Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose $\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. Our framework consists of three components: (1) $\texttt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof; (2) a Progressive Multi-Stage SFT strategy that mimics the human learning process, teaching the model proof writing, planning, and insight identification; and (3) $\texttt{InsightPO}$, a policy optimization method that assigns structured rewards over this insight hierarchy. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque. We study multi-class linear classification in the hard no-margin regime and make the computation identifiable by enforcing feature- and label-permutation equivariance at every layer. This enables interpretability while maintaining functional equivalence and yields highly structured weights. From these models we extract an explicit depth-indexed recursion: an end-to-end identified, emergent update rule inside a softmax transformer, to our knowledge the first of its kind. Attention matrices formed from mixed feature-label Gram structure drive coupled updates of training points, labels, and the test probe. The resulting dynamics implement a geometry-driven algorithmic motif, which can provably amplify class separation and yields robust expected class alignment.

LLMs see the world as a single stream of text, partitioned into roles like <user> or <tool>. We trace prompt injection to role confusion: models perceive the source of text from how it sounds, not its labeled role. A command hidden in a webpage hijacks an agent simply because it sounds like <user> text, despite its <tool> label. We design role probes to measure how LLMs internally perceive "who is speaking," and find that injected text occupies the same representational space as the trusted role it imitates. We demonstrate this with CoT Forgery, a zero-shot attack that injects fabricated reasoning into user prompts and tool outputs. Models mistake the forgery for their own thoughts, yielding 60% attack success against frontier models with near-zero baselines. Strikingly, the degree of role confusion predicts attack success before a single token is generated. This mechanism generalizes beyond CoT Forgery to standard agent prompt injections, revealing prompt injection as a measurable consequence of role perception. To the model, sounding like a role is indistinguishable from being one.

Cultural values are expressed not only through language but also through visual scenes and everyday social practices. Yet existing evaluations of cultural values in language models are almost entirely text-only, leaving it unclear whether culture-conditioned judgments remain stable when response options are visualized. We introduce ValueGround, a benchmark for evaluating culture-conditioned visual value grounding in multimodal large language models (MLLMs). Built from World Values Survey questions, ValueGround uses minimally contrastive image pairs to represent opposing response options while controlling irrelevant variation. Given a country, a question, and an image pair, a model must choose the image that best matches the country's value tendency without access to the original response-option texts. Experiments across six MLLMs and 13 countries show that models perform substantially worse with visualized response options than with the original textual options, with average accuracy dropping from 72.8% to 62.6%. Our benchmark provides a controlled testbed for studying cross-modal transfer of culture-conditioned value judgments.

Vision-Language-Action (VLA) policies have emerged as a versatile paradigm for generalist robotic manipulation. However, precise object placement under compositional language remains challenging for end-to-end VLA policies. Slot-level placement requires reliable slot grounding and centimeter-level geometric precision. To this end, we propose AnySlot, a framework that reduces compositional complexity by introducing an explicit spatial visual goal between language grounding and control. AnySlot converts language into a visual goal by rendering a spatial marker at the intended slot, then executes this goal with a goal-conditioned VLA policy. This hierarchical design decouples high-level slot selection from low-level execution, improving semantic accuracy and spatial robustness. Furthermore, recognizing the lack of benchmarks for such precision-demanding tasks, we introduce SlotBench, a structured simulation benchmark with nine task categories for evaluating spatial reasoning in slot-level placement. Extensive experiments show that AnySlot significantly outperforms flat VLA baselines and modular grounding methods in zero-shot slot-level placement.

Accurate distance estimation from monocular cameras is essential for intelligent monitoring systems. In many deployments, image coordinates are mapped to ground positions using planar homographies initialized by manual selection of corresponding regions. Small inaccuracies in this initialization propagate into systematic distance distortions. This paper derives an explicit relationship between homography perturbations and the resulting distance error, showing that the error grows approximately quadratically with the true distance from the camera. Based on this model, two simple correction strategies are evaluated: regression-based estimation of the quadratic error function and direct optimization of the homography via coordinate-based gradient descent. A large-scale simulation study with more than 19 million test samples demonstrates that regression achieves higher peak accuracy when the model is reliably fitted, whereas gradient descent provides greater robustness against poor initial calibration. This suggests that improving geometric calibration may yield greater performance gains than increasing model complexity in many practical systems.

As Large Language Models (LLMs) are increasingly deployed in real-world applications, reliable uncertainty quantification (UQ) becomes critical for safe and effective use. Most existing UQ approaches for language models aim to produce a single confidence score -- for example, estimating the probability that a model's answer is correct. However, uncertainty in natural language tasks arises from multiple distinct sources, including model knowledge gaps, output variability, and input ambiguity, which have different implications for system behavior and user interaction. In this work, we study how the source of uncertainty impacts the behavior and effectiveness of existing UQ methods. To enable controlled analysis, we introduce a new dataset that explicitly categorizes uncertainty sources, allowing systematic evaluation of UQ performance under each condition. Our experiments reveal that while many UQ methods perform well when uncertainty stems solely from model knowledge limitations, their performance degrades or becomes misleading when other sources are introduced. These findings highlight the need for uncertainty-aware methods that explicitly account for the source of uncertainty in large language models.

By combining complementary benefits of short- and long-exposure images, Dual-Exposure Imaging (DEI) enhances image quality in low-light scenarios. However, existing DEI approaches inevitably suffer from producing artifacts due to spatial displacement from scene motion and image feature discrepancies from different exposure times. To tackle this problem, we propose a novel Event-based DEI (E-DEI) algorithm, which reconstructs high-quality images from dual-exposure image pairs and events, leveraging high temporal resolution of event cameras to provide accurate inter-/intra-frame dynamic information. Specifically, we decompose this complex task into an integration of two sub-tasks, i.e., event-based motion deblurring and low-light image enhancement tasks, which guides us to design E-DEI network as a dual-path parallel feature propagation architecture. We propose a Dual-path Feature Alignment and Fusion (DFAF) module to effectively align and fuse features extracted from dual-exposure images with assistance of events. Furthermore, we build a real-world Dataset containing Paired low-/normal-light Images and Events (PIED). Experiments on multiple datasets show the superiority of our method. The code and dataset are available at github.

Feature optimization -- specifically Feature Selection (FS) and Dimension Selection (DS) -- is critical for the efficiency and generalization of large-scale recommender systems. While conceptually related, these tasks are typically tackled with isolated solutions that often suffer from ambiguous importance scores or prohibitive computational costs. In this paper, we propose ShuffleGate, a unified and interpretable mechanism that estimates component importance by measuring the model's sensitivity to information loss. Unlike conventional gating that learns relative weights, ShuffleGate introduces a batch-wise shuffling strategy to effectively "erase" information in an end-to-end differentiable manner. This paradigm shift yields naturally polarized importance distributions, bridging the long-standing "search-retrain gap" and distinguishing essential signals from noise without complex threshold tuning. Extensive experiments across four benchmarks validate that ShuffleGate consistently outperforms state-of-the-art methods in both Feature and Dimension Selection tasks. It achieves a 15\times speedup over permutation baselines and demonstrates extreme scalability by processing 270M parameters in just 700 seconds. Finally, in a top-tier industrial deployment, it compressed input dimensions by 10\times, yielding a 91% increase in training throughput while serving billions of daily requests without performance degradation.

Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, Fourier-based variants inherently truncate high-frequency components in spectral space, resulting in the loss of small-scale structures and degraded prediction quality at high resolutions when trained on low-resolution data. While diffusion-based enhancement methods can recover multi-scale features, they introduce substantial inference overhead that undermines the efficiency advantage of neural operators. In this work, we introduce MeanFlow-Enhanced Neural Operators (MENO), a novel framework that achieves accurate all-scale predictions with minimal inference cost. By leveraging the improved MeanFlow method, MENO restores both small-scale details and large-scale dynamics with superior physical fidelity and statistical accuracy. We evaluate MENO on three challenging dynamical systems, including phase-field dynamics, 2D Kolmogorov flow, and active matter dynamics, at resolutions up to 256$\times$256. Across all benchmarks, MENO improves the power spectrum density accuracy by up to a factor of 2 compared to baseline neural operators while achieving up to $14\times$ faster inference than the state-of-the-art Denoising Diffusion Implicit Model (DDIM)-enhanced counterparts, effectively bridging the gap between accuracy and efficiency. The flexibility and efficiency of MENO position it as an efficient surrogate model for scientific machine learning applications where both statistical integrity and computational efficiency are paramount.

We examine whether human psychometric questionnaires can serve as reliable tools for characterizing and predicting LLM behavior in everyday user interactions. We analyze eight open-source LLMs by comparing their value and personality profiles derived from two different methods: Likert self-reports on established questionnaires (PVQ-40/21 and BFI-44/10) and generation probabilities over value-laden responses to everyday user queries. The two profiles diverge substantially. Within-construct item consistency, often cited as evidence of stable LLM dispositions, disappears in generation probabilities. We attribute this gap to the fact that explicit lexical cues in established questionnaire items allow models to recognize the target construct and respond in alignment-consistent, socially desirable ways, whereas realistic user queries provide no such cues. In addition, demographic persona prompts shift models' responses to human questionnaires in ways consistent with real human patterns, but no such shifts appear in the generation probabilities of responses to realistic user queries, showing their limited ability to simulate the behaviors of target demographics in real-world user interactions. Overall, our study shows that human psychometric questionnaires are insufficient tools for predicting LLM behavior and suggests generation-based profiling as a more accurate measure.

General-purpose world models promise scalable policy evaluation, optimization, and planning, yet achieving the required level of robustness remains challenging. Unlike policy learning which primarily focuses on optimal actions, a world model needs to be reliable over a vast space of suboptimal actions, which are often underrepresented in action-labeled robot interactions. To address this challenge, we propose World Action Verifier (WAV), a framework that enables world models to identify their own prediction errors and self-improve. The key idea is to decompose action-conditioned state prediction into two independently verifiable factors: state plausibility and action reachability. We show that verifying these factors is significantly more tractable than direct forward prediction due to two underlying asymmetries: the broader availability of action-free data and the lower dimensionality of action-relevant features. Leveraging these asymmetries, we augment a world model with (i) a diverse subgoal generator obtained from video corpora and (ii) a sparse inverse model that infers actions from a subset of state features. By enforcing cycle consistency among proposed subgoals, inferred actions, and forward rollouts, WAV provides an effective verification mechanism in under-explored regimes, where existing methods often fail. Across nine tasks spanning MiniGrid, RoboMimic, and ManiSkill, our method achieves 2x higher sample efficiency while improving downstream policy performance by over 22%.

This paper presents EBuddy, a voice-guided workflow orchestrator for natural human-machine collaboration in industrial environments. EBuddy targets a recurrent bottleneck in tool-intensive workflows: expert know-how is effective but difficult to scale, and execution quality degrades when procedures are reconstructed ad hoc across operators and sessions. EBuddy operationalizes expert practice as a finite state machine (FSM) driven application that provides an interpretable decision frame at runtime (current state and admissible actions), so that spoken requests are interpreted within state-grounded constraints, while the system executes and monitors the corresponding tool interactions. Through modular workflow artifacts, EBuddy coordinates heterogeneous resources, including GUI-driven software and a collaborative robot, leveraging fully voice-based interaction through automatic speech recognition and intent understanding. An industrial pilot on impeller blade inspection and repair preparation for directed energy deposition (DED), realized by human-robot collaboration, shows substantial reductions in end-to-end process duration across onboarding, 3D scanning and processing, and repair program generation, while preserving repeatability and low operator burden.

We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We also extend our analysis to dynamic regret, obtaining the first guarantees with optimal $\sqrt{P_T}$ path-length dependencies without prior knowledge of $P_T$. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore $Ω(\sqrt{dT})$ rate for adversarial linear bandits on the Euclidean ball, which is of independent interest.

Convolutional neural networks (CNNs) achieve state-of-the-art performance in medical image analysis yet remain opaque, limiting adoption in high-stakes clinical settings. Existing approaches face a fundamental trade-off: post-hoc methods provide unfaithful approximate explanations, while inherently interpretable architectures are faithful but often sacrifice predictive performance. We introduce TTE-CAM, a test-time framework that bridges this gap by converting pretrained black-box CNNs into self-explainable models via a convolution-based replacement of their classification head, initialized from the original weights. The resulting model preserves black-box predictive performance while delivering built-in faithful explanations competitive with post-hoc methods, both qualitatively and quantitatively. The code is available at https://github.com/kdjoumessi/Test-Time-Explainability

Drones equipped with overhead manipulators offer unique capabilities for inspection, maintenance, and contact-based interaction. However, the motion of the drone and its manipulator is tightly linked, and even small attitude changes caused by wind or control imperfections shift the end-effector away from its intended path. This coupling makes reliable tracking difficult and also limits the direct use of learning-based arm controllers that were originally designed for fixed-base robots. These effects appear consistently in our tests whenever the UAV body experiences drift or rapid attitude corrections. To address this behavior, we develop a reinforcement-learning (RL) framework with a transformer-based double deep Q learning (DDQN), with the core idea of using an adaptive beam-search planner that applies a short-horizon beam search over candidate control sequences using the learned critic as the forward estimator. This allows the controller to anticipate the end-effector's motion through simulated rollouts rather than executing those actions directly on the actual model, realizing a software-in-the-loop (SITL) approach. The lookahead relies on value estimates from a Transformer critic that processes short sequences of states, while a DDQN backbone provides the one-step targets needed to keep the learning process stable. Evaluated on a 3-DoF aerial manipulator under identical training conditions, the proposed meta-adaptive planner shows the strongest overall performance with a 10.2% reward increase, a substantial reduction in mean tracking error (from about 6% to 3%), and a 29.6% improvement in the combined reward-error metric relative to the DDQN baseline. Our method exhibits elevated stability in tracking target tip trajectory (by maintaining 5 cm tracking error) when the drone base exhibits drifts due to external disturbances, as opposed to the fixed-beam and Transformer-only variants.

Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potential process and increases its effective order through Kirchhoff-inspired cascade composition. A single Kirchhoff Neural Cell implements a stable first-order update, while serially composed cells form higher-order dynamical operators within one block. This construction is interpretable, numerically stable and compatible with common neural backbones. Theoretical analysis shows that cascaded cells induce end-to-end high-order operators, and controlled experiments demonstrate that intra-block high-order construction differs from generic depth stacking, especially on derivative-sensitive measures. Across steady-state operator learning, long-horizon physical forecasting and ImageNet-1K recognition, CHONN improves structural fidelity, rollout stability and visual representation learning. These results identify high-order circuit composition as a general principle for neural dynamics modeling.

Benchmarking large language models (LLMs) and agents in multi-turn interactive scenarios is essential for understanding their practical capabilities. However, existing evaluation protocols are highly heterogeneous, differing significantly in dataset formats, model interfaces, and evaluation pipelines, which severely impedes systematic comparison. In this work, we present UniDial-EvalKit (UDE), a unified evaluation toolkit for assessing interactive AI systems. The core contribution of UDE lies in its holistic unification: it standardizes heterogeneous data formats into a universal schema, streamlines complex evaluation pipelines through a modular architecture, and aligns metric calculations under a hierarchical scoring aggregation. It also supports efficient large-scale evaluation through parallel generation and scoring, as well as checkpoint resume to eliminate redundant computation. Leveraging UDE, we conduct an extensive evaluation across diverse multi-dimensional benchmarks. Our empirical analysis shows that no single system consistently outperforms others across all benchmarks, while current memory agents often fail to surpass full-context baselines. Further analyses highlight several future directions, including benchmark deduplication and more adaptive memory architectures.

Large language models excel on objectively verifiable tasks such as math and programming, where evaluation reduces to unit tests or a single correct answer. In contrast, real-world enterprise work is often subjective and context-dependent: success hinges on organizational goals, user intent, and the quality of intermediate artifacts produced across long, multi-tool workflows. We introduce LH-Bench, a three-pillar evaluation design that moves beyond binary correctness to score autonomous, long-horizon execution on subjective enterprise tasks. The pillars are: (i) expert-grounded rubrics that give LLM judges the domain context needed to score subjective work, (ii) curated ground-truth artifacts that enable stepwise reward signals (e.g., chapter-level annotation for content tasks), and (iii) pairwise human preference evaluation for convergent validation. We show that domain-authored rubrics provide substantially more reliable evaluation signals than LLM-authored rubrics (kappa = 0.60 vs. 0.46), and that human preference judgments confirm the same top-tier separation (p < 0.05), evidence that expert-grounded evaluation can scale without sacrificing reliability. We release public datasets and report results on two environments: Figma-to-code (33 real .fig tasks against the Figma API via MCP) and Programmatic content (41 courses comprising 183 individually-evaluated chapters on a course platform serving 30+ daily users).

Self-improvement training, where models learn from self-generated solutions, promises sustained capability gains but suffers from a pervasive failure mode: across multiple rounds, compounding reasoning errors cause accuracy to stall or degrade. We trace this drift to standard filtering criteria that retain solutions based solely on final answer correctness, which lets lucky guesses (correct answers with flawed reasoning) contaminate the training data. We propose Verified Self-Improvement (VSI), a framework that conditions data retention on step-level structural integrity rather than just the final output. VSI validates solutions by recomputing arithmetic steps via a computer-algebra library (sympy), checking intermediate consistency, and enforcing domain constraints. Evaluating VSI on GSM8K with Qwen3-4B-Thinking across 5 rounds of self-improvement against four baselines (no verification, outcome verification, majority voting, and VSI with DPO) shows that VSI rejects approximately 34% of correct-answer solutions, successfully isolating lucky guesses. This cleaner training signal drives sustained accuracy gains across all rounds (80.5% to 91.0%), whereas outcome verification plateaus and unverified training collapses. Finally, converting VSI checks into DPO preference pairs trains the model to distinguish sound reasoning from lucky answers, boosting reward accuracy from 46% to 63%. VSI offers a simple, reproducible recipe for robust self-improvement whenever automated reasoning checks are available.

Performance gains of Vision Language Models (VLMs) obtained by fine-tuning are generally based on ad hoc data collection and annotation of real-world scenes. Despite the improvements, this process is often prone to biases, errors, and distribution imbalance, resulting in overfitting and imbalanced performance. Although a few studies have explored synthetic data generation, they typically lack control over data distribution and annotation quality. In this work, we re-evaluate the potential of model fine-tuning by exploring a fully controlled data generation and annotation pipeline, obtaining bias-free data with balanced distribution and clean annotations. Using the spatial reasoning task of identifying the absolute position of an object as a use case, we fine-tune state-of-the-art VLMs and conduct exhaustive evaluations on both synthetic and real-world benchmarks, including transferability to real-world scenes. Our experiments reveal two key findings: 1) fine-tuning on balanced data yields uniform performance across the visual scene and mitigates common biases with as few as 130 samples; and 2) fine-tuning on synthetic stimuli improves performance by 13% on real-world data (COCO), outperforming models fine-tuned on the full COCO train set.

Accurately modeling opinion change through social interactions is crucial for understanding and mitigating polarization, misinformation, and societal conflict. Recent work simulates opinion dynamics with role-playing LLM agents (RPLAs), but multi-agent simulations often display unnatural group behavior, such as premature convergence, and lack empirical benchmarks for assessing alignment with real human group interactions. We introduce DEBATE, a large-scale benchmark for evaluating the authenticity of opinion dynamics in multi-agent RPLA simulations. DEBATE contains multi-round public messages and private Likert-scale beliefs from U.S.-based participants across 107 topics; the cleaned benchmark used in our experiments contains 2,788 participants in 697 groups, enabling evaluation at the utterance and group levels and supporting future individual-level analyses. We instantiate "digital twin" RPLAs with seven LLMs and evaluate across two settings: next-message prediction and full dynamics simulation, using stance-based opinion-dynamics metrics. In zero-shot settings, RPLA groups exhibit strong opinion convergence relative to human groups. On the held-out group split, supervised fine-tuning (SFT) for Llama-3.1-8B-Instruct improves auxiliary stance alignment and reduces group-level convergence error, though discrepancies in opinion change and belief updating remain. DEBATE enables rigorous benchmarking of simulated opinion dynamics and supports future research on aligning multi-agent RPLAs with realistic human interactions.

Vision-Language Models like CLIP are extensively used for inter-modal tasks which involve both visual and text modalities. However, when the individual modality encoders are applied to inherently intra-modal tasks like image-to-image retrieval, their performance suffers from the intra-modal misalignment. In this paper we study intra-modal misalignment in CLIP with a focus on the role of the projectors that map pre-projection image and text embeddings into the shared embedding space. By analyzing the form of the cosine similarity applied to projected features, and its interaction with the contrastive CLIP loss, we show that there is an inter-modal operator responsible for aligning the two modalities during training, and a second, intra-modal operator that only enforces intra-modal normalization but does nothing to promote intra-modal alignment. Via spectral analysis of the inter-modal operator, we identify an approximately isotropic subspace in which the two modalities are well-aligned, as well as anisotropic directions specific to each modality. We demonstrate that this aligned subspace can be directly obtained from the projector weights and that removing the anisotropic directions improves intra-modal alignment. Our experiments on intra-modal retrieval and classification benchmarks show that our training-free method reduces intra-modal misalignment, greatly lowers latency, and outperforms existing approaches across multiple pre-trained CLIP-like models. The code is publicly available at: https://github.com/simomagi/IsoCLIP.

Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships: \[ \log \tilde q_t(i) = α_t \left( \log q_t(i) + \log b_t(i) \right) + c_t, \] where $q_t$ and $\tilde q_t$ are pre- and post-elicitation probabilities, $b_t$ is an externally constructed evidence signal, and $α_t$ is an empirical descriptor of the prompting configuration. Across 4,975 reasoning problems from GPQA Diamond, TheoremQA, MMLU-Pro, and ARC-Challenge, evaluated on multiple instruction-tuned model families, we observe approximate log-ratio relationships with mean $R^2 \approx 0.76$ over about $1.3 \times 10^5$ candidate-level observations. Coefficients vary across elicitation settings, but qualitatively similar relationships persist across evaluated conditions. Robustness analyses using alternative statistical representations, prompting configurations, held-out evaluation, and token-level log-probabilities suggest that the observed structure is not tied to one prompting procedure or probability estimation method. The main contribution is not the algebraic form itself, which is related to generalized Bayesian updating and probability-transformation frameworks, but the empirical observation that diverse inference-time prompting pipelines repeatedly exhibit reproducible log-ratio structure under controlled conditions. The framework provides a protocol-sensitive perspective for analyzing calibration, evidence amplification, uncertainty propagation, and interaction sensitivity in inference-time LLM pipelines.

A foundational assumption in linguistics holds that sound-meaning relations are largely arbitrary. Here we show that this assumption fails at the level of individual phonemes: each English phoneme carries a structured, multidimensional semantic profile that is recoverable from text, perceived across languages, and grounded in articulation. Three large language models independently detected consistent semantic structure across nine perceptual dimensions in 220 pairwise letter contrasts. Native English speakers (N = 93) confirmed these associations in a preregistered forced-choice task (85.3% agreement with model predictions), and listeners of five typologically diverse languages (N = 155) replicated the effect under audio presentation (73.2%-81.9% accuracy). Articulatory features predicted the structure with cross-validated R^2 of 0.56-0.98, indicating that the bodily act of producing a sound systematically shapes the meaning it conveys. These findings reframe phoneme-level iconicity as a pervasive, embodied property of the phonological system.

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo recovery of executable mechanisms from weights without relying on human-written target programs. However, applying this paradigm to Transformer is complicated by representation entanglement (e.g., superposition), where features encoded in overlapping directions substantially hinder the recovery of symbolic expressions. We propose the Discrete Transformer, an architecture explicitly designed to bridge the gap between continuous representations and discrete symbolic logic. By injecting discreteness through temperature-annealed sampling, our framework effectively leverages hypothesis testing and symbolic regression to extract human-readable programs. Empirically, the Discrete Transformer achieves performance comparable to the RNN-based MIPS baseline on shared discrete tasks, while broadening extraction to tasks with continuous-valued intermediate computations. Finally, we show that architectural inductive biases provide fine-grained control over synthesized programs, establishing the Discrete Transformer as a controllable testbed for algorithm extraction and Transformer interpretability.

Anonymization is often assumed to protect privacy once explicit identifiers are removed, because re-identification has historically required specialized expertise, tailored algorithms, and manual corroboration. We show that LLM-based agents weaken this barrier: by combining scattered, individually non-identifying cues with public evidence, they reconstruct real-world identities, sometimes even during benign tasks. We evaluate this risk across three settings -- classical linkage incidents, a controlled benchmark (\emph{InferLink}) that varies fingerprint type, task framing, and attacker knowledge, and open-ended human--AI interaction traces. In the sparsest regime of the Netflix Prize deanonymization setting, agents reconstruct 79.2\% of identities, against 56.0\% for a classical matching baseline; on \emph{InferLink}, they link individuals even without an explicit re-identification request, and more often once one is given. In redacted human--AI interaction traces, agents further resolve anonymized profiles to specific individuals by corroborating contextual cues with public evidence. These findings suggest that privacy evaluations for agentic systems should measure not only what information is accessed or disclosed, but also what identities can be inferred.

Large language models (LLMs) are increasingly deployed as automated evaluators that assign numeric scores to model outputs, a paradigm known as LLM-as-a-Judge. However, standard Reinforcement Learning (RL) methods typically rely on binary rewards (e.g., 0-1 accuracy), thereby ignoring the ordinal structure inherent in regression tasks; for instance, they fail to recognize that predicting 4 is significantly better than predicting 1 when the ground truth is 5. Conversely, existing regression-aware approaches are often confined to Supervised Fine-Tuning (SFT), limiting their ability to explore optimal reasoning paths. To bridge this gap, we propose \textbf{REAL} (\underline{RE}gression-\underline{A}ware Reinforcement \underline{L}earning), a principled RL framework designed to optimize regression rewards, and also proven to be optimal for correlation metrics. A key technical challenge is that the regression objective is explicitly policy-dependent, thus invalidating standard policy gradient methods. To address this, we employ the generalized policy gradient estimator, which naturally decomposes optimization into two complementary components: (1) exploration over Chain-of-Thought (CoT) trajectory, and (2) regression-aware prediction refinement of the final score. Extensive experiments across model scales (8B to 32B) demonstrate that REAL consistently outperforms both regression-aware SFT baselines and standard RL methods, exhibiting significantly better generalization on out-of-domain benchmarks. On Qwen3-32B specifically, we achieve gains of +8.40 Pearson and +7.20 Spearman correlation over the SFT baseline, and +18.30/+11.20 over the base model. These findings highlight the critical value of integrating regression objectives into RL exploration for accurate LLM evaluation.

Neural networks often learn the parts of a task but fail on novel combinations of those parts. We argue that this failure is architectural: a decoder generalizes compositionally only when it respects the algebraic laws of the task, i.e. when it descends from freely generated sequences to the quotient determined by those laws. We make this principle constructive by compiling Higher Inductive Type (HIT) specifications into neural architectures. Basepoints, path constructors, and 2-cells are mapped to base constraints, generator networks, structural concatenation, and learned homotopies. The resulting transport decoders are strict monoidal functors by construction: decoding a concatenated word is concatenation of independently generated loop segments. In contrast, we prove that softmax self-attention cannot simultaneously satisfy strict monoidal composition and descent to any non-trivial compositional quotient. Experiments on the torus, wedge of circles, and Klein bottle validate the predicted hierarchy: functorial decoders outperform non-functorial alternatives by $2$--$10\times$, and a learned 2-cell closes a $46\%$ error gap precisely on words exercising the Klein-bottle relation. These results suggest that compositional generalization should be enforced as functorial structure in the architecture, rather than learned from examples alone.