (3) multistage data-level balancing through feature-space clustering and oversampling of minority clusters; (4) algorithm-level balancing using a novel Latent-Density Weighted Loss (LDWL) to emphasize rare samples in latent and target spaces; and (5) attention-based gated fusion for final regression. Experimental results on benchmark datasets demonstrate that the proposed framework consistently improves predictive performance compared to standalone regressors and existing imbalanced regression approaches.

Generating molecules that simultaneously satisfy drug-like properties and conform to the 3D structure of a target protein is a core challenge in structure-based drug design (SBDD). Existing generative approaches, however, often rely on costly post-hoc processing during Sampling or require carefully curated datasets during training, yet still achieve modest gains. These limitations are especially pronounced in multi-objective settings, where balancing conflicting criteria remains a core challenge. To address these challenges, We propose FTDiff, a reinforcement learning fine-tuning framework tailored for diffusion-based molecular generation under structural constraints. To ensure stable and sample-efficient optimization, FTDiff adopts a group relative policy optimization (GRPO) style strategy. Furthermore, FTDiff builds upon a time-free pretrained diffusion model and incorporates a fast sampling mechanism that reduces the number of denoising steps, significantly accelerating both training and inference while maintaining generation quality. By optimizing a fixed threshold-aware reward, FTDiff effectively guides the model to produce valid, diverse, and high- quality molecules that balance multiple drug design objectives. Extensive experiments on benchmark datasets demonstrate that FTDiff consistently outperforms prior methods, without requiring expensive post-hoc optimization or intricate data engineering.

Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder characterized by challenges in communication and behavior. This study examines the relationship between ethnicity and ASD traits, along with behavioural scores, sex and neonatal jaundice across three ethnic groups: White Europeans, Asians, and Middle Eastern individuals. We perform a logistic regression and show that ethnicity has a significant effect on incidence of ASD. White Europeans are 81% increased risk of ASD and Middle Easterners are at 79% reduced risk of ASD compared to Asians. We also confirm earlier studied which show that neonatal jaundice is a significant predictor of ASD, while male children are at much higher risk of ASD compared to female children. These results suggest the need for diagnostic frameworks and interventions that account for ethnic in the presentation and assessment of ASD traits

The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors. In order to leverage the geometry of the space, we formulate the learning of such matrices as optimization on a Riemannian quotient manifold. We propose a novel block-diagonal Riemannian metric derived from the pullback of the Frobenius inner product. The metric is shown to be invariant under these symmetries. We develop a Riemannian gradient descent algorithm that uses a tuning-free Gauss–Newton step size and scales linearly in the number of observed entries per iteration. The versatile framework of Riemannian quotient optimization enables both first-order and second-order Riemannian methods, the latter through a closed-form connection and the Riemannian Hessian. Experiments on real and synthetic datasets illustrate the efficacy of our proposed Riemannian approach.

The choice between cross-attention and concatenation for multimodal fusion remains governed by practitioner intuition rather than principled understanding. In this paper, we demonstrate that feature alignment quality, not data scale alone, is the primary determinant of which fusion strategy excels. Through controlled experiments on Flickr8k using two feature extraction backbones (ResNet18 and CLIP ViT-B/32), we show that concatenation outperforms cross-attention by 4.1-5.1 percentage points across all tested scales (2048-16384 samples) when features are pre-aligned by a vision-language pretraining objective. We provide a theoretical explanation grounded in sample complexity analysis: concatenation requires O(d_v + d_t) samples to learn its fusion projection, while cross-attention requires O(d_v * d_t) samples to learn bilinear attention weights, over 256 times as many for 512-dimensional CLIP features. When features are already aligned, the approximation error gap between the two methods vanishes, and concatenation's sample efficiency dominates at all practical dataset sizes. An alignment degradation study confirms a monotonic trend: as feature alignment degrades, concatenation's advantage grows from 1.3% to 2.8%. These findings provide a principled decision framework for fusion method selection in multimodal systems, with direct implications for the design of Multimodal Large Language Models.

When a language model answers a factual question, where does its internal state go? We asked four open models (Llama-3.1-8B, Qwen2.5-7B, Gemma-2-9B and Llama-3.2-1B) 2,256 factual questions whose answers recur, such as the country a person is a citizen of. At every layer, we recorded the state from which the answer is produced. Questions that receive the same answer converge on a shared region of state space, which we summarise by its centre, the answer centroid. The answer becomes readable within a single layer. In every model, the share of questions whose state lies nearest its own answer's centroid jumps at one layer, between 47% and 71% of the way through the network. The centroids follow the answer the model gives rather than the question: the centroid of a country learned from questions about people's citizenship also identifies that country in questions about towns and films. The model also uses the centroids. After the jump, moving the state of a wrongly answered question to the right answer's centroid makes the model give the right answer in 83%-97% of cases late in the network, against 2%-4% for a random move of the same size. Before the jump, moves of the same size almost never work. Near misses, in which the model answers wrongly but picks the right option in multiple choice, can be seen from the onset layer, where the right answer's centroid is already among the nearest to the state. This signal is about as informative as the right answer's rank in the model's final output, and more informative than the model's confidence in its reply.

Classical models of strategic classification treat agents' responses to a deployed classifier as cosmetic: features change, but true labels do not. We study an improvement-aware variant in which strategic responses can change outcomes: agents choose post-deployment features strategically at a cost, and labels are then drawn from a fixed conditional outcome law. We formalize this problem for linear classifiers under a single-index qualification model and linear-decomposable costs. Under these assumptions, agents' best responses reduce to a closed-form shift of the decision boundary, and the resulting improvement-aware classification problem is learnable with linear sample complexity. As post-deployment labels are unavailable a priori, we begin by establishing a generalization bound with oracle access to the outcome law. One of our main contributions is a practical plug-in algorithm that replaces the oracle with an estimate, together with a bound on its improvement-aware error. We also show that the optimal classifier for standard strategic classification is a better proxy for the improvement-aware objective than the non-strategic Bayes-optimal classifier. Experiments on semi-synthetic and synthetic data support these findings and the plausibility of our assumptions.

Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems. While Physics-Informed Neural Networks (PINNs) successfully solve differential equations, current architectures remain inherently domain-specific. The extraction of domain-invariant entropy representations across fundamentally different physical laws remains unexplored. This paper introduces a unified Physics-Informed Deep Learning (PIDL) framework that simultaneously enforces differential equation residuals and information-theoretic bounds within a single neural architecture. We demonstrate this framework via two canonical studies: (i) a thermodynamic continuous stirred-tank reactor (CSTR) model solving governing ODEs, where a Softplus constraint strictly enforces the Second Law of Thermodynamics; and (ii) an information-theoretic financial market model solving the inverse Fokker-Planck PDE to infer latent drift and diffusion coefficients, guaranteeing diffusion positivity via a Softplus constraint while naturally inducing Shannon entropy. Three model variants are evaluated: two domain-specific baselines and one shared-encoder architecture. The PIDL framework guarantees absolute thermodynamic admissibility with zero Second-Law violations and exhibits exceptional data efficiency, retaining >90% predictive accuracy using merely 30% of available training data. Furthermore, a post-hoc Ruppeiner Riemannian geometric analysis of the learned entropy surface successfully identifies thermodynamic phase instabilities. This methodology provides a robust, domain-agnostic architecture for physics-constrained entropy modeling, advancing applications in sustainable process design and quantitative financial risk assessment.