arXiv subjects
Publications and source records attributed to Xiao Li.
For every integer $k\ge1$, we prove that each nonempty bounded set in real $\ell_1^{4k+1}$ has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: $J(\ell_1^5)=3/4$. If a Hadamard matrix of order $4k$ exists, then $J(\ell_1^{4k-1})=J(\ell_1^{4k})=J(\ell_1^{4k+1})=(4k-1)/(4k)$. The upper bound for every $k\ge1$ has been formalized in Lean.
Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.
Privileged 3D supervision uses additional geometric information during training to guide RGB-based visuomotor policy learning, without requiring geometric inputs at deployment. However, low reconstruction error does not ensure that visual representations capture geometry useful for control. We identify three limitations that weaken this supervision: proprioceptive shortcuts, dominant-view reliance, and reconstruction objectives dominated by task-irrelevant geometry. To address these limitations, we propose Latent Encoding with Aligned Privileged Geometry (LEAP). Our framework uses an auxiliary decoder to reconstruct point clouds within the manipulation workspace from visual features alone, while retaining proprioception for action prediction. Alongside full reconstruction, we introduce wrist-view dropout and partial reconstruction targets matched to the retained wrist, encouraging the encoder to capture complementary local geometry. The auxiliary decoder is removed at inference, leaving only RGB observations and robot state as policy inputs. Extensive experiments on RoboTwin, ManiSkill, and real-world tasks demonstrate consistent and substantial improvements over Diffusion Policy and ACT, with only a small increase in parameter count and no reduction in inference speed.
Multi-shot long-form video generation remains challenging due to identity drift and compounding inconsistencies across shots. Existing methods encode past shots as compressed context, implicit features, or retrieved frames, making it hard to tell whether new visual evidence is another view of an existing appearance, an evolved state of the same identity, or a newly introduced entity. We propose EvoState, an agentic framework that formulates multi-shot generation as entity-centric evolving visual state management, following a state-observation-update-propagation cycle. An entity-centric Visual State Memory separates persistent identity anchors from their evolved states and observations, so each shot retrieves the required state, accumulates complementary views, and reactivates earlier appearances without conflating them. A Visual State Analyzer reconciles the text-visual-memory triplet by observing generated visual evidence, updating generation conditions according to realized outcomes and memory states, and propagating inferred state transitions into memory and future prompts. As a result, generation is conditioned on an evolving state history grounded in what has been realized, rather than solely on planned textual descriptions. Experiments on our curated StoryBench benchmark demonstrate substantial improvements in identity preservation, state-transition correctness, and narrative coherence over state-of-the-art methods.
Post-training is central to mathematical reasoning in modern large language models (LLMs), but endpoint pass@1 alone underidentifies what has changed. Gains may reflect newly reachable solutions, cheaper sampling of latent solutions, surface robustness, or memorisation. We compare three post-training paths under a common diagnostic readout: our sufficiently trained off-policy distillation trajectories, released Qwen3 off-policy-plus-on-policy distillation endpoints, and a released DeepSeek-Math endpoint trained with Group Relative Policy Optimisation (GRPO). Our probe uses cross-surface pass@K over verbatim prompts, paraphrases, numerical isomorphisms, and translations, plus consistency, distribution-shape, and verified supervised-fine-tuning (SFT) membership analyses. We find two regimes. On easier AMC problems, large-K ceilings are near saturation, so post-training mainly compresses sample cost. On harder AIME problems, post-training expands the large-K ceiling over the base model: sufficient off-policy distillation already raises this ceiling, Qwen3 released endpoints raise it further, and DeepSeek-Math GRPO does not dominate sufficient off-policy distillation at large K. English-dominant distillation improves non-English reasoning but preserves language-tier gaps. A controlled-overfit audit finds limited sensitivity in current SFT-membership probes. Compression is one regime of post-training, not a universal explanation.
Open-source reasoning models provide unequal access to reasoning capability across languages. When a model can solve a problem but cannot deliver a complete solution in the user's language, language becomes an access barrier rather than merely a source of performance variation. We audit Qwen3 checkpoints on competition-mathematics tasks in eleven languages. Across the ten non-English languages, only 15.4-17.9% of problems receive a correct, terminating solution with visible reasoning in the requested language in any of 16 samples, compared with 92.9% in English. To identify the source of this disparity, we evaluate thirteen endpoints from one model family, spanning released checkpoints, multilingual supervised fine-tuning (SFT) at two scales, controlled SFT ablations, and three reinforcement-learning (RL) reward formulations. We jointly track correctness, language adherence, termination, and delivery efficiency. The dominant bottleneck shifts across post-training stages. Released models often reason in English. Multilingual SFT restores target-language reasoning, but accuracy declines across multilingual, English-only, and single-language SFT runs, showing that this cost is not specific to multilingual mixing; non-English reasoning traces additionally become prone to non-terminating loops. RL restores termination in both arms at no cost in accuracy, but only the arm whose reward includes a language term delivers: rewarding correctness alone returns the model to English. Together, these stages establish a constructive post-training path from English-pivoted capability to multilingual reasoning that is reliably delivered.
Recent approaches to reinforcement learning (RL) post-training for large language models increasingly remove the critic to reduce training instability and memory overhead. Even where a critic is trained, it is discarded once training ends, although it has learned to predict outcomes. We revisit this trend and show that a pretrained critic's ability to predict future outcomes can make it a valuable asset for efficient long-horizon reasoning. First, we find that instability in critic-based RL for long chain-of-thought reasoning is largely an optimization artifact: keeping policy updates small and low in variance restores stable convergence. Second, a well-pretrained critic estimates the posterior probability of eventual success from later trajectory states and unfinished prefixes. Its predictions provide outcome-derived, dense, per-prefix learning signals that, during policy optimization, require neither completed rollouts, step-level annotations, nor external reward labels. Building on this insight, we introduce Reward-Free Policy Optimization (RFPO), which repurposes a single calibrated, frozen critic as a rollout-level reward, a value baseline for generalized advantage estimation, and a success forecaster for unfinished prefixes. We further show that binarizing the debiased score stops the policy from exploiting the critic's length bias. Binarized, RFPO matches supervised PPO without a single label in the training loop, while cutting compute and memory overhead. This makes RFPO well suited to long-horizon reasoning tasks, where outcomes arrive late and generation dominates cost: because rollouts can be rewarded before they finish, training no longer has to pay for waiting on every trajectory to complete. Our findings challenge the prevailing critic-free paradigm and establish critic-based, reward-free optimization as a scalable and computationally efficient path for LLM post-training.
On-policy distillation, where a student learns from a stronger teacher's feedback on its own outputs, is a common way to pass reasoning to smaller models. We analyze what it transfers at small scale, distilling Qwen3-8B into Qwen3 4B, 1.7B and 0.6B students, in thinking mode (reason at length, then end the reasoning and answer) and, for comparison, in non-thinking mode (no separate reasoning phase). Long reasoning needs two abilities, solving a problem and knowing when it is solved, and we find that distillation transfers the first, but in thinking mode not the second. Solving improves at every size, up to two ceilings, which we measure comprehensively across both modes and all student sizes: a student's single attempt never exceeds what it could already reach in many attempts before training, and the smaller the student, the further it stays below the teacher. Stopping is where the modes part. In non-thinking mode every student keeps stopping; in thinking mode students stop ending their reasoning early in training, and the smaller the student, the less of this ability survives: the teacher signals a stop almost only where a student already ends its reasoning, so distillation teaches no new stops; it only keeps the student's existing stops that land on a right answer, and a weak student has few such stops. The smallest students often reach the right value but do not commit to it: they either rarely mark it or mark it and write past it. Together, these results describe how small students behave under on-policy distillation, and a diagnostic that separates answer marking, correctness and stopping.
Brain-to-image retrieval seeks to identify the visual stimulus that elicited a non-invasive neural response. Candidate images are typically represented by pretrained vision models, whose internal representations vary in abstraction across depth. Existing methods usually train the neural encoder to recover a fixed final-layer visual target. Under this formulation, the visual hierarchy is reduced to a single prescribed endpoint, preventing representations at other depths from directly shaping the visual target. This limitation motivates learning how information across visual depths should contribute to the retrieval target. To this end, we introduce NeuroGlyph, which learns a trial-independent visual target from multiple depths of a frozen visual backbone. NeuroGlyph decomposes the target into factor-specific subspaces. Each subspace learns an image-conditioned allocation over visual depth. The resulting subspaces are fused into a single embedding for retrieval. Across THINGS-EEG and THINGS-MEG, NeuroGlyph outperforms final-layer supervision in all controlled comparisons. It also surpasses the post hoc best fixed-layer oracle in three of four comparisons. Parameter-matched ablations support both factorized target construction and image-conditioned depth allocation. Under comparable 200-way retrieval protocols, NeuroGlyph achieves the strongest system-level performance in six of eight reported metrics. These results support learning retrieval targets across the visual hierarchy rather than prescribing one visual depth.
Language-conditioned manipulation requires both precise contact-rich control and robust reasoning over language, scenes, and long horizons. End-to-end Vision-Language-Action (VLA) models provide strong local visuomotor skills, but they are trained on in-distribution task trajectories and often fail under deployment perturbations such as semantic retargeting, goal re-binding, spatial-layout shifts, and unstable local contacts. LLM coding agents provide complementary semantic and compositional reasoning, but purely analytic primitives struggle with irregular grasping, constrained placement, and articulated-object interaction. We present Harness VLA, a memory-augmented agentic framework that exposes a frozen VLA as a retryable contact-rich primitive and composes it with a small fixed library of analytic primitives for grounding, staging, transport, navigation, and release. Rather than expanding the skill library, the harness learns the operating range of these fixed primitives from task-specific execution traces, global success rules, and failure models. By lifting semantic re-grounding, non-contact execution, and VLA re-staging to the planner while reserving the frozen VLA for local contact-rich phases, Harness VLA extends pretrained VLAs beyond their original trajectory distribution without finetuning. Across perturbed tabletop, household kitchen, and clean-to-randomized bimanual manipulation, Harness VLA improves over the strongest relevant baselines by 38.6 and 25.4 percentage points on LIBERO-Pro and RoboCasa365, respectively, and reaches 58.4% on RoboTwin C2R. Real-world demonstrations on dual-Franka robots further show target redirection, grasp recovery, and new task compositions with the same frozen VLA. Code is available at https://github.com/RLinf/RPent.
This paper investigates a fundamental question in stripeless erasure coding based on symmetric balanced incomplete block designs (SBIBDs): how many replicas per object are precisely required to guarantee recovery from any set of at most $p$ node failures? We refine the known sufficient recovery guarantee for the generalized SBIBD $(v,k,λ)$ construction. One replica is necessary and sufficient for $p=1$, and $q=λ(p-1)+2$ replicas ($q\le k$) guarantee recovery for $p\ge2$. Recovery takes one round for $p=2$ and at most two rounds in general. To study the tightness of this count, we define the universal replica threshold $q^\ast(A,p)$ for a fixed zero-diagonal SBIBD representative~$A$. We determine $q^\ast(A,p)$ for $p=1$ and $p=2$. For $p\ge3$, we identify pairwise separated sets and private target permutations as the structures determining whether the sufficient count is tight or can be further reduced. These conditions give exact thresholds for all but the case where $λ>1$ and $A$ contains no pairwise separated set of size~$p$. We improve the bounds for this remaining case and leave its exact threshold open. Finally, we give sufficient conditions for pairwise separated sets and show how affinity relabeling can realize private target permutations.
The rapid capability gains of frontier language models are widely attributed to improved reasoning abilities, yet this cannot be verified as raw CoT traces in closed-source systems are hidden. By registering a simple custom tool through a standard API feature, we induce frontier models to externalize intermediate reasoning. Because these traces may reflect post-hoc rationalization rather than genuine reasoning, we first evaluate against native CoT on open-source models and extend to closed-source frontier models including GPT-6 Astra. We find that the extracted reasoning matches native reasoning performance and substantially outperforms no-reasoning baselines, across competition mathematics, science, and code generation. We then characterize how frontier models structure their intermediate reasoning. Across token efficiency, reasoning-step types, and induced reasoning trees, we identify systematic differences in how models externalize, compress, and organize reasoning. We find that Astra exhibits token-efficient directed reasoning, selecting a correct trajectory earlier, while resolving elementary steps internally and externalizing only crucial reasoning. These findings provide a behavioral lens on frontier-model reasoning beyond benchmark scores.
AT2019aalc is considered a repeating tidal disruption event (TDE) candidate occurring in an active galactic nucleus (AGN). In this paper, we highlight previously unnoticed but intriguing features that include a brief optical dimming prior to the rise of the main flare and a significantly lower post-flare luminosity compared to the pre-flare level. By applying a time-dependent obscured TDE model to AT2019aalc, we successfully reproduce its light curves with the tidal disruption of a $1.122_{-0.176}^{+0.246}\rm M_\odot$ main-sequence star by a $1.862_{-0.259}^{+0.255} \times 10^7{\rm M_\odot}$ supermassive black hole (SMBH). Both the pre-flare dimming and the reduced post-flare luminosity are attributed to obscuration of the intrinsic AGN emission. The total energy of the event derived from our fit is $1.24\times10^{51}$ ergs and about 0.2 ${\rm M_\odot}$ of debris mass is accreted by the SMBH. In addition, the $g-r$ color of the net flare in AT2019aalc exhibits a continuous reddening trend during the first flare, consistent with a gradual increase in $E(B-V)$ predicted by the obscured TDE model. These results suggest that AT2019aalc can be considered a second member of the recently proposed class of obscured TDE candidates hosted in AGNs. } \keywords{galaxies: active-galaxies: nuclei-quasars: supermassive black holes-quasars: individual (AT2019aalc)-transients: tidal disruption events.
We establish a discrete $H^1$-Korn inequality for finite element spaces satisfying a second order weak continuity condition. This implies that classical $H^2$-nonconforming elements satisfy the discrete Korn inequality. Based on this result, we develop a stabilized Morley finite element method for linear strain gradient elasticity using only piecewise quadratic polynomials. Thanks to the discrete $H^1$-Korn inequality, this method does not require any penalty parameter. We prove that the method is robust with respect to both $λ$ and $ι$. Numerical experiments confirm the theoretical results.
Vision-language-action (VLA) policies based on flow matching generate action chunks through repeated evaluations of an action expert. Increasing the number of integration steps raises inference cost, but does not necessarily improve closed-loop success. We propose Coda, which reallocates part of this integration budget to a single learned endpoint correction. A frozen policy first completes a few-step noise-to-action trajectory; a lightweight Transformer then predicts a demonstration-supervised residual using the candidate action, source noise, and shared observation-prefix cache. Only the corrector is trained. On 50 RoboTwin Easy tasks, five-step Coda improves success from 71.64% to 74.68% over the matched five-step baseline, while reducing forward latency by 30.2% relative to the default ten-step policy. A two-step configuration achieves 71.88% success with a 2.12$\times$ speedup. An independent 13-task control shows a 5.69-percentage-point gain at nearly equal latency, supporting correction as an effective alternative to additional integration. The same design also improves frozen official SmolVLA, raising two-step success from 60.8% to 69.4%. These results show that endpoint correction improves the quality-latency trade-off of frozen flow-matching policies.
Methods for streaming language models are often discussed alongside long-context and memory systems, although they solve different problems. An attention sink can stabilize autoregressive generation over an indefinitely long stream while the model remains unable to use content that has left its recent-token cache. We argue that this distinction should be explicit in system claims and evaluation. We introduce three horizons: the stability horizon, over which predictive behavior remains well behaved; the access horizon, over which past content can still causally affect the output; and the utility horizon, over which a task retains acceptable performance. We show constructively that the stability horizon can be infinite while the access and utility horizons are finite. We then propose ThreeH, an evaluation contract that measures all three horizons under a common state and compute budget. Applying the framework to attention-sink streaming clarifies its strength, constant-memory, stable generation, without treating anchor tokens as semantic memory. The framework exposes roles for cache policies, recurrent state, retrieval, and external memory. Experiments on 128K-token streams, delayed binding recall, and delayed decisions show that attention sinks preserve local modeling but not content beyond the active cache; recurrent and retrieval state extend the semantic horizon.
Large-scale multiple-input multiple-output (MIMO) detection is fundamental to modern wireless networks but constrained by performance-complexity trade-offs. Existing detectors, whether classical or learning-based, often fall short in either scalability or generalizability across heterogeneous scenarios. To overcome these limitations, we introduce a wireless-native graph foundation model (GFM) tailored for large-scale MIMO detection. The proposed GFM employs a physics-informed hybrid architecture, integrating the local correlation extraction of message passing neural networks with the global attention of graph Transformers, encoding the physical interference patterns from the expectation propagation algorithm. Via extensive pre-training, this synergy enables the learning of a general-purpose detection mapping scalable across antenna dimensions and channel conditions. For rapid downstream deployment, parameter-efficient fine-tuning is leveraged to adapt the GFM to specific non-ideal system regimes with minimal overhead. To enhance inference efficiency, a mixture-of-experts mechanism is embedded at downstream deployment to dynamically activate only the necessary sub-modules. Evaluations show that the proposed GFM consistently outperforms classical detectors and advanced data-driven baselines in accuracy, configuration generality, and cross-scenario transferability across various challenging zero-shot and few-shot conditions.
We describe the architecture and ablations of Qwen3.8-Flash-Next, a sparse mixture-of-experts model with 125B parameters, 6B activated per token, and additional 51B parameters of n-gram embedding tables held off the accelerator. On fourteen pre-training benchmarks the model leads the 397B-A17B predecessor on eight and trails it on the rest by at most 2.6 points, at 1/3 the activated parameters, 1/3 the training tokens, and roughly 1/9 the training FLOPs. Token mixing uses a layer-wise hybrid of Gated DeltaNet (GDN) and global attention, with one full-attention layer in every four; at continued-pretraining time those full-attention layers are replaced by Qwen Sparse Attention (QSA), which scores context at micro-block granularity with a compressed lightweight indexer. The residual stream is widened to four branches and read through an elementwise gate, a design we call the Gated Residual (GR). Capacity is added outside the backbone by a single n-gram embedding layer whose tables are prefetched from host memory. We evaluate every candidate change along three axes: loss together with downstream benchmarks; the cost of the change in training, prefill and decode; and its effect on the optimal hyperparameters and training stability. Loss and downstream accuracy do not always move together: enlarging the n-gram vocabulary lowers loss monotonically while downstream accuracy saturates. The architecture and the Muon optimizer together shift the optimal learning rate and batch size upwards, render batch-size warmup unnecessary, and substantially improve stability under stress tests. Loss, benchmarks, efficiency and stability form one design problem. Solved jointly, they yield a recipe that is simultaneously more efficient, more capable and more stable.