Papers

How do people build abstract, reusable knowledge from sequential experience under bounded cognitive resources? To answer this question, we integrate rate-distortion theory with recent advances in program induction to describe how prior knowledge shapes which future structures are cheap to encode and easy to discover. We formalize this in a hierarchical Adaptor Grammar (HAG) with distinct local (within-task) and global (across-task) libraries, governed jointly by constraints on memory and computation. In simulations, HAG achieves better rate-distortion trade-offs and stronger generalization than fixed grammars or shallow chunking methods. In an online melodic sequence-learning experiment, participants' recall errors reflected systematic simplifications and reaction times increased at inferred program boundaries. Trial-by-trial fits further showed that hierarchical libraries best explained individual differences in both recall and out-of-sample continuation choices, outperforming all alternative models. These findings cast structured learning as bounded program induction in which the order of experience shapes future abstractions a learner builds.

The goal of artificial intelligence is to create agents capable of general, adaptive behaviour in open-ended environments. Guided by the "Bitter Lesson", we argue that the most effective path toward this goal is to systematically remove human priors and allow intelligence to naturally emerge through interaction with a "Big World" that is orders of magnitude more complex than the agent itself. We propose the mobile Graphical User Interface (GUI) as a practical proxy for such a world and introduce Darwin Mobile Agent, an open-source infrastructure designed as a foundation for autonomous reinforcement learning in this domain. This framework addresses the data-collection bottleneck in real-world mobile interactions by using an asynchronous agent-environment loop across parallel cloud-phone instances. We further propose a conceptual roadmap to systematically remove human priors from three fundamental pillars of a self-evolving agent: task curricula, outcome verification, and memory management. We validate that the Darwin infrastructure provides the stability and scalability required for the first stage of this roadmap: policy optimisation in the GUI domain. This work establishes the practical and theoretical foundation necessary to move toward truly autonomous, self-evolving GUI agents.

Multi-agent debate improves the reliability of large language models (LLMs) through iterative peer critiques. However, fixed topologies often introduce persistent positional biases, amplify unreliable agents, and cause high sensitivity to role assignments. We introduce Permutation-Equivariant Adaptive Routing Multi-Agent Debate (PEAR), an inference-time train-free protocol that dynamically reconfigures communication roles and sparse topologies across consecutive debate rounds. By strategically switching agent-to-role assignments based on evolving agent states, PEAR prevents any agent from permanently occupying a privileged network position or distributes influence more evenly across the debate. We theoretically characterize PEAR as an equivariant sparse router: it preserves accuracy under agent relabeling while reducing routing complexity and improving generalization. Comprehensive empirical evaluations across four reasoning benchmarks and six diverse LLM backbones demonstrate PEAR significantly improves average accuracy over the strongest debate baselines. The code is available at https://github.com/EVIEHub/PEAR.

Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable. Yet, many real-world reasoning problems are inductive: agents must infer uncertain beliefs from sparse, ambiguous observations. There are challenges to using standard fine-tuning methods for inductive reasoning, including difficulties in curating large-scale, high-quality labeled datasets and in handling targets that are inherently distributional. In this work, we introduce a novel approach, called Program-based Posterior Training (PPT), to address these limitations: we use an LLM to generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses to queries, and then fine-tune on these probabilistic soft labels. Using this approach, we fine-tune LLMs on 10,000 programmatically generated scenarios and evaluate on held-out motifs, human-labeled judgments, and external benchmarks. Overall, PPT substantially improves estimation accuracy on held-out inductive tasks, increases alignment with human judgments, and transfers to external benchmarks for estimation and calibration. Additionally, the gains in raw calibration are not subsumed by post-hoc temperature scaling, showing that the models have more deeply internalized uncertainty compared to output rescaling. Together, these results suggest that probabilistic-program-mediated fine-tuning is a promising approach for post-training LLMs to reliably perform approximate inductive inference.

Korean folk painting (minhwa) is built from a small vocabulary of auspicious symbols, a tiger for protection, a pair of birds for marital harmony, a peony for wealth, that recur across many of its painted genres. This suggests an obvious computational approach, identify which symbols appear in a painting and read the genre from the inventory. Working with a public corpus that pairs whole paintings, eight-field bilingual curatorial captions, and a separate set of expert object crops, we find that this approach does not work. A model given only a list of which symbols a painting contains predicts the genre far worse than a model that fuses the image with the curatorial text, and forcing the genre representation to be object-grounded actively hurts accuracy. The visual evidence on which the genre prediction rests is nonetheless localized and inspectable. A leakage-safe object evidence map projected from a part-level detector is spatially faithful to where curators isolated symbolic objects and to a patch-based surrogate's own gradient saliency. We name this configuration a faithful-but-insufficient dissociation. The part-level explanation is honest about what the part-level model sees, yet the genre target turns on how symbols are arranged rather than on which ones appear. The same lens separates a content label that survives transfer to held-out source institutions, genre, from a style label that does not, era, a prediction we confirm on two further labels in the corpus. We release the multimodal system, a worked-example reading of one painting's evidence map against its catalogue, and a set of evaluation cautions that recur in long-tailed heritage collections.

Self-healing smart grids can quickly adjust their network configuration during outages to minimize power disruptions. During an outage, several actions can be taken, such as network reconfiguration through switching operations and emergency load shedding. However, traditional machine learning methods for outage mitigation are not well suited for smart grids due to their slow response time and high computational cost. To address these challenges, recent studies have explored reinforcement learning to automatically perform network reconfiguration. In these approaches, the control policy is typically modeled using a graph neural network (GNN). However, conventional GNNs operate in the spatial domain and may fail to capture important relationships in the frequency domain. Frequency-domain information is particularly useful for modeling global structural patterns and system-wide interactions in power networks. In this paper, we propose a spectral graph reinforcement learning framework for outage management in distribution networks to enhance system resilience. Our model learns the optimal power restoration policy using a spectral graph neural network. We evaluate the proposed method on three modified IEEE test systems: the 13-bus, 34-bus, and 123-bus networks. Experimental results show that our approach achieves near-optimal performance in real time and generalizes well across a wide range of outage scenarios.

Customer churn prediction is essential across data-driven industries such as insurance, digital banking, eCommerce, and subscription platforms, where retaining existing customers is typically more cost-effective than acquiring new ones. Predicting churn on structured datasets remains challenging due to class imbalance, nonlinear feature interactions, and heterogeneous feature types. Tree-based ensemble methods consistently demonstrate strong performance in these contexts, often outperforming conventional neural networks. This study introduces a validated hybrid architecture that integrates feature-tokenized transformers (FT-Transformer) with gradient-boosted trees through calibration-aware stacking. The proposed framework addresses persistent gaps in statistical validation, probability calibration, and reproducibility found in prior research. The FT-Transformer captures higher-order feature interactions using self-attention, while XGBoost captures gradient-boosted decision boundaries with complementary inductive biases. Class imbalance is handled using class-weighted loss functions, thereby avoiding synthetic oversampling and preserving minority-class distributions. The models are ensembled using out-of-fold (OOF) stacking with a logistic regression meta-learner, which recalibrates overconfident base model outputs and learns optimal combination weights. On a public bank churn dataset, the hybrid model achieves 62.10% F1, 0.861 AUC-ROC, and 0.647 PR-AUC, outperforming the Multi-Layer Perceptron (MLP) baseline by 3.37 F1 points and 0.027 AUC under 5x5 cross-validation with 95% confidence intervals reported. Ablation studies demonstrate that both the transformer component and stacking strategy contribute materially to performance. The proposed methodology offers a reproducible and extensible reference architecture for contemporary churn prediction on structured tabular data.

A trained model is usually described by its weights, as if the weights fixed its behavior. In practice the same weights are run by different programs. Training uses high-precision accumulation and fixed tensor shapes, while serving uses low-precision arithmetic, fused attention kernels, a paged key-value cache, and dynamic batching. These programs produce different next-token distributions from identical weights. We make this dependence explicit by indexing a policy by the kernel that executes it, and we propose kernel contracts, which state how far a serving kernel may drift from a reference kernel on each slice of traffic and what the serving system should do when a limit is exceeded. We prove non-asymptotic bounds that link the logit difference between two kernels to total-variation and KL divergence, to the change in expected reward, to the bias of policy gradients computed from rollouts generated by another kernel, and to whether the greedy token can change. We test the bounds and the contracts in GPU experiments on Qwen2.5-7B-Instruct with Hugging Face and vLLM. The bounds hold on every prompt we measured. Lower precision, a different serving engine, and a different batch size each change the generated token on some prompts, and these changes concentrate on prompts where the model is nearly undecided between two tokens. A kernel can therefore look fine on aggregate metrics while behaving differently on exactly these prompts. Checking a contract separately on each slice of traffic catches these cases.

As Low Earth Orbit has grown more crowded with space debris, the need for reliable and efficient debris removal solutions becomes more urgent. An active tether-net system with maneuverable units is one of the promising solutions to this problem, whose success is dependent on the robustness of the net maneuver and closing decisions. These in turn are impacted by the uncertainties attributed to i) noisy observation of the target debris state (e.g., sensing errors), and ii) imperfect simulations of the complex net dynamics and net/debris interaction behavior, over which the decision system is trained. This paper focuses on the first of these two uncertainty sources, and presents a pipeline to propagate and quantify the resulting uncertainty in the debris capture performance expressed in terms of Capture Quality Index (CQI). This quantification is uniquely performed for both an active tether-net using a fixed baseline control and one using a trained neuro-control policy to guide the net maneuver during the deployment phase. Two different uncertainty quantification (UQ) techniques, namely Sobol's variance-based sensitivity analysis and perturbation-based method are exploited. A high-fidelity simulator and a lower-fidelity surrogate-based environment are used to demonstrate trade-offs between prediction accuracy versus ease of resolving uncertainties.

This paper extends MST-Direct, a Matching-via-Sinkhorn-Transport approach for multivariate geostatistical simulation, from the original bivariate, unconditional, small-grid formulation to multivariate, conditional, and large-grid settings. We address the three main limitations identified in the original work: (i) scalability beyond a few thousand nodes through a sparse, candidate-restricted Sinkhorn matcher with O(nC) memory complexity; (ii) extension to multiple variables by matching target value tuples onto an independent FFT-MA Gaussian backbone that reproduces a prescribed variogram; and (iii) hard-data conditioning by fixing observed data tuples at their spatial locations while conditioning the backbone through kriging. Because the transport plan remains a permutation of the target tuples, the multivariate joint distribution is preserved exactly. The method is validated using the same six-variate, heteroscedastic, strongly nonlinear reference distribution employed in Direct Multivariate Simulation (DMS), under both unconditional (200x200) and conditional (100x100, 200 hard-data samples) scenarios, and is benchmarked against the Projection Pursuit Multivariate Transform (PPMT). Results show that MST-Direct reproduces the joint distribution with zero histogram error, exactly honours hard data, and accurately reproduces the prescribed spatial correlation structure, whereas PPMT remains an approximation. Index Terms-Optimal transport, Sinkhorn algorithm, geostatistical simulation, multivariate simulation.

We present CARTOGRAPH, a verification layer for AI scientists that couples unresolved-subspace experiment steering (select), explicit ambiguity closure (resolve), and residual-based library inadequacy detection (refuse). Under a local linear-Gaussian bridge, raw unresolved projection is the isotropic unresolved Fisher-information trace, while CARTOGRAPH-A is the exact unresolved A-optimal rule; closed-form EIG and Box-Hill arise as local comparators rather than global equivalents. Across five testbeds, CARTOGRAPH-A beats raw projection 129W/0T/15L at d = 8 (p < 10^-21) in a replicated structured cascade. More distinctively, the framework tentatively identifies three out-of-library pharmacokinetic mechanisms and then revokes those identifications as residuals expose structural misfit, while one perturbed in-library control stays identified throughout. In low-dimensional pharmacokinetic and filtered EPA settings, near-ties against disagreement are predicted by theory and observed. Finally, in a retrospective audit of 40 positive claims from the published A-Lab autonomous materials system, the refuse guard flags all 4 claims later marked inconclusive under manual reanalysis while passing 32/36 confirmed claims. Code is available at https://github.com/ai4science-boed/cartograph.git

Regulatory stress testing frameworks, including the Comprehensive Capital Analysis and Review (CCAR) and the Internal Capital Adequacy Assessment Process (ICAAP), require robust Stressed Value-at-Risk (SVaR) estimation under forward-looking macroeconomic scenarios. Traditional parametric approaches often exhibit numerical instability under extreme shocks, reducing the reliability of capital projections. This paper extends the Hybrid Gaussian Process Regression Historical Simulation (GPR-HS) framework of Vadrevu (2026) to forward-looking stress scenarios, demonstrating stability across three regimes: West Asia War, Climate Risk, and AI Bubble/Regulation. A key contribution is the Scenario-Averaged Covariance Stabilization (SACS) framework, which constructs stress covariance as a weighted aggregation of historical crisis regimes, providing stable and interpretable dependence structures. Stressed return paths are generated over a 252-day horizon using deterministic drift and stochastic residuals, while volatility is modeled via Gaussian Process Regression with Aggressive Noise Initialization (ANI). The framework exhibits consistent convergence across all assets and scenarios. SVaR ranges from -2.1020% to -2.2231%, with the coherence property |SES| > |SVaR| preserved. The results support GPR-HS with SACS as a stable and regulator-aligned approach for forward-looking SVaR and SES estimation in CCAR and ICAAP applications.

Manifold-constrained hyper-connections (mHCs) have recently been proposed as a principled extension of hyper-connections, where the residual mixing matrices are constrained to be doubly stochastic via projection onto the Birkhoff polytope. In practical mHC implementations, this constraint is enforced by Sinkhorn-Knopp iterations, and the backward pass relies on unrolling the iterative solver. This design introduces substantial computation and memory overhead, and may also yield inaccurate projections when the algorithm converges slowly on challenging inputs, undermining the intended norm-control and stability guarantees of mHCs. In this work, we focus on the practically important 4x4 Birkhoff projection setting and develop an end-to-end acceleration framework. By leveraging the dual formulation, we reduce the problem to a three-dimensional unconstrained convex problem and solve it with Newton's method, achieving fast convergence and high accuracy. For the backward pass, we replace the unrolled differentiation with implicit differentiation, yielding exact gradients without storing intermediate states. To exploit massive parallelism, we design a warp-level CUDA kernel that uses only register-level primitives, avoiding global and shared memory I/O. Extensive experiments against representative open-source baselines demonstrate that the proposed solver yields substantially more reliable doubly stochastic projections – especially when the input magnitude is large – and achieves significant end-to-end speedups (including the backward pass), reaching over 20x acceleration at large batch sizes while maintaining orders of magnitude smaller marginal errors.

Despite Japan being one of the world's largest advanced democracies, the development of election forecasting models for its national elections remains limited. This study introduces nonlinear machine-learning forecasting models, based on decision tree and ensemble learning methods, for predicting the outcomes of Japanese lower-house elections. To assess the methodological benefits of our approach, we replicated the theoretical framework and dataset of Lewis-Beck and Tien's (LBT) foundational statistical forecasting model for Japanese elections. Our models demonstrated moderately but consistently improved predictive accuracy compared to LBT's model in both in-sample and out-of-sample evaluations, suggesting that nonlinear algorithms offer an alternative approach to classical linear methods in capturing complex electoral dynamics. This study represents one of the earlier applications of nonlinear machine-learning techniques to single-country election forecasting. It offers a replicable framework that, when combined with the country-specific electoral theories of other nations, may enhance the predictive performance of forecasting models in broader national contexts.

Key-value (KV) caching for shared prefixes is essential for high-throughput large language model (LLM) serving, but it faces critical challenges in emerging diffusion language models (DLMs). In DLMs, bidirectional attention means that updating any token dynamically alters the entire context and its corresponding KVs. Thus, existing caching techniques developed for LLMs, which assume that KVs remain invariant once computed, corrupt the shared prefix KVs. Our experiments show that applying these techniques to DLMs causes model accuracy to collapse to near zero. To unlock high-throughput DLM serving, we propose bidirectional prefix caching, BiCache, the first KV caching technique for shared prefixes in DLMs. BiCache is designed based on key observations from our comprehensive analysis: shared prefix KVs remain stable and reusable in shallow layers, while the depth of shallow layers depends on the fraction of shared prefix tokens in each request. Thus, BiCache dynamically identifies a safe layer depth for reusing shared prefix KVs and eliminates redundant computation. Evaluations demonstrate that BiCache significantly improves serving throughput by 36.3%-98.3% compared to existing techniques without accuracy collapse (only 0-1.8% difference).

Scientific knowledge is increasingly dispersed across vast and heterogeneous scientific literature, where important claims are often implicit, evolving, and internally debated. While large language models (LLMs) have shown impressive performance in information extraction and summarization, their ability to recover latent scientific consensus remains unclear. Here, we investigate this problem in the context of high-temperature superconductivity (HTS), a long-standing and highly debated topic in condensed matter physics, as a challenging testbed. Using near 18,000 highly-cited publications over the past seven decades, we construct a structured knowledge graph linking competing superconducting mechanisms, material families, evidential modalities, and citation relations. We find that LLM-extracted representations recover coherent and physically interpretable structures, including family-dependent mechanism profiles, evidence-specific correlations, and citation-mediated temporal evolution of scientific beliefs. Ablation studies on LLM further show that the global structure remains robust across prompting, decoding, and model variations. Our results suggest that LLMs can indeed serve as scalable tools for deciphering scientific knowledge in domains characterized by competing interpretations and evolving knowledge.

Accurate carbon emission monitoring is critical for climate policy and emerging regulatory mechanisms such as the EU Carbon Border Adjustment Mechanism, yet city-level high-frequency monitoring data remain extremely scarce, severely limiting data-hungry deep learning models. Time series generation is a natural remedy, but existing GAN and diffusion-based generators often provide limited explicit supervision for the domain structure of carbon emission data: they may match marginal distributional statistics while insufficiently preserving cross-variable correlations between CO$_2$ and co-emitted pollutants and meteorological factors, and tend to collapse the first-difference statistics of atmospheric measurements, producing sequences that are smooth on average but lack the realistic step-wise variability of the underlying signals. We propose TriHead-GAN, a Transformer-based adversarial framework whose triple-head discriminator jointly supervises three complementary aspects of the joint distribution: distributional authenticity via a Wasserstein critic, cross-variable dependency via leakage-free regression of the target variable, and step-wise temporal smoothness via adjacent-difference prediction. The generator combines global self-attention with local temporal convolution, per-step noise injection, and an anti-smoothing loss that matches first-difference statistics. Experiments on the self-collected Changsha Carbon dataset, two public carbon datasets (China, US), and the ETTh1 benchmark show that TriHead-GAN achieves favorable performance over mainstream baselines on the vast majority of settings, and that the resulting synthetic windows improve downstream forecasting accuracy in low-resource carbon monitoring scenarios.

Scientific data annotation, such as tracking animals in video or proofreading neural reconstructions, remains bottlenecked by the "last mile" problem: even with strong automation, verification and correction consume substantial human effort. Standard approaches train models to directly predict annotations, discarding the rich supervision in how experts navigate, click, verify, and correct. We introduce a framework for studying behavioral cloning on scientific annotation: 9 synthetic tasks paired with synthetic annotations that simulate realistic human strategies including exploration, mistake correction, and strategic decision-making. Our experiments reveal several findings. First, skills emerge hierarchically: models learn GUI mechanics before task-critical decisions, and commit fewer mistakes than the training data while retaining the ability to correct errors when they occur. Second, scaling models on multi-task behavioral cloning shows that larger models are more data efficient within our scale range. Third, multi-task pretraining enables efficient fine-tuning to new tasks, while training from scratch fails entirely. Fourth, linear probes reveal that models internally represent latent variables of the annotation process such as task phase and data position; interestingly, we find a shared mistake representation that generalizes across different annotation tasks. Overall, our framework establishes systematic benchmarks and identifies key bottlenecks, providing a foundation for scaling behavioral cloning to real-world scientific data annotation.

Reinforcement Learning (RL) has long been a powerful solution to various problems in communication networks. However, traditional RL models still face with several limitations. Not only do they rely on large numbers of interactions with the environment, but they are also limited in terms of modeling long-term relationships and tackling partial observability. In recent years, the Transformer model has demonstrated the ability to enhance RL models, allowing them to overcome these issues. Particularly, the self-attention mechanism within the Transformer enables efficient modeling of long-range dependencies and global correlations, as well as accelerates training processes and handles heterogeneous data modalities. In this paper, we present a comprehensive survey of Transformer-based RL algorithms and their applications in communication networks. Specifically, the paper provides the mathematical background of RL and Transformer architectures, along with insights into key issues such as resource allocation, computation offloading, routing, and trajectory control, and network security. We conclude the paper by discussing challenges, open issues, and notable future research directions, including Transformer-enhanced DRL algorithms for semantic communication and network optimization.

Electrocardiography (ECG) remains central to cardiovascular screening, yet interpretation remains largely manual and episodic. Clinical practice relies on brief resting ECGs and, when required, long-duration ambulatory recordings, both generating data that require resource-intensive review. Consequently, subtle morphological changes or progressive drift preceding clinically apparent abnormalities may go unnoticed. We propose a motif-based framework that defines beat-aligned ECG motifs as interpretable cardiac signatures and quantifies morphological drift and deviation across short and long-term monitoring. Motifs are representative cardiac cycles capturing dominant morphology. We introduce three interpretable drift metrics: deviation from a normal sinus rhythm (NSR), deviation from a personalised baseline, and a motif instability index. Motifs are extracted by selecting beats that minimise Dynamic Time Warping (DTW) distance within fixed windows. We evaluate these metrics on short (PTB-XL) and long-duration (MIT-BIH Arrhythmia) ECG datasets. Interpretability is achieved through representative motif overlays and fiducial-based visualisations, enabling direct inspection of morphological changes. In MIT-BIH, the proposed metrics significantly separated predominantly normal from arrhythmic subjects (p<0.01). In PTB-XL, NSR deviation distinguished normal from abnormal ECGs across major diagnostic subtypes (p<1e-4, Cliff's delta up to 0.93). ECG motifs provide an interpretable representation of cardiac morphology, supporting scalable longitudinal monitoring and early detection of morphology-driven change.

Brain-computer interfaces (BCIs) are limited by low signal-to-noise ratio in modalities such as electroencephalography, which requires multiple trials to reliably decode user intentions. This induces a speed-accuracy trade-off, whereby higher accuracy comes at the cost of speed. The speed-accuracy balance is application-dependent, motivating controllable trade-offs. Conventional metrics, such as the Information Transfer Rate, combine speed and accuracy obscuring their dependence and potentially introducing biases. In this study, we propose an evaluation framework independent of classifier, paradigm, and early-stopping strategy that separates speed and accuracy. We employ two measures, Gain (relative speed improvement) and Conservation (relative accuracy preservation), and combine them into a tunable Gain-Cons Balance controlled by {\alpha}, regulating the speed-accuracy trade-off. The parameter adjusts the operating point without modifying the classifier, facilitating deployment across scenarios. The framework was evaluated on P300 event-related potential paradigms using public recordings from 63 subjects as well as multiple classifiers and early-stopping strategies to achieve distinct operating points in speed-accuracy and bitrate. Results show that tuning {\alpha} yields fast, accurate, or balanced BCI behaviours, demonstrating explicit control of the speed-accuracy trade-off. The method supports subject-level performance prediction and improves explainability of BCI behaviour. Further analysis of the Information Transfer Rate reveals a systematic bias toward speed, explained by the proposed framework through the Gain and Conservation measurements. Overall, this work establishes the speed-accuracy trade-off as a controllable design variable validated on public P300-based paradigms, enabling transparent evaluation and application-specific optimization of BCIs.

Modern time series architectures face a fundamental trade-off: channel-independent models scale well with increasing data volume but ignore critical inter-channel dependencies, while channel-dependent models are expressive but remain “dimension-bounded”, struggling to generalize across heterogeneous datasets.To bridge this gap, we introduce Unicorn (Universal Correlation Network), a framework for scalable, multi-dataset pretraining on high-dimensional time series. At the core of Unicorn is a latent prototype codebook that decouples correlation modeling from specific channel identities. By projecting heterogeneous channels into a shared latent space, UniCorN learns identity-agnostic, reusable interaction patterns that transfer across domains with diverse dimensionalities and semantics. Extensive experiments show that Unicorn significantly outperforms state-of-the-art forecasting architectures, particularly in few-shot transfer scenarios, offering a scalable path toward multivariate time series foundation models.

Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) – but if the SDE is integrated once per observation gap, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion – trajectory-law invariance to the observation schedule – together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A $2 \times 2$ encoder $\times$ integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency $p < 1/256$) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.

In-context learning \ – performing tasks based on examples given in the prompt \ – is an important capability that has emerged in large language models and has received significant attention in both theory and practice. Existing theoretical work often focuses on settings where the learning uses information purely from the prompt. However, many practical instances of in-context learning require the model to retrieve factual knowledge stored in the model's parameters, with the context serving to identify which knowledge is relevant. In this work, we study how in-context learning leverages factual knowledge recall. We formalize this behavior by introducing the in-context factual recall (IC-recall) task, where a transformer is provided a context of (subject, answer) pairs generated from a hidden relation, along with a query subject, and must both infer this hidden relation and retrieve the corresponding answer. Factual knowledge is modeled by the transformer having access to a simple pre-constructed MLP associative memory storing (subject, relation, answer) triplets. We analyze the supervised fine-tuning dynamics of a one-layer transformer on IC-recall data and prove that the model successfully performs IC-recall by converging to a particular pairwise attention pattern. This fine-tuning stage requires a very small number of samples \ – only polylogarithmic in the number of stored knowledge triplets. Experiments verify our theoretical predictions and show that the pairwise attention pattern emerges even when the MLP layer is pretrained instead of constructed.

When a language model sees a document contradicting its training knowledge, it must choose: follow the document or trust itself. Prior work proved this choice depends on how well-known the fact is. We ask: does the model's chain-of-thought (CoT) reasoning faithfully report this mechanism? We introduce introspective faithfulness and test it across 200 questions, 8 models, and 4 prompt conditions. We find CoT reasoning is highly stable across opposite decisions: flip pairs retain 96% of same-answer similarity (d=0.34; confirmed by ROUGE-L, d=0.45). Yet self-rated confidence carries a faint genuine signal: for obscure facts where entity fame is uninformative, confidence still predicts decisions (p<0.001) and tracks item-level knowledge (r=0.134). GPT-4o is the only model with statistically reliable reasoning-decision coupling. Claude Sonnet 4.6 shows the widest confidence range (SD=1.39) but near-zero pooled correlation because the confidence-decision relationship reverses between conditions; a temperature ablation confirms this is model-specific. Internal thinking tokens show greater decision-sensitivity than user-facing CoT (p=0.033). CoT decomposes into a decision-invariant knowledge display (~96%) and a thin confidence layer with weak but real signal. For monitoring: read confidence, not the argument.

Audio large language models (Audio LLMs) demonstrate strong performance on speech understanding tasks, yet their ability to understand paralinguistic information remains limited. To systematically quantify this issue, we introduce VoxParadox, an adversarial benchmark with 2,000 verified examples, spanning 10 paralinguistic tasks, created with controlled speech synthesis to intentionally mismatch transcript claims and speaking style, enabling direct measurement of speech paralinguistic understanding. Evaluation of a diverse set of Audio LLMs reveals consistently low accuracy on acoustic ground truth and a strong tendency to follow language-implied (incorrect) answers. To understand the cause of this gap, we perform layer-wise probing and find that (i) paralinguistic cues can degrade in deeper encoder layers and at the encoder–LLM interface, and (ii) even when such cues are available in audio tokens, the language model frequently ignores them. To address these problems, we propose Prompt-Conditioned Layer Mixer (PCLM), which adaptively combines information from multiple audio layers based on the input prompt, and pair it with Direct Preference Optimization (DPO) to explicitly prefer acoustically supported options over language-implied alternatives. These methods substantially improve Audio LLM paralinguistic understanding, improving Audio Flamingo 3 from 17.40% to 65.20% on VoxParadox, and from 37.74% to 54.78% on MMSU paralinguistic subset. Our project page is available at https://voxparadox.github.io/.

We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations of lattice polytopes. dualGNN operates on a generalization of the dual graph of a triangulation, with edges labeled by `signed circuits' – combinatorial invariants from the theory of oriented matroids. We show that these circuits are necessary and sufficient to determine a triangulation's regularity from the graph, provided certain magnitude information is retained. The model is independent of the polytope's point count and invariant under its orientation-preserving symmetries ($\mathrm{SL}(d,\mathbb{Z}) \ltimes \mathbb{Z}^d$), and our masking procedure further guarantees that every rollout produces a fine triangulation (in 2D). On unseen polygons with $N_\mathrm{pts} \leq 40$, dualGNN is the only sampler we tested that is consistent with uniform sampling across all our diagnostics (KL divergence from uniformity, collision counts, and sample autocorrelation). The model is small ($\sim92$k parameters) and trains in $\sim7.5$ hours on a single consumer GPU. We apply dualGNN to string theory, sampling Calabi-Yau threefolds uniformly at $h^{1,1}=86$; we also sample CYs at $h^{1,1}=128$, observing no deviations from uniformity, but our diagnostics are weaker here. Code, training scripts, and pretrained models are available at https://github.com/natemacfadden/dualGNN (pip install dualgnn), and dualGNN is integrated into CYTools.

We study the query complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to polynomial approximation barriers and a characteristic \(\sqrt{\kappa}\) dependence on the condition number. We show that this barrier disappears when the sampler is allowed to query smoothed scores, namely gradients of the logarithms of the Gaussian-convolved densities. For a Gaussian target with precision matrix \(\Lambda\), a smoothed-score query at noise level \(\tau\) gives access to the resolvent \((\Lambda+\tau^{-1}I)^{-1}\). Combining geometrically spaced noise levels with sinc-quadrature rational approximation, we obtain a sampler with $q=O\!\left(\bigl(\log\kappa+\log(e\sqrt d/\delta_{\rm TV})\bigr)\log(e\sqrt d/\delta_{\rm TV})\right)$ smoothed-score queries for total variation error \(\delta_{\rm TV}\), improving the condition-number dependence from \(\sqrt{\kappa}\) to logarithmic. We also study finite-bit gradient oracles. Using coordinatewise quantization of the transformed smoothed-score answers and a final dithering step, we obtain a sampling scheme whose total communicated gradient information is polylogarithmic in \(\kappa\); in particular, for fixed dimension and accuracy, the bit complexity is \(O(\log^2\kappa)\). To complement these upper bounds, we introduce a channel-synthesis, or reverse-Shannon, converse technique for sampling lower bounds. This converts total-variation simulation guarantees into communication requirements and yields an \(\Omega(\log\kappa)\) lower bound on the required gradient information. Together, these results identify smoothed scores as a provably more informative oracle for sampling and give nearly matching upper and lower bounds for its finite-bit complexity.

Recent advances in large language models have enabled natural language to serve as a flexible interface for controlling complex systems, but often at the cost of large-scale multimodal training or weakened domain-specific inductive biases. In structured decision-making domains such as chess, specialized policy networks achieve strong performance but lack semantic controllability, while prompt-conditioned language models are more flexible yet typically exhibit weaker domain grounding. We propose $\textbf{UniMaia}$, a framework for prompt-conditioned policy modulation that adapts a frozen Lc0-based chess policy network using a parameter-efficient text encoder and a ControlNet-style conditioning mechanism. UniMaia enables semantic control over gameplay, including opening selection and player strength, while preserving the pretrained policy representations. We further introduce $\textbf{UniMaia-Aux}$, which incorporates auxiliary temporal conditioning and behavioral prediction objectives. To support this work, we construct a large-scale metadata-augmented Lichess dataset, develop a semi-automated prompt-generation pipeline, and introduce benchmarks spanning both prompt-conditioned and metadata-conditioned settings. UniMaia achieves state-of-the-art expected accuracy on several prompt-conditioned benchmarks and competitive top-move accuracy on general instruction-following tasks, while remaining competitive with dedicated metadata-conditioned approaches on human move prediction benchmarks. UniMaia-Aux further improves expected accuracy and behavioral modeling across several evaluation settings, with modest trade-offs in top-move accuracy. Overall, our results demonstrate that prompt-conditioned control of domain-specific policy networks is feasible without end-to-end multimodal training, while highlighting trade-offs between controllability and predictive performance.

Self-Distillation Policy Optimization (SDPO) provides dense token-level credit assignment for reinforcement learning with large language models by leveraging the model's own feedback-conditioned predictions as a self-teacher. Unlike GRPO, however, whose group-relative advantage naturally concentrates learning on a sweet spot of intermediate-difficulty questions, SDPO's KL-based advantage lacks an implicit notion of difficulty awareness. We analyze this gap through the lens of GRPO's advantage normalization. Extending the learnability framework to normalized rewards, we show that normalization absorbs the variance term $p(1-p)$, equalizing leading-order learnability across questions and leaving $\sqrt{p(1-p)}$ as the sole residual scaling factor in the per-question gradient. This analysis yields a simple prescription: weight each question's SDPO loss by $[\hat{p}(1-\hat{p})]^{1/2}$, resulting in SC-SDPO, a scale-consistent variant of SDPO. The proposed weights are obtained as a zero-cost byproduct of on-policy rollouts with batch-adaptive normalization, inducing an implicit curriculum that dynamically tracks the model's evolving competence. Experiments on scientific reasoning and tool-use benchmarks demonstrate that SC-SDPO consistently improves over SDPO, yielding gains of +3.2/+4.3 (mean@16/maj@16) on Qwen3-8B and +1.8/+3.0 on OLMo-3-7B, while preserving stable training dynamics throughout optimization.