Near-critical Ornstein–Zernike theory for the planar random-cluster model
arXiv:2510.13648v3 Announce Type: replace Abstract: We develop an Ornstein–Zernike theory for the two-dimensional random-cluster model with $1 \leq q
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arXiv:2510.13648v3 Announce Type: replace Abstract: We develop an Ornstein–Zernike theory for the two-dimensional random-cluster model with $1 \leq q
arXiv:2602.21160v3 Announce Type: replace-cross Abstract: In safety-critical classification, the cost of failure is often asymmetric, yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), that cannot distinguish whether a model's ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector $C_k(x)=\sigma_k^{2}/(2\mu_k)$, with $\mu_k{=}\mathbb{E}[p_k]$ and $\sigma_k^2{=}\mathrm{Var}[p_k]$ across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the $1/\mu_k$ weighting corrects boundary suppression and makes $C_k$ comparable across rare and common classes. By construction $\sum_k C_k \approx \mathrm{MI}$, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of $C_k$, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class $C_k$ reduces selective risk by 34.7\% over MI and 56.2\% over variance baselines; (ii) out-of-distribution detection on clinical and image benchmarks, where $\sum_k C_k$ achieves the highest AUROC and the per-class view exposes asymmetric shifts invisible to MI; and (iii) a controlled label-noise study in which $\sum_k C_k$ shows less sensitivity to injected aleatoric noise than MI under end-to-end Bayesian training, while both metrics degrade under transfer learning. Across all tasks, the quality of the posterior approximation shapes uncertainty at least as strongly as the choice of metric, suggesting that how uncertainty is propagated through the network matters as much as how it is measured.
Contactless body measurement technologies are becoming increasingly significant for smart health monitoring, digital health applications, and remote patient assessment. Traditional anthropometric measurements typically necessitate physical contact and trained personnel, which may constrain scalability in remote healthcare settings. In this study, we introduce a depth camera-based framework for estimating human body measurements utilizing 3D point cloud data. An Orbbec Astra 2 depth camera was employed to capture RGB images, depth maps, and 3D point clouds of participants. The captured point cloud was processed using Python-based tools, including Open3D, NumPy, and OpenCV, to segment the human body from the background. Key anthropometric measurements, such as height and arm span, were computed. The measurements were obtained through a combination of spatial filtering and landmark selection on the 3D point cloud, followed by the projection of the computed measurements onto the corresponding RGB image using camera intrinsic parameters. In addition to linear measurements, the approximate body volume and visible surface area were estimated using voxel-based occupancy analysis and mesh-based surface reconstruction methods. The experimental results from a single depth capture demonstrated that accurate body measurements and geometric estimates could be obtained from depth camera data without physical contact. This study provides a foundation for future real-time systems that integrate depth sensing with intelligent health monitoring and generative AI models for smart healthcare applications.
arXiv:2606.13313v1 Announce Type: cross Abstract: Let $\delta_n^L$ be the maximal density of a lattice sphere packing in the $n$-dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $\delta_n^L \geq c n^2 2^{-n}$ where $c>0$ is a universal constant. In higher dimension, even for non-lattice sphere packings, this new lower bound is a substantial improvement. Klartag's proof uses the probabilistic method in two different ways. The first, very standard, relies on the statistical properties of a uniformly chosen random lattice. The second, completely new, studies the stochastic evolution of an ellipsoid constrained to contain non nonzero lattice points in the interior.
arXiv:2606.24780v1 Announce Type: new Abstract: Progress in deep learning is, at scale, more a matter of systems engineering than of modelling: the behaviour of a model in training (its throughput, its memory footprint, and the numerical fidelity of the result) is determined less by the architecture itself than by how that architecture is expressed on the hardware. To achieve absolute control over this hardware expression while abstracting away systems complexity to make modelling seamless and eliminating the need for repetitive orchestration logic, BluTrain was architected from first principles as a robust, lightweight, and architecture-general training framework in standard C++ and the core CUDA programming model. Every layer is implemented natively: a typed tensor module with reverse-mode autograd, a linear-algebra library, a caching allocator, a multi-mode distributed-execution module, and an MLIR-based deep-learning compiler. In formal evaluations training a 124M-parameter GPT-2 baseline in FP32 on an 8-GPU 6000 Ada system, BluTrain outperforms industry-standard baselines in both throughput (sustaining an average of 407K tokens/s versus PyTorch's 395K tokens/s) and memory efficiency (achieving up to a 22% footprint reduction), while strictly preserving numerical fidelity and converging to a marginally lower final validation loss. With every layer explicitly open to native tuning, the performance ceiling is the framework's own to raise.
Prior work synthesizes tool-use LLM datasets by first generating a user query, followed by complex tool-use annotations like depth-first search (DFS). This leads to inevitable annotation failures and low efficiency in data generation. We introduce ToolGrad, an agentic framework that inverts this paradigm. ToolGrad first constructs valid tool-use chains through an iterative process guided by textual "gradients", and then synthesizes corresponding user queries. This "answer-first" approach led to ToolGrad-500, a dataset generated with more complex tool use, lower cost, and almost 100% pass rate. Experiments show that ToolGrad models outperform those trained on expensive baseline datasets and proprietary LLMs. The ToolGrad source code, dataset, and models are available at https://github.com/zhongyi-zhou/toolgrad.
arXiv:2606.15868v1 Announce Type: new Abstract: Next activity prediction (NAP) is a cornerstone of predictive process monitoring (PPM), enabling organizations to move from retrospective analysis to proactive process steering. The PPM field has progressed from classical machine learning through deep learning architectures such as LSTMs and Transformers to large language models (LLMs). Despite growing model complexity, no benchmark jointly compares LLMs, Transformers, LSTMs, and simple baselines in a direct sequence modeling setting for NAP. In this paper, we fill this gap with a systematic benchmark. We compare vocabulary-adapted LLMs, Transformers trained from scratch, LLM-distilled Transformers, and LSTMs against a simple counting-based argmax baseline across seven real-life event logs. Our results tell a David vs. Goliath story: pretraining confers no consistent improvement over training from scratch, model size shows little effect on performance, and on most datasets the argmax baseline matches or approaches the performance of billion-parameter LLMs.
Large reasoning models typically follow a read-then-think paradigm: they observe the complete input, reason over a static context, and then produce the answer. Yet many real-world scenarios are inherently dynamic, such as audio and video stream, where information arrives as a continuous stream and models must reason, update, and respond under partial observations. Recent streaming reasoning methods allow models to think while reading, but they largely rely on supervised imitation of pre-constructed trajectories, which limits their flexibility. In this paper, we propose AdaSR, an adaptive streaming reasoning framework that enables models to reason during input streaming and perform final deliberation once the stream is complete, learning when to think, and how much computation to allocate across different stages. To optimize this hierarchical reasoning process, we introduce Hierarchical Relative Policy Optimization (HRPO), which decomposes policy optimization into streaming reasoning and deep reasoning phases, providing more fine-grained advantage assignment instead of uniformly distributing a single sequence-level advantage over all tokens. HRPO integrates format, accuracy, and adaptive thinking rewards to enforce valid reasoning protocols, preserve final task performance, and encourage latency-aware computation allocation. Experiments show that AdaSR achieves a better balance among reasoning accuracy, computational efficiency, and streaming latency compared with supervised fine-tuning baseline. We release our code at https://github.com/EIT-NLP/StreamingLLM/tree/main/AdaSR.
arXiv:2606.19298v1 Announce Type: new Abstract: We prove that if $p/q$ is a continued fraction convergent of $1/e$ with $q\geq 3$, then, for the secretary problem with $q$ applicants, the optimal number of initially rejected applicants is $p$.
arXiv:2606.14415v1 Announce Type: new Abstract: Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods
End-to-end structure predictors, such as AlphaFold2, typically output only the dominant conformational state of a given protein, which is biased by the training data set. Existing strategies for recovering alternative conformations are often computationally expensive and offer limited biological interpretability. Here, we present SteerAF, an inference-time optimization framework based on AlphaFold2 that leverages information encoded in the distogram derived from deep multiple sequence alignments (MSAs) to predict alternative protein conformations. Across four benchmark datasets, SteerAF matches or surpasses existing methods in predicting alternative conformations for the majority of systems. Sparse MSA-feature modifications generated via block gradient ascent exhibit a strong correlation with experimentally characterized functional residues, recovering them with approximately 50% precision in the tested proteins. Furthermore, SteerAF enables effective decoy selection in the absence of experimental structures, and its predictions can serve as seed structures for molecular dynamics simulations to map conformational landscapes. Thus, SteerAF provides an efficient and interpretable approach for predicting alternative conformations, offering a framework that can be extended to other similar predictors and problems.
arXiv:2606.19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks. We solve a non-convex Lipschitz-regularized training program by introducing a convex restriction that can be efficiently solved to global optimality. Our approach can be employed as a post-processing step by taking a pre-trained network as an initial solution to then solving the convex program whose optimal network is guaranteed to be no worse than the initial one. We illustrate the improvements of our training procedure with experiments using real world datasets for regression tasks under an adversarial setting. We show numerically that solving our proposed convex program yields networks with lower objective values on the Lipschitz-regularized program compared to existing methods. Additionally, we show that on certain datasets, networks obtained using our convex training program are both more accurate and robust with respect to adversarial attacks.
Large Language Models (LLMs) have achieved strong performance across natural language processing tasks, yet reliable reasoning remains an open challenge. Although modern LLMs show progress in structured inference, multi-step problem solving, and contextual understanding, their reasoning behavior is often inconsistent and sensitive to prompting strategies, task design, and model scale. This survey provides a systematic analysis of more than 300 recent papers from arXiv, Semantic Scholar, Google Scholar, Papers with Code, and the ACL Anthology to examine how reasoning capabilities emerge in LLMs and where they fail. We make three main contributions. First, we introduce a structured taxonomy of LLM reasoning research, covering Chain-of-Thought reasoning, multi-hop reasoning, mathematical reasoning, common sense reasoning, visual and temporal reasoning, code and algorithmic reasoning, retrieval-augmented reasoning, tool-augmented and agentic reasoning, and reinforcement learning-based reasoning. Second, we analyze methodological trends across these paradigms, including prompting methods, model architectures, training objectives, reward modeling, and evaluation benchmarks. Third, we synthesize recurring limitations and failure modes, such as reasoning hallucinations, brittle multi-step inference, weak causal abstraction, and poor cross-domain generalization. By organizing a rapidly expanding literature, this survey offers a unified view of the current capabilities and limitations of reasoning in LLMs. We also identify emerging research directions, including meta-reasoning, self-evolving reasoning frameworks, multimodal reasoning, and socially grounded reasoning. Overall, this work aims to serve as a reference for developing more robust, interpretable, and generalizable reasoning systems in future language models.
Autoregressive video diffusion models enable streaming generation, opening the door to long-form synthesis, video world models, and interactive neural game engines. However, their core attention layers become a major bottleneck at inference time: as generation progresses, the KV cache grows, causing both increasing latency and escalating GPU memory, which in turn restricts usable temporal context and harms long-range consistency. In this work, we study redundancy in autoregressive video diffusion and identify three persistent sources: near-duplicate cached keys across frames, slowly evolving (largely semantic) queries/keys that make many attention computations redundant, and cross-attention over long prompts where only a small subset of tokens matters per frame. Building on these observations, we propose a unified, training-free attention framework (FAST-AR) for FAST-AutoRegressive diffusion, consisting of three components: TempCache compresses the KV cache via temporal correspondence to bound cache growth; AnnCA accelerates cross-attention by selecting frame-relevant prompt tokens using fast approximate nearest neighbor (ANN) matching; and AnnSA sparsifies self-attention by restricting each query to semantically matched keys, also using a lightweight ANN. Together, these modules reduce attention, compute, and memory and are compatible with existing autoregressive diffusion backbones and world models. Experiments demonstrate up to x5 - x10 end-to-end speedups while preserving near-identical visual quality and, crucially, maintaining stable throughput and nearly constant peak GPU memory usage over long rollouts, where prior methods progressively slow down and suffer from increasing memory usage.
On-policy distillation (OPD) improves student models by training them on trajectories induced by their own policy, making it a promising approach for mitigating exposure bias in agent training. However, most OPD studies focus on single-turn settings, while realistic LLM agents interact with environments over multiple turns. In this regime, early errors can alter future observations and compound across the trajectory, and standard dense token-level OPD becomes brittle, as it may over-penalize semantically valid alternatives, reinforce local degeneracies such as repeated actions, and propagate unreliable teacher supervision on off-distribution histories. We propose SAGE-OPD, a verifier-free selective intervention framework specifically designed for multi-turn OPD. Instead of applying teacher supervision uniformly across all turns, SAGE-OPD first observes environment feedback and uses teacher judgment to decide whether each student response should be skipped or intervened on. To further address compounding errors, SAGE-OPD weights token-level distillation by teacher confidence, reducing the influence of uncertain teacher distributions on corrupted or ambiguous histories. Finally, SAGE-OPD applies loss normalization to preserve the overall loss scale of standard OPD while retaining selective turn-level weighting. Experiments on agent tasks show that SAGE-OPD consistently improves over baselines, achieving up to a 13.3% relative improvement in ALFWorld unseen success rate over standard OPD. Ablation studies further demonstrate that turn-level intervention, teacher confidence weighting, and loss normalization provide complementary benefits. Our results suggest that effective multi-turn OPD should remain on-policy, but teacher supervision should be selectively allocated to turns where intervention is necessary and reliable.
A world model predicts environment dynamics based on current observations and actions, serving as a core cognitive mechanism for reasoning and planning. In this work, we investigate how world modeling based on language models can further push the boundaries of general agents. (i) We first focus on building foundation models for agentic environment simulation. We introduce Qwen-AgentWorld-35B-A3B and Qwen-AgentWorld-397B-A17B, the first language world models capable of simulating agentic environments covering 7 domains via long chain-of-thought reasoning. Leveraging more than 10M environment interaction trajectories of 7 domains in real-world environments, we develop Qwen-AgentWorld through a three-stage training pipeline: CPT injects general-purpose world modeling capabilities from the state transition dynamics and augmented professional corpora, SFT activates next-state-prediction reasoning, and RL sharpens simulation fidelity through a tailored framework with hybrid rubric-and-rule rewards. To evaluate language world models, we present AgentWorldBench, a comprehensive benchmark constructed from real-world interactions of 5 frontier models on 9 established benchmarks. Empirical results demonstrate that Qwen-AgentWorld significantly outperforms existing frontier models. (ii) Beyond foundation models, we further investigate two complementary paradigms through which world modeling enhances general agents. First, as a decoupled environment simulator, Qwen-AgentWorld supports scalable and controllable simulation of thousands of real-world environments for agentic RL, yielding gains that surpass real-environment training alone. Second, as a unified agent foundation model, world-model training acts as a highly effective warm-up that improves downstream performance across 7 agentic benchmarks. Code: https://github.com/QwenLM/Qwen-AgentWorld
arXiv:2605.00432v2 Announce Type: replace Abstract: Online conformal prediction must balance fast adaptation to distribution shift against stable coverage: feedback-driven methods react quickly but become volatile, while strongly discounted Bayesian methods lag and inflate intervals at tight coverage. We introduce State-Adaptive Bayesian Conformal Prediction (SA-BCP), which forms the predictive quantile as a gated convex combination of long-term temporal inertia and local spatial evidence from a kernel density estimate, controlled by a single interpretable evidence threshold $K$. We establish three results: (i) asymptotic marginal validity of the resulting intervals; (ii) a closed-form expression for the MSE-optimal threshold, $K^*_{\mathrm{MSE}}=\alpha(1-\alpha)/M^{\mathcal{T}}$, trading the coverage-indicator (Bernoulli) variance against the temporal structural bias $M^{\mathcal{T}}$; and (iii) a rolling-origin procedure for selecting $K$ online – consistent under stationarity, with $O(\sqrt{T\log N})$ regret against the best fixed $K$ and, for a segmented variant, a sublinear dynamic-regret bound under bounded drift. Across four financial-volatility and weather datasets, three target coverage levels, and eight baselines (including the strongest recent conditional-quantile methods, SPCI and KOWCPI), SA-BCP attains at-or-above-nominal coverage in most settings while producing substantially sharper intervals – up to roughly $3\times$ lower Winkler score than discounted Bayesian CP at the tightest coverage – and a coverage-matched audit confirms these efficiency gains are not an artifact of under-coverage. We disclose one principal limitation: a volatility-specialized conformal-GARCH competitor remains more efficient on its home volatility-base series, though it does not transfer across domains.
Although the beneficial effects of sodium–glucose cotransporter 2 (SGLT2) inhibition in heart failure (HF) have been well established, it is unknown whether SGLT2 inhibition confers benefit in carriers of rare variants in cardiomyopathy-associated genes. Here we evaluated whole-exome sequencing data from the randomized DECLARE-TIMI 58 trial, in which adults with type 2 diabetes and increased cardiovascular risk were randomized to dapagliflozin or placebo treatment. Pathogenic or likely pathogenic variants (P/LP) in high-confidence cardiomyopathy genes were identified, and treatment effects on hospitalization for HF (HHF) were compared between carriers of such variants and noncarriers. Among 12,685 patients for whom sequence data were obtained, 121 carried a cardiomyopathy variant (76 dilated cardiomyopathy, 25 hypertrophic cardiomyopathy and 25 arrhythmogenic cardiomyopathy). Over a median follow-up of 4.2 years, dapagliflozin lowered the risk of HHF more strongly in carriers (hazard ratio 0.18, 95% confidence interval 0.04–0.86) than in noncarriers (hazard ratio 0.70, 95% confidence interval 0.57–0.86; P interaction 0.03). Absolute risk reduction was 13.0% in carriers and 1.0% in noncarriers (P interaction 0.03). Most carriers (82%) had no prior HF, and in carriers without prior HF, treatment with dapagliflozin reduced the absolute risk of HHF by 12.8%, compared with a reduction of 0.6% in noncarriers (P interaction 0.01). The findings from this cohort of older and high-risk patients raise the possibility that SGLT2 inhibitor treatment should be started early to prevent HF in individuals who carry P/LP cardiomyopathy variants. These results need to be confirmed in a prospective, dedicated trial of preventive HF treatments in carriers of P/LP cardiomyopathy-associated variants. In a whole-exome sequencing analysis, the beneficial effects of the SGLT2 inhibitor dapagliflozin in reducing the risk of future heart failure hospitalization in individuals with type 2 diabetes were markedly greater in individuals who carried a cardiomyopathy-associated genetic variant compared with noncarriers, suggesting a personalized preventative therapy based on genetic information.
Mean opinion score (MOS) prediction models are widely used as proxy metrics in text-to-speech (TTS) research, yet their ability to capture quality differences beyond acoustic fidelity remains unclear. We investigate this via controlled perturbations on speech: acoustic degradation, prosodic errors, and manipulation of speaker-specific characteristics such as pitch and speaking rate. We obtained MOS predictions for these speech samples from both human listeners and the model, and analyzed the differences in their perceptual characteristics. Results show that most models track acoustic degradation well, while all are insensitive to prosodic errors despite large subjective score drops. For speaker characteristics, models exhibit a double dissociation: strong mean fundamental frequency (F0) biases absent in human ratings, yet insensitivity to speaking rate and F0 variability that humans notice. These findings highlight limitations of scalar MOS prediction beyond acoustic fidelity.
arXiv:2606.13733v1 Announce Type: cross Abstract: Multi-agent systems (MAS) were expected to overcome the limitation of single-agent systems (SAS) through collaboration. However, under typicality conditions on the task's constraint graph and bounded inter-agent communication, we prove that the success probability of a MAS is closely tied to the connectivity of task constraints, where each agent has limited information-processing capacity. Specifically, the success probability decays exponentially with an information bottleneck that emerges from partitioning the task's constraint graph among agents. We define this quantity as the minimum cut cost $C_{\min}$ of the potential constraint graph of each task. This information-theoretic bound applies to both open systems with external feedback and closed systems without. We validate our theory on both synthetic experiments and real-world empirical data from SWE-bench submissions. From our framework, effective MAS design should incorporate task-inherent constraints alongside engineering optimization, and when $\Cmin$ is high, practitioners should restructure tasks rather than simply scaling agents or communication.
This paper proposes a Linear Programming (LP)-based local search framework for fine-tuning pretrained transformer models with explicit control against overfitting. The approach formulates transformer fine-tuning as a bilevel optimization-based regularization problem, in which model parameters and regularization hyperparameters are jointly updated. Information collected during initial warm-up iterations, including validation gradients and training Hessian information, is used to construct a local descent direction by solving an LP that minimizes a scaled directional derivative while preserving training optimality. This validation-aware descent direction enables focused local updates of both parameters and regularization hyperparameters, reducing overfitting without requiring repeated full retraining cycles. The resulting method, termed Linear Programming-based Fine-Tuning (LiFT) for transformers, differs from conventional fine-tuning by systematically identifying task-specific updates rather than relying on heuristic or grid-based hyperparameter selection. Experiments on GPT-2 Small fine-tuned on WikiText-2 demonstrate that LiFT enables effective adaptation through selective tuning of transformer blocks and regularization parameters, yielding consistent improvements in test perplexity across multiple layer configurations and regularization settings, with particularly pronounced gains in overfitting-prone scenarios. Beyond empirical performance, LiFT establishes a principled connection between transformer fine-tuning, bilevel optimization, local search, and regularization theory.
As natural language corpora expand at an unprecedented rate, manual annotation remains a significant methodological bottleneck in corpus linguistic work. We address this challenge by presenting a scalable pipeline for automating grammatical annotation in voluminous corpora using large language models (LLMs). Unlike previous supervised and iterative approaches, our method employs a four-phase workflow: prompt engineering, pre-hoc evaluation, automated batch processing, and post-hoc validation. We demonstrate the pipeline's accessibility and effectiveness through a diachronic case study of variation in the English evaluative consider construction (consider X as/to be/{\O} Y). We annotate 143,933 'consider' concordance lines from the Corpus of Historical American English (COHA) via the OpenAI API in under 60 hours, achieving 98%+ accuracy on two sophisticated annotation procedures. A Bayesian multinomial GAM fitted to 44,527 true positives of the evaluative construction reveals previously undocumented genre-specific trajectories of change, enabling us to advance new hypotheses about the relationship between register formality and competing pressures of morphosyntactic reduction and enhancement. Our results suggest that LLMs can perform a range of data preparation tasks at scale with minimal human intervention, unlocking substantive research questions previously beyond practical reach, though implementation requires attention to costs, licensing, and other ethical considerations.
arXiv:2410.01492v3 Announce Type: replace-cross Abstract: The recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The purpose of this note is twofold. First, we introduce a $q$-deformed version of the Witten zeta function using the Chern-Simons theory at level $k$. We analyze the large $k$ limit of this function and show that it converges to an integer multiple of the classical Witten zeta function of $G$, where the integer multiple is precisely the order of the center of the group. This analysis provides an alternative way to compute the classical zeta functions, and we present some examples. Next, we study the quantum state associated with the $S^3$ complement of torus links of type $T_{p,p}$ and show that we can write the Rényi entropies at finite $k$ in terms of $q$-deformed Witten zeta functions. Using our first result, we obtain the $k \to \infty$ limit of the Rényi entropies and find that the entropies converge to finite values, which can be written in terms of the classical Witten zeta functions evaluated at positive integers. Since Witten zeta functions naturally appear in the symplectic volumes of moduli spaces of flat connections on Riemann surfaces, we give a geometric interpretation of the $k \to \infty$ limit of the Rényi and entanglement entropies in terms of these volumes. The results of this paper reveal an intriguing connection between topological entanglement, number-theoretic structures arising from Witten zeta functions, and the geometry of moduli spaces.
arXiv:2606.23838v1 Announce Type: new Abstract: When two or more parameters or labels produce similar data, they are degenerate, or hard to distinguish. Degeneracies render both label prediction and inverse problems difficult, since both machine learning algorithms and probabilistic samplers rely on the distinguishability of data and its gradients with respect to parameters. However, identifying degeneracies in physical models or real-world datasets can be elucidating about the choice of model or the underlying process that produces the data. We present the degeneracy distillery, a method that (1) detects and (2) resolves degenerate parameter combinations (a) automatically and (b) symbolically, from parameter-data (or parameter-simulation) pairs alone, through estimation and flattening of the Fisher information matrix. By exploring the information geometry of the likelihood, we characterize degeneracies as an intrinsic property of the physical model, requiring no realised data observation. We demonstrate our approach on a range of synthetic and real-world problems, discovering symbolic coordinate transformations that identify the combinations of parameters of a model which yield independent effects on the data. The resulting coordinates flatten the Fisher information in expectation globally, in contrast to posterior-based methods that flatten only at a single point, and substantially reduce the simulation budget required for downstream neural posterior estimation. In test cases we require up to $10\times$ fewer simulations for posterior estimation at matched validation calibration whilst simultaneously gaining physical insight on the system.
With the rapid advancement of large language models, evaluating human-likeness in open-ended conversation has become increasingly important. However, human-likeness is a form of tacit knowledge that humans perceive intuitively, yet the underlying criteria resist explicit formulation. Human judgments vary widely, with strong agreement on some cases and legitimate disagreement on others. Meanwhile, the criteria behind human judgments remain implicit, leaving no clear basis for constructing cases. Further, what counts as human-likeness is not static, but evolving with model capability and human expectations. Despite progress in evaluation methods such as expert-authored benchmarks, Reward Models, and self-evolving benchmarks, none addresses all three challenges simultaneously. Therefore, we propose GrowLoop, a self-evolving conversation evaluation system that continuously adapts as models advance and scenarios shift. Starting from minimal human seed annotations, LLM agents iteratively extract and refine evaluation rubrics through Heuristic Learning. Human-AI agreement is required where annotators converge, while only plausibility is expected where they diverge. Moreover, the Rubric-Case co-evolution mechanism enables continuous evolution. When the evaluation target shifts, new human seeds expand the system's coverage accordingly. When applied to human-likeness evaluation in open-ended conversation, the AI judge guided by these rubrics not only substantially outperforms existing methods in alignment with human judgments, but also uncovers issues that annotators overlook. The resulting benchmark effectively discriminates models across capability tiers and reveals where they fall short, while generalizing to new scenarios and adapting as models advance. Our work shifts the benchmarking paradigm from manual updates or difficulty scaling to comprehensive, continuous self-evolution.