Factor

AI is changing what leaders must judge, explain, learn, and coordinate, yet existing measures do not capture these behaviors at the level needed to study leadership in AI-enabled work. We develop the AI Leadership Battery, which organizes 36 behaviorally specific subdimensions into 11 theory-specified content families. Following established scale-development procedures, the research used deductive item generation; content validation of definitional correspondence and definitional distinctiveness; exploratory factor analysis and item reduction; confirmatory factor analysis in independent samples; and tests of internal consistency reliability, convergent validity, discriminant validity, and criterion-related and incremental validity. Across the development and validation studies, the analyses provided evidence for the Battery's content, multidimensional structure, reliability, and distinction from selected orbiting constructs. The Battery also contributed additional information beyond orbiting constructs across organizational growth, decision speed, customer/stakeholder response capability, AI-enabled team performance, AI-enabled work experience, AI security and risk management, and AI adoption and integration. The resulting measure provides researchers with a behavioral framework for examining how leaders in AI-enabled work regulate judgment, learning, adaptation, transparency, and accountability.

Neural 3D scene editing is often evaluated by semantic alignment alone, although a convincing result may alter unrelated content or become inconsistent across views. We introduce EditBench3D, a representation-agnostic benchmark that treats editing as controlled information replacement. It evaluates four complementary properties: instruction fidelity, spatial locality, cross-view consistency, and preservation of non-target content. The protocol combines visibility-aware 3D target supports, paired descriptions, held-out cameras, and five edit families covering appearance, material, geometry, and object-level changes. We evaluate eight representative NeRF, 3D Gaussian Splatting, hybrid, and proxy-based editors on 240 scene-edit pairs. The study shows that semantic fidelity is only weakly associated with the other editing properties, and that no single method is optimal across all dimensions. Explicit Gaussian editors offer a strong overall balance, whereas direct proxy manipulation provides the most conservative edits at the cost of open-ended fidelity. These findings support reporting editability as a multi-objective profile rather than a single semantic score.

Language-guided robots need persistent scene memories to follow instructions, revisit objects, and resolve references to objects encountered over time. While much of language-guided scene-memory retrieval has emphasized spatial or relational references, many everyday object references specify objects by multiple persistent attributes, such as category, material, size, or surface appearance. We formalize this problem as attribute-compositional retrieval, where a fixed object-centric scene memory is queried with natural language to retrieve the object satisfying the requested attributes. To investigate this capability directly, we introduce a controlled evaluation protocol with fixed scene memories and attribute-defined targets, separating retrieval from perception and annotation ambiguities. We then propose FRAME, which turns language into query-relevant attribute weights, uses learned readouts to estimate per-attribute evidence from object embeddings, and ranks objects by aggregating this evidence according to the query. Across held-out scenes and object assets, FRAME outperforms representative scene-memory retrieval baselines while reducing post-decomposition object scoring to lightweight matrix-vector computation. These results position attribute-compositional retrieval as a complementary scene-memory capability for language-guided robots, showing that persistent object attributes can be exposed as composable evidence for accurate and efficient multi-attribute retrieval.

Automated alpha factor discovery searches symbolic trading signals from price-volume panels and order-book data under a fixed evaluation budget. Existing single- and multi-agent program-search systems can overfit predictive proxies that fail after execution costs and repeatedly explore redundant factor families, limiting execution robustness and behavioral diversity. We introduce GoAnt, a quality-diversity multi-agent search framework that combines non-communicating Explorer, Exploiter and Connector workers with a shared adaptive Mental Map and a compact Queen dispatcher. The Mental Map organizes candidates by leakage-free execution profiles and retains one elite per niche, while the Queen reallocates the evaluation budget from explicit search-state summaries. We also define a map-independent effective-yield protocol that counts high-quality, mutually nonredundant factors directly from each method's evaluation records, giving archive-based and map-free systems the same ruler. On real A-share microstructure data spanning 2023--2026, GoAnt reaches quality-weighted yields of 41.8 and 47.6 in price-volume and order-book settings, improving the strongest baseline by 57% and 97% under matched budgets. Its locked populations retain 0.64 and 0.67 of in-sample quality out of sample, compared with 0.61 and 0.63 for a static map.

Large language models (LLMs) demonstrate strong performance on standard content moderation benchmarks. However, these benchmarks often aggregate multiple moderation criteria into a single label, making it unclear whether models can disentangle them and reliably apply each criterion when making decisions. To study whether LLMs exhibit criterion-conditioned behaviour, we introduce Diagnostic Evaluation of COntent (DECO), a criterion-independent factorisation of content that enables controlled, criterion-level evaluation. We also introduce pairwise evaluation to compare model outputs across different criteria for the same input. Across four moderation datasets and four LLMs, we find that strong benchmark performance can hide substantial failures at the criterion level. Models struggle most when correct decisions depend not on overall harmfulness, but on the specific aspect of the content that the criterion requires them to assess. Our results highlight a key limitation of current content moderation benchmarks: strong performance on aggregated labels does not provide sufficient evidence that LLMs can reliably evaluate content with respect to individual moderation criteria. These findings call for the development of evaluation methods that explicitly measure criterion-conditioned behaviour.

Recent advances in LLM agents enable a new paradigm for asset pricing, which we call Agentic Empirical Asset Pricing (AEAP): systems that autonomously conduct the scientific discovery process itself. We define AEAP and identify its core building blocks. Existing evaluation practices backtest only the outputs (factors or trades), not the autonomous discovery system that produced them. We focus on factor discovery, contributing a reference architecture, a rigorous evaluation standard for discovered factors, and a method for out-of-sample backtesting the discovery system. As a concrete instance of that architecture, we evaluate SEADS against five re-implemented baselines on two US equity panels using this standard: no single metric ranks the systems consistently, motivating evaluation on multiple axes at once. A separate rolling re-execution then asks the complementary question of whether the discovery process itself, not one static output, is reliable. We also report negative findings and limitations that surface further evaluation pitfalls for future AEAP systems.

Traditional finance relies on experts to hand-craft factors through a principled process grounded in economic rationale. Recent LLM-based multi-agent systems have automated this process, scaling factor mining far beyond manual effort. However, these automated approaches optimize directly for returns and rarely check whether a generated factor still expresses the economic hypothesis that motivated it. We identify this inconsistency between mathematical form and economic meaning as a structural failure mode of return-oriented automation. The resulting factors blur the line between real signals and spurious correlations and break down across regime shifts. We propose FaVOR (Factor Validation through Observable Reasoning), an agentic framework that restructures factor mining around hypothesis-level evidence rather than return outcomes. In place of the standard hypothesis-to-formula leap, FaVOR enforces a three-stage consistency loop tying mathematical form to economic rationale throughout. (1) Decomposition splits a broad economic hypothesis into independent observable conditions. (2) Validation checks whether each factor reflects its intended condition. (3) Integration merges them into a composite whose structure remains interpretable. On the CSI 500 and S&P 500 in 2025, FaVOR outperforms existing baselines while remaining effective across regimes. FaVOR shows that hypothesis-grounded factor discovery produces signals that are interpretable by construction, regime-robust, and economically faithful. The code is available at https://github.com/damilab/FaVOR.

We study recursive self-improvement at the level of quantitative-investment research: whether an autonomous system can use evidence from earlier experiments to improve the hypotheses and candidates proposed in later iterations. We present AQuA, which comprises two separate language-model-driven research systems: one for symbolic factor discovery and one for trainable model development. The two systems do not share agents, memories, candidate spaces, or research state. Instead, each independently closes its own research loop by retaining validated evidence and using it to guide subsequent proposals. In this bounded sense, both systems implement recursive self-improvement at the level of the research process. Each system also uses its own sealed sandbox, which fixes the data splits, feature and label definitions, and evaluator while allowing the model to act only through constrained factor expressions or configuration diffs. The factor system, a manager-mediated multi-agent pipeline, discovers and combines factors into a signal that reaches a combined information coefficient of about $0.190$ on a crypto universe. The model system, a config-driven loop over a hybrid time-series architecture, reaches a per-stock information coefficient of $+0.0843$ on US equities and converts it into a threshold long/short strategy with a held-out Sharpe of up to $+2.50$ at a two-leg cost. The strategy is positive in every year from 2021 to 2025.

Whether an additional general dimension is necessary beyond correlated first-order factors is a property of the population covariance matrix, not of any estimator or design. This research establishes when that property can be decided. Where the general and group loadings are proportional within every cluster the bifactor structure is covariance-equivalent to correlated factors, so no sample size separates them (Proposition 1); where that proportionality fails in every cluster, three items per cluster and some mild regularities leave no $K$-factor model with diagonal uniquenesses able to reproduce the covariance matrix (Theorem 1); and between them lies a mixed boundary, located numerically here and turning on cluster resistance. Distinguishability is therefore graded, measured by the population distance to the $K$-factor class. Because that question is conditional on a first-order structure which is itself uncertain, a two-step procedure is developed within partially exploratory factor analysis, delivering a structure only when it reproduces across adjacent counts and treating non-delivery as legitimate. Simulation shows that a unanimous count can accompany a structure that fails to reproduce, and that absorbed local dependence can imitate a general factor, the error growing with sample size while stability indicators stay clean. Four empirical datasets illustrate the possible outcomes.

Low-rank adaptation (LoRA) represents large language model (LLM) updates with two compact matrix factors, i.e., $A$ and $B$, providing an efficient way to fine-tune large models in federated learning paradigm. Inspired by the asymmetric roles of the LoRA factors, we study whether $A$ should be shared across clients while $B$ remains client-specific (Share-A/Local-B), or whether $B$ should instead be shared while $A$ remains client-specific (Share-B/Local-A). With a least-squares surrogate, we reveal that Share-A/Local-B requires the client-specific LoRA update matrices to use a common rank-$r$ input-side space, whereas Share-B/Local-A requires a common rank-$r$ output-side space. The two strategies therefore incur different projection residuals, indicating that the preferred strategy is the one with the smaller aggregate residual across clients. With this insight, we propose Federated Adaptive Factor Sharing Low-Rank Adaptation (FedAS-LoRA), which selects the sharing side before training to enhance fine-tuning performance. To enable adaptive factor selection before training, we design a Rank-Aware Shared-Subspace Sufficiency (RSS) metric, which effectively assesses whether a shared rank-$r$ input subspace is sufficient for the local data distributions using representations extracted from a frozen LLM backbone. Experiments across different tasks, data distributions, LoRA ranks, and participation settings confirm the effectiveness of RSS and the superior performance of FedAS-LoRA.

Large multi-call LLM systems pose a scientific problem that query-level routing does not capture: the value of a model depends on where it enters a dependent computation and on the deployment that surrounds that call. Existing routers typically decide \emph{where} to spend a stronger model while treating the benefit of the substitution itself as known. We separate these two decisions through a predicate-action factorization and evaluate it in controlled solve-merge-verify workflows spanning 8-64 solve calls and four three-tier model ladders. The resulting evidence reveals a consistent principle beneath apparently conflicting outcomes. On numeric frequency counting, all-strong reduces RMSE from 4.818 to 1.538 in the Mixed Qwen/GPT ladder, whereas the average Qwen-only ordering reverses. Input-matched interventions further show that the same medium-to-strong action has sharply different value across roles and scales. A semantic task-and-contract shift reverses the Mixed ordering again, while allocation ablations distinguish useful sparse placement from under-coverage and indiscriminate escalation. Together, these results establish model substitution as a deployment-conditioned action rather than a property implied by a tier label, and they provide a practical sequence for large-scale workflow routing: calibrate the action, resolve its role-conditioned effect, and then optimize its placement.

We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal. For arbitrary positive row marginals of equal total mass, the joint KL projection reduces exactly to a strictly convex gauge-fixed dual with only $r-1$ effective variables; its Hessian is a sum of categorical covariance terms and admits $O((n+m)r)$ matrix-free Hessian--vector products. The projection theorem is objective-independent. We then specialize this geometry to doubly stochastic (DS) graph learning through $W=U\operatorname{Diag}(g)^{-1}V^\top$, where row-simplex factors with a common column mass induce an exactly DS graph without materializing an $n\times n$ optimization variable. Combined with observed-edge sparse fitting, a stochastic anchor-reduced manifold regularizer, and Bregman backtracking, the resulting mirror-descent method preserves exact feasibility at every accepted step. Under a nonvanishing latent-mass condition, it satisfies sufficient decrease and an $O(1/N)$ mirror-stationarity bound, while strictly positive accumulation points are KKT stationary. Matched clustering experiments show competitive accuracy, feasibility residuals near numerical precision, and favorable anytime behavior without a dense learned graph.

This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces. MGFA uses a geodesic factor model within each mixture component, providing greater expressiveness than mixtures of Riemannian radial distributions and enabling clustering of manifold-valued data with anisotropic subpopulations. We establish root-$n$ consistency for the MGFA maximum likelihood estimator (MLE), thereby filling a theoretical gap for mixtures of Riemannian radial distributions as a special case. We also propose an iterative estimation algorithm and implement it on spheres, shape spaces, and hyperbolic spaces. Numerical experiments show that MGFA substantially outperforms competing methods in well-specified regimes while remaining robust under model misspecification. Finally, case studies on corpus callosum and left hippocampus shape datasets demonstrate MGFA's effectiveness for both 2D contour and 3D shape analysis.

Compositional analysis of frozen vision encoders should determine both what changed and where it changed. Standard factor probes score these axes separately, however, and can reward multiple operations that reuse the same predicted slot. We call this failure operation laundering. We introduce an injectively aligned leave-one-cell-out protocol over support x operation grids and SO-OPF, a readout that factors cell energy into support salience and a competitive operation posterior. This formulation separates two questions that aggregate scores conflate: whether the carrier composes held-out bindings when the grid is known, and whether that grid can be recovered from flat cell labels. With frozen DINOv3 features, known factorial assignment reaches 0.874 injective accuracy on Shapes3D-Extended and 0.799 on globally image-disjoint COCO; learning the assignment from flat labels reaches 0.769 and 0.762, respectively. Under matched-axis-aware supervision on Shapes3D, the factored carrier improves learned-assignment accuracy from 0.653 to 0.841 over a dense carrier and eliminates its laundering gap. SigLIP2 replicates the COCO separation. A rebuilt MuJoCo substrate exposes a boundary: learned-assignment accuracy is 0.569 with DINOv3 and 0.484 with SigLIP2, with substantial slot collapse. Thus factored readout and injective evaluation recover held-out bindings on two substrates while exposing, rather than hiding, a renderer-specific failure boundary; they do not establish universal recovery from flat labels.

Tabular Foundation Models (TFMs) are currently the best approach to tabular prediction problems. They are constructed as transformers that approximate the Bayesian posterior predictive distribution based on a pre-training prior. These univariate predictors can be converted into multivariate ones autoregressively by sampling one target and adding it to the features. However, the faithfulness of the resulting joint has not been investigated. Furthermore, TFMs cannot be evaluated against the posterior itself, at least not on real-world datasets, because the ground-truth distribution is unknown. We therefore propose asking a different question: could a model's predictions result from any joint distribution? To answer this question, we pose two requirements that any such model must satisfy. The first is marginalization consistency, which demands that marginalized conditionals are equal to directly predicted marginals. The second is factorization consistency, which demands that different factorization orders result in equal joint distributions. Every TFM that we evaluate violates both of these requirements for both classification and regression across all datasets.

Factorized generative models commonly regularize a latent style variable z_s by matching its marginal distribution to a fixed Gaussian prior and interpret this as evidence that the style representation is independent of class information. We show that this interpretation is incorrect. Matching only the marginal distribution places no constraint on the class-conditional distributions, allowing the latent style to remain highly predictive of the label despite appearing perfectly Gaussian in aggregate. We derive an exact decomposition showing that this mismatch is one of four conditions required for factorized sampling, and demonstrate that eliminating it is necessary but not sufficient to obtain the intended factorization. Empirically, our case-study model and four representative latent baselines achieve near-zero global MMD while still allowing a linear probe to recover class labels with 74%--100% accuracy (10% chance level). Our model reaches 99.15% clustering accuracy, whereas externally evaluated class-conditional generation succeeds only 16% of the time. This leakage remains under six independent perturbations involving model capacity, curriculum, prior geometry, and supervision across two datasets. Four mitigation strategies reduce probe accuracy to 21%--46%, although they leave within-class dependence largely unchanged. A post-hoc conditional prior improves externally evaluated class generation to 0.97 on MNIST without retraining but reaches only 0.41 on CIFAR-10, while an empirical style bank achieves 0.88 on CIFAR-10. These results demonstrate that no divergence computed solely on the marginal distribution of the style latent can certify independence from class labels, and that reporting marginal statistics alone does not verify the property commonly claimed in factorized generative models.

GUI agents must remember both useful experience from earlier tasks and unfinished progress in the current interaction. Latent memory offers a compact solution by compressing multimodal trajectories into a few continuous tokens. Existing methods, however, usually map each trajectory to one fixed memory block and train it mainly through next-action supervision. This creates three practical problems: important details may be lost during compression, the same memory block must serve different decision stages, and irrelevant retrieved trajectories may still mislead the agent. We introduce FocusMem, which separates these responsibilities within a compact latent-memory interface. A role-aware content basis encourages episodic memory to retain reusable experience and working memory to retain task progress. A state-conditioned readout generates a decision-specific view of the same stored evidence, while a lightweight trust gate can suppress memory blocks that appear irrelevant to the current step. All components are trained while the GUI policy remains frozen. Across five GUI-agent benchmarks, FocusMem consistently outperforms a fully matched action-only fixed-memory baseline and prior latent memory adaptations. Further analysis shows that semantic and functional supervision preserve complementary information, state-conditioned readout is more robust as surrounding trajectory context grows, and the trust gate reduces the harm caused by injected irrelevant episodic evidence. These results show that effective latent memory depends not only on compressing past interaction, but also on what is retained, what is exposed, and what is allowed.

Sonic seasoning research has shown that listeners attribute systematic gustatory and emotional meaning to sound, and text-to-music generative artificial intelligence has recently been used to render gustatory prompts as musical stimuli. Whether the taste-sound correspondences acquired by such models hold beyond the cultural context in which they were validated remains untested. We extended a single-country study to a three-country online experiment conducted in Argentina, Italy, and Japan (N = 361). Participants first indicated their preference between base and fine-tuned MusicGen excerpts generated from four taste prompts (sweet, sour, bitter, salty), and then rated fine-tuned excerpts on twelve taste, emotion, and thermal descriptors. Preference for the fine-tuned model was confirmed in Argentina and Italy but not in Japan, and the salty prompt yielded the weakest correspondence in all three cohorts. Ratings differed substantially between countries, yet the main effect of country was no longer detectable once ratings had been standardized within participant, whereas the interactions characterizing the mapping of prompts onto descriptors remained essentially unchanged. Much of the apparent cross-cultural divergence is therefore attributable to differences in scale use; a structural component nevertheless persists. In addition an exploratory factor analysis indicated that the twelve descriptors were organized along different latent dimensions in each cohort. These results indicate that cross-cultural variation in AI-mediated sonic seasoning operates at two levels: the overall level at which taste is attributed to a given stimulus, and the relational structure of those attributions. Evaluations of generative music systems across populations should accordingly distinguish response-style bias from genuine perceptual reorganization.

{AdaBoost.MH} reduces multi-class classification to a collection of binary subproblems and enjoys the classical boosting-type convergence guarantee under a weak learning condition. A more structured variant, Factorized {AdaBoost.MH}, uses base classifiers of the form $\mathbf{h}(x)=α\mathbf{v} \bm{\varphi}(x)$, where a single binary classifier $\bm{\varphi}$ is shared across all classes and the label dependence is carried by a vote vector $\mathbf{v} \in\{\pm1\}^K$. This factorization is algorithmically attractive and achieves better performance in practice, but its convergence depends on whether one can always choose a vote vector with sufficiently large induced binary weight mass. Previous work resolved this question with a lower bound $\max\{1/n,1/\sqrt{2K}\}$, which still leaves a dimension-dependent slowdown relative to the original {AdaBoost.MH} analysis. In this paper, we sharpen this combinatorial step. For the minimax quantity $\mathfrak{W}_{n,K}$ governing the factorized edge, we prove $\mathfrak{W}_{n,K} = C_{\min\{n+1,K\}}$, where $C_q=1$ for $q=1$, $C_q=q/(3q-4)$ for even $q\ge2$, and $C_q=(q+1)/(3q-1)$ for odd $q\ge2$. Since $C_q\downarrow 1/3$, our bounds show that $\mathfrak{W}_{n,K}=Θ(1)$ uniformly over $n$ and $K$. Consequently, Factorized {AdaBoost.MH} achieves the same boosting-type convergence rate as {AdaBoost.MH} up to a universal constant factor, removing the previously suggested additional dependence on $n$ or $K$ in the number of boosting rounds.

Despite the many variants of DeepONet that have been proposed, query-based operator networks still struggle with shock-dominated and low-viscosity PDEs, whose sharp moving discontinuities and slowly decaying solution spectra challenge finite-dimensional separable representations. In this work, we propose \emph{Feature Interaction Modeling Operator} (FM-Operator), a point-wise query neural operator that explicitly models feature construction and interactions between sensor observations and query coordinates. Our design is motivated by a reinterpretation of the canonical DeepONet aggregation through the lens of multiplicative interactions. Specifically, the branch--trunk inner product admits the equivalent form $\boldsymbol{b}(u)^\top \boldsymbolτ(y)=\boldsymbol{1}^\top \operatorname{diag}(\boldsymbol{b}(u))\,\boldsymbolτ(y)$, revealing that the two representations interact only along corresponding latent dimensions and therefore constitute a diagonally constrained multiplicative interaction. This observation suggests that, beyond improving the individual branch and trunk networks, the structure through which function and query representations interact is itself an important inductive bias in point-wise operator learning. FM-Operator accordingly redesigns both feature construction and feature interaction, enabling structured information exchange beyond the conventional branch--trunk coupling while retaining point-wise query evaluation. Experiments across multiple PDE benchmarks demonstrate that FM-Operator consistently outperforms vanilla DeepONet and achieves clear improvements over the strong Shift-DeepONet baseline. These results suggest that explicitly designing representation construction and interaction provides a promising direction for improving the effectiveness of DeepONet-style query-based neural operators.

There is a growing need for reliable and culturally validated instruments to assess psychological dependency on large language models (LLMs), particularly as LLMs are increasingly used for task execution, decision-making, and communication in organizational and work-related settings. This need is especially relevant for Spanish-speaking populations, where LLM adoption is rapidly expanding, yet validated psychometric tools remain scarce. The present study reports the first validation of the Spanish version of the Large Language Model Dependency Scale (LLM-D12-SP), extending prior validations conducted in English- and Arabic-speaking samples. The LLM-D12 is a two-dimensional instrument assessing Instrumental Dependency (reliance on LLMs for performing tasks and supporting decisions) and Relationship Dependency (psychological reliance on LLMs for companionship and social interaction). A total of 386 Spanish-speaking participants (M = 28.0 years, SD = 6.1; 55% male) completed the LLM-D12-SP. Confirmatory factor analysis supported the original two-factor structure. The scale demonstrated good internal consistency (Cronbach's alpha = 0.89 total; 0.86 Instrumental; 0.85 Relationship). Discriminant validity analyses indicated that the two subscales represent related but distinct constructs. External validation showed that both dependency dimensions were positively associated with internet addiction and perceived trustworthiness of LLMs, while showing weak or no association with need for cognition. Together with prior English and Arabic validations, these findings establish cross-linguistic support for the scale's structure and provide a psychometrically sound tool for investigating psychological aspects of LLM use in organizational contexts.

Genomic language models achieve strong performance across regulatory-genomics tasks, yet what these models internally represent remains opaque, and the field lacks a principled procedure for verifying that an apparent concept'' inside a model is real rather than an artifact of sequence composition. We introduce a framework that combines sparse dictionary learning with causal intervention to extract, validate, and causally test interpretable features in genomic foundation models. Training top-$k$ sparse autoencoders on the hidden activations of two architecturally distinct models, Nucleotide Transformer ($6$-mer tokenization) and DNABERT-2 (byte-pair encoding), we recover thousands of monosemantic features that map to transcription-factor (TF) sequence motifs. We show that the naive validation of such features against position weight matrices is severely confounded by GC composition and repetitive elements, producing hundreds of spurious TF features'', and we develop a composition-matched, binding-resolved protocol that removes these confounds. Critically, we move beyond correlation: by ablating individual dictionary directions during the model's forward pass and measuring the induced shift in the model's own predictive distribution, we establish that specific features are \emph{causally} used to represent cell-type-specific TF binding, not merely motif presence. Across three transcription factors (CTCF, GATA1, REST) and both architectures, causally validated binding features emerge reproducibly ($7$--$14$ of $15$ tested features per condition), while two classes of negative control, scrambled binding labels and randomly selected features, yield no detectable signal. The framework is purely computational, uses only public data, and provides a reusable standard for interpretability claims in genomic deep learning.

This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Such a model is motivated by transfer learning and latent factor regression, where one seeks stable low-dimensional representations for both interpretation and robust out-of-sample prediction of the response $Y$. Leveraging the invariance principle, we show that the invariant and heterogeneous factors are disentangled under a minimal structural condition. Based on this, we propose ATLAS, an Auxiliary-label and invariance-guided Transfer via Latent Alignment across heterogeneous environmentS. ATLAS is a unified procedure that leverages the invariance principle to separate aligned invariant and unaligned heterogeneous factors, and further exploits supervision from auxiliary labels to extract prediction-invariant and transferable factors from those unaligned heterogeneous factors. ATLAS yields near-oracle performance for downstream latent factor regression, enables transferable prediction in new environments through the full latent signal when auxiliary labels are available, and reduces to robust invariant-factor-only prediction otherwise. We establish sharp non-asymptotic error bounds for recovering invariant and heterogeneous factors, identifying all the response-invariant factors, and estimating the invariant signal in $Y$.

This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting. Machine learning problems are specified as sketches: graphs with commutativity conditions $\mathcal D$, limit cones $\mathcal L$, and colimit cocones $\mathcal K$, generalizing the usual scalarization of loss functions or vector space assumptions. Non-compositionality is defined purely as failure of a universal factorization problem, not as arithmetic error between the desired and actual predictions. Given a learning sketch $\mathbb S=(S,\mathcal D,\mathcal L,\mathcal K)$, whose underlying graph is $S$, and a model $D:J \rightarrow C$, the base defect is the obstruction to factorization $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(D))$. The tangent lift applies the tangent functor $T$ to obtain $TD:J \rightarrow C$, and LINCS is defined as the obstruction $\mbox{Obs}(\mbox{Fact}_{\mathbb S}(TD))$ -- asking whether infinitesimal perturbations preserve the compositionality constraints.The paper also introduces Tangent Learning Sketches, which are sketches equipped with Cockett-Cruttwell tangent structure. The paper defines the INC endofunctor, which iterates the tangent lift, producing a tower $D,TD,T^2D, \cdots$ of factorization problems. ML is thereby formulated as the search for a coalgebraic fixed point where successive tangent unfoldings stabilize ($νT_{\mbox{INC}}$). Using the Aczel--Mendler theorem, we prove existence of a final INC coalgebra whenever $T_{\mbox{INC}}$ admits a set-based class realization that creates its final carrier. A detailed experimental evaluation of LINCS is underway in a number of concrete ML settings, including deep learning, large language models, and reinforcement learning, and is described in companion papers.

As generative AI (GenAI) becomes increasingly embedded in undergraduate academic writing, how students rely on these tools, rather than simply whether they use them, has become a central question for learning, academic integrity, and educational equity. Existing measures of reliance were developed inductively, focused on discrete problem-solving tasks, and validated mainly with homogeneous samples. This study developed and validated the GenAI Reliance Types Scale (GenAI-RTS), a 20-item instrument measuring four theoretically derived types of GenAI reliance: Strategic, Instrumental, Dependent, and Dialogic. Validation followed the multisource framework of the Standards for Educational and Psychological Testing, drawing on a survey of 382 undergraduates at a U.S. Minority-Serving Institution and interviews with 14 purposively sampled students. Confirmatory factor analyses of six competing models supported a five-factor structure in which Strategic Reliance comprises two facets, Deliberate Use and Critical Evaluation, alongside Instrumental, Dependent, and Dialogic factors (CFI = .92, RMSEA = .08; DWLS CFI = .98, RMSEA = .07). Subscale reliability was acceptable to good (omega = .75-.88), and scalar measurement invariance held across gender, first-generation status, and STEM/non-STEM majors, to our knowledge the first such evidence for a GenAI reliance instrument. Rasch analysis indicated that a five-point response format would improve category functioning. Strategic reliance was positively associated with AI literacy, and the reliance types differentiated students across multiple writing process and outcome variables. The GenAI-RTS offers researchers and educators a theoretically grounded, psychometrically validated instrument for identifying undergraduate reliance profiles and supporting research, assessment, and AI literacy intervention.

Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.

This paper introduces numerical optimizations for maximizing throughput on GPU when solving large batches (10,000 to over 100,000) of sequential quadratic programming (SQP) iterations, where all problems have the same structure. The optimizations are implemented in a toolbox WarpMPC for model-predictive control (MPC) in JAX and Warp. Based on the insight that all MPC problem instances in a batch share the same sparsity in time, cost, and constraints, we propose unrolling sparse linear factorizations and solves, which dominate alternating direction method of multipliers (ADMM) solver runtime. We avoid memory access bottlenecks and wasting computations via optimized memory layout, padding-reducing segmentation of the unrolled factorization, and dependency level scheduled backsolves, additionally accelerating sensitivity computation. We achieve throughputs of 8,000 to 250,000 SQP iterations per second on nonlinear cartpole, quadrotor, and humanoid robot benchmarks, outperforming baselines by 3$\times$ to 25$\times$. We illustrate practical usefulness by synthesizing a dataset and training a neural network approximation of an MPC in under 4 minutes that stabilizes a nano quadrotor in hardware experiments.

Cooperative multi-agent reinforcement learning is well suited to problems with large parameter spaces and exploitable local structure, such as the tuning of electrostatically-defined quantum-dot arrays. However, if parameter cross-talk is strong, a non-stationary environment from the perspective of any individual agent can destabilize learning - the same effect that plagues manual tuning of such systems. We propose using a factored representation of the action space, learned online, to decouple agents and minimize their interference. Our framework, QADAPT, uses this factorization to efficiently learn shared policies based on local measurements and rewards. With this modular strategy, we achieve zero-shot generalization to unseen quantum device sizes and maintain an approximately constant number of convergence steps to reach target regimes. This work provides a scalable route toward the rapid calibration of large-scale quantum processors.

In partially exploratory factor analysis (PEFA), the loading structure and factor numbers are weakly specified. The regularized variational approximation for partially confirmatory factor analysis (PCFA VA) recovers this structure via Bayesian variable selection, using spike and slab priors to assign inclusion probabilities to unspecified loadings. This research introduces a post selection assessment framework for this approach. We convert converged solutions into covariance models using either hard selection (thresholding probabilities into a sparse pattern) or soft selection (retaining them as weights for effective parameter counts). We derive the resulting degrees of freedom, absolute fit diagnostics (RMSEA, SRMR, CFI, TLI), and relative criteria (AIC, BIC, ELBO). To determine factor numbers, we propose a scale free gain rule with a sustained drop guard. Simulations show absolute indices successfully track loading recovery and flag under factoring. While raw criteria over factor, our gain rule accurately recovers true dimensionality, with the ELBO variant proving most robust. Finally, a 100 item PID 5 example demonstrates that our model fits better than a confirmatory 25 facet model and concordantly recovers major structures across disjoint specifications.

Process industries rely on time-series forecasting and soft sensing to estimate quality variables that are hard to measure online. Labeled data are scarce, operating regimes change frequently, and retraining models or rebuilding alignment pipelines for each scenario is costly. Such settings often provide variable tables and process documents that record variable names, units, physical meanings, and process roles. However, standard time-series backbones usually treat inputs as anonymous numerical columns. Existing text-enhanced methods also rarely make the semantic-logical relations between input variables and the prediction target available to the model within each numerical window. To address this problem, this article proposes Task-Semantic Field Factorization (TSF), a large language model (LLM)-guided framework. TSF builds a task-semantic field from task protocols and variable documents before training and uses the LLM only for offline semantic construction. Online training and inference remain with conventional time-series backbones. During training and inference, the current numerical window activates variable semantics, so semantic information participates in each prediction and supports adaptation to different prediction targets and operating shifts. On multiple complex industrial forecasting and soft-sensing tasks, TSF reduces MAE by 6.4% on average in improved settings, with the largest reduction reaching 25.5%. It adds only about 1.8--3.0k parameters, with less than 0.008 ms/step of additional online inference overhead. These results show that TSF turns existing process documents into measurable forecasting gains across backbones and semantic generators while remaining lightweight for deployment.

Episode mining aims to extract subsequences of events that possess certain distinctive properties and constitute facts valuable to the user. Maximal frequent episode mining concentrates on discovery of frequently-appearing subsequences, which are not included into any other larger frequent subsequence. The state-of-the-art for this problem is the MaxFEM algorithm which enumerates possible subsequences, while applying various pruning techniques to accelerate the search. However, this is a computationally-intensive problem: reducing the minimum number of required subsequence occurrences or increasing the length of the subsequence both substantially raise running time, which limits practical use of MaxFEM. In this paper we describe our efforts in designing a high-performing algorithm for this problem. For this we: 1) develop an efficient C++ implementation of MaxFEM, and 2) devise an efficient technique to parallelizing it. As the result, we propose an improved parallel MaxFEM variant, which we call ParMaxFEM. Additionally, we integrate the improved algorithm into Desbordante - a high-performance, open-source data profiler with deep Python integration that treats patterns as first-class entities and allows users to develop their custom programs that can include discovery and validation of patterns. To evaluate our approach we compare both C++ implementations with the original SPMF implementation. Experiments demonstrated that our reimplemented version provides up to $8\times$ speedup over the SPMF baseline, while our parallelization technique provides up to $35\times$ improvement overall (on 8 cores).

Device-free 3D human pose estimation using commodity WiFi Channel State Information (CSI) enables privacy-preserving and illumination-robust human sensing, but its deployment is limited by poor cross-environment generalization. Unlike images, CSI measurements do not have a spatially localized correspondence to body parts and are heavily affected by multipath propagation, causing models that regress absolute poses to entangle body structure with environment-specific location cues. Within a single environment this coupling is benign: an end-to-end absolute-pose variant, RePos-D, already achieves state-of-the-art accuracy on Person-in-WiFi-3D (86.9 mm MPJPE, a 3.4% gain over the previous best WiFi method, DT-Pose). Across environments, however, the same model overfits position and suffers significant performance degradation. We therefore propose RePos, a factorized framework that separates root-relative pose estimation from root localization. By preventing absolute-pose supervision from affecting the structure branch, RePos learns environment-invariant pose representations. Specifically, it groups CSI features into body-part-aware latent tokens that skeleton-guided modeling refines into the pose, while a separate amplitude-based network estimates the root position through a differentiable spatial-decomposition module. Under the strict MM-Fi cross-environment protocol, RePos achieves MPJPEs of 254.4-296.1 mm, a 10-21% reduction over existing WiFi-based methods. The improvement remains consistent across activity protocols, leave-one-environment-out splits, and leakage-free few-shot transfer. Analysis of the learned features shows that relative-pose representations remain largely position-agnostic, while root localization retains environment dependence, indicating distinct generalization behavior for structure and localization.

Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization. We propose a unified framework, termed direction-magnitude decomposition (DMD), that decomposes the optimization variable to improve optimization efficiency even when the target rank is unknown. We develop two DMD-based approaches and establish their theoretical advantages on the canonical problem of matrix factorization. The first, overparameterized DMD, uses a rank $r$ larger than necessary and enjoys faster convergence as $r$ increases. The second, recursive DMD, is motivated by the incremental eigenpair learning, or saddle-to-saddle, behavior of overparameterized DMD. It achieves lower memory and computational costs, complementing overparameterized DMD. Both approaches are exponentially faster than gradient descent applied to the BM formulation. Numerical experiments on matrix factorization, sensing, and completion corroborate our theoretical findings and demonstrate the practical effectiveness of DMD.

Modern LLM deployments often combine quantization with higher sampling temperatures to reduce cost, latency, or repetition, yet safety evaluations usually treat these as fixed implementation details. We test whether models that are safe at FP16 with greedy decoding remain safe after quantization and stochastic sampling, or whether the two factors amplify each other. We evaluate 8 instruction-tuned models from five families across 3 precisions and 6 temperatures, covering 144 configurations on 7 harmfulness benchmarks and generating about 2.0 million responses, which are scored by a six-judge safety ensemble. Contrary to concerns that low-bit deployment erodes alignment, we find that standard quantization is approximately safety-neutral: for 7 of 8 models, AWQ INT4 keeps attack success within about 1.6 percentage points of FP16 or lowers it, with clear degradation only for SmolLM3-3B (34.5% to 44.1%). However, the larger risk comes from sampling: higher temperatures sharply increase decision instability, with DFR reaching 41.9% at T = 1.0, even when average ASR changes only modestly. The two factors do not compound: our Compound Degradation Index remains sub-additive (-0.071 to +0.018), indicating that quantization partially offsets rather than amplifies temperature-induced degradation. Finally, a per-benchmark breakdown shows that single-benchmark evaluation badly understates risk: several models scoring 0% on AdvBench exceed 80% on ManyHarm. Standard INT4/INT8 quantization can therefore be reasonable for well-aligned models, but safety claims should report multi-sample stability across multiple benchmarks rather than rely on a single benchmark at greedy decoding.

The common factor analytic model is related to Helmholtz and Boltzmann machines, can be conceived as a linear autoencoder, or can be thought of as a single-hidden-layer generative neural network. We thus consider it a basal generative representation learner that can be used as a minimal model for studying the foundational characteristics of (deep) generative model architectures. We focus on the fundamental problem of indeterminacy in latent factor projections. This indeterminacy implies that, even when the intrinsic dimension of the latent vector is known, regularity conditions are met, and rotational indeterminacy is resolved, an inherent indefiniteness in the retrieval of causative latent sources remains: they will be uncertain, distributionally deviant, and non-unique. This can have major implications for data representation but remains an elusive issue, even to practitioners and theorists well-versed in the factor model. Moreover, this classic psychometric problem is intricately related to the modern issue of latent variable collapse in the variational autoencoder framework for deep generative modeling. Here, we assess this indeterminacy from various perspectives and show how these are mathematically and conceptually related and we discuss subsequent implications for the Psychometrics, Statistics, and Artificial Intelligence communities. We show that one has latent factor determinacy across all its facets when the feature-dimension grows to infinity. This feeds into an essentially distribution-free estimation approach in the sample case when the number of features grows very large. We conclude, as these are emergent properties at scale, that the factor model is suited for representation learning of very-high-dimensional data.

Training-free compression methods for large language models (LLMs) often use calibration data to guide compression decisions. ROCKET, a recent method combining sparse-dictionary factorization with multi-choice knapsack problem (MCKP) allocation, derives its per-layer factorization from an output reconstruction objective but uses weight-space Frobenius error as the MCKP allocation cost. We investigate whether aligning the allocation cost with the output-space objective improves compressed model fidelity. On Qwen3-8B at 50% compression, our ROCKET-ActCost achieves +0.8 percentage points higher average accuracy across 8 zero-shot benchmarks (53.1% vs 52.3%), but increases WikiText perplexity by 16% (61.46 vs 52.98). This accuracy-perplexity tradeoff reveals that different allocation objectives favor different downstream metrics. The high correlation ($>$0.99) between weight-space and output-space errors limits allocation divergence, explaining the modest effect size. On Llama-3.2-1B at 20% compression, the two methods produce near-identical results (53.3% vs 53.5% accuracy, 14.45 vs 14.66 PPL), suggesting that the effect of the cost function is minor at lower compression ratios.

Large language models (LLMs) are increasingly used to generate, classify, and annotate data whose outputs feed downstream hypothesis tests. However, LLM-based research is easy to p-hack: a researcher can tune the prompts, decoding parameters, or output format until a desired result is reached. We propose a protocol to mitigate p-hacking in LLM-based research: preregistering the experiment and eligible models, and then running it on the first eligible LLM that is released after the preregistration. The researcher finalizes the procedure on current models, preregisters the analysis plan together with a set of eligible future models, and runs the confirmatory analysis on the first eligible model released afterward. Because this model does not exist at commitment time, it cannot be hacked against; furthermore, configurations that hack one model frequently do not transfer to the next. We evaluate the protocol on two tasks whose true values are known. Across 20 models from four providers and 11 LLM-analysis configurations, the protocol would have blocked successful transfer of the p-hack in 73.9% and 72.7% of cases in the two tasks. Additional analyses reveal that mitigation remains substantial under several stress tests. Finally, putting money where our mouth is, we followed our own protocol and preregistered our experiment. The preregistered experiment confirmed the protocol's effectiveness: out of the 7 configurations that hacked the prior model, the hacking failed to carry over in 6 configurations on the first eligible model released afterward.

Probe-based uncertainty estimation (UE) has emerged as a prominent approach to detect hallucinations in Large Language Models (LLMs) by learning uncertainty from internal model signals. Yet, recent methods vary simultaneously across feature design, training data construction, and evaluation setting, obscuring what actually drives performance. To address this issue, we propose a factorised study of probe-based UE under matched conditions. Our results show that raw hidden states and attention features are difficult to outperform in-domain. However, under distribution shift, structured and compressed features are more robust, suggesting that in-domain performance alone is insufficient to measure progress. Furthermore, prompting and label construction significantly affect probe behaviour. Building on these best-practice findings, we train benchmark-based pretrained probes that transfer reasonably well to open-ended factual generation, providing a stable off-the-shelf baseline. Our work encourages more deployment-oriented evaluation of probe-based uncertainty estimators. The code repository is available at https://github.com/ponhvoan/ProbeUE.

Many real-world control problems involve hybrid discrete-continuous action spaces. For example, steering and signaling in autonomous driving, and aiming and firing in robotics or video-games. Despite real-world hybrid factorization and reinforcement learning framework support for complex action spaces (e.g., Gymnasium, PettingZoo, TorchRL, SeedRL, Mujoco, etc), the default environments within those frameworks often implement uniform action space configurations (LunarLander, Walker2D, Cheetah, SMAC, SUMO, Ant, Atari). Landmark hybrid-action benchmarks (RoboCup 2D HFO, SC2LE, Platform, CARLA, etc) are mostly heavyweight or archival implementations originating from papers which test one or a small number of competing factorization methods on one kind of control. This article provides a cross-sectional study of factorization methods [independent networks, shared encoder, VDN, QPLEX, Joint, Auto-Regressive] on each of three families of algorithms [PPO, SAC, DQN] across three action spaces [discretized, hybrid, continuous] over four lightweight environments [Platform, hybrid-LunarLander, Hybrid-Shoot, CoopPush]. Accounting for some invalid pairings such as joint-continuous, we are left with 220 configurations to analyze each method. We provide two new C++ parallel gymnasium and petting-zoo compliant environments [CoopPush, Hybrid-Shoot] to isolate particular challenges such as state-dependent inter-action dependence. Finally, we introduce VDN-PPO and PPO-MIX which use a branching critic to assign credit to multi-headed PPO. These variants out-perform all other tested PPO factorizations. Our results suggest that branching dueling architectures balance compute and performance most effectively, with Auto-Regressive actions reaching the highest performance overall and native continuous SAC outperforming discrete and hybrid algorithms, albiet both at increased computational cost.

Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory. We formulate it as a reinforcement learning problem in two directions, bottom-up and top-down. To address the challenge of a fast-growing combinatorial search space, we introduce FactorLibrary, which stores factorizable subexpressions that serve as reusable subgoals across training episodes. We trained a bottom-up agent with Gumbel-PPO-MCTS and two top-down agents with PPO+MCTS and SAC. The PPO+MCTS top-down agent exhibited the most stable performance, finding certified optimal circuits up to complexity $8$ with a success rate of $91.8\%$.

Modern finance relies heavily on complex machine learning models to find patterns in the stock market. However, as these AI models get more complicated, they often memorize short-term market noise instead of finding companies with real, lasting value. We designed this research to test if Benjamin Graham's classic value investing rules could act as a mathematical "low-pass filter" to keep these modern models in check. We built three different sets of features - pure Graham rules, modern market factors, and a mix of both - and tested them against highly complex models (XGBoost and AutoGluon) using 20 years of S&P 500 data. By applying a strict buy-and-hold strategy over a four-year test period (March 2022 to March 2026), the results showed that more complex algorithms do not always win. While the AutoGluon model captured high returns (222.68%), it suffered a substantial 39.78% drop because it bought volatile tech stocks right before the market crashed. On the other hand, the pure Graham Random Forest achieved the highest overall return (232.13%) with much less risk (1.38 Calmar Ratio). Furthermore, the Combined Random Forest successfully mixed momentum with Graham's rules, making a 202.91% return while keeping the lowest maximum drop (34.53%) of any model tested. Ultimately, this research proves that Graham's "margin of safety" isn't outdated; it is actually a highly effective way to prevent modern AI from taking on too much risk.

Black-box optimization (BBO) deals with problems where objective functions lack explicit analytical forms and are expensive to evaluate. Factorization machine with quadratic-optimization annealing (FMQA) constructs a surrogate model using a factorization machine (FM) and optimizes it with an Ising machine. Conventional FMQA applies a single integer-binary encoding throughout the optimization process, although the encoding best suited to surrogate learning may differ from the one best suited to Ising-machine solution search. We propose a stage-dependent FMQA framework and derive conversion formulas between one-hot and domain-wall QUBO matrices that preserve the surrogate objective over feasible integer states up to an additive constant. We evaluate the OhDw variant, which employs one-hot encoding for learning and domain-wall encoding for search, on the Rastrigin function with input dimensions N = 2 and 5 and discretization levels q = 61 and 301. Across all conditions, the dominant factor governing optimization performance is the encoding used in the learning stage, with one-hot encoding consistently yielding lower residual errors than domain-wall or binary encoding. The additional benefit of switching to domain-wall encoding for solution search is condition-dependent. For N = 5 and q = 301, OhDw achieves a lower residual error and solutions closer to the global optimum than one-hot-only FMQA, whereas for N = 5 and q = 61 the latter achieves a lower residual error. These results indicate that one-hot encoding in the learning stage is the primary performance driver and that stage-dependent encoding can provide further improvement under finer discretization.

Latent action pretraining learns representations of visual change from pairs of observations, but existing methods typically encode each transition as a single unstructured representation that entangles transition extent and transition mode. We introduce Polar Latent Actions with Radial structure (PoLAR), which imposes a radial-direction structure on latent actions, encouraging radius to encode transition extent and direction to retain transition mode. PoLAR uses temporal offset between two observations as a weak proxy for transition extent, encouraging latent action from observation pairs separated by larger temporal gaps to occupy larger radii. We instantiate this structure in hyperbolic space, whose expanding volume with radius offers a natural fit for more diverse transition modes at larger extents. Across in-task and large-scale pretraining settings, PoLAR improves downstream policy performance in simulation and real-world robot experiments, outperforming latent action baselines and strong pretrained VLAs. These results suggest that the geometry of the latent action space is an important design choice for transferring visual pretraining to downstream robot policy learning.

We re-interpret Transformer pretraining as a fast-slow, singularly perturbed flow along depth, with untied weights as its non-autonomous feature. The linearised dynamics is a depth-ordered product of layer maps. Along a token-homogeneous reference trajectory, the linearised layer factorises along the eigenbasis of a frozen attention kernel. Past a computable saturation depth, the flow factors through the block coarse-graining -- in other words, running the layers is running the coarse variable, dually. Weight perturbations supported on the decaying bundle move neither the persistent component of the distinguished trajectory nor the frozen kernel to first order, so the framework partitions parameter space into visible and invisible directions, with the cross-block coupling of the slow path sitting entirely on the visible side. How large a gate the slow path can carry is bounded by a stability margin. On the data side: if block emissions follow an exponential family, block-mean pooling captures all the information the slow path can use; but if neighbouring blocks carry no shared structure, no cross-block channel can help the prediction, and the gate amplitude is invisible in the prediction risk. Stability delimits what the architecture may do; the data decides what it will.

Muon is an optimizer that computes updates using the polar factor of the momentum matrix and has shown strong empirical performance across a range of training settings. A key component of Muon is the Newton-Schulz iteration used to compute this polar factor. Although this avoids the cost of an exact singular value decomposition, it remains expensive in practice because it is applied at every optimization step. At the same time, the momentum matrix changes smoothly over training, suggesting strong temporal correlation in the corresponding polar factors. In this paper, we exploit this structure and propose CacheMuon, a temporal preconditioning method that reuses information from previous optimization steps to approximate the polar factor at the current step. This reduces redundant orthogonalization computation across iterations. We analyze CacheMuon as an inexact Muon update, with error controlled by fresh-solver error and cache staleness. Empirically, CacheMuon provides a controllable quality-efficiency frontier: conservative thresholds closely match fresh Muon on language-model and vision training while reducing orthogonalization FLOPs, whereas more aggressive thresholds yield larger arithmetic savings at the cost of modest validation-quality degradation.

We present an interpretable machine learning pipeline to decompose Cross-Sectional Equity Return Predictability into auditable factor contribution. We apply an XGBoost model with TreeSHAP attribution and conduct stress testing on 3632 Chinese A-share stocks from 2009 until 2019. Using 60-month, rolling windows over 55 months of out-of-sample data, XGBoost obtains a mean AUC of 0.547 and +2.38%/month (Newey-West t = 5.94; Annualized Sharpe 2.23) long-short spread for the top vs bottom quintiles. This alpha is persistent after adjusting for the Carhart four-factor model (+2.31%/month; t = 7.48). SHAP Decomposition indicates that behavioral signals (turnover and momentum) account for 58.2% of predictive attribution compared to 10.7% for valuation ratios, on average, across 55 industry groups. Ablation analysis serves to cross-validate this ranking and provides evidence that SHAP and ablation diverge in a manner that highlights feature substitutability structure that is largely invisible to either method used in isolation.

Contact-rich manipulation requires force sensitivity, but many robot arms lack dedicated force sensors due to their high cost. We present Neural External Torque Estimation (NEXT), a data-driven method that estimates external joint torques without needing any dedicated force sensors. NEXT trains in 1 minute from only 10 minutes of free-motion data, yet achieves estimates comparable to dedicated joint-torque sensors. NEXT enables force-feedback teleoperation on low-cost arms and improves policy learning through Force-Informed Re-Sampling Training (FIRST), which up-samples pre-contact and contact segments during behavior cloning. Across five long-horizon tasks, FIRST outperforms prior force-aware policies by over 17% in task progress. Together, NEXT and FIRST bring force-aware teleoperation and policy learning to off-the-shelf robots without additional sensing hardware. Video results and code are available at https://jasonjzliu.com/factr2

We present GHOST, a framework for learning visuomotor manipulation policies that generalize beyond the training distribution. GHOST factorizes control into (i) a high-level policy that predicts the next sub-goal as a distribution over 3D end-effector poses from multi-view RGB-D observations, and (ii) a low-level goal-conditioned controller that executes embodiment-specific actions. To condition image-based policies on 3D goals, we introduce a simple spatial interface that projects predicted goals into the image plane and represents them as end-effector heatmaps. Across a suite of manipulation tasks, this hierarchical factorization consistently improves performance and robustness compared to a flat Diffusion Policy. Further, we show that this hierarchical interface also makes it easy to incorporate human demonstrations without relying on (noisy) action retargeting. As sub-goals are largely embodiment-agnostic, we train the high-level policy on human video to specify how learned skills should be applied and composed, while keeping the low-level policy trained purely on robot data. This hierarchy enables adaptation to novel objects and task variations using a small number of human demonstrations.

Court simulation bridges legal education and judicial practice, yet human-based simulations are costly and difficult to scale. Large language models (LLMs) offer a scalable alternative, but existing court-simulation research mainly focuses on criminal cases. Civil litigation is more common in practice and harder to simulate because its claims, liability, and remedies are more flexible. We present a multi-agent court simulation framework for Chinese civil cases. The framework organizes role-based interaction through a five-stage civil trial procedure and integrates memory module and statute retrieval to support long-process adjudication. Experiments show that the framework produces reliable civil judgments, with clear strengths in liability allocation and multi-item adjudication. Further experiments show that memory quality substantially affects downstream simulation quality. Through a five-layer factor framework, we analyze how legal grounding, information conditions, judicial capability and role orientation, organizational pressure, and social context affect the framework's reliability and behavior. These results support the effectiveness of the proposed framework for civil court simulation. The dataset and code are available at: https://github.com/foggpoy/Civil-Court.

Large language models (LLMs) trained predominantly on English data encode substantial world knowledge, yet often fail to express it reliably in other languages, a phenomenon known as cross-lingual factual inconsistency. To study and address this, we introduce PolyFact, a large-scale parallel multilingual factual QA dataset containing 100K Wikidata-grounded facts across 12 typologically diverse languages. Using PolyFact, we compare light continual pretraining (CPT), supervised fine-tuning (SFT), and reinforcement learning via Group Relative Policy Optimization (GRPO) for improving cross-lingual factual recall in Qwen-2.5-7B and OLMo-2-1124-7B. We find that GRPO consistently outperforms SFT, improving both cross-lingual consistency and generalization to unseen languages, while CPT on parallel data yields limited additional gains. Mechanistic analyses further show that GRPO reorganizes multilingual routing by reducing language specialization in MLP layers and attention heads, thereby promoting more shared cross-lingual representations. We release our code, models, and dataset.

Continuous-time event data, in which entities emit instantaneous events over time, arises naturally across many domains such as neuroscience, seismology, and social networks. Non-negative matrix factorization (NMF) is a natural tool to uncover interpretable structure in such data, but it has so far only been applied after binning or smoothing the entity-level counting measures. This preprocessing step comes with the risk of erasing entity-level heterogeneities and fine-grained temporal features. In this paper, we introduce EventNMF, a continuous-time non-negative factorization model that operates directly on event times: each entity's events are modeled as a Poisson process whose intensity factorizes through a non-negative B-spline basis, and a simple estimation procedure recovers interpretable temporal templates shared across entities. The resulting method is mathematically principled, easy to implement, and computationally efficient. We further show that standard binned-count approaches arise as the special case of degree-zero splines, explore bias-variance tradeoffs and compare against existing methods on a synthetic latent factor model, and demonstrate the effectiveness of EventNMF on several real-world applications.

Contrastive Analysis aims to separate factors that are common between two data distributions from those that are salient to only one of them. Existing contrastive methods are based on generative models (e.g., VAEs or GANs) that often suffer from limited reconstruction and image quality, which hampers effective latent factor separation and limits their applicability to high-fidelity image generation and edition. We propose a novel conditioning framework for diffusion models that enables contrastive decomposition without compromising generation quality. We first train a prompt-free, image-conditioned diffusion model, and then learn to decompose the conditioning into a common and a salient factor, using weak supervision. We prove that the additive contrastive factorization, commonly assumed in prior work, is identifiable under mild conditions. This factorization enables targeted operations by swapping or interpolating only the salient factor.

Marginal inference in discrete graphical models forces a choice between exactness and scalability: exact algorithms are intractable for high-treewidth graphs, while iterative approximations (Belief Propagation, variational methods) sacrifice convergence guarantees on frustrated topologies. We argue that this dichotomy stems from a mismatched inductive bias: iterative methods abandon the sequential elimination structure that makes exact inference correct. We introduce In-Context Graphical Inference (ICG-I), an autoregressive Graph Transformer that restores this structure by mimicking Variable Elimination with learned, Tensor- Train-compressed intermediate factors, paired with a Dirichlet output layer and Weighted Conformal Prediction for calibrated, distribution-free coverage guarantees under topological shift. We prove that TT compression errors propagate at most lincarly through the autoregressive chain, that the Dirichlet-Multinomial loss is a proper scoring rule, and that WCP maintains coverage with a quantifiable degradation under estimated density ratios. We conducted intensive experiments to evaluate ICG-I and achieved state-of-the-art performance across all benchmarks. ICG-I reduces MAE from 0.041 (best baseline) to 0.020 on standard instances and achieves 0.048 on N=500 frustrated spin glasses where BP diverges entirely.

Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes. Latent factorization of tensors (LFT) extracts target knowledge from DWDNs via low-rank embedding. However, similar to many machine learning models, the performance of LFT heavily depends on the selection of hyperparameters. In practice, these parameters are often tuned manually or through grid search, which requires significant computational resources and human effort. Motivated by this challenge, this paper proposes an automated hyperparameter optimization framework based on Differential Evolution (DE) for LFT (DE-LFT). The proposed method integrates DE into the training process of the LFT model to automatically learn optimal regularization parameters $λ_1$, $λ_2$ and $λ_3$. As a result, the model can adaptively search the hyperparameter space and improve prediction accuracy. Experimental results on four real-world datasets demonstrate that the proposed approach achieves lower MAE and RMSE compared with manually tuned baselines while reducing the need for extensive parameter tuning.

Multi-task learning (MTL) aims to construct a joint model for multiple tasks by sharing a common representation across domains. To achieve this goal, existing optimization-centric methods either balance task gradients or modify the shared architecture. However, as these approaches remain agnostic to the content of the shared representation, they fail to disentangle task-relevant structure from spurious context, leading to negative transfer and poor generalization. To overcome this limitation, we propose Causal Orthogonal Representations for Multi-Task Learning (CORE-MTL), a causally motivated representation-centric framework that encourages a structured semantic-residual factorization of the shared representation, concentrating task-relevant structure in the semantic stream while relegating nuisance variation to the residual stream. We instantiate this framework in the visual domain by leveraging physical priors for structured scenes and statistical constraints for attributes. Theoretically, our method enjoys a tighter out-of-distribution generalization bound than optimization-centric methods and reduces task gradient interference without explicit gradient projection or reweighting. Empirically, CORE-MTL consistently outperforms existing methods on visual multi-task benchmarks in both in-distribution and out-of-distribution settings. Code is publicly available at https://github.com/Hope-Rita/CORE-MTL.

Robot learning must produce policies that generalize to new combinations of constraints, teammates, and environments. To achieve this, we must structurally factor the policy, which is a choice that dictates what generalizes, what requires retraining, and what remains entangled. Existing methods span a wide spectrum, from expecting structure to emerge from data scaling, to hand-designing it via hierarchies, skill libraries or learned specializations. In this paper, we study what we argue is the most fundamental factorization in robotics: separating the world from the task. We investigate the conditions under which this factorization is principled. World factors are properties of the embodied system and the environment; they exist independently of intent. Task factors are defined by the task's logic over what the world admits. We formalize this asymmetry through Bayesian model evidence: it aligns with the data-generating process, maintains high likelihood through an analytical world model, and reduces the Occam razor's penalty on task parameters. We instantiate this factorization by pairing AICON, a differentiable graph of recursive estimators and interconnections that is compositional, operates without task-specific data, and propagates cost gradients to actuators, with a compact, learned policy that modulates gradient paths. Gradients serve as the interface between the two factors: they carry world structure through the graph and task structure through costs, enabling low-dimensional learning while preserving structural generalization. We test the world/task factorization across three problems that encompass heterogeneous robots, environments, task logic and sensorimotor modalities. Our framework outperforms end-to-end baselines and analytical heuristics in all settings, generalizes zero-shot to out-of-distribution configurations, and transfers to real hardware without retraining.

Visual Prompting (VP) has emerged as an efficient paradigm for adapting large-scale pre-trained vision models to downstream tasks by incorporating learnable prompts at the input level. However, existing VP methods typically employ dense pixel-level prompts, which often suffer from redundant perturbations, limited generalization and energy inefficiency. To overcome these limitations, we propose to integrate brain-inspired spiking learning into visual prompt learning tasks. As we know that spiking neuron can perform inexpensive information processing by transmitting the input data into discrete spike trains and return sparse outputs. Inspired by this, we propose \textbf{Lo}w-\textbf{R}ank visual \textbf{S}pike \textbf{P}rompting (LoRSP), a novel framework that learns dynamic low-rank sparse visual prompts naturally via a Spiking neuron learning mechanism. The core idea of LoRSP is to exploit the brain-inspired sparse firing mechanism of spiking neurons to generate pixel-level sparse prompt for each instance. To be specific, we first construct a series of prompt factors via low-rank factorization to capture distinct prompt subspaces. These prompt factors are then fed into an SNN architecture, which performs the integrate-and-fire process to emit spikes. As a result, our LoRSP generates a \emph{sparse} visual prompt while maintaining the low-rank constraint. This design enables instance-specific selective prompting, leading to more compact and robust adaptation across diverse downstream tasks. Extensive experiments on five heterogeneous vision backbones and multiple benchmarks demonstrate that LoRSP achieves competitive performance while requiring fewer tunable parameters compared to existing VP methods.

Multi-LLM systems use multiple language models to deliberate, judge each other's outputs, or coordinate as agents. Their value depends on the models producing measurably different conversational behaviors when given the same input. Prior offline studies recommend drawing one model per family for behavioral diversity, because LLMs prefer outputs from their own family when rating one another in isolation. Whether the same family label predicts behavior in interactive multi-LLM systems, the setting that real deployed systems use, has not been tested. We study this with a 940,000-chain 11-checkpoint corpus and a 1.6M-chain same-base Llama factorial. On our validated headline metric, hedging, a reasoning-distilled Llama checkpoint shifts by 18% depending on which same-base partner it replies to, more than any cross-family hedging gap in the controlled subset. Qwen, closed-API, and runtime checks suggest the pattern is not isolated, while repair and challenge analyses remain exploratory because their surface-cue detectors are weaker. Overall, the results identify post-training recipe as a first-class axis for multi-LLM panel composition and show that model family alone is an incomplete proxy for conversational diversity.

Message-passing neural networks (MPNNs) are widely used for molecular property prediction, but their deployment as monolithic architectures makes it difficult to identify how specific message-passing operators affect performance. We present an operator-level factorial benchmark that decomposes 2D molecular MPNNs into the three families of message-seed initialization, node-edge fusion, and node update operators. The resulting 84 configurations are benchmarked on ten MoleculeNet datasets under a shared experimental setup and statistical analysis protocol. Across this controlled design, performance variation is associated primarily with message construction rather than update complexity. Message-seed initialization shows significant family-level effects for both regression and classification, node-edge fusion shows a significant family-level effect for regression with descriptive advantages for concatenation-based mixing, and the update family shows no statistically supported effect for either endpoint family. A representation probe into the Quinethazone molecule further demonstrates that concatenation-based mixing can better differentiate chemically distinct heteroatoms and withstand oversmoothing than Hadamard gating. Representative configurations selected separately for classification and regression recover competitive performance relative to established molecular graph neural network (GNN) baselines, ranking numerically best on eight of ten benchmark datasets. These empirical results are interpreted through concise mechanistic analyses of representative node-edge fusion and update operators. Our findings provide empirical design heuristics for molecular MPNNs by turning model design from a search over monolithic architectures into a targeted assessment of where and how chemical information enters the message-passing pipeline.

This study reports findings from a cross-sectional survey (n = 72) of higher education practitioners examining beliefs, behaviors, and institutional conditions related to artificial intelligence (AI) integration in teaching and learning. Grounded in the DOT Framework, which integrates design thinking and open systems theory, the study investigates AI familiarity, usage patterns, design-oriented practices, and pedagogical beliefs. Exploratory factor analysis of 19 belief items identified a three-factor structure: AI Functional Capabilities, Oversight and Governance, and Instructor Collaboration and Planning (α = .90). Results indicate that practitioners hold favorable views of AI as a pedagogical support while maintaining strong commitments to human oversight and critical evaluation. Reported practices emphasize iterative prompting and content generation, with less consistent use of needs assessment and feedback loops. Institutional barriers including limited policy, training, and infrastructure were widely reported. These findings provide preliminary empirical support for the DOT Framework as a descriptive model of practitioner beliefs and practices, while also highlighting gaps between design-oriented theory and current implementation. The study contributes an initial measurement structure and identifies directions for confirmatory validation and outcome-based research linking AI-supported design practices to instructional quality.