arXiv subjects

Zijian Zeng

Publications and source records attributed to Zijian Zeng.

At least 19 recordsLinked to original sources

arXiv2026

Multiplicity-Isolated Cores and Chromatic Symmetric Reconstruction of Trees

Stanley's tree-isomorphism conjecture asks whether the chromatic symmetric function distinguishes nonisomorphic trees. We give a reconstruction criterion that permits repeated leaf-component orders. For a proper tree, collapse each leaf component to its center and record its order as a vertex weight. We prove that the chromatic symmetric function reconstructs the tree whenever every nonleaf vertex of this weighted core has a weight that occurs nowhere else in the core. Repetitions among core leaves are unrestricted. The proof uses only the leading star-basis partition and the coefficients immediately above it. As a consequence, the conjecture holds for an infinite class of diameter-six trees not covered by the condition that all leaf-component orders are distinct. We also give a canonical integer-partition model for arbitrary diameter-six trees and an exact cut-partition implementation intended for further work. The unrestricted diameter-six case remains open.

math.CO↗

arXiv2026

A Counterexample to the Tang Zhang Schatten Norm Conjecture and Sharp Positive Results

For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p. $$ Tang and Zhang conjectured an explicit formula for every finite $p>1$. We disprove the conjecture with two explicit real $2\times 2$ rank-one matrices at $p=3/2$. The comparison is certified by seven strict rational inequalities and, in particular, places the attained ratio above $207/200$, while the conjectured constant lies below $207/200$. On the positive side, we prove the conjectured sharp bound for every family of rank-at-most-one summands when $2\leq p<\infty$, and classify all equality cases. We also prove the corresponding endpoint statement for $p=\infty$. Finally, for arbitrary complex matrices, we establish the conjectured sharp constant in the case $m=2$, $p=4$.

math.CO↗

arXiv2026

On the Impossibility of Unbiased and Length-Invariant Policy Optimization with Outcome Rewards

Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.

cs.LG↗

arXiv2026

ThinkReset: Learnable Intermediate Interface Construction for Bounded-Context Long-Horizon Reasoning

Long chain-of-thought reasoning improves performance on complex problems, but it also introduces redundancy accumulation, context overflow, and error anchoring. We argue that under bounded context windows, the core bottleneck is not trajectory compression or test-time control, but the absence of a reusable intermediate interface that can replace discarded history and support continued solving. We further identify a key failure mode of outcome-reward-driven long-chain reinforcement learning: when the model has not solved the task before the window is nearly exhausted, the final-answer reward encourages premature guessing rather than continued careful reasoning. We propose ThinkReset, a text-space instantiation of this view. ThinkReset explicitly constructs reusable intermediate interfaces through interface writeback and reset, and directly optimizes post-reset continuation success. Across multiple long-horizon reasoning benchmarks, this perspective consistently improves success rates under fixed context windows.

cs.AI↗

arXiv2026

State commitment learning: training language models to distinguish computation from memory

Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.

cs.LG↗

arXiv2026

Scaffold-Mediated Post-Training: Co-Evolving Model Parameters and Procedural Scaffold Graphs

Post-training of large language models optimizes only parameters, while inference-time procedural scaffolds are typically designed independently of parameter training. This disconnect makes it difficult to automatically acquire and internalize complex strategies. We propose scaffold-mediated post-training: procedural scaffolds are organized into an evolvable graph structure that co-evolves with model parameters through discovery, distillation, and dynamic recompilation. We instantiate this paradigm as Skill Training. On FeatureBench, automatically discovered skills improve the passed rate by 8.1pp, and after progressive distillation the model still achieves a 27.7% passed rate without any external scaffold (distillation retention rate 85.2%, defined as post-distillation / with-skill passed rate), significantly outperforming standard SFT on the same data.

cs.CL↗

arXiv2026

DexSim2Real: Foundation Model-Guided Sim-to-Real Transfer for Generalizable Dexterous Manipulation

Sim-to-real transfer remains a critical bottleneck for deploying dexterous manipulation policies learned in simulation to real-world robots. Existing approaches rely on manually designed domain randomization or task-specific adaptation, limiting their generalizability across diverse manipulation scenarios. We present DexSim2Real, an integrated framework that leverages vision-language foundation models to bridge the sim-to-real gap for dexterous manipulation. Our system combines three components: (1) Foundation Model-Guided Domain Randomization (FM-DR), which uses a vision-language model as a visual realism critic to optimize simulation parameters via closed-loop CMA-ES, complementing text-based approaches like DrEureka with direct visual feedback; (2) a Tactile-Visual Cross-Attention Policy (TVCAP) that adapts cross-attention visuo-tactile fusion to zero-shot sim-to-real RL; and (3) a Progressive Skill Curriculum (PSC) that builds on LLM-based task decomposition with a difficulty scheduler tailored to contact-rich dexterous tasks. Extensive experiments on six challenging manipulation tasks with blinded evaluation demonstrate that DexSim2Real achieves a 78.2% average real-world success rate, outperforming DrEureka and DeXtreme while reducing the sim-to-real performance gap to only 8.3%.

cs.RO↗

arXiv2026

HELM: Harness-Enhanced Long-horizon Memory for Vision-Language-Action Manipulation

Vision-Language-Action (VLA) models fail systematically on long-horizon manipulation tasks despite strong short-horizon performance. We show that this failure is not resolved by extending context length alone in the current reactive execution setting; instead, it stems from three recurring execution-loop deficiencies: the memory gap, the verification gap, and the recovery gap. We present HELM, a model-agnostic framework that addresses these deficiencies with three components: an Episodic Memory Module (EMM) that retrieves key task history via CLIP-indexed keyframes, a learned State Verifier (SV) that predicts action failure before execution from observation, action, subgoal, and memory-conditioned context, and a Harness Controller (HC) that performs rollback and replanning. The SV is the core learning contribution: it consistently outperforms rule-based feasibility checks and ensemble uncertainty baselines, and its effectiveness depends critically on access to episodic memory. On LIBERO-LONG, HELM improves task success rate by 23.1 percentage points over OpenVLA (58.4% to 81.5%), while extending the context window to H=32 yields only a 5.4-point gain and same-budget LoRA adaptation remains 12.2 points below HELM. HELM also improves long-horizon performance on CALVIN and substantially boosts recovery success under controlled perturbations. Ablations and mechanism analyses isolate the contribution of each component, and we release LIBERO-Recovery as a perturbation-injection protocol for evaluating failure recovery in long-horizon manipulation.

cs.LG↗

arXiv2026

Reducing Credit Assignment Variance via Counterfactual Reasoning Paths

Reinforcement learning for multi-step reasoning with large language models (LLMs) typically relies on sparse terminal rewards, which creates a poorly conditioned credit-assignment problem: the final feedback is propagated uniformly across all intermediate decisions. This leads to high gradient variance, unstable training, and many ineffective updates, ultimately limiting sustained model improvement. We propose a counterfactual-comparison framework for credit assignment. For each input, the framework samples multiple reasoning trajectories and treats their differences as implicit approximations to alternative decisions. This yields an implicit process-level advantage estimator that converts sparse terminal rewards into step-sensitive learning signals. Building on this framework, we introduce Implicit Behavior Policy Optimization (IBPO), which substantially improves training stability and the performance ceiling on mathematical and code-reasoning benchmarks. Our results point to a promising direction for unlocking the reasoning potential of LLMs.

cs.LG↗

arXiv2026

Rethinking the Comparison Unit in Sequence-Level Reinforcement Learning: An Equal-Length Paired Training Framework from Loss Correction to Sample Construction

This paper investigates the length problem in sequence-level relative reinforcement learning. We observe that, although existing methods partially alleviate length-related phenomena, a more fundamental issue remains insufficiently characterized: the comparison units used during training lack inherent comparability. Building on this observation, we propose a new perspective: the length problem should not be viewed merely as a loss-scaling or normalization bias, but rather as a \emph{comparison unit construction} problem. We further establish a sample-construction-based training framework that, instead of applying post-hoc corrections to unequal-length responses, proactively constructs equal-length, alignable, and comparable training segments during generation. Within this framework, we propose EqLen, a concrete method applicable to group-relative comparison algorithms such as GRPO, GSPO, and RLOO. Through dual-track synchronous generation, prefix inheritance, and segment masking, EqLen efficiently collects effective equal-length training segments and enables stable

cs.LG↗

arXiv2026

Internalizing Outcome Supervision into Process Supervision: A New Paradigm for Reinforcement Learning for Reasoning

The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning signals that can guide intermediate reasoning steps. Existing approaches either rely on outcome-level rewards for sequence-level optimization, which makes precise credit assignment difficult, or depend on externally constructed process supervision, which is costly and difficult to scale sustainably. To address this, we propose a new perspective: reinforcement learning for reasoning can be understood as the problem of internalizing outcome supervision into process supervision. From this perspective, we introduce a supervision-internalization method for reinforcement learning for reasoning, enabling the model to automatically extract process-level learning signals through identifying, correcting, and reusing failed reasoning trajectories, thereby achieving finer-grained policy optimization under outcome-only supervision. We further abstract this idea into a new training paradigm, in which the model continually generates and refines its own internal process supervision during reinforcement learning, opening a new path for fine-grained credit assignment in reinforcement learning for reasoning that differs from externally provided process supervision.

cs.LG↗

arXiv2026

Design Conditions for Intra-Group Learning of Sequence-Level Rewards: Token Gradient Cancellation

cs.LG↗

arXiv2026

Difference Feedback: Generating Multimodal Process-Level Supervision for VLM Reinforcement Learning

Vision--language models (VLMs) are increasingly aligned via Group Relative Policy Optimization (GRPO)-style training. However, relying solely on terminal outcome rewards yields sparse credit assignment in multi-step reasoning, weakening the linkage between visual evidence and intermediate steps and often causing unstable optimization and visual hallucinations. We propose Differential Feedback, which automatically constructs token/step-level supervision masks by repairing erroneous reasoning trajectories, explicitly marking the key positions that require correction. Without costly large-scale step-by-step human annotations, our method enables process-level visual alignment and can be seamlessly integrated into existing GRPO-like frameworks. Experiments on multimodal reasoning benchmarks including MMMStar and MathVista show an average 3% improvement under matched compute budgets. Our approach offers an effective, low-cost solution for accurate vision--reasoning process alignment.

cs.CV↗

arXiv2026

PoseStreamer: A Multi-modal Framework for 3D Tracking of Unseen Moving Objects

Six degree of freedom (6DoF) pose estimation for novel objects is a critical task in computer vision, yet it faces significant challenges in high-speed and low-light scenarios where standard RGB cameras suffer from motion blur. While event cameras offer a promising solution due to their high temporal resolution, current 6DoF pose estimation methods typically yield suboptimal performance in high-speed object moving scenarios. To address this gap, we propose PoseStreamer, a robust multi-modal 6DoF pose estimation framework designed specifically on high-speed moving scenarios. Our approach integrates three core components: an Adaptive Pose Memory Queue that utilizes historical orientation cues for temporal consistency, an Object-centric 2D Tracker that provides strong 2D priors to boost 3D center recall, and a Ray Pose Filter for geometric refinement along camera rays. Furthermore, we introduce MoCapCube6D, a novel multi-modal dataset constructed to benchmark performance under rapid motion. Extensive experiments demonstrate that PoseStreamer not only achieves superior accuracy in high-speed moving scenarios, but also exhibits strong generalizability as a template-free framework for unseen moving objects.

cs.CV↗

arXiv2025

Double-Layered Silica-Engineered Fluorescent Nanodiamonds for Catalytic Generation and Quantum Sensing of Active Radicals

Fluorescent nanodiamonds (FNDs) hosting nitrogen-vacancy (NV) centers have attracted considerable attention for quantum sensing applications, particularly owing to notable advancements achieved in the field of weak magnetic signal detection in recent years. Here, we report a practical quantum-sensing platform for the controlled production and real-time monitoring of ultra-short-lived reactive free radicals using a double-layered silica modification strategy. An inner dense silica layer preserves the intrinsic properties of NV centers, while an outer porous silica layer facilitates efficient adsorption and stabilization of hydroxyl radicals and their precursor reactants. By doping this mesoporous shell with gadolinium (III) catalysts, we achieve sustained, light-free generation of hydroxyl radicals via catalytic water splitting, eliminating reliance on external precursors. The mechanism underlying this efficient radical generation is discussed in detail. The radical production is monitored in real time and in situ through spin-dependent T1 relaxometry of the NV centers, demonstrating stable and tunable radical fluxes, with concentration tunable across a continuous range from approximately 100 mM to molar levels by adjusting the catalyst condition. This study extends the technical application of nanodiamonds from relaxation sensing to the controlled synthesis of reactive free radicals, thereby providing robust experimental evidence to support the advancement of quantum sensing systems in intelligent manufacturing.

quant-ph↗

arXiv2025

CrossRay3D: Geometry and Distribution Guidance for Efficient Multimodal 3D Detection

The sparse cross-modality detector offers more advantages than its counterpart, the Bird's-Eye-View (BEV) detector, particularly in terms of adaptability for downstream tasks and computational cost savings. However, existing sparse detectors overlook the quality of token representation, leaving it with a sub-optimal foreground quality and limited performance. In this paper, we identify that the geometric structure preserved and the class distribution are the key to improving the performance of the sparse detector, and propose a Sparse Selector (SS). The core module of SS is Ray-Aware Supervision (RAS), which preserves rich geometric information during the training stage, and Class-Balanced Supervision, which adaptively reweights the salience of class semantics, ensuring that tokens associated with small objects are retained during token sampling. Thereby, outperforming other sparse multi-modal detectors in the representation of tokens. Additionally, we design Ray Positional Encoding (Ray PE) to address the distribution differences between the LiDAR modality and the image. Finally, we integrate the aforementioned module into an end-to-end sparse multi-modality detector, dubbed CrossRay3D. Experiments show that, on the challenging nuScenes benchmark, CrossRay3D achieves state-of-the-art performance with 72.4 mAP and 74.7 NDS, while running 1.84 faster than other leading methods. Moreover, CrossRay3D demonstrates strong robustness even in scenarios where LiDAR or camera data are partially or entirely missing.

cs.CV↗

arXiv2025

Practice on Long Behavior Sequence Modeling in Tencent Advertising

Long-sequence modeling has become an indispensable frontier in recommendation systems for capturing users' long-term preferences. However, user behaviors within advertising domains are inherently sparse, posing a significant barrier to constructing long behavioral sequences using data from a single advertising domain alone. This motivates us to collect users' behaviors not only across diverse advertising scenarios, but also beyond the boundaries of the advertising domain into content domains-thereby constructing unified commercial behavior trajectories. This cross-domain or cross-scenario integration gives rise to the following challenges: (1) feature taxonomy gaps between distinct scenarios and domains, (2) inter-field interference arising from irrelevant feature field pairs, and (3) target-wise interference in temporal and semantic patterns when optimizing for different advertising targets. To address these challenges, we propose several practical approaches within the two-stage framework for long-sequence modeling. In the first (search) stage, we design a hierarchical hard search method for handling complex feature taxonomy hierarchies, alongside a decoupled embedding-based soft search to alleviate conflicts between attention mechanisms and feature representation. In the second (sequence modeling) stage, we introduce: (a) Decoupled Side Information Temporal Interest Networks (TIN) to mitigate inter-field conflicts; (b) Target-Decoupled Positional Encoding and Target-Decoupled SASRec to address target-wise interference; and (c) Stacked TIN to model high-order behavioral correlations. Deployed in production on Tencent's large-scale advertising platforms, our innovations delivered significant performance gains: an overall 4.22% GMV lift in WeChat Channels and an overall 1.96% GMV increase in WeChat Moments.

cs.IR↗

arXiv2025

Multi-Layer GRPO: Enhancing Reasoning and Self-Correction in Large Language Models

The Group Relative Policy Optimization (GRPO) algorithm has demonstrated considerable success in enhancing the reasoning capabilities of large language models (LLMs), as evidenced by DeepSeek-R1. However, the absence of intermediate supervision in GRPO frequently leads to inefficient exploration dynamics. A single error in a complex reasoning chain can invalidate the entire solution, resulting in abrupt reward vanishing and compromising training stability.To address these challenges, we propose MGRPO (Multi-layer GRPO). MGRPO operates in two layers: the first layer employs standard GRPO to generate an initial response. This response, along with the original query, is then fed into a second-layer GRPO process. This second layer is specifically trained to identify and correct errors in the initial response, effectively creating a self-correction loop. This mechanism provides implicit process-level supervision by rewarding successful error correction, without requiring an explicit, densely-annotated reward model. Experimental results on several mathematical reasoning benchmarks demonstrate that MGRPO significantly outperforms standard GRPO, achieving superior performance by fostering both reasoning and self-correction abilities.

cs.LG↗