Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning. Studies of the internal representations of Large Language Models (LLMs) support their ability to parse text when predicting the next word, while representing semantic notions independently of surface form. Yet, which data statistics make these feats possible, and how much data is required, remain largely unknown. Probabilistic context-free grammars (PCFGs) provide a tractable testbed for studying these questions. However, prior work has focused either on the post-hoc characterization of the parsing-like algorithms used by trained networks; or on the learnability of PCFGs with fixed syntax, where parsing is unnecessary. Here, we (i) introduce a tunable class of PCFGs in which both the degree of ambiguity and the correlation structure across scales can be controlled; (ii) provide a learning mechanism -- an inference algorithm inspired by the structure of deep convolutional networks -- that links learnability and sample complexity to specific language statistics; and (iii) validate our predictions empirically across deep convolutional and transformer-based architectures. Overall, we propose a unifying framework where correlations at different scales lift local ambiguities, enabling the emergence of hierarchical representations of the data.

Policy-gradient methods are widely used in reinforcement learning, yet training often becomes unstable or slows down as learning progresses. We study this phenomenon through the noise-to-signal ratio (NSR) of a policy-gradient estimator, defined as the estimator variance (noise) normalized by the squared norm of the true gradient (signal). Our main result is that, for (i) finite-horizon linear systems with Gaussian policies and linear state-feedback, and (ii) finite-horizon polynomial systems with Gaussian policies and polynomial feedback, the NSR of the REINFORCE estimator can be characterized exactly-either in closed form or via numerical moment-evaluation algorithms-without approximation. For general nonlinear dynamics and expressive policies (including neural policies), we further derive a general upper bound on the variance. These characterizations enable a direct examination of how NSR varies across policy parameters and how it evolves along optimization trajectories (e.g. SGD and Adam). Across a range of examples, we find that the NSR landscape is highly non-uniform and typically increases as the policy approaches an optimum; in some regimes it blows up, which can trigger training instability and policy collapse.

Effective e-commerce risk management requires in-depth case investigations to identify emerging fraud patterns in highly adversarial environments. However, manual investigation typically requires analyzing the associations and couplings among multi-source heterogeneous data, a labor-intensive process that limits efficiency. While Large Language Models (LLMs) show promise in automating these analyses, their deployment is hindered by the complexity of risk scenarios and the sparsity of long-tail domain knowledge. To address these challenges, we propose Sherlock, a framework that integrates structured domain knowledge with LLM-based reasoning through three core modules. First, we construct a domain Knowledge Base (KB) by distilling structured expertise from heterogeneous knowledge sources. Second, we design a two-stage retrieval-augmented generation strategy tailored for case investigation, which combines input contextual augmentation with a Reflect & Refine module to fully leverage the KB for improved analysis quality. Finally, we develop an integrated platform for operations and annotation to drive a self-evolving data flywheel. By combining real-time hotfixes through KB updates with periodic logic alignment via post-training, we facilitate continuous system evolution to counteract adversarial drifts. Online A/B tests at JD dot com demonstrate that Sherlock achieves an 82% Expert Acceptance Rate (EAR) and a 386.7% increase in daily investigation throughput. An additional 90-day evaluation shows that the flywheel successfully recovers from performance decay caused by changing tactics twice, raising the EAR ceiling by around 3.5% through autonomous model updates.

Structural modeling is a fundamental component of computational engineering science, in which even minor physical inconsistencies or specification violations may invalidate downstream simulations. The potential of large language models (LLMs) for automatic generation of modeling code has been demonstrated. However, non-executable or physically inconsistent outputs remain prevalent under stringent engineering constraints. A framework for physics-consistent automatic building modeling is therefore proposed, integrating domain knowledge construction, constraint-oriented model alignment, and verification-driven evaluation. CivilInstruct is introduced as a domain-specific dataset that formalizes structural engineering knowledge and constraint reasoning to enable simulation-ready model generation. A two-stage fine-tuning strategy is further employed to enforce constraint satisfaction and application programming interface compliance, substantially reducing hallucinated and non-conforming outputs. MBEval is presented as a verification-driven benchmark that evaluates executability and structural dynamics consistency through closed-loop validation. Experimental results show consistent improvements over baselines across rigorous verification metrics. Our code is available at https://github.com/Jovanqing/AutoBM.

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on sampling costs, stopping once sufficient consistency is reached. Although the exact posterior is computationally intractable, we further introduce an efficient "L-aggregated" stopping policy that tracks only the L-1 most frequent answer counts. Theoretically, we prove that L=3 is all you need: this coarse approximation is sufficient to achieve asymptotic optimality, and strictly dominates prior-free baselines, while having a fast posterior computation. Empirically, this identifies the most consistent (i.e., mode) LLM answer using fewer samples, and can achieve similar answer accuracy while cutting the number of LLM calls (i.e., saving on LLM inference costs) by up to 50%.

Kullback-Leibler (KL) divergence regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise regimes. Using a unified information-geometric framework, we introduce KL analogs by replacing the Fisher-Rao geometry in the dynamical formulation of the KL with transport-based geometries, and derive closed-form expressions for common distribution families. Between elliptic distributions, these divergences remain finite for degenerating equal covariances and yield a geometric interpretation of regularization heuristics used in Kalman ensemble methods. We demonstrate the utility of these divergences in KL-regularized optimal control. In the fully tractable setting of linear time-invariant systems with Gaussian process noise, the classical KL reduces to a quadratic control penalty that becomes singular as process noise vanishes. Our variants remove this singularity and yield well-posed problems. In both the double integrator and cart-pole examples, the resulting controls preserve nontrivial feedback and achieve better closed-loop performance.

Scaling Multimodal Large Language Models (MLLMs) to long-form speech is bottlenecked by the explosive growth of input tokens. Unlike images or videos, audio lacks overlapping information, making extreme 1-token compression highly susceptible to the loss of fine-grained acoustic cues. To overcome this, we propose FastSLM, a token-efficient architecture featuring the Hierarchical Temporal Abstractor (HTA). HTA progressively distills non-overlapping acoustic features across multiple temporal scales, achieving an extreme compression rate of 1.67 tokens per second a 97% reduction without losing critical context. Experimental results show that FastSLM achieves competitive performance with state-of-the-art models on long-form benchmarks despite operating with significantly fewer FLOPs and parameters. The source code and model checkpoints are available at https://anonymous.4open.science/r/FastSLM-8BD3.

We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate distributions $μ$ and $ν$ to a rank histogram on $\{ 0, \ldots, K\}$ and measure its deviation from uniformity via a discrete $f$-divergence, yielding a rank-statistic divergence estimator. We prove that the resulting estimator of the divergence is monotone in $K$, is always a lower bound of the true $f$-divergence, and we establish quantitative convergence rates for $K\to\infty$ under mild regularity of the quantile-domain density ratio. To handle high-dimensional data, we define the sliced rank-statistic $f$-divergence by averaging the univariate construction over random projections, and we provide convergence results for the sliced limit as well. We also derive finite-sample deviation bounds along with asymptotic normality results for the estimator. Finally, we empirically validate the approach by benchmarking against neural baselines and illustrating its use as a learning objective in generative modeling experiments.

As the role of modern Graphics Processing Units (GPUs) becomes increasingly essential for several computing tasks, analyzing their past and current progress is paramount for determining future constraints on scientific research. This is particularly compelling in the Artificial Intelligence (AI) domain, where rapid technological advancements and fierce global competition have led the United States to recently implement export control regulations limiting international access to advanced AI chips. Consequently, this paper examines technical progress in NVIDIA datacenter GPUs from the mid-2000s through 2025. Our main results identify doubling times of 1.43 and 1.67 years for FP16 and FP32 dense operations, while FP64 doubling times range from 2.05 to 3.79 years. Off-chip memory size and bandwidth have grown at slower rates than computing performance, doubling every 3.29 to 3.41 years, whereas the release prices and power consumption roughly doubled every 5.03 and 15 years, respectively. Moreover, our cross-vendor comparison of the top-performing GPUs per year shows that NVIDIA's performance advantage is narrowing, but not enough to compel a major market shift. Finally, we quantify the potential implications of current U.S. export control regulations and the consequent performance gaps, which the recently proposed policy changes could shrink from 23.6X to 3.54X.

We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator with data-driven clamping bounds, whose population risk matches the private minimax rate up to logarithmic factors. Using this estimator, we construct private test statistics that achieve the same asymptotic relative efficiency as the non-private, most powerful tests while maintaining conservative type I error control. In addition to our theoretical results, our numerical experiments show that our private tests outperform competing DP methods and offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.

Many materials properties depend on higher-order derivatives of the potential energy surface, yet machine learned interatomic potentials (MLIPs) trained with a standard loss on energy, force, and stress errors can exhibit error in curvature, degrading the prediction of vibrational properties. We introduce phonon fine-tuning (PFT), which directly supervises second-order force constants of materials by matching MLIP energy Hessians to DFT-computed force constants from finite displacement phonon calculations. To scale to large supercells, PFT stochastically samples Hessian columns and computes the loss with a single Hessian-vector product. We also use a simple co-training scheme to incorporate upstream data to mitigate catastrophic forgetting. On the MDR Phonon benchmark, PFT improves Nequix MP by 55% on average across phonon thermodynamic properties and achieves state-of-the-art accuracy among models trained on Materials Project trajectories. PFT also generalizes to improve properties beyond second-derivatives, improving thermal conductivity predictions that rely on third-order derivatives of the potential energy.

Kleinberg and Mullainathan recently proposed a formal framework for studying the phenomenon of language generation, called language generation in the limit. In this model, an adversary gives an enumeration of example strings from an unknown target language, and the algorithm is tasked with correctly generating unseen strings from the target language within finite time. Refined notions of non-uniform and uniform generation were later introduced by Li, Raman, and Tewari (2025), and a noisy model was introduced by Raman and Raman (2025), which allows the adversary to insert extraneous strings. A natural question in the noisy model is to quantify the effect of noise, by studying the impact of each additional extraneous string. We show two complementary results in this setting. We first show that for both uniform and non-uniform generation, a single noisy string strictly reduces the set of collections that can be generated, thus answering an open question in Raman and Raman (2025). Then, we show for both uniform and non-uniform generation that generation with a single noisy string is equivalent to generation with any finite amount of noise, sharply contrasting with the strict hierarchy for noisy generation in the limit shown by Bai, Panigrahi, and Zhang (2026). Finally, we leverage our previous results to provide the first known characterization for non-uniform noise-dependent generatability.

ECG-Language Models (ELMs) extend recent advances in Multimodal Large Language Models (MLLMs) to automated ECG interpretation. However, most existing ELMs inherit Vision-Language Model (VLM) design choices and rely on pretrained ECG encoders, introducing substantial architectural and training complexity. Inspired by encoder-free VLMs, we introduce ELF, a family of three encoder-free ELM architectures that remain competitive with, and often outperform, prior state-of-the-art ELMs across two datasets despite substantially simpler architectures and training pipelines. All code and data is available at github.com/ELM-Research/ECG-Language-Models.

Large Language Models remain vulnerable to adversarial prompts that elicit toxic content even after safety alignment. We present ToxSearch, a black-box evolutionary framework that tests model safety by evolving prompts in a synchronous steady-state loop. The system employs a diverse set of operators, including lexical substitutions, negation, back-translation, paraphrasing, and two semantic crossover operators, while a moderation oracle provides fitness guidance. Operator-level analysis shows heterogeneous behavior: lexical substitutions offer the best yield-variance trade-off, semantic-similarity crossover acts as a precise low-throughput inserter, and global rewrites exhibit high variance with elevated refusal costs. Using elite prompts evolved on LLaMA 3.1 8B, we observe practically meaningful but attenuated cross-model transfer, with toxicity roughly halving on most targets, smaller LLaMA 3.2 variants showing the strongest resistance, and some cross-architecture models retaining higher toxicity. These results suggest that small, controllable perturbations are effective vehicles for systematic red-teaming and that defenses should anticipate cross-model reuse of adversarial prompts rather than focusing only on single-model hardening.

Vision-Language-Action (VLA) models are increasingly deployed in safety-critical robotic applications, yet their security vulnerabilities remain underexplored. We identify a fundamental security flaw in modern VLA systems: the combination of action chunking and delta pose representations creates an intra-chunk visual open-loop. This mechanism forces the robot to execute K-step action sequences, allowing per-step perturbations to accumulate through integration. We propose SILENTDRIFT, a stealthy black-box backdoor attack exploiting this vulnerability. Our method employs the Smootherstep function to construct perturbations with guaranteed C2 continuity, ensuring zero velocity and acceleration at trajectory boundaries to satisfy strict kinematic consistency constraints. Furthermore, our keyframe attack strategy selectively poisons only the critical approach phase, maximizing impact while minimizing trigger exposure. The resulting poisoned trajectories are visually indistinguishable from successful demonstrations. Evaluated on the LIBERO, SILENTDRIFT achieves a 93.2% Attack Success Rate with a poisoning rate under 2%, while maintaining a 95.3% Clean Task Success Rate.

Materials synthesis procedures are predominantly documented as narrative text in papers, protocols, and laboratory records, placing them beyond the reach of conventional data-driven optimization frameworks. This language-native character poses a particular challenge for complex, multistage processes such as the preparation of boron nitride nanosheets (BNNS), where outcomes depend on path-dependent choices in exfoliation, functionalization, and functionalization. Here, we recast synthesis planning of the materials as a text reasoning problem enabled by a lightly structured knowledge substrate that preserves the procedural logic and causal contexts while exposing computable elements for retrieval. Built on this representation, our framework combines semantic matching, lexical search, and parameter-aware filtering to support retrieval-augmented generation with more accurate and better-grounded synthesis guidance. We further introduce experience-augmented reasoning, in which iteratively refined text guides distilled from multi-source narratives support hypothesis generation, failure diagnosis, and protocol revision. We validated the framework in the targeted exfoliation of BNNS, a synthesis problem governed by multivariate constraints and limited transferability of literature protocols across laboratory settings. By integrating dispersed literature evidence with experimentally observed failure modes, the system converged within only three iterative rounds on a high-performing protocol that yielded high-quality ultrathin nanosheets meeting the target specifications, substantially shortening what is often a prolonged cycle of expert-led trial-and-error. By enabling language-native reasoning over procedural knowledge, this framework moves AI beyond literature assistance toward active synthesis planning, adaptation and acceleration in complex materials workflows.

We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order methods for min-max optimization is relatively limited, as obtaining global rates of convergence with second-order information can be much more involved. In this paper, we examine how second-order information is used to speed up extra-gradient methods, even under inexactness. In particular, we show that the proposed methods generate iterates that remain within a bounded set and that the averaged iterates converge to an $ε$-saddle point within $O(ε^{-2/3})$ iterations in terms of a restricted gap function. We also provide a simple routine for solving the subproblem at each iteration, requiring a single Schur decomposition and $O(\log\log(1/ε))$ calls to a linear system solver in a quasi-upper-triangular system. Thus, our method improves the existing line-search-based second-order min-max optimization methods by shaving off an $O(\log\log(1/ε))$ factor in the required number of Schur decompositions. Finally, we evaluate our method on both synthetic benchmarks and a real-world application arising from AUC maximization on standard LIBSVM datasets, and find that the proposed second-order approach delivers stronger practical efficiency than representative first-order methods on these problems.

Early diagnosis of attention-deficit/hyperactivity disorder (ADHD) in children plays a crucial role in improving outcomes in education and mental health. Diagnosing ADHD using neuroimaging data, however, remains challenging due to heterogeneous presentations and overlapping symptoms with other conditions. To address this, we propose a novel parameter-efficient transfer learning approach that adapts a large-scale 3D convolutional foundation model, pre-trained on CT images, to an MRI-based ADHD classification task. Our method introduces Low-Rank Adaptation (LoRA) in 3D by factorizing 3D convolutional kernels into 2D low-rank updates, dramatically reducing trainable parameters while achieving superior performance. In a five-fold cross-validated evaluation on a public diffusion MRI database, our 3D LoRA fine-tuning strategy achieved state-of-the-art results, with one model variant reaching 71.9% accuracy and another attaining an AUC of 0.716. Both variants use only 1.64 million trainable parameters (over 113x fewer than a fully fine-tuned foundation model). Our results represent one of the first successful cross-modal (CT-to-MRI) adaptations of a foundation model in neuroimaging, establishing a new benchmark for ADHD classification while greatly improving efficiency.

In recurrent neural networks (RNNs) used to model biological neural networks, noise is typically introduced during training to emulate biological variability and regularize learning. The expectation is that removing the noise at test time should preserve or improve performance. Contrary to this intuition, we find that continuous-time RNNs (CTRNNs) often perform best at or near the training noise level. This noise preference typically arises when noise is injected inside the neural activation function; networks trained with noise injected outside the activation function perform best with zero noise. The phenomenon arises robustly in diverse tasks for large enough training noise; we also show the phenomenon arising in feedforward neural networks, not just in RNNs. Our analyses show that the phenomenon stems from noise-induced shifts of fixed points (stationary distributions) in the underlying stochastic dynamics of the RNNs. These fixed point shifts are noise-level dependent and bias the network outputs when the noise is removed, degrading performance. Analytical and numerical results show that the bias arises when neural states operate near activation-function nonlinearities, where noise is asymmetrically attenuated, and that performance optimization incentivizes operation near these nonlinearities; such performance incentives exist for networks with noise inside, but not outside, the activation function, explaining why only noise-in networks show the preference. Thus, networks can overfit to the training noise itself rather than just to the input-output data. The phenomenon is distinct from stochastic resonance, wherein nonzero noise enhances signal processing. Our findings reveal that training noise can become an integral part of the computation learned by neural networks, with implications for understanding neural population dynamics and for the design of robust artificial RNNs.

In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs, SIAM J. Sci. Comput., 47(2), C501-C528, 2025. FEONet realizes the parameter-to-solution map on a finite element space and admits a training procedure that does not require training data, while exhibiting high accuracy and robustness across a broad class of problems. However, its computational cost increases and accuracy may deteriorate as the number of elements grows, posing notable challenges for large-scale problems. In this paper, we propose a new sparse network architecture motivated by the structure of the finite elements to address this issue. Throughout extensive numerical experiments, we show that the proposed sparse network achieves substantial improvements in computational cost and efficiency while maintaining comparable accuracy. We also establish theoretical results demonstrating that the sparse architecture can approximate the target operator effectively and provide a stability analysis ensuring reliable training and prediction.

Timing and burst patterns can leak through encryption, and an adaptive adversary can exploit them. This undermines metadata-only detection in a stand-alone consumer gateway. Therefore, consumer gateways need streaming intrusion detection on encrypted traffic using metadata only, under tight CPU and latency budgets. We present a streaming IDS for stand-alone gateways that instantiates a lightweight two-state unit derived from Network-Optimised Spiking (NOS) dynamics per flow, named \emph{NOS-Gate}. NOS-Gate scores fixed-length windows of metadata features and, under a $K$-of-$M$ persistence rule, triggers a reversible mitigation that temporarily reduces the flow's weight under weighted fair queueing (WFQ). We evaluate NOS-Gate under timing-controlled evasion using an executable \emph{worlds} benchmark that specifies benign device processes, auditable attacker budgets, contention structure, and packet-level WFQ replay to quantify queue impact. All methods are calibrated label-free via burn-in quantile thresholding. Across multiple reproducible worlds and malicious episodes, at an achieved $0.1\%$ false-positive operating point, NOS-Gate attains 0.952 incident recall versus 0.857 for the best baseline in these runs. Under gating, it reduces p99.9 queueing delay and p99.9 collateral delay with a mean scoring cost of $\approx 2.09\,μ\mathrm{s}$ per flow-window on CPU.

Natural Language Processing (NLP) systems are increasingly used in sensitive domains such as healthcare, finance, and government, where they handle large volumes of personal and regulated data. However, these systems introduce distinct risks related to security, privacy, and regulatory compliance that are not fully addressed by existing AI governance frameworks. This paper introduces the Secure and Compliant NLP Lifecycle Management Framework (SC-NLP-LMF), a comprehensive six-phase model designed to ensure the secure operation of NLP systems from development to retirement. The framework, developed through a systematic PRISMA-based review of 45 peer-reviewed and regulatory sources, aligns with leading standards, including NIST AI RMF, ISO/IEC 42001:2023, the EU AI Act, and MITRE ATLAS. It integrates established methods for bias detection, privacy protection (differential privacy, federated learning), secure deployment, explainability, and secure model decommissioning. A healthcare case study illustrates how SC-NLP-LMF detects emerging terminology drift (e.g., COVID-related language) and guides compliant model updates. The framework offers organizations a practical, lifecycle-wide structure for developing, deploying, and maintaining secure and accountable NLP systems in high-risk environments.

Securing Agentic Artificial Intelligence (AI) systems requires addressing the complex cyber risks introduced by autonomous, decision-making, and adaptive behaviors. Agentic AI systems are increasingly deployed across industries, organizations, and critical sectors such as cybersecurity, finance, and healthcare. However, their autonomy introduces unique security challenges, including unauthorized actions, adversarial manipulation, and dynamic environmental interactions. Existing AI security frameworks do not adequately address these challenges or the unique nuances of agentic AI. This research develops a lifecycle-aware security framework specifically designed for agentic AI systems using the Design Science Research (DSR) methodology. The paper introduces MAAIS, an agentic security framework, and the agentic AI CIAA (Confidentiality, Integrity, Availability, and Accountability) concept. MAAIS integrates multiple defense layers to maintain CIAA across the AI lifecycle. Framework validation is conducted by mapping with the established MITRE ATLAS (Adversarial Threat Landscape for Artificial-Intelligence Systems) AI tactics. The study contributes a structured, standardized, and framework-based approach for the secure deployment and governance of agentic AI in enterprise environments. This framework is intended for enterprise CISOs, security, AI platform, and engineering teams and offers a detailed step-by-step approach to securing agentic AI workloads.

The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training. However, extensions of this approach to non-smooth settings remain in their early stages, often relying on interpolation assumptions or requiring knowledge of the optimal solution. In this work, we propose a novel SPS variant, Safeguarded SPS (SPS$_{safe}$), for the stochastic subgradient method, and provide rigorous convergence guarantees for non-smooth convex optimization with no need for strong assumptions. We further incorporate momentum into the update rule, yielding equally tight theoretical results. Comprehensive experiments on convex benchmarks and deep neural networks corroborate our theory: the proposed step size achieves competitive performance to existing adaptive baselines and exhibits stable behavior across a wide range of problem settings. Finally, in the context of deep neural network training, the gradient norms under our step size do not collapse to (near) zero, indicating robustness to vanishing gradients.

Even LLMs that appear safe during evaluation can still produce harmful responses in deployment. Because stochastic sampling yields different responses to the same prompt, low-probability harmful outputs can still reach users at scale. Common human evaluation workflows generate many random samples per prompt and review them in static spreadsheets. The practice scales poorly, forcing evaluators to repeatedly reread near-duplicate prefixes. To address this, we present InFerActive, an interactive system that visualizes sampling results as a navigable tree of readable phrases, allowing evaluators to filter, explore, and extend the generation space on demand. InFerActive utilizes breadth-first sampling, a novel tree construction procedure that matches the harmful-response coverage of random sampling while requiring up to 5.0x fewer samples. Two controlled user studies (N = 12 each) demonstrate that InFerActive significantly improves evaluation efficiency and coverage over both spreadsheet and basic tree baselines.

Variational inference (VI) approximates a target density $p$ by the best match $q$ in a family of tractable distributions. The best variational approximation is found by minimizing a divergence between distributions, $D(p||q)$, and several divergences have been proposed as objective functions for VI, with different choices leading to different approximations. We show that even when these divergences have different minimizers, the resulting approximations all abide by certain symmetry-matching principles. Specifically, our results hold for all $f$-divergences, a broad class which includes the reverse and forward Kullback-Leibler divergences and the $α$-divergences. We show that in the presence of even symmetry, any stationary point of an $f$-divergence is guaranteed to recover the mean of $p$ and likewise, in the presence of elliptical symmetry, any stationary point is guaranteed to recover its correlation matrix. To obtain these guarantees we assume that $p$ and $q$ are unimodal, but notably we do not require them to be log-concave, light-tailed, or even everywhere-smooth. These guarantees generalize a previous result obtained for the reverse Kullback-Leibler divergence when $p$ is log-concave. They also extend to cases where the target density $p$ only exhibits symmetry along some but not all of its coordinates. These partial symmetries arise naturally in Bayesian hierarchical models, where the prior induces a challenging geometry but still possesses axes of symmetry.

Detecting the anomalies of web applications, important infrastructures for running modern companies and governments, is crucial for providing reliable web services. Many modern web applications operate on web APIs (e.g., RESTful, SOAP, and WebSockets), their exposure invites intended attacks or unintended illegal visits, causing abnormal system behaviors. However, such anomalies can share very similar logs with normal logs, missing crucial information (which could be in database) for log discrimination. Further, log instances can be also noisy, which can further mislead the state-of-the-art log learning solutions to learn spurious correlation, resulting superficial models and rules for anomaly detection. In this work, we propose MINES which infers explainable API invariants for anomaly detection from the schema level instead of detailed raw log instances, which can (1) significantly discriminate noise in logs to identify precise normalities and (2) detect abnormal behaviors beyond the instrumented logs. Technically, MINES (1) converts API signatures into table schema to enhance the original database shema; and (2) infers the potential database constraints on the enhanced database schema to capture the potential relationships between APIs and database tables. MINES uses LLM for extracting potential relationship based on two given table structures; and use normal log instances to reject and accept LLM-generated invariants. Finally, MINES translates the inferred constraints into invariants to generate Python code for verifying the runtime logs. We extensively evaluate MINES on web-tamper attacks on the benchmarks of TrainTicket, NiceFish, Gitea, Mastodon, and NextCloud against baselines such as LogRobust, LogFormer, and WebNorm. The results show that MINES achieves high recall for the anomalies while introducing almost zero false positives, indicating a new state-of-the-art.

Reichel (2025) defined the bariance as a pairwise-difference measure that can be rewritten in linear time using only scalar sums. We extend this idea to the covariance matrix by showing that the standard matrix expression involving the uncentered Gram matrix and a correction term is algebraically identical to the pairwise-difference definition while avoiding explicit centering. The computation then reduces to one outer product of dimension p-by-p and a single subtraction. Benchmarks in Python show clear runtime gains, especially when BLAS optimizations are absent. Optionally faster Gram-matrix routines such as RXTX (Rybin et al., 2025) further reduce overall cost.

Selecting an effective docking algorithm is highly context-dependent, and no single method performs reliably across structural, chemical, and protocol regimes. MolAS is a lightweight algorithm-selection model that predicts per-algorithm performance from pretrained protein and ligand embeddings using attentional pooling and a shallow residual decoder. With hundreds to a few thousand labelled complexes, MolAS achieves up to a 15 percentage-point absolute improvement over the single-best solver (SBS) and closes 17--66\% of the Virtual Best Solver (VBS)--SBS gap across five docking benchmarks. Analyses of selection frequencies, margin-conditioned reliability, and benchmark-level oracle structure indicate that MolAS is most effective when the workflow-defined oracle landscape has low winner entropy and a reasonably separable top-solver region, but degrades under protocol mismatch that shifts solver rankings and changes the induced labels. These results suggest that, in the evaluated regime, robustness is limited less by representational capacity than by workflow- and protocol-induced instability in solver hierarchies, positioning MolAS as an in-domain selector for fixed pipelines and as a diagnostic tool for assessing when docking algorithm selection is well-posed.

We introduce a framework for simulating macroeconomic expectations in survey experiments using LLM-based economic agents (LLM Agents). We construct LLM Agents equipped with several functional modules that retrieve personal characteristics, prior expectations, and dynamic external information. We validate our framework by recapitulating three representative survey designs covering various expectations across different types of respondents. Our results show that LLM Agents generate expectation distributions highly similar to human data and capture human-aligned qualitative patterns in open-ended responses. Evaluation reveals that priors are crucial for matching distributions, whereas personal and external information drive human-like thought processes. Our findings offer guidance for narrowing the belief gap between generative AI and humans at the aggregate level while delineating the boundaries of the framework.