Papers

How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank. We show that both quantities can change under an information-preserving invertible reparameterization, so neither is intrinsically a concept dimension. We distinguish model-defined population quantities (generating dimension, sufficient linear dimension, and minimum guarding rank) from procedure-defined quantities such as stopping count and cumulative edit rank. In a population Gaussian construction, an invertible shear preserves the prediction problem and all three quantities, yet changes the cumulative Euclidean erasure count from one to two. The separation holds for Moore–Penrose ordinary least squares and every finite nonnegative ridge weight. For a two-output full-QR procedure matching our motivating video analysis, cumulative edit rank similarly changes from two to the ambient dimension four. Conversely, the complete cumulative metric-QR trajectory is affine-equivariant when its positive-definite metric, probe, regularizer, and tie-breaking are transported consistently; exact covariance is one corollary, not a canonical semantic metric. In a known-rank finite-sample Adam/QR calibration, identity mixing stops after one accepted update in all 20 large-sample runs, whereas each tested shear $a\in\{.5,.75,1,1.25,2\}$ accepts at least two updates in all 20 runs. Controlled reparameterizations of frozen V-JEPA2 features preserve rank-zero predictions yet alter later Euclidean trajectories under practical optimization. These visual contact experiments are stress tests, not estimates of contact dimension. Iterative erasure therefore returns a procedure-relative estimand jointly determined by representation geometry and the full measurement procedure, not a semantic dimension by itself.

Not all clicks are equal. Industrial ads ranking decouples conversion probability into click-through rate (CTR) and post-click conversion rate (CVR), yet treats every click as the same event. In reality, users provide a free, self-generated signal of intent through their physical UI interactions. Different click types on the same ad exhibit a 4-fold difference in actual conversion rates. By conflating these signals, the standard CVR model under-predicts high-intent clicks and over-predicts low-intent ones, which is a bias masked by near-perfect aggregate calibration. We propose MARCO (Multi-intent Ads Ranking Composition Optimization), a framework that resolves this bias by decomposing each click by intent. Using the logged click type as a free behavioral label, MARCO trains per-intent CVR heads on homogeneous populations, and at serving time composes their per-intent CVR estimates under a predicted distribution over intents. Theoretically, we prove that decomposition never raises population risk, give the exact headroom under squared loss and non-negativity under the deployed loss, and show through a routing-efficiency dial how much of it reaches serving. Because the population-optimal score is unchanged, any gain is a finite-capacity estimation and calibration effect that we validated both offline and online. For deployment at scale, we further cast multi-impression, multi-click attribution as credit assignment with a bias-variance tradeoff analogous to RL return estimation, showing last-impression, first-click attribution is the low-bias, low-variance, deterministic choice under production constraints, and derive three consistency conditions enforced end-to-end at scale. Deployed at binary intent granularity, MARCO corrects per-intent calibration to approximately 100%, lifts conversions per click by +2.80%, and drives +0.98% cumulative improvement in topline metrics.

Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval–Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.

Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.

Sparse autoencoders (SAEs) have helped uncover mechanistic explanations for LLM behaviours such as reasoning, jailbreaking etc., via understanding the corresponding task-relevant and causally effective features. To evaluate such mechanistic explanations, downstream studies must distinguish surface lexical features from genuinely high-level ones. However, neither an autointerp-based semantic description nor causal steering utility fully resolves the abstraction level of a feature. To this end, we introduce Feature Nonlocality (FNL), defined as the entropy of the normalized per-position influence on an SAE feature's activation. We report that FNL correlates with existing LLM-based proxy metrics of feature semantic abstractness, and successfully distinguishes context-dependent reasoning features from token-driven ones, correctly assigning the higher FNL to the contextual feature in $73$–$84\%$ of randomly drawn pairs that consist of one contextual and one token-level feature. We demonstrate two downstream applications. We audit SAE-based features used for jailbreak mitigation and find surprisingly that most effective features are positional features with low FNL rather than genuinely recognizing harmful intents. We report that steering high-FNL features in DeepSeek-R1-Distill-Llama-8B improves MATH-500 accuracy by $4.6$ points over the unsteered model and outperforms steering low-FNL features, though the gains are model-specific. We conclude that FNL provides an LLM-independent, label-free, correlational witness of the abstraction level of an SAE feature, with applications in evaluating mechanistic explanations as well as selecting features for downstream interventions.

Static load balancers cannot mitigate a backend that is degraded rather than down: round-robin and least-connections keep routing traffic to a server returning HTTP 500s until an operator intervenes. We ask whether a Large Language Model can replace the static routing policy itself, reading HAProxy and Prometheus telemetry every 10 seconds and isolating faulty servers through guardrailed calls to the HAProxy Data Plane API. On a reproducible benchmark with a persistent structural fault built into roughly one-third of a heterogeneous fleet, we sweep 15 open-weight models across five families (0.35B to 35B total parameters; dense, mixture-of-experts, and efficient-sparse architectures), reasoning modes, fleet scales of 3 to 9 backends, and two routing algorithms, totaling 240 runs. We find a capability threshold near 3B active parameters. Below it, LLM policies are typically unreliable and sometimes worse than no policy; above it, every model, regardless of architecture, saturates near an 88% reduction in client-perceived 5xx errors over the static baseline. The threshold is approximate: Gemma 4 E2B clears it with 2B active parameters, while the dense 3B Granite 4.0 Micro does not. The availability gain has costs. Draining concentrates load onto surviving servers, inflating tail latency 2.6 to 2.8 times, and enabling reasoning multiplies token spend roughly tenfold, overrunning the control interval and degrading effectiveness. The efficient operating point is a supra-threshold model in its cheapest non-reasoning mode, wrapped inside deterministic guardrails.

The multi-armed bandit problem is a central framework in sequential decision-making, extensively studied under sub-Gaussian reward assumptions. However, real-world applications often involve heavy-tailed reward distributions and decentralized, information-asymmetric interactions. We study multi-agent multi-armed bandits with heavy-tailed rewards under three information-asymmetry regimes: unobserved actions with common rewards, observed actions with independent rewards, and unobserved actions with independent rewards. We develop robust decentralized algorithms for each setting and derive regret guarantees that nearly match centralized heavy-tailed rates. Experiments on a Pareto-distributed reward environment validate our theoretical findings and illustrate the trade-offs between synchronization, coordination, and exploration across the three regimes.

Anchor-based pointwise LLM reranking scores each candidate against a shared reference passage to recover cross-document context at pointwise cost. We study when this actually helps, using GCCP/PAGC as a representative method. Our study is reproduction-first. We use reproduction as a starting point for a controlled component-level stress test of anchor-based pointwise reranking. Our initial reimplementation, based only on the paper text, achieves 0.24 nDCG@10 instead of the reported 0.66, revealing that several undocumented implementation details are necessary to reproduce the method. After identifying and recovering eight such details, we reproduce the reported results within 1.6% and use the validated implementation for controlled analysis. We find that the core contrastive scoring idea is robust under rigorous statistical correction. However, two design choices held fixed in the original paper are less reliable. First, we find that combining the contrastive score with the standard pointwise relevance score helps when the first-stage retriever is BM25, but gives little or no benefit when the first-stage retriever is a stronger dense model such as E5. Second, the paper's more complex method for constructing the anchor is unnecessary. A much simpler anchor, built by interleaving the top-ranked sentences, matches or outperforms it across datasets. These findings are consistent across different LLM backbones, including a 4-bit quantized 72B model. Overall, anchor-based pointwise reranking is effective, but its gains come mainly from contrastive scoring rather than from the more complex aggregation and anchor-construction choices, and they appear under narrower conditions than the original evaluation suggests.

Motivated by decentralized applications, we study cooperative multi-agent bandits in continuous (Lipschitz) action spaces when the Lipschitz constant is unknown. We consider three information structures: (A)~unobserved actions with common rewards, (B)~observed actions with independent rewards, and (C)~unobserved actions with independent rewards. In each case we design and analyze an algorithm that estimates the Lipschitz constant, chooses a discretization of the joint action space, and applies a cooperative bandit method to the induced discrete problem. Players never communicate once learning starts, so the central difficulty is that they must reach the same discretization from their own data. We prove regret guarantees showing that common rewards and observable actions each supply this agreement for free, and that in their absence agreement can still be bought, through a dithered quantization of the estimate, at no cost in the leading order of the regret.

Accurate physical-layer modeling is increasingly essential for reliable ultra-wideband operation and capacity optimization, especially under the intensified inter-channel stimulated Raman scattering (ISRS) effect. This paper proposes the link-adaptive digital twin (LA-DT) for hybrid-amplified ultra-wideband links to overcome the generalization and speed limitations of existing methods, achieving accurate modeling and robust generalized signal-to-noise ratio (GSNR) estimation across diverse links. First, to address EDFA heterogeneity, the GSNR modeling task is decomposed into three key power predictions: ASE, NLI, and signal powers before EDFA entry. Second, to enhance cross-scenario generalization, three dedicated DT models are developed using a novel neural architecture with linear modulation layers (LMLs). Third, for rapid adaptation to unseen scenarios with limited data, three domain discriminators guide few-shot fine-tuning of the LMLs. Fourth, the LA-DT explicitly accounts for Raman amplifier (RA) insertion loss, improving practical deployment reliability. Results across 35 scenarios show that LA-DT reduces RMSE for NLI, ASE, and signal power predictions to 0.151, 0.111, and 0.113 dBm with improvements of 56.0%, 58.4%, and 52.7% over the baseline,and achieves an average GSNR estimation RMSE of 0.114 dBm (55.8% improvement). For 12 unseen scenarios, the LA-DT maintains high accuracy through few-shot fine-tuning with only 20 samples per scenario, achieving an average GSNR RMSE of 0.159 dB and demonstrating strong adaptability and robustness.

Accurate pre-deployment estimation of CNN inference cost–energy, latency, and peak memory–is increasingly critical as models are deployed on resource-constrained GPU platforms. Existing approaches rely on FLOPs, latency measurements, or single-device profiling as energy proxies, overlooking the non-linear interactions between architectural design and hardware load. We present a workload characterization study of 13 419 CNN configurations on two GPU platforms (RTX 5090 and RTX 3080) under GPU telemetry, revealing that energy, latency, and memory exhibit fundamentally distinct scaling behaviors: energy and latency diverge by 3x under high computational demand, and cross-GPU transferability differs by target–energy and latency require platform-specific models while memory transfers well across the two tested platforms. Building on these characterization findings, we develop CARB, a cascade-blended ensemble that jointly predicts all three targets with R2 ~0.99, and a two-stage deployment screening workflow that eliminates over 90% of candidates in seconds, reducing large design spaces to a Pareto-prioritized shortlist validated against real hardware.

Personalized Federated Reinforcement Learning (PFRL) takes a decentralized approach to storing and accessing information based on past experiences while keeping each client's data private during the learning of each client's policy. Many current methods for PFRL rely heavily on exploiting existing reinforcement learning reward signals to derive an optimal policy for each client, thereby neglecting exploration in non-stationary or sparse-reward environments. In this work, we introduce a new exploration-driven framework, Exploration-Driven Personalized Federated Reinforcement Learning via Intrinsic Motivation (EDPFRL-IM), that leverages an inherent curiosity-driven exploration at each client to promote local exploration and protect client privacy. Furthermore, to facilitate policy discovery via exploration in previously unexplored state spaces, clients add an intrinsic random network distillation (RND) signal to their extrinsic reward. Additionally, the server does not have access to clients' raw experiences or local gradient estimates; instead, the server sends global exploration priors and collects minimal novelty summaries from each client to enable both diverse and coordinated exploration among clients. Experiments in benchmark environments show that our framework outperforms average PFRL benchmarks in policy personalization and sample efficiency, primarily in delayed and sparse reward systems. Overall, EDPFRL-IM enables the integration of a flexible exploratory learning structure into federated reinforcement learning systems while preserving client privacy.

Large language models (LLMs) are widely applied across chemical tasks, such as molecular property prediction, which underpins drug discovery. Molecular LLMs represent a molecule through several modalities, notably a 1D SMILES sequence or a 2D molecular graph. Both encode molecular information implicitly, so the contribution of individual substructures remains opaque. Retrieval and augmentation methods add context, but from external sources. However, the cues chemists reason over are the internal substructures that drive a property up or down. We propose MR-MoL, a multi-granular rationale-guided molecular LLM that supplies this evidence directly. A fine-tuned GNN scores each substructure through masking, and the most influential ones are serialized as a ranked, direction-tagged rationale that the LLM reads alongside the SMILES sequence and molecular graph. The rationale spans three levels of granularity: Murcko scaffolds with their side chains, BRICS fragments, and functional groups. This is, to our knowledge, the first method to expose GNN-derived attributions to an LLM as evidence for property prediction. On eight MoleculeNet tasks, MR-MoL achieves the best overall results among generalist models and narrows the gap to specialist models tuned for each task. Five diagnostics further confirm that the model reads the rationale rather than merely benefiting from its presence. Its direction, rank, and substructure each shape the prediction, and its attributions reproduce known structure-property relationships.

Popularity bias in recommendation systems arises when a majority user class generates disproportionate interaction data, causing the system to increasingly favour it while degrading recommendation quality for niche users. While extensive empirical evidence of popularity bias exists, the dynamics leading to its emergence are not well understood. In this work, we study the coupled evolution of recommender model updates and user engagement through the lens of dynamical systems. We formulate a stochastic process and analyse its asymptotic behaviour through an ordinary differential equation (ODE) framework grounded in two-time-scale stochastic approximation. We characterise the equilibrium points of this dynamical system, and derive conditions under which popularity bias is provably emergent, as well as conditions under which symmetric retention of all user classes is possible. We conduct experiments on synthetic data and real-world production logs derived from a large-scale commercial music recommendation platform to validate our theoretical results.

Offline-to-online (O2O) reinforcement learning aims to leverage policies pretrained on static datasets while improving them through online interaction. However, directly reusing an offline-trained critic can hinder online fine-tuning: as the policy and data distribution change rapidly, value estimates inherited from offline training may become misaligned with the online environment, leading to inaccurate policy improvement and inefficient exploration. To address this problem, we introduce Critic-Free Pretraining: an efficient paradigm that completely abandons the approach of offline critic training, allowing a freshly initialized critic to adapt without inheriting biased estimates. CFP is compatible with various mainstream O2O algorithms and consistently matches or improves upon conventional O2O algorithms across a diverse set of tasks, with particularly pronounced gains on several challenging tasks.

Fair representation learning with a continuous sensitive attribute $S$ requires a representation $Z$ that is statistically independent of $S$. Existing criteria, including generalized demographic parity, the expectation of integral probability metrics (EIPM), and mutual information, enforce this independence by averaging a per-value discrepancy between the conditional law $P_{Z \mid S=s}$ and the marginal $P_Z$ over the law of $S$. This approach requires a nonparametric surrogate for the conditional law at each sensitive value. We propose evaluating independence through a single joint discrepancy $d\left(P_{Z, S}, P_Z \otimes P_S\right)$ between the joint law and the product of its marginals. We establish a disintegration identity; on decomposable witness classes it equals the conditional-integral functional that EIPM and generalized demographic parity instantiate. By reaching the same target without the conditional law, this discrepancy can be estimated directly from samples via a dependence statistic rather than conditional smoothing. We take the Hilbert-Schmidt independence criterion (HSIC) as an instance of the joint discrepancy $d$ to investigate the statistical efficiency of replacing the conditional formulation. The HSIC estimator is a closed-form $O\left(n^2\right)$ statistic that converges at the $O\left(n^{-1 / 2}\right)$ rate, in contrast to the nonparametric $O\left(n^{-2 / 5}\right)$ rate of the conditional-route estimators. We prove this instance is equivalent to the conditional maximum mean discrepancy (MMD) integral up to an explicit spectral tail. The corresponding algorithmic implementation, i.e., FRHSIC, attains fairness-accuracy tradeoffs comparable to conditional-route basel es while reducing per-epoch training time.

Incremental learning models are required to learn new classes sequentially without catastrophic forgetting, while operating under parameter and memory constraints. In the Noisy Intermediate-Scale Quantum (NISQ) era, although quantum neural networks offer advantages in feature mapping, hardware limitations restrict circuit width. Furthermore, traditional quantum classifiers are constrained by the number of orthogonal basis states, limiting their capacity to accommodate a continually growing number of categories. Thus, we introduce a novel quantum incremental learning framework based on trainable mixed-state prototypes. Its original design incorporates new classes by adding class prototypes rather than increasing the circuit width of the shared quantum backbone. The use of mixed-state prototypes is another key contribution, since they have representation capabilities to represent information than a single pure-state prototype. And the decomposable mixed-state calculation provides lower production costs and a convenient Hilbert-Schmidt (HS) distance metric for classification. Simulation results show that our model achieves high-dimensional feature concentration using a minimal number of qubits, while demonstrating lower computational complexity and robust representation in incremental learning tasks compared with classical baselines.

Large language models (LLMs) are increasingly used as costly, on-demand components in real systems, but calling them indiscriminately can waste substantial compute, latency, and serving budget. The key deployment question is therefore not only whether an LLM helps on average, but when it is worth calling. We identify a common failure mode, which we call acquisition collapse: an LLM signal can appear useful in aggregate or post hoc, yet still provide too little before-call information to support reliable selective use. We introduce RAISE (Reward-SNR Actionability in Signal Evaluation), a pre-routing diagnostic framework for testing whether available evidence supports selective use before committing to a routing strategy. We instantiate RAISE with Structured Hypothesis Embeddings (SHE), a frozen-LLM intent signal for recommendation using one LLM call per user, and evaluate it through controlled, retrospective, and fresh-cohort studies and a prospective offline pilot whose audit decisions are frozen before independent outcomes are revealed. Across these settings, predictable incremental benefit, not average lift alone, distinguishes settings with recoverable selective value; deployment additionally depends on cost and operational constraints. Seemingly strong oracle or subgroup gains can disappear under independent evaluation. More broadly, RAISE reframes costly inference as an information-acquisition problem: before paying for an expensive model, tool, sensor, or measurement, first test whether its value is predictable at decision time. This principle motivates cost-aware acquisition in settings ranging from agent tool use and stronger-model consultation to robotic sensing and clinical decision pipelines.

Forecast accuracy is often used as a proxy for temporal structure discovery, but predictive performance and structural identifiability are not equivalent. Different temporal mechanisms can achieve similar forecast errors, while small forecast differences may still contain sufficient information for recovery. In this work, we study when forecast-only structural selection can be trusted. We show that a vanishing forecast margin does not necessarily imply structural ambiguity, and establish a stability perspective that evaluates structural separation relative to uncertainty in the selection objective. This perspective provides both a sufficient condition for reliable selection and a continuous measure of selection difficulty. Experiments across controlled and end-to-end settings demonstrate that forecast margin alone is insufficient, while the proposed stability measure better characterizes when forecast-based structural selection succeeds or fails. Our results suggest that predictive accuracy should be treated as evidence for structure discovery only when its separation is sufficiently robust.

Large Language Models (LLMs) deployed as AI agents frequently exhibit user specification-grounding failures, executing hallucinated, undesired actions to force a resolution rather than expressing uncertainty. Existing detection methods fail to provide actionable, real-time correction as they either do not localize the hallucinations, or incur prohibitive inference latency. We introduce the Latent Critic, a lightweight low-rank adapter (LoRA) that operates concurrently with a frozen base LLM's generation to actively restructure the transformer's residual stream—amplifying latent grounding signals and translating them into localized, natural language feedback within a single sequence. By refining the base model's native uncertainty signals, this manipulation of the latent space enables reliable, granular detection without the overhead of secondary inference loops. Mechanistic analysis via activation patching and layer-wise probing shows that this rank-invariant behavior restructures pre-existing uncertainty geometry into a linearly separable representation that transfers more reliably than base model representations alone. Using tool-calling as an instantiation of granular hallucinations, we validate the detection and downstream improvements enabled by the Latent Critic architecture across Qwen and Llama-based models. Demonstrating superior real-time efficacy, our approach significantly outperforms equivalent-scale fine-tuned external detectors, semantic entropy baselines, and passive internal probes in isolating hallucinations, achieving 0.966 AUROC and >80% accuracy in localization (e.g., ungrounded: date). When deployed in a closed-loop ReAct environment, the Critic acts as a negligible latency guardrail, intercepting hallucinations before execution to prevent undesired actions while simultaneously leveraging this specific localized feedback to enable efficient agent self-correction.

A slew of recent works develop agents for solving research problems end-to-end, a paradigm increasingly referred to as autoresearch. Such agents have inspired large industry investment, motivated by their potential to automate time-consuming human labor and customize machine learning solutions for specialized applications. In this paper, we study the modeling pipeline at the core of these autoresearch systems and identify common failure modes when they are applied to tabular datasets: (1) they waste compute resolving the same bugs over and over again; (2) they often fail to tune hyperparameters even when they have a large remaining compute budget; (3) the tree-search algorithms that power them do not explore; and (4) they perform data analysis, mimicking the humans whose data they are trained on, but do not use that analysis to make downstream decisions. We explore targeted interventions and find that a global debug consultant that shares discovered runtime constraints across all branches of the search tree, prompt- and control-level enhancements, and refined tree-search algorithms successfully recover wasted compute. Our results show that large gains in autoresearch agent performance are achievable through agentic design alone, holding the underlying language model fixed.

Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications. Despite this progress, however, little was known about lower bounds for such methods beyond the classical $\Omega(T^{-2})$ benchmark for general first-order methods. In this work, we present a new lower bound of $\Omega(T^{-1.9319})$ for the last-iterate convergence rate of gradient descent with predetermined nonnegative stepsize schedules. This result provides rigorous evidence that stepsize schedules alone cannot accelerate plain GD to the optimal $O(T^{-2})$ convergence rate. The proof was developed by GPT-5.6 Sol Pro under the authors' guidance.

We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver). The Euclidean part establishes three core theorems: (1) circuit separation—IDA achieves exact retrieval with $\mathcal{O}(1)$ resources while softmax requires $\Omega((\log n)^2)$ width; (2) a Polyak–Lojasiewicz inequality with $\Omega(e^{\Delta^2/\sqrt{d}}/\Delta^2)$ stronger constant than softmax, implying linear convergence, $\mathcal{O}(\log n)$ Lipschitz scaling under a low-rank/clustering assumption, $\Theta(1)$ Hessian spread, and absence of spurious local minima; (3) a width-independent effective rank bound that limits noise memorization—softmax memorizes arbitrary labels when $d_h\ge n$, while IDA limits test error to $\mathcal{O}(\eta^2)$. The non-Euclidean extension then builds upon this prototype, replacing Euclidean distance with hyperbolic geodesic distance for storage and spherical geodesic distance for routing. The Riemann GeoResolver framework comprises ten integrated modules: four HIDA operators spanning $\Theta(n^2)$ to $\Theta(1)$ per token; Hyperbolic Curvature Compression (HCC) with provable error bounds; HyperGate with gradient lower-bound theorem; Spherical Inverse Distance Attention (SIDA) with sphere-analog PL inequalities; Dynamic Memory Genesis (DMG) with $\mathcal{O}(\log T)$ regret bounds; and Geodesic Sparse Routing (GSR) with quality and communication bounds. The Euclidean theorems are proved in full; the non-Euclidean extension theorems are proved with analogous arguments. This work establishes a theoretical arc: from Euclidean attention as a special case, to hyperbolic memory, to spherical retrieval.

Large Language Models (LLMs) are typically evaluated on standard written Vietnamese, yet everyday communication frequently involves regional dialects that preserve meaning but differ in surface form. Existing Vietnamese dialect work largely addresses this issue through dialect-to-standard normalization instead of measuring how the model fails under Vietnamese dialectal inputs. To address this gap, we present the first systematic evaluation of LLM robustness to Vietnamese dialect variation across multiple tasks, quantifying performance degradation and failure patterns. We introduce VialectBench (Vietnamese Dialects Benchmarking), a controlled benchmark for testing whether model decisions remain stable across six Vietnamese dialect groups. VialectBench contains 400 Standard Vietnamese source instances and 2,400 human-written dialectal rewrites spanning emotion recognition (ER), natural language inference (NLI), question answering (QA), and multiple-choice question answering (MCQA). Dataset evaluation with a fixed reference language model shows that the dialectal rewrites induce a measurable model-relative likelihood shift while remaining nearly equal in length to their Standard counterparts. Across ten instruction-tuned models, dialectal inputs reduce average performance by 2.82%, and no evaluated model is fully dialect-invariant. All four tasks are affected, with QA showing the largest average degradation. Robustness also varies substantially across dialect groups: PNT3 and PNT2 cause the largest average performance drops, at 6.17% and 4.73%, respectively, whereas PNB slightly improves average performance by 0.42%. The Central dialect group (PNT1-PNT4) also yields the highest average harmful-flip rate across all models, at 6.54%. These findings show that strong performance on Standard Vietnamese does not guarantee reliable behavior under meaning-preserving regional variation.

Web search, product search, and question-answering retrieval systems often assign a relevance label and confidence score to each query-candidate pair. The relevance label describes how well a page, product, or passage matches the query, while the confidence often guides downstream use or fallback decisions. Post-hoc calibration is therefore needed because misaligned confidence can make systems over-trust wrong predictions or unnecessarily defer correct ones. However, calibration mainly aligns confidence with average correctness, and does not remove predicted-label-dependent reliability differences that remain within the same calibrated confidence level. We address this gap with Label-wise Monotone Reliability Projection (MRP), which learns label-wise monotone functions that map calibrated confidence to correctness reliability while preserving the original predicted labels and class probabilities. The resulting reliability score reranks fixed predictions according to residual risk. Across six information access relevance datasets and multiple post-hoc calibrators, MRP improves reliability reranking and average fallback utility while preserving full-coverage accuracy and ECE. Structural ablations show that the main gains come from label-wise residual reliability rather than from global confidence remapping. We further analyze when MRP reliability scores can be embedded back into top-label probability geometry, showing that this projection is useful as a compatibility analysis but is distinct from the main reliability-reranking objective. The implementation will be made publicly available.

Reinforcement learning (RL) for large language models is moving toward multi-turn agentic workloads, where rollout tasks repeatedly pause for external environments, resume with growing contexts, and finish at highly variable times. In this setting, RL training goodput, measured by training throughput, matters more than raw GPU occupancy: GPU waiting and repeated prefill recomputation are pure overhead. We present TideRL, a readiness-aware elastic RL system with Continuous Task Batching, Resource-Aware Ref-Actor Pipelining, and Elastic Resource Scaling. CTB preserves useful rollout state, $\textrm{RA}^2\textrm{P}$ selects between decoupled streaming and colocated aggregation from the ready backlog and arrival interval, and ERS moves ranks between rollout and training using the same readiness signals. Across text-only and multi-modal agentic workloads, TideRL improves RL training goodput by up to 5.6$\times$ over synchronous baselines and over 33% over asynchronous baselines, while reaching similar task performance. It also improves KV cache hit rate by 1.58$\times$, reduces per-step training time by up to 44.3%, and cuts total waiting time by up to 77.6%.

Intracytoplasmic sperm injection (ICSI) operators frequently adjust the field-of-view (FOV) during procedures, which interrupts workflow and increases procedure time. Conventional microscopes require manual objective lens switching and illumination adjustments to achieve different FOV sizes. We propose an AI-based automatic FOV adjustment method integrated with a view-expansive microscope. This microscope enables the simultaneous acquisition of a large FOV and high-resolution images using a single objective lens through multiview imaging with galvanometer mirrors and high-speed vision, thereby eliminating the need for physical lens exchanges. Our method utilizes a long short-term memory (LSTM) model to predict the appropriate FOV size based on real-time analysis of the pipette's position and velocity, combined with the operator's gaze position. The AI model is trained using ICSI procedure data from an expert with over five years of micromanipulation experience. Experimental evaluation with novice operators reveals that the proposed automatic FOV adjustment system significantly improves the ICSI procedure speed, reducing the average task completion time from 60.5 to 48.0 s (p < 0.001). The experiments also demonstrate that this improvement enables novice operators to achieve ICSI working speeds equivalent to those of expert operators.

What if judges already behave like algorithms? As artificial intelligence and algorithms are deployed in many settings, including the judicial system, many have debated whether judges should be allowed to rely on them. Instead, we ask whether judges follow predictable, algorithmic-like rules already. If judges already follow consistent, formula-like rules based on discrete and static factors such as criminal history, age, and charge type, then judicial behavior may be improved. However, if judges rely on individualized information that cannot be identified through court data, then standards-based decision-making may be more challenging to understand or improve. This work explores these questions by studying judicial decision-making in misdemeanor bail hearings in Harris County, Texas. Using available court data, we investigate whether magistrate judges follow what resembles an algorithm; whether they consider the same variables in their decision-making; and whether they are consistent with themselves and with each other. To do this, we train machine learning models for each judge, measure variable importance metrics to determine important variables for each judge's decision-making, and analyze outcomes of similar cases for judges. Our results reveal that these judges generally behave algorithmically: their decisions can be captured by small, interpretable formulas. However, in some cases, judges differ substantially, leading to surprising inconsistency and unequal treatment across similar defendants. Identifying cases where algorithms do not explain judicial decision-making can improve the justice system by focusing attention on decisions where individualized standards, rather than rules, better explains outcomes.

ELVAE places an input-dependent normal–inverse-gamma (NIG) hierarchy at each VAE latent coordinate, separating location uncertainty $u_{\mathrm{epi}}=\beta/[\nu(\alpha-1)]$ from conditional variability $u_{\mathrm{var}}=\beta/(\alpha-1)$. The marginalized latent law, however, identifies only the three quotient coordinates $(\gamma,\alpha,c)$ with $c=\beta(1+1/\nu)$; reconstruction is blind to one $(\nu,\beta)$ fiber direction. A companion theoretical analysis shows that the complete NIG prior and forward KL select a unique prior-relative canonical representative on each fiber, so canonical inverse allocation is not a fourth independent information channel. Empirically, trained inverse evidence $1/\nu$ remains the strongest sensitivity-ranking score. At $\tau_{\mathrm{epi}}=1$, the three-seed mean high/low-$u_{\mathrm{epi}}$ semantic-transition ratios are 1.98 on MNIST and 1.66 on Fashion-MNIST, falling to 1.33 and 1.16 under scale-matched controls. In the 20-draw MNIST component study with equal per-anchor perturbation energy, $1/\nu$ gives high/low ratios 1.69 and 1.65 under the $u_{\mathrm{epi}}$ and $u_{\mathrm{var}}$ fields and 1.69 (95% interval 1.45–1.97) under a geometry-free isotropic field, whereas $u_{\mathrm{var}}$ reverses the isotropic ordering to 0.76. Under the experimental prior, canonical $1/\nu_{\mathrm{can}}$ is a strictly increasing transform of $T=c/[\alpha(\gamma^2+2)]$ and is bounded above by $3+\sqrt{10}$. Thus ELVAE exposes a controllable sensitivity mechanism whose trained four-output realization is operationally informative, while the exact reconstruction-visible information remains three-dimensional and baseline image quality is a separate question.

Mixture-of-experts (MoE) models have recently moved beyond routing a fixed number of complete experts. Shared-expert designs preserve reusable knowledge, fine-grained methods vary computation within experts, and dynamic routers adapt the number of active experts. Yet these decisions are usually made independently, overlooking a basic dependency: extracting reusable computation changes both what remains and how much expert capacity the remainder needs. We study this dependency by decomposing sparsely upcycled feed-forward experts into key-value channels. Co-activated experts align at a subset of value positions; removing these positions changes expert preference; and greater shared coverage is associated with lower residual expert demand. These observations lead to one principle: share first, then route what remains. We instantiate it in UniF-MoE, a unified framework for token-adaptive MoE computation. Each expert is partitioned into aligned blocks. A shared-demand score sets the shared block count and pathway weight, key prototypes select the shared content, and the complementary demand determines the residual expert count through cumulative routing mass. A Gram regularizer separates and normalizes router embeddings, promoting diverse routing directions, sparse expert overlap, and a simple routing geometry. Experiments on DomainBed and GLUE show that this unified design improves predictive performance over representative static and dynamic MoEs while reducing activated computation, inference latency, and memory. Code is available at https://github.com/existence0420/UniF-MoE.