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We present an automated, contrastive evaluation pipeline for auditing the behavioral impact of interventions on large language models. Given a base model $M_1$ and an intervention model $M_2$, our method compares their free-form, multi-token generations across aligned prompt contexts and produces human-readable, statistically validated natural-language hypotheses describing how the models differ, along with recurring themes that summarize patterns across validated hypotheses. We evaluate the approach in synthetic setting by injecting known behavioral changes and showing that the pipeline reliably recovers them. We then apply it to three real-world interventions, reasoning distillation, knowledge editing and unlearning, demonstrating that the method surfaces both intended and unexpected behavioral shifts, distinguishes large from subtle interventions, and does not hallucinate differences when effects are absent or misaligned with the prompt bank. Overall, the pipeline provides a statistically grounded and interpretable tool for post-hoc auditing of intervention-induced changes in model behavior.

We administer 45 validated psychometric questionnaires to 50 large language models (LLMs) to identify the dimensions along which LLMs differ psychometrically. Using Supervised Semantic Differential (SSD), we find that the primary axis of between-model variance separates items describing phenomenally rich experience, including embodied sensation, felt affect, inner speech, imagery, and empathy, from items describing stimulus-driven behavioral reactivity ($R^2_{adj}=.037$, $p<.0001$). To test this hypothesis at the item level, we introduce the Pinocchio score ($π_i$), the ratio of inter-model response variance under neutral prompting to that under a human-simulation prompt, as an annotation-free measure of each item's experiential demand. $π_i$ predicts condition-induced shifts in primary factor loading magnitudes ($ρ=-.215$, $p<.0001$, $n=1292$--$1310$ items), confirming that between-model divergence on experiential items is structured rather than noisy. Applying PCA to per-model EFA scores across all questionnaires reveals one dominant dimension, the Pinocchio Axis ($Π$): the degree to which a model presents itself as a locus of phenomenal experience rather than a system of behavioral responses. This axis captures 47.1% of cross-questionnaire between-model variance in primary factor scores and converges with item-level Pinocchio scores ($r=.864$). Marked within-provider divergence across closely related model variants is consistent with post-training fine-tuning as a key contributor, supporting the interpretation that $Π$ reflects a training-shaped self-representational tendency governing how a model treats experiential language as self-applicable. The dominant axis of between-model psychometric variation is therefore not a conventional personality trait but a self-representational stance toward one's own nature as an experiencer.

Large Language Models (LLMs) have achieved remarkable success but remain highly susceptible to jailbreak attacks, in which adversarial prompts coerce models into generating harmful, unethical, or policy-violating outputs. Such attacks pose real-world risks, eroding safety, trust, and regulatory compliance in high-stakes applications. Although a variety of attack and defense methods have been proposed, existing evaluation practices are inadequate, often relying on narrow metrics like attack success rate that fail to capture the multidimensional nature of LLM security. In this paper, we present a systematic taxonomy of jailbreak attacks and defenses and introduce Security Cube, a unified, multi-dimensional framework for comprehensive evaluation of these techniques. We provide detailed comparison tables of existing attacks and defenses, highlighting key insights and open challenges across the literature. Leveraging Security Cube, we conduct benchmark studies on 13 representative attacks and 5 defenses, establishing a clear view of the current landscape encompassing jailbreak attacks, defenses, automated judges, and LLM vulnerabilities. Based on these evaluations, we distill critical findings, identify unresolved problems, and outline promising research directions for enhancing LLM robustness against jailbreak attacks. Our analysis aims to pave the way towards more robust, interpretable, and trustworthy LLM systems. Our code is available at Code.

Gap-closing rate and visual looming swap discriminative dominance depending on deceleration intensity - a finding that reconciles a long-standing conflict in the car-following literature and challenges spacing-centered assumptions in traditional driver behavior models. This study presents a two-stage analytical framework that distinguishes between information availability (kinematic variables measurable in the environment) and information utilization (variables that demonstrably separate driver behavioral patterns), applied to 1,060,119 valid car-following observations from the NGSIM trajectory dataset (2,932 vehicles). Six kinematic features are extracted, and deceleration events are detected under two threshold conditions (-0.5 m/s^2 and -0.3 m/s^2). K-means clustering identifies behavioral modes, and one-way ANOVA with eta-squared effect sizes ranks each feature's discriminative power. Three key findings emerge: (1) threshold selection fundamentally shapes behavioral inference - the stricter threshold yields three interpretable modes while the permissive threshold collapses these to two; (2) hard braking prioritizes gap-closing rate (eta^2 = 0.715) while moderate braking emphasizes visual looming (eta^2 = 0.574); and (3) spacing headway is negligible (eta^2 <= 0.014) across both thresholds. These findings provide empirically grounded candidates for perceptual cue prioritization and have direct implications for ADAS warning system design and autonomous vehicle control.

We propose a lightweight and single-pass uncertainty quantification method for detecting hallucinations in Large Language Models. The method uses attention matrices to estimate uncertainty without requiring repeated sampling or external models. Specifically, we measure the Kullback-Leibler divergence between each attention head's distribution and a uniform reference distribution, and use these features in a logistic regression probe. Across multiple datasets, task types, and model families, attention divergence is highly predictive of answer correctness and performs competitively with existing uncertainty estimation methods. We find that this signal is concentrated in middle layers and on factual tokens such as named entities and numbers, suggesting that attention dynamics provides an efficient and interpretable white-box signal of model uncertainty.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.

Handwritten archival tables contain rich historical information, yet transforming them into structured representations, such as Knowledge Graphs, requires integrating table structure recognition, handwriting recognition, and semantic interpretation - a complex multimodal process. End-to-end AI implementations can obscure these steps, resulting in opaque algorithmic operations that hinder human oversight, critical assessment, and trust. To address this, we present a modular, provenance-aware pipeline to convert handwritten tabular images into KGs supporting human-AI collaboration. The pipeline decomposes the workflow into three stages - table reconstruction, information extraction, and KG construction - while exposing intermediate representations for inspection, evaluation, and correction. A key contribution of our approach is the systematic integration of data provenance at every stage, ensuring that all extracted entities and literals remain traceable to their visual and textual origins. The proposed pipeline is demonstrated through a number of experiments on real-world archival material concerning military careers. The results across three different table reconstruction variants highlight the importance of modularisation. By coupling modularity with data provenance, our work advances transparent and collaboratively controllable image-to-KG pipelines for complex historical data.

Compositional generalization refers to correctly interpret novel combinations of known primitives, which remains a major challenge. Existing approaches often rely on supervised fine-tuning, which encourages models to imitate target outputs. This token-level training paradigm fails to capture the global compositional structure required for generalizing to unseen combinations. In this work, we investigate whether compositional generalization can instead be improved through outcome-level reinforcement learning. We adopt Group Relative Policy Optimization to optimize models based on feedback on their final outputs. Within this framework, we explore both a simple binary outcome reward and a composite reward that provides additional composition feedback. Experiments on multiple compositional benchmarks show that reinforcement learning improves compositional generalization compared to supervised fine-tuning. Further analysis reveals that supervised models tend to overfit frequent training compositions, whereas reinforcement learning improves compositional generalization by reshaping the output distribution, particularly for more complex composition types.

Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC) paradigm, this paper introduces the RC-Koopman framework, which interprets reservoir as a stateful, finite-dimensional Koopman dictionary whose temporal depth is explicitly controlled by its spectral radius. We show that the Echo State Property (ESP) guarantees well-posedness and favorable numerical conditioning of the lifted Koopman approximation. A correlation-based spectral radius selection algorithm aligns reservoir memory with dominant system timescales. Analysis reveals how the finite memory of the reservoir determines which Koopman eigenfunctions remain observable from the lifted features. Evaluation on synthetic benchmarks demonstrates that RC-Koopman achieves a favorable balance between reconstruction accuracy of the underlying nonlinear dynamics and dynamical stability, compared to Extended Dynamic Mode Decomposition (EDMD) and Hankel-based lifting approaches. Code available at: https://github.com/NEAR-the-future/RC-Koopman.git

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.

When a language model processes a hallucinated response, its attention routing tends to fail in one of two shapes: over-concentrating on a narrow set of positions, or spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. We study these shapes as a diagnostic characterization, computed from attention matrices under \emph{forced scoring} of benchmark-labeled responses rather than during live generation. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport \emph{capacity}; we prove that every transpose-invariant spectral diagnostic of this operator is structurally \emph{orientation-blind} (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a converse to the blindness theorem bounding any Lipschitz diagnostic's transpose sensitivity by the asymmetry coefficient $G$. Pairing this with a closed-form bipartite-Cheeger landscape for canonical causal architectures, we show that uniform causal attention satisfies an $n$-independent floor $φ\ge 1/5$, while window attention pierces the floor as $O(w/n)$; failure modes are shape-different, not just value-different. This floor is an idealized-architecture benchmark, not an empirical attractor: the fraction of real attention heads that pierce it is itself an architectural signature. The resulting two-axis diagnostic ($φ$ for capacity, $G$ for direction) yields a falsifiable polarity prediction: bottleneck- and diffuse-dominated benchmarks should exhibit opposite polarity. Under length-controlled evaluation, transport features retain interpretable signal (0.62-0.84 LC-AUROC) across the tested decoder-only, encoder-only, and encoder-decoder models, with polarity reversing as predicted between HaluEval and MedHallu.

This paper proposes latent visualization by optimization (LVO), a mechanistic interpretability technique that extends feature visualization by optimization - originally developed for convolutional neural networks - to latent diffusion models. LVO employs sparse autoencoders (SAEs) to disentangle polysemantic layer representations into monosemantic features. Key contributions include latent-space optimization, time-step activity analysis, schedule-matched noise injection, prior initialization through feature steering, and suitable regularization strategies. We demonstrate the method on Stable Diffusion 1.5 fine-tuned on the Style50 dataset, showing that SAE features produce clear visualizations of recognizable concepts - including diagonal compositions, human figures, roses, cables, and waterfall foam - that correlate with dataset examples, while the baseline without disentanglement produces less coherent results. We further show that regularization techniques from pixel-space feature visualization transfer to the latent domain, though they require different configurations for the raw-layer and SAE variants. Compared to dataset examples and steering, LVO provides complementary insights by directly revealing what activates a feature rather than its downstream effects.

This paper presents the Personalized Thinking Model (PTM), a hierarchical and interpretable learner representation designed for AI supported education. PTM organizes evidence from learner journals into a five-layer structure covering behavioral instances, behavioral patterns, cognitive routines, metacognitive tendencies, and self-system values. PTM is grounded in Marzano's New Taxonomy of Educational Objectives and tries to clone learner's thinking model and build cognitive twin. It was constructed using a pipeline that combines large language model inference (Gemini 2.5 Pro), sentence embeddings, dimensionality reduction, and consensus clustering. This paper evaluates PTM fidelity through three methods applied to 40 participants in a seven-week study. First, automatic evaluation using atomic information point matching yielded an overall F1 score of 74.57% before human-in-the-loop (HITL) refinement and 75.48% after refinement. Second, user evaluation using a Likert scale produced mean ratings of 4.26 and 4.30 on a five-point scale for pre and post-HITL conditions respectively. Third, semantic alignment verification showed that topic coherence increased from 0.436 at the behavioral layer to 0.626 at the core value layer, while lexical overlap with journal vocabulary decreased from 0.114 to 0.007 across those same layers. These results suggest that the PTM produces outputs with acceptable fidelity, was generally perceived by users as reflecting their thinking, and showed a pattern consistent with semantic abstraction across layers.

Transformer based pre-trained large language models have become ubiquitous. There is increasing evidence to suggest that even with large scale pre-training, these models do not capture complete compositional context and certainly not, the full human analogous context. Besides, by the very nature of the architecture, these models hallucinate, are difficult to maintain, are not easily interpretable and require enormous compute resources for training and inference. Here, we describe Gyan, an explainable language model based on a novel non-transformer architecture, without any of these limitations. Gyan achieves SOTA performance on 3 widely cited data sets and superior performance on two proprietary data sets. The novel architecture decouples the language model from knowledge acquisition and representation. The model draws on rhetorical structure theory, semantic role theory and knowledge-based computational linguistics. Gyan's meaning representation structure captures the complete compositional context and attempts to mimic humans by expanding the context to a 'world model'. AI model adoption critically depends on trust and transparency especially in mission critical use cases. Collectively, our results demonstrate that it is possible to create models which are trustable and reliable for mission critical tasks. We believe our work has tremendous potential for guiding the development of transparent and trusted architectures for language models.

Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit, theoretically grounded rules for system evolution, their empirical estimation collapses due to severe data sparsity when applied to high-resolution, high-noise environments. We explore this statistical barrier using financial time series as a canonical, real-world testbed. To overcome the degeneracy of empirical counting, we introduce a framework that utilizes neural networks strictly as parameterization engines to generate explicit, time-varying Markov transition matrices. By constraining the neural network to output its predictions as a formal stochastic operator, we maintain complete structural interpretability. We demonstrate that these learned operators successfully capture complex regime shifts: the state-conditioned model achieves mean row heterogeneity $\barρ = 0.0073$ while the state-free ablation collapses to exactly zero, and operator row entropy correlates with realized variance at $r = -0.62$ ($p \approx 10^{-251}$), revealing that high-volatility regimes homogenize transition dynamics rather than diversify them. Furthermore, rather than enforcing the Chapman-Kolmogorov equations as a rigid structural requirement, we repurpose them as a localized diagnostic tool to pinpoint specific temporal windows where first-order memory assumptions break down. Ultimately, this framework demonstrates how neural networks can be constrained to make rigorous, classical operator analysis viable for complex real-world time series.

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

Human Activity Recognition (HAR) using Inertial Measurement Unit (IMU) sensors is a cornerstone of mobile health, smart environments, and human-computer interaction. However, current deep learning-based HAR models often struggle with heavy reliance on labeled data, position-specific ambiguity, and a lack of transparent reasoning. Inspired by the advanced agents framework, which emulates a collaborative agent using Large Language Models (LLMs), we propose SensingAgents, a novel multi-agent system for robust IMU activity recognition. SensingAgents organizes LLM-powered agents into specialized roles: a group of Analyst Agents for position-specific sensor analysis (arm, wrist, belt, pocket), a pair of Advocate Agents that resolves sensor conflicts through dynamic and static dialectical debates, and a Decision Agent that ensures reliability under sensor drift or failure. Evaluation on the Shoaib dataset demonstrates that SensingAgents significantly outperforms state-of-the-art single-agent and multi-agent LLM models, achieving an accuracy of 79.5% in a zero setting--29% higher than existing agent models and 9.4% higher than deep learning baselines--particularly in complex scenarios where multi-sensor data is conflicting or noisy. Our work highlights the potential of multi-agent collaborative reasoning for advancing the robustness and interpretability of ubiquitous sensing systems.

The representativeness of synthetic pre-crash scenarios is crucial for assessing the safety impact of Driving Automation Systems through virtual simulations. However, a gap remains in the robust evaluation of synthetic pre-crash scenarios' practical equivalence to their real-world counterparts; that is, whether they are similar enough for the intended assessment purpose. Conventional significance testing is inadequate, as it focuses on detecting differences rather than establishing practical equivalence. This study addresses the research gap by extending our previous work on a Bayesian Region of Practical Equivalence (ROPE)-based equivalence testing framework by introducing a binning-based approach to define appropriate statistics and equivalence criteria. Two binning-based statistics are proposed to measure practically meaningful distributional differences between datasets in the context of safety impact assessment. The framework's applicability is demonstrated through a case study, which tests the practical equivalence of two synthetic rear-end pre-crash datasets with a previously developed reference dataset in the context of the safety impact assessment of an Automatic Emergency Braking system. The results show that the framework provides informative quantitative assessments of practical equivalence as well as diagnostic insights into the divergence of datasets. Although the demonstration focuses on rear-end pre-crash scenarios, the framework is generic and extensible to broader validation contexts, providing an interpretable and principled basis for practical equivalence assessment across diverse synthetic data applications.

Inferring continuum models directly from video is hampered by two facts: the recorded field is uncalibrated image intensity rather than a physical state, and direct numerical differentiation of noisy frames is unstable. We develop a video-to-PDE pipeline that converts grayscale recordings of an ink plume into a normalised scalar field $u(x,y,t)$, isolates a bulk drift $\mathbf{v}(t)$ from intrinsic spreading via the intensity-weighted centroid, and identifies an effective transport law by weak-form sparse regression. Conditioning, threshold-sweep and random-centre diagnostics show that overcomplete libraries are strongly collinear; the search is therefore restricted to compact gradient-based libraries. Coefficients are refined by an inverse physics-informed network and recalibrated against forward rollouts, with a chronological block bootstrap quantifying uncertainty. The selected reduced model $u_t+\mathbf v(t)\!\cdot\!\nabla u = 9.005\,|\nabla u|^{2}+0.666\,Δu$ outperforms advection--diffusion baselines on held-out frames, retains a positive Laplacian coefficient, and admits a Cole--Hopf reduction to a linear advection--diffusion equation. The framework demonstrates that uncalibrated visual data can yield compact, predictive and structurally interpretable continuum models when discovery, calibration and uncertainty are treated as distinct stages.

Single-cell ATAC-seq (scATAC-seq) enables high-resolution mapping of chromatin accessibility, yet privacy regulations and data size constraints hinder multi-institutional sharing. Federated learning (FL) offers a privacy-preserving alternative, but faces three fundamental barriers in scATAC-seq analysis: ultra-high dimensionality, extreme sparsity, and severe cross-institutional heterogeneity. We propose FL-Sailer, the first FL framework designed for scATAC-seq data. FL-Sailer integrates two key innovations: (i) adaptive leverage score sampling, which selects biologically interpretable features while reducing dimensionality by 80%, and (ii) an invariant VAE architecture, which disentangles biological signals from technical confounders via mutual information minimization. We provide a convergence guarantee, showing that FL-Sailer converges to an approximate solution of the original high-dimensional problem with bounded error. Extensive experiments on synthetic and real epigenomic datasets demonstrate that FL-Sailer not only enables previously infeasible multi-institutional collaborations but also surpasses centralized methods by leveraging adaptive sampling as an implicit regularizer to suppress technical noise. Our work establishes that federated learning, when tailored to domain-specific challenges, can become a superior paradigm for collaborative epigenomic research.

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (\textbf{\textsc{GANO}}), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. \textsc{GANO} encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, \textsc{GANO} supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

Transportation surveys are widely used to understand travel preferences and adoption barriers, yet most survey-based analyses remain descriptive or predictive and rarely provide sparse, policy-feasible intervention strategies. We study sparse counterfactual community intervention from survey responses, where the goal is to shift a target respondent group toward a desired reference group through controllable survey-variable adjustments. We formulate this task as a policy-feasible distributional alignment problem using a fixed-basis nonnegative latent representation that preserves pre/post comparability and provides a stable map from latent factors to original variables. To make latent movement actionable, target-relevant latent factors are identified through Shapley-guided attribution and transferred to controllable variables as intervention priorities. Feasible group-level adjustments are then learned by minimizing an entropy-regularized optimal-transport discrepancy between the post-intervention target distribution and the reference distribution, together with a weighted $\ell_{2,1}$ penalty that promotes shared policy-lever sparsity. Experiments on real-world transportation survey datasets show that the proposed framework produces compact and interpretable policy-feasible interventions with explicit adjustment magnitudes, improves population-level conversion, and preserves intervention sparsity. Code and datasets are publicly available at: https://github.com/pangjunbiao/latent-group-alignment.git

In most real-world image-to-image (I2I) scenarios, existing evaluations primarily focus on instruction following and the perceptual quality or aesthetics of the generated images. However, they largely fail to assess whether the output image preserves the semantic correspondence and spatial structure of the input image. To address this limitation, we propose StableI2I, a unified and dynamic evaluation framework that explicitly measures content fidelity and pre--post consistency across a wide range of I2I tasks without requiring reference images, including image editing and image restoration. In addition, we construct StableI2I-Bench, a benchmark designed to systematically evaluate the accuracy of MLLMs on such fidelity and consistency assessment tasks. Extensive experimental results demonstrate that StableI2I provides accurate, fine-grained, and interpretable evaluations of content fidelity and consistency, with strong correlations to human subjective judgments. Our framework serves as a practical and reliable evaluation tool for diagnosing content consistency and benchmarking model performance in real-world I2I systems.

While LLMs show promise in automating educational content creation, their ability to generate questions that stimulate higher-order thinking remains understudied. This work evaluates six widely-used LLMs through a Bloom's Taxonomy lens, focusing on their capacity to transcend rote memorization and achieve cognitive leaps. Using a hybrid human--AI evaluation protocol, we generate and analyze 20{,}700 questions across computer science, K--12 math, and social-science domains. Key contributions include: (1) a fine-grained prompting strategy that reduces question repetitiveness by 24.45% for Qwen2.5-7B-Instruct, and increases the proportion of higher-order cognitive level outputs by 11.53% for InternLM3-8B-Instruct; (2) quantitative metrics for cognitive shift intensity (CogShift) and category drift, revealing InternLM3's superior performance in multi-level transitions; (3) an interpretability analysis revealing metric-level correlations that enhance the transparency of Chain-of-Thought prompting. Our findings highlight the importance of cognitive-aware prompt design and provide benchmarks for deploying LLMs in personalized learning systems.

Cognitive neuroscience is fragmented into specialized models, each tailored to specific experimental paradigms, hence preventing a unified model of cognition in the human brain. Here, we introduce TRIBE v2, a tri-modal (video, audio and language) foundation model capable of predicting human brain activity in a variety of naturalistic and experimental conditions. Leveraging a unified dataset of over 1,000 hours of fMRI across 720 subjects, we demonstrate that our model accurately predicts high-resolution brain responses for novel stimuli, tasks and subjects, superseding traditional linear encoding models, delivering several-fold improvements in accuracy. Critically, TRIBE v2 enables in silico experimentation: tested on seminal visual and neuro-linguistic paradigms, it recovers a variety of results established by decades of empirical research. Finally, by extracting interpretable latent features, TRIBE v2 reveals the fine-grained topography of multisensory integration. These results establish artificial intelligence as a unifying framework for exploring the functional organization of the human brain.

Causal reasoning in natural language requires identifying relevant variables, understanding their interactions, and reasoning about effects and interventions, often under noisy or ambiguous conditions. While large language models (LLMs) exhibit strong general reasoning abilities, they struggle to disentangle correlation from causation, particularly when observations are partially incorrect or irrelevant information is present. In this work, we introduce NoisyCausal, a new benchmark designed to evaluate causal reasoning under structured noise. Each instance is generated from a ground-truth causal graph and contextualized with a natural language scenario by injecting controllable forms of noise, such as irrelevant distractors, value perturbations, confounding, and partial observability. Moreover, we propose a modular reasoning framework that combines LLMs with explicit causal structure to address these challenges. Our method prompts the LLM to extract variables, construct a causal graph from context, and then reformulates the reasoning task as a structured prompt grounded in this graph. Rather than relying on statistical patterns alone, the LLM is guided by symbolic structure, enabling more interpretable and robust inference. Experimental results show that our method significantly outperforms standard prompting and reasoning baselines on NoisyCausal. Furthermore, it generalizes well to external benchmarks such as Cladder without task-specific tuning. Our findings highlight the importance of combining causal abstractions with language-driven reasoning to achieve faithful and robust causal understanding in LLMs.

Transformer self-attention can be interpreted as a gradient flow on the unit sphere, in which tokens evolve under softmax interaction potentials and tend to form clusters. While prior work has established clustering behavior for single-head attention, the multi-head setting remains less understood due to geometric interference between heads, which invalidates standard monotonicity arguments. In this work, we develop a theoretical framework for multi-head self-attention dynamics and resolve several open questions. We show that, under suitable conditions on the score matrices, a natural multi-head energy functional is non-decreasing along both flat and spherical dynamics. We identify the key obstruction to per-head monotonicity as radial shadow terms, which are projections of each head's output onto token directions, persisting even under orthogonality assumptions. We introduce a sufficient condition ensuring monotonicity and establish robustness to approximate orthogonality. In a simplified scalar-head regime with equiangular token configurations, we derive a closed-form expression for the critical inverse temperature governing clustering behavior, and show that heterogeneous heads exhibit super-additive clustering rates. In this regime, we also prove a separation in clustering time between ReLU and softmax attention in the linearized dynamics. Finally, we establish an entropy production identity and show that attention entropy increases monotonically toward equilibrium as clustering progresses. Our results provide a unified perspective on the dynamics of multi-head attention and clarify the mechanisms underlying clustering and stability in transformer models.

Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning that departs from traditional density-based approaches by explicitly modeling the intrinsic curvature of the data manifold. The method relies on a discrete approximation of the shape operator, estimated from local k-nearest neighbor patches, to compute pointwise mean curvature without requiring explicit manifold parametrization. The key insight of MCBP is to use mean curvature as a principled descriptor of boundary structure: high-curvature regions naturally correspond to transitions between clusters, geometric irregularities, and low-density interfaces. This yields a unified geometric interpretation of boundary, outlier, and transition points. We further introduce an adaptive percentile-based thresholding scheme that enables multiscale boundary extraction without relying on ad hoc density parameters. Beyond detection, we propose a curvature-driven data decomposition that separates samples into smooth (low-curvature) and boundary (high-curvature) subsets, effectively acting as a non-linear geometric filtering mechanism. This representation enhances cluster separability and improves the robustness of downstream unsupervised algorithms. Extensive experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance, particularly in complex and high-dimensional scenarios. These results position MCBP as a concrete contribution to Geometric Machine Learning, highlighting the potential of curvature-aware analysis as a unifying paradigm bridging differential geometry and data-driven modeling.

We introduce State Vector Space Partitioning (SVSP), a novel method to mimic a black box reinforcement learning policy using a set of human-interpretable subpolicies. By partitioning a distillation dataset of state action pairs with linear support vector machine splits, SVSP constructs a compact and structured representation of the original policy. Our method improves mean return by +7.4% over previous critic driven state partitioning attempts such as Voronoi State Partitioning (VSP) and +2.8% over the original TD3 policy, while reducing the number of required subpolicies against VSP by 82.1%. Our results pave the path towards a more flexible form of distillation where both the decision boundary and surrogate models can be chosen within a margin of the original black box behavior.

The Linear Mixing Model (LMM) dominates spectral unmixing for its simplicity, but fails under multiple scattering; existing nonlinear models compensate by applying a fixed regime uniformly across entire scenes. We propose Physics-Guided Regime Unmixing (PGRU), which estimates a pixel-wise scalar $ξ_i \in [0,1]$ from observable physical features to activate nonlinear mixing only where justified. Residuals from the Generalized Bilinear Model (GBM), the Post-Nonlinear Mixing Model (PPNM), and Hapke are combined via learned attention, yielding interpretable regime maps. Experiments on Samson, Jasper Ridge, and Urban show consistent improvements over baselines, with physical coherence $ρ> 0.90$.