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Lei Yu

Publications and source records attributed to Lei Yu.

At least 19 recordsLinked to original sources
arXiv2026

A Sharp Fisher-Information Inequality for Boolean Pairs: Proof of the Amari--Kobayashi Conjecture

Consider two terminals that observe correlated uniform binary vectors and separately compress their observations to one bit. We prove that, for every blocklength and every correlation parameter in $(-1,1)$, the Fisher information retained by the resulting pair of bits is maximized by matching parity functions of an appropriate degree, thereby resolving a conjecture of Amari and Kobayashi. The proof combines a Fourier-based bound on the derivative of the normalized covariance with a scalar inequality for signed polynomials subject to a global range constraint.

cs.IT↗
arXiv2026

Exact Second-Order Asymptotics for the Gaussian Gray--Wyner Problem

We revisit the Gray-Wyner problem of lossy compression of bivariate Gaussian sources under the quadratic distortion measure and derive the exact second-order asymptotics. Specifically, we first identify the boundary rate tuples using the explicit first-order asymptotics by Yu (TIT 2023) and then characterize the tradeoff among three second-order coding rates subject to a constraint on the joint excess-distortion probability. Our main contribution is the achievability proof, where we derive a covariance shell covering lemma that is analogous to the type covering lemma for the discrete case. In particular, our covering lemma classifies the source sequences into power shell types via their empirical covariance matrix. For each such power shell type, we derive sufficient conditions on the compression rates so that covering within distortion levels are achievable. Finally, asymptotical analysis via the Berry-Esseen theorem yields the desired result.

cs.IT↗
arXiv2026

What Hallucinations Have We Measured? Semantic Illusion, Confabulation, and Expressed Uncertainty

Hallucination remains one of the most critical challenges in deploying large language models (LLMs) reliably and safely. Yet the term is used inconsistently across the research community. We argue for a strict definition of hallucinations in LLMs. First, hallucinations should be confident incorrectness, kept separate from expressed uncertainty (UNK)1. UNK reveals that the model may be wrong, whereas a hallucination does not reveal it and is therefore more dangerous in practice. Conflating the two obscures their distinct behaviors and makes them hard to study. Second, hallucinations should be split by a simple re-elicitation test: does any semantically equivalent prompt recover the correct response? This test probes whether the relevant knowledge2 is accessible. If none does, the knowledge is likely absent or inaccessible, and the error type is a confabulation (CF) that likely requires external knowledge or retraining; if some does, the knowledge is accessible from the model but applied inconsistently, and the error type is a semantic illusion (SI) that simple prompt or decoding changes can mitigate3. Re-evaluating 14 recent hallucination methods under this taxonomy yields three findings. (1) Detection methods flag UNK more often than hallucinated responses (i.e., SI and CF). (2) Mitigation methods are far more effective for SI than for CF. (3) Latent signals are more informative than output-level signals for CF. An audit of recent hallucination papers shows that most conflate these categories. We recommend reporting CF, SI, and UNK separately, and introduce a practical labeling protocol that needs only a modest number of semantically equivalent prompts.

cs.CL↗
arXiv2026

On the Fundamental Limits of Bistatic ISAC Over Vector Channels

This paper studies the fundamental limits of bistatic integrated sensing and communications (ISAC) systems over vector channels. We first consider a class of parallel channels in which, on each component channel, the channel from the transmitter (Tx) to the communication receiver (Rx) is degraded with respect to the channel from the Tx to the sensing Rx, or vice versa, where the direction of degradation may vary across component channels. For this class of channels, we establish matching achievability and converse results, which yield a single-letter characterization of the capacity-distortion function $C(D)$. For parallel Gaussian channels with additive Gaussian states, the evaluation of the capacity-distortion-power function $C(D,P)$ under the squared error distortion measure reduces to a joint power and distortion allocation problem across the component channels. We then extend the analysis to general vector channels and derive single-letter lower and upper bounds on $C(D)$. In particular, for vector Gaussian channels with additive Gaussian states, we prove the optimality of Gaussian superposition coding without requiring a global degradation order between the communication and sensing channels, by combining the channel enhancement technique with a matrix extremal inequality based on Fisher information. This leads to an exact characterization of $C(D,P)$.

cs.IT↗
arXiv2026

See, Foresee, Act: Intent-Aware World Modeling for Proactive Retail Assistance

World models allow agents to anticipate action consequences, but proactive assistance also requires interpreting incomplete observations and deciding whether to intervene before a user asks for help. We propose See-Foresee-Act and instantiate it as the Proactive Intent World Model (PIWM) for retail assistance. See preserves role-relevant observable evidence alongside AIDA-BDI customer states; Foresee predicts one-step consequences for candidate actions; Act explicitly compares those consequences, including non-intervention. GuidanceSalesBench supplies predominantly synthetic supervision linking observations, states, candidate outcomes, and decisions. On 509 Full test examples, consequence-based selection achieves 63.65% decision accuracy, compared with 45.38% for direct decision output, an improvement of 18.27 percentage points. These results support candidate-consequence comparison for decision reasoning in this retail task. Code and data will be released after consent verification and upon publication.

cs.CL↗
arXiv2026

An explicit dimension-free isoperimetric plateau in the cube

We prove that, in every dimension, the relative Euclidean isoperimetric profile of the unit cube equals one whenever the prescribed volume differs from one half by at most $6.25\times10^{-12}$. The only minimizers in this interval are coordinate slabs. This answers Glaudo's question on the existence of a dimension-free central plateau. The proof combines a dimension-free local optimality estimate for slabs, established through BV slicing and a small-support estimate, with a quantitative Gaussian rigidity argument that forces the normal of an approximating half-space to be close to a coordinate direction.

math.MG↗
arXiv2026

Learning with a Single Rollout via Pass@k Policy Optimization

Group Relative Policy Optimization (GRPO) typically requires multiple rollouts per prompt to estimate relative credit, incurring substantial sampling cost and exacerbating training asynchrony. This limitation is particularly severe for scientific reasoning agents, where each trajectory may involve long-horizon reasoning, multiple turns, and parallel sub-runs. We study single-rollout reinforcement learning, where only one rollout is collected per prompt, and find that naive training can stagnate or become severely unstable. We introduce Single-Rollout Pass@k Policy Optimization (SR-PPO), which combines Monte Carlo token-level advantage estimation with Pass@k gradient reweighting. An online critic without large-scale pretraining is used both as a prefix-dependent baseline for credit assignment and to estimate the Pass@k gradient weight. Using only one rollout per prompt, SR-PPO achieves stable learning and performance comparable to GRPO across reasoning and logic benchmarks, even under off-policy drift that degrades the performance of standard Pass@1 PPO. A key factor in this stability is Pass@k reweighting, which emphasizes harder prompts while downweighting high-success prompts, for which imperfect credit estimates tend to produce noisier policy updates. Through analyses of critic quality, gradient noise, and update behavior, we investigate how Pass@k reweighting stabilizes single-rollout learning and why residual critic errors may limit SR-PPO's ability to outperform GRPO.

cs.LG↗
arXiv2026

Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models

Reasoning errors can propagate into later decisions and memory. This survey synthesizes 312 papers and first-party reports on text-based reasoning hallucinations around three questions: what evidence is observable, what study designs establish, and which corrective actions the evidence supports. UIPCA records unsupported premises (U), invalid inferences (I), dependent reuse (P), visible answer-trace consistency (C), and action-policy failures (A). Across 58 reviewed sources, no comparison establishes that a specified intervention improves reasoning while reducing factual reliability under matched conditions. The synthesis connects diagnosis to verification, repair, selective release, and persistent-state control across memory, tools, and training feedback.

cs.AI↗
arXiv2026

Probe with Participation Trophies: Random-Reward RL as a Probe of LLM Capability

We connect the spurious-reward paradox to a model's reachability and propose random-reward reinforcement learning (RL) as a useful tool for the probing enterprise, addressing a decade-long debate over what probing performance actually reveals about a model. There are two prevailing explanations for the surprising finding that even random rewards can improve the performance of large language models (LLMs): one attributes the gains to particular mechanisms within RL training; the other to data contamination. Our results motivate a different view: spurious-reward RL can probe a model's reachability, or what further training can attain from its current state under specified constraints, beyond what is reflected in its current performance. Two OLMo checkpoints with the same accuracy on synthetic arithmetic (3.5%), for example, reach 8.5% and 55% in their best runs under the same correctness-rewarded RL. Examining OLMo checkpoints across pre-training and mid-training reveals three distinct regimes of training response: early on, RL produces little improvement even when correct answers are rewarded; later in pre-training, rewarding correct answers becomes effective while random rewards remain weak; and, upon entering mid-training, even random rewards can produce large gains. A similar ordering appears in a number-masked supervised fine-tuning (SFT) analysis of these checkpoints, suggesting that the pattern is not specific to a particular RL mechanism. Moreover, RL with random rewards offers a distinctive perspective on what training can make an LLM do, since its reward signal supplies no information about which answers are correct. By asking what training can attain without correctness feedback, it addresses the label-leakage side of a central problem in decodability-based probing: whether a successful probe reveals the model's capabilities or learns the task itself.

cs.CL↗
arXiv2026

Activation-Conditioned Self-Distillation

On-policy self-distillation uses a model as its own teacher to provide dense supervision for reasoning, often through reference-solution conditioning. Providing privileged information does not by itself ensure effective token-level supervision throughout long responses. We introduce Activation-Conditioned Self-Distillation (ACSD), which extracts a steering vector by contrasting activations of self-generated trajectories that reach verified correct answers within a generation budget with those of all remaining trajectories. A frozen copy of the base model applies this vector at each prediction position, and the student learns from its next-token distributions on student-generated prefixes. Outcome verification is used for direction construction and calibration; distillation requires neither problem-specific reference text nor teacher parameter updates. The distilled student is used alone at inference. On each of five models, ACSD achieves the highest mean accuracy over four mathematical benchmarks among the evaluated methods. On DeepSeek-R1-0528-Qwen3-8B, mean mathematical accuracy reaches 71.9\% and LiveCodeBench v6 pass@12 reaches 70.9\%, compared with 69.0\% and 66.3\% for the reference-conditioned OPSD baseline. Contrasts among correct trajectories also support distillation, and extracted directions can be reused across mathematical training datasets. On fixed student trajectories, ACSD maintains more stable late-position logit-update magnitudes than OPSD.

cs.LG↗
arXiv2026

Leaky Students: Membership Inference against On-Policy Distillation

On-policy distillation (OPD) trains a student to match a teacher's next-token distributions on student-generated trajectories. However, privileged information supplied to the teacher for OPD training may contain sensitive data. Whether the student leaks private information about the records supplied to the teacher during distillation remains poorly understood. To the best of our knowledge, we present the first systematic study of membership inference in this setting. We find that fresh student trajectories expose sparse membership signals that fixed reference-answer losses often miss. These signals are mixed with probability changes caused by training on other records. We introduce Leaky, which samples fresh trajectories from the target model and compares its token log-probabilities with the maximum across matched reference models trained without the candidate records. It applies Leaky ReLU to the resulting gaps, preserving positive gaps and downweighting negative gaps as an approximate correction for incidental positive gaps in non-members. Across fifteen targets spanning mathematics, medical question answering, and code generation, Leaky outperforms all evaluated baselines and achieves mean AUROC 0.875, compared with 0.614 for the strongest baseline on each target in the main evaluation. On the same sampled trajectories, the strongest baseline achieves mean AUROC 0.826. These results show that students trained through OPD can expose the membership of records used for teacher supervision, even when fixed reference-answer losses provide little evidence of membership.

cs.LG↗
arXiv2026

On Average Distance, Level-1 Fourier Weight, and Chang's Lemma

We study the maximum level-$1$ Fourier weight of Boolean functions, which is equivalent to the minimum average-distance problem on the hypercube. We first determine the dimension-free optimum at sufficiently small densities: there exists a universal $a_{0}>0$ such that the maximum level-$1$ Fourier weight for Boolean functions of mean smaller than $a_{0}$ is asymptotically attained by Hamming balls as the dimension $n\to \infty$. The key ingredient is an eventual Gaussian stop-loss domination inequality for normalized Rademacher sums. We then use an induction argument to improve the classical level-$1$ bound (Chang's lemma) in both the small- and large-density regimes. We apply these estimates to strengthen the Friedgut--Kalai--Naor theorem, study the corresponding average-distance problem in Euclidean space, and derive a sharp form of Chang's original lemma for $\mathbb{F}_{2}^{n}$: Hamming balls maximize the dimension of the span of the large Fourier coefficients.

math.CO↗
arXiv2026

S2Planner: Multi-Scale Semantic Planner for End-to-End Autonomous Driving

We present S2Planner, a trajectory planner that combines three front-facing cameras with ego-motion history and the current driving command. A fine-tuned DINOv3 backbone and a Spatial Tuning Adapter produce multi-scale image features; a coarse-to-fine decoder then uses trajectory self-attention and camera-projected cross-attention to refine candidate waypoints. The contribution is the integration of ego-conditioned trajectory initialization with iterative, geometry-guided sampling of multi-scale image features, rather than a new visual backbone or attention operator. On the NAVSIM v1 non-reactive evaluation, the previously reported navtest run obtained 88.03 PDMS. Because that run was selected using navtest performance, this number is exploratory and cannot be interpreted as an unbiased test estimate. Validation-selected evaluation on unexposed data, repeated runs, and computational measurements are needed to establish generalization and efficiency.

cs.CV↗
arXiv2026

Timed Rule-Based Supervision of an End-to-End Autonomous Parking Policy

We study whether a manually specified runtime supervisor can correct recurring failures of an existing end-to-end parking policy in a fixed CARLA parking lot. The vision-based Transformer architecture is inherited from Yang et al.; our contribution is a timed, rule-based Parametric Safety Shield (PSS) applied to its control outputs. The PSS uses hand-calibrated speed, position, and duration thresholds to intervene in observed failure modes, including boundary exits, delayed braking, and stalled or oscillatory control. In the reported closed-loop evaluation, 16 held-out target slots and six initial poses are each evaluated in four rounds (384 attempts per configuration). Target success increases from 327/384 (85.16%) for the retrained policy to 375/384 (97.66%) with the PSS; mean position and orientation errors among successful attempts are 0.21m and 0.33 degrees. These results show an improvement within this simulator setup. The repeated attempts share one map, vehicle, and sensor configuration, and the PSS uses simulator world coordinates; thus the results do not establish generalization to other lots or real vehicles, or a formal safety guarantee.

cs.RO↗
arXiv2026

Sharp Small-Volume Isoperimetry from Log-Sobolev Inequalities

Let $I_{\inf}(a):=\lim_{n\to\infty}I_{n}(a)=\inf_{n\ge1}I_{n}(a)$ be the asymptotic isoperimetric profile for product of a weighted Riemannian manifold satisfying $\mathrm{CD}(0,\infty)$ and, more broadly, for product of a nonsmooth subspace with density that can be approximated by a sequence of densities satisfying $\mathrm{CD}(0,\infty)$. We establish the following identity: \[ \lim_{a\downarrow0}\frac{I_{\inf}(a)}{a\sqrt{2\ln(1/a)}}=\sqrt{K_{\mathrm{LS}}}, \] where $K_{\mathrm{LS}}$ is the optimal log-Sobolev constant. The same argument also yields the large-deviation and moderate-deviation asymptotics for isoperimetry.

math.MG↗
arXiv2026

Stability for the 2D Micropolar equations near Couette flow via Green's function method

In this paper, we use the Green's function method to study the stability of solutions to micropolar equations in the whole space. An essential difficulty in estimating the Green's function lies in treating a coupled system of equations with variable coefficients, which is completely different from previous Green's function analyses for scalar equations. We propose a dominant factor extraction method to overcome this difficulty. Based on sharp Green's function estimates for the micropolar system, we prove that if the initial data (m_0, ω_0) satisfy \|(m_0, ω_{0})\|_{L^1\cap L^{\infty}}\leq c_0μ^{3/4} for some small constant c_0 independent of the viscosity coefficient μ, then the corresponding solution remains of order O(μ^{3/4}) under the effect of the Couette flow. Meanwhile, we establish the optimal decay estimates of solutions in the general L^p norm. More importantly, the dominant factor extraction method developed in this work provides a general framework for the stability analysis of complex coupled fluid systems.

math.AP↗