arXiv subjects

Yuanda Xu

Publications and source records attributed to Yuanda Xu.

At least 19 recordsLinked to original sources

arXiv2026

Composing What Each Teacher Learned: Delta Distillation for Multi-Teacher On-Policy Learning

Multi-teacher on-policy distillation (MOPD) is used in two settings. In common-domain composition, several teachers score each student rollout from one prompt domain and their signals form a single target; in routed-domain distillation, prompts from different domains are assigned to the corresponding specialist. Both settings usually transfer each teacher's endpoint policy, which mixes what post-training changed with preferences inherited from the teacher's base. We introduce $Δ$-MOPD, which transfers each teacher's teacher-minus-base logit shift re-anchored at the student's frozen initialization, and compare it with endpoint supervision in both settings while holding teacher selection fixed. We first expose the mechanism that impedes endpoint transfer: inherited base pull can exceed the post-training shift. Removing it reduces the teacher-term norm ratio and target--student KL. Across our experiments, the results suggest that shift targets are particularly useful when teacher signals are combined at a state. With three composed teachers, $Δ$-MOPD exceeds endpoint composition by $4.11$ Math and $1.95$ five-benchmark points; with two, it matches endpoint accuracy. Under phased routing, it achieves higher mean performance in both phase orders and reduces the observed order gap from $10.50$ to $6.42$ points. Under interleaved routing, where each update involves one teacher, the two targets perform comparably. The phased results provide supporting evidence that the benefit may extend to signals accumulated across training phases. Target construction is thus an independent design axis in MOPD, complementary to teacher selection. The experiment repo could be find at https://github.com/HJSang/Delta-MOPD

cs.LG↗

arXiv2026

Reconstruction-Optimized Expert Pruning for Mixture-of-Experts Language Models

Mixture-of-Experts (MoE) models reduce computation through sparse expert activation, but deployment still requires storing a large number of expert parameters. We study post-training expert pruning using task-domain calibration data as a subset-selection problem: given a pretrained MoE layer, select a fixed number of experts that best reconstruct its original output. Exact subset search is combinatorial and becomes intractable for modern MoE models with many experts per layer. We develop OptEP, a scalable continuous relaxation that directly optimizes differentiable expert-selection variables, followed by a lightweight reconstruction-based update of the retained expert weights. Across multiple MoE architectures and tasks spanning mathematical reasoning and code generation, our approach improves over the strongest existing expert-pruning baselines, with absolute accuracy gains of up to 15.05% on Qwen3-30B-A3B, 14.55% on Qwen3-235B-A22B, 11.06% on GLM-4.5-Air, and 16.20% on Mixtral-8x7B. The improvements are particularly pronounced under aggressive pruning, demonstrating that reconstruction-driven expert selection and weight adaptation can preserve substantially more of the original model's performance while reducing the number of retained experts.

cs.LG↗

arXiv2026

Amplified moments and a refinement of the quasi-Riemann hypothesis

Recently, OpenAI announced a uniform $7/8$ zero-free half-plane for finite-order Hecke $L$-functions over $\mathbb{Q}(\sqrt{-3})$, together with its transfer to Dirichlet $L$-functions. Assuming the analytic inputs of that work, we improve the boundary from $7/8=0.875$ to $8748867/10000000=0.8748867$ for the same families. The improvement combines a relaxed direct estimate with an amplified first moment of the reflected numerator, obtained from the existing fourth-moment estimate. A two-stage parameter argument yields the stated boundary without strengthening the inverse-moment estimate.

math.NT↗

arXiv2026

A matching lower bound for the sextic large sieve and structured prime moments

We study the contrast between the large-sieve norm and the second moment of structured prime coefficients for sextic residue characters over the Eisenstein integers. For squarefree row and column ideals of norms at most A and B, we prove a lower bound of order (AB)^(-epsilon) times (A + B + A^(5/6) B^(1/3) + A^(1/3) B^(5/6)), matching de Faveri's upper bound throughout the full parameter range. In particular, the squared full-cutoff norm at balance is at least Q^(7/6 - epsilon). The proof uses the uniform unmarked character moments of OpenAI's September 2026 manuscript, a Gauss second moment uniform in moving prime exclusions, and a centered comparison that transports a squarefree-row signal between column scales. With the additional unmarked inverse moment and buffered zero detector from the same source, we derive a low-height zero-density estimate and bound the second moment of a fixed smooth prime sum by Q^((37 - 10 sqrt(6))/6 + epsilon). We also treat bounded convolutions of independently weighted large primes. An appendix retains the first version's unbalanced lower bound and its exponent 17/16, without using the additional plain or inverse moment estimates.

math.NT↗

arXiv2026

Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated to the model and reward density where it is most informative. We identify a reward-density principle: sparse sequence-level reward is most useful on models that can explore and discover better behavior, while dense token-level teacher supervision is better suited for compressing that behavior into a smaller deployment model; accordingly, scarce labeled data should be used upstream on the strongest available teacher, then transferred downstream as dense supervision. We evaluate this rule through a four-stage workflow:teacher RL, forward-KL warmup, on-policy distillation, optional post-bridge student RL on verifiable math and code generation with Qwen3, Llama, and Qwen2.5 models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student ($79.3\%$ vs.\ $75.9\%$ on MATH; $25.2\%$ vs.\ $19.8\%$ on AIME~2024), while transfer from the same teacher before RL underperforms. A component ablation confirms that each stage is load-bearing: the RL-improved teacher adds $7.8$ absolute points on MATH over a raw teacher of the same size, the forward-KL warmup adds $1.7$, and on-policy distillation adds $3.3$. The teacher-quality ordering: raw-teacher transfer $<$ direct GRPO $<$ RL-teacher transfer, replicates on Llama-3.1-8B-Instruct with a Llama-3.3-70B-Instruct teacher and on Qwen2.5-7B-Instruct for code generation with a Qwen2.5-32B-Instruct teacher. The operational lesson is to avoid spending scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge. The OPD implementation used in our experiments is available at https://github.com/HJSang/OPSD_OnPolicyDistillation.

cs.LG↗

arXiv2026

Budgeted KV-Cache Repair for Evolving Contexts

Language-model agents revise their working context as information becomes obsolete, but deleting text does not erase its influence on cached computation. Later key-value (KV) states remain conditioned on the deleted content, while recomputing the entire retained suffix can be costly. We introduce budgeted KV-cache repair: recovering task performance by recomputing a user-chosen fraction of the retained suffix. Comparing repair allocations under identical relevance scores and token budgets, we find that refreshing coherent regions can substantially outperform refreshing isolated tokens. This finding motivates Semantic-Unit Refresh (SUR), which allocates the budget to query-relevant text regions using inexpensive embedding scores, without training or an auxiliary transformer forward. To execute these repairs efficiently, a layer-packed executor processes selected states together at each layer while preserving full causal cache access. Across five models, SUR achieves strong recovery in controlled deletion tasks while recomputing only 2-5% of the suffix. On four natural multi-hop QA datasets, it achieves near-full-recompute exact match at a 5% budget with lower post-edit latency. The executor accelerates fragmented refresh by up to 16.1x over interval-wise execution.

cs.AI↗

arXiv2026

LatentPress: Context Compression Beyond Text and Vision

Compressed context is usually carried as human-readable text or as rendered images that must be decoded, even when its consumer is a language model. We introduce LatentPress, which writes conversational histories and long documents into a third representation: continuous memory tokens that a frozen decoder reads directly through its input-embedding interface, with no text reconstruction at inference. A small reader-matched writer compresses $4$-$16\times$ while training only an adapter (4.2M-26.2M parameters, $\sim\!0.1\%$ of the decoder). On LongMemEval, LatentPress reaches $0.504$ accuracy at $7.70\times$ compression versus $0.490$ for uncompressed evidence, outperforming text summaries (0.184) and OCR-based compression (0.426 to 0.312). On LongBench-QA, in-domain writers match or exceed raw-context reading at $4$-$8\times$ compression, while $16\times$ trails raw. Writing takes 43ms per conversation, roughly an order of magnitude faster than text summarization or OCR reconstruction, and reading is $5$-$9\times$ faster than raw context or cached OCR. We validate the interface under two transfer settings, zero-shot from UltraChat to LongMemEval memory QA and from LongMemEval-derived QA to unseen LongBench document domains, establishing direct soft tokens as a practical machine-facing context interface beyond text and vision. The implementation of the experiments could be found at: https://github.com/HJSang/LatentPress.

cs.LG↗

arXiv2026

Hierarchical Reinforcement Learning with Stable Temporal Abstraction for Language Model Agents

Hierarchical reinforcement learning improves long-horizon control by organizing primitive actions around persistent subgoals and assigning credit at multiple temporal scales. Recent hierarchical language agents bring these benefits to interactive tasks by explicitly separating subgoal planning from action execution. We observe, however, that an explicit hierarchy does not by itself determine how stable the resulting temporal abstraction is: the learned boundary policy may replace the subgoal almost every turn, making it effectively transient, or retain a subgoal after it has stopped being appropriate. We call this temporal abstraction instability. We propose Stable Temporal Abstraction via Constrained Optimization (STAC), a constrained boundary-policy optimization method that represents premature replanning and stale persistence as constraint costs. STAC applies the resulting Lagrangian costs only to the sampled boundary decision, leaving the underlying algorithm's rewards, critic targets, subgoal advantages, and primitive-action advantages unchanged. Across two backbones and two benchmarks, STAC improves success over a strong hierarchical baseline by $8.1$ and $7.9$ points on ALFWorld and WebShop with Qwen3-0.6B, and by $23.5$ and $15.8$ points with Llama-3.2-1B-Instruct.

cs.AI↗

arXiv2026

CONTRAMEM: Learning Self-Evolving Procedural Memory from Contrasting Multi-Model Trajectories

Autonomous computer-use agents are increasingly applied to long-horizon tasks requiring coordinated application calls, persistent state tracking, and verifier-sensitive writes, yet they remain prone to procedural failures: misreading application state, tool semantics, or task progress. Procedural memory promises more consistent decisions and less redundant exploration, but constructing high-quality memory without model training remains challenging. We introduce CONTRAMEM, a source-flexible, training-free framework for self-evolving procedural memory that treats same-task outcome variation as supervision: differences in correctness, efficiency, recovery, and failure modes expose outcome-relevant procedural distinctions, distilled into a compact bank of app-level Function Cards and task-level Skill Cards that evolves through localized curation rather than append-only accumulation or whole-bank rewriting. On held-out GAIA2/ARE computer-use tasks, CONTRAMEM more than doubles the success rate across the three source-model targets (26.2% to 55.3%), with consistent per-model gains (GPT-5.5: 27.5 to 61.0; Claude Sonnet 4.6: 28.0 to 52.5; DeepSeek V4 Pro: 23.0 to 52.5). The same bank transfers unchanged to the unseen Qwen3.7 Plus (18.5 to 35.5), indicating transferable procedural knowledge rather than model-specific behavior. The same construction carries over unchanged to AppWorld, beating both no memory and its own single-source self-memory variant for all three mid-tier agents on both public test splits. Under a matched trajectory budget, heterogeneous multi-model trajectories yield stronger memory than self- or same-model multi-rollout memory: the margin comes from contrastive behavioral diversity, not stronger source agents or more sampling.

cs.AI↗

arXiv2026

Smaller Models, Better Rejects: Preference Distillation Scaling

Preference distillation typically treats a teacher response as preferred and the student's own response as rejected. This assumes that self-generated failures are the most informative negatives and that rejects must come from a model at least as large as the student, making generation costly at scale. We find neither assumption holds: across students from 7B to 72B, smaller frozen models generate rejects with less inference compute yet train stronger students than self-generated rejects, before and after sequence-level knowledge distillation, on code generation and mathematical reasoning. To explain this result, we derive a finite-horizon utility bound for Direct Preference Optimization in a linearized feature model. The bound characterizes favorable reject distributions and motivates three interventions. First, mixing rejects from smaller and student-scale models improves performance as the smaller model's share increases. Second, reassigning rejects to other prompts and shuffling their code tokens still outperform length-matched gibberish, showing that task structure contributes to reject utility. Third, selecting candidates with lower likelihood under the reference policy improves net transfer when higher-likelihood candidates provide less useful contrast. Lower-likelihood selections outperform higher-likelihood ones for every source. These results suggest that effective rejects preserve task structure while limiting coupling to the reference policy, and that smaller frozen models can provide them at low cost.

cs.LG↗

arXiv2026

PersonaEval: Persona-Based User Simulation for Evaluating Interactive Applications

Real user studies are important for understanding how people interact with systems under test or already deployed. In practice, however, they are often costly, time-consuming, and difficult to scale. To address these challenges, we introduce PersonaEval, a persona-based user simulation framework that approximates real-user behavior across diverse interactive settings. PersonaEval connects simulated users drawn from existing persona datasets to task-specific application interfaces and collects the interaction trajectories and outcomes. PersonaEval provides a plug-and-play evaluation workflow in which the application being evaluated can be easily changed. In this demo, we present PersonaEval on three forms of interactive applications: surveys, chatbots, and web applications. Together, these examples show that PersonaEval can support repeatable, parallelizable, and scalable evaluation across different interaction settings, while producing user-oriented feedback and task-specific behavior.

cs.HC↗

arXiv2026

MicroVerse: An Instrument for Measuring Self-Authored Identity Drift in Long-Horizon Multi-Agent Language-Model Simulations

Long-horizon, multi-agent language model (LM) simulations are widely proposed for studying social behavior, yet instruments to measure whether persona-conditioned agents maintain identity fidelity under sustained pressure are lacking. We present MicroVerse, a behavioral-science instrument that measures identity drift in generative agents. Agents carry an immutable "soul file" (core values, moral boundaries, personality, goals) and inhabit a resource-scarce 50 x 50 environment where water is a non-respawning survival constraint. Scarcity is operationalized via a per-tick existence-cost gradient. The eight-verb action space maps directly to moral boundaries (trade, talk, attack, scavenge). Using a three-layer memory architecture, agents periodically revise a mutable current identity against their immutable original soul via importance-triggered reflection. To mitigate survivor bias, MicroVerse decouples measurement from behavior using uniform longitudinal engine snapshots every N ticks alongside a forced-end snapshot of all living and dead agents. Identity drift is scored offline using a paraphrase-aware, value-anchored, multi-register diff rather than raw cosine similarity. We evaluate the instrument via a controlled seed run (n = 25) and a reflection-threshold sweep (thresholds {40, 80, 150}) to determine if drift dynamics are gate artifacts or threshold-robust properties. We report two primary findings: (1) Anti-self-deception emerges unprompted as the single largest semantic category of identity modification (27 of 111 added boundaries, 24%). (2) The system is threshold-robust; lower gates accelerate and increase revision frequency but preserve drift direction. All empirical results are strictly preliminary existence proofs and effect shapes (one model, one seed per arm, n = 25) rather than statistical significance claims.

cs.CL↗

arXiv2026

MatrAIx: Simulating the World with 8.3 Billion Persona Agents

Human evaluation of AI systems and digital products is costly, slow, and difficult to scale. Offline evaluations are more scalable but often abstract away human diversity and interactive behavior. We therefore introduce MatrAIx, a population-scale simulated-user evaluation infrastructure for testing AI systems and digital products with heterogeneous users. MatrAIx has three core components: First, Persona 8B contains 8.3 billion persona records represented by 1,290 categorical dimensions. Records are either sampled from a dependency graph that preserves correlated attributes or derived from human-authored profiles. We release a quality-filtered coreset of approximately 1 million personas, comprising 599,847 human-grounded and 400,000 synthetic records. Second, the MatrAIx Playground provides four environments in which diverse users evaluate and interact with digital products: Survey, AI Chatbot, Web, and App. Third, MatrAIx provides 1,010 application tasks spanning more than 25 domains, including Commerce, Software, Finance, and Healthcare. We conducted 18,189 evaluation trials across eight representative tasks. Persona agents were powered by three LLMs: Claude Opus 4.8, GPT 5.5, and Claude Haiku 4.5. The resulting feedback captures how decisions and preferences vary across persona backgrounds, including hesitation after a price increase, willingness to continue after an AI assistant fails, and latency tolerance. We conducted two main validation studies: First, a 400-trial controlled study evaluated persona adherence across ten behavioral attributes and all four environments. The declared behavior was expressed or correctly suppressed in 366 trials (91.5%). Second, human and LLM judges evaluated the extraction quality of human-grounded personas. Overall, MatrAIx provides an end-to-end infrastructure for evaluating AI systems and digital products with diverse simulated human users.

cs.AI↗

arXiv2026

TRIAGE: Role-Typed Credit Assignment for Agentic Reinforcement Learning

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that the Bayes-optimal role-measurable correction is the L2 projection of the per-segment advantage residual onto the role variable, and that TRIAGE's fixed role constants approximate this projection, reducing advantage estimation error whenever the judge is reliable; we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional $10.4\%$ and $14.8\%$ relative to GRPO.

cs.LG↗

arXiv2026

TREK: Distill to Explore, Reinforce to Refine

Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-$r$ proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.

cs.LG↗

arXiv2026

CRISP: Compressed Reasoning via Iterative Self-Policy Distillation

Reasoning models often generate far more tokens than a task requires, which raises inference cost and can compound errors. We introduce CRISP (Compressed Reasoning via Iterative Self-Policy Distillation), an on-policy self-distillation method that teaches a model to reason more concisely by distilling its own concise behavior back into itself. The method uses a single idea: condition the same model on a "be concise" instruction to obtain teacher logits, then minimize the per-token reverse KL divergence between the student and this teacher on the student's own rollouts. It requires no ground-truth answers, no token budgets, and no difficulty estimators. The reverse-KL objective is naturally difficulty-adaptive: it compresses easy problems aggressively while preserving the reasoning steps that hard problems require. On Qwen3-14B, CRISP cuts reasoning length by up to 56% on MATH-500 and 38% on the harder AIME 2024, while improving MATH-500 accuracy by up to 3.3 points over the base model and holding AIME 2024 accuracy within about one point. This behavior generalizes across model sizes and families: Qwen3-8B shows the same compression with accuracy preserved, and DeepSeek-R1-Distill-Llama-8B improves accuracy on all five benchmarks while shortening its responses. General capabilities are preserved across all three models. Code is available at https://github.com/HJSang/OPSD_Reasoning_Compression.

cs.LG↗

arXiv2026

TIP: Token Importance in On-Policy Distillation

On-policy knowledge distillation (OPD) trains a student on its own rollouts under token-level supervision from a teacher. Not all token positions matter equally, but existing views of token importance are incomplete. We ask a direct question: which tokens carry the most useful learning signal in OPD? Our answer is that informative tokens come from two regions: positions with high student entropy, and positions with low student entropy plus high teacher--student divergence, where the student is overconfident and wrong. Empirically, student entropy is a strong first-order proxy: retaining $50\%$ of tokens with entropy-based sampling matches or exceeds all-token training while reducing peak memory by up to $47\%$. But entropy alone misses a second important region. When we isolate low-entropy, high-divergence tokens, training on fewer than $10\%$ of all tokens nearly matches full-token baselines, showing that overconfident tokens carry dense corrective signal despite being nearly invisible to entropy-only rules. We organize these findings with TIP (Token Importance in on-Policy distillation), a two-axis taxonomy over student entropy and teacher--student divergence, and give a theoretical explanation for why entropy is useful yet structurally incomplete. This view motivates type-aware token selection rules that combine uncertainty and disagreement. We validate this picture across three teacher--student pairs spanning Qwen3, Llama, and Qwen2.5 on MATH-500 and AIME 2024/2025, and on the DeepPlanning benchmark for long-horizon agentic planning, where Q3-only training on $<$$20\%$ of tokens surpasses full-token OPD. Our experiments are implemented by extending the OPD repository https://github.com/HJSang/OPSD_OnPolicyDistillation, which supports memory-efficient distillation of larger models under limited GPU budgets.

cs.LG↗

arXiv2026

PACED: Distillation and On-Policy Self-Distillation at the Frontier of Student Competence

Standard LLM distillation treats all training problems equally -- wasting compute on problems the student has already mastered or cannot yet solve. We empirically show that this inefficiency has a precise gradient-level signature: the cross-problem gradient signal-to-noise ratio (SNR) follows a bell curve over student pass rate, collapsing at both extremes. We propose PACED, which weights each problem by $w(p) = p(1{-}p)$ where $p$ is the student's empirical pass rate -- concentrating training on the zone of proximal development. This requires only student rollouts, no architectural changes, and no hyperparameters. We prove the Beta kernel $w(p) = p^α(1{-}p)^β$ is the leading-order optimal weight family arising from the SNR boundary-collapse structure, and is minimax-robust under misspecification (worst-case efficiency loss $O(δ^2)$). Across Qwen3, Qwen2.5, and Llama-3 families, PACED sets a new state of the art in our experimental setting on MATH-500, AIME~2024, and AIME~2025, improving over unweighted distillation by up to $\mathbf{+8.2}$ and over the strong AKL baseline by up to $\mathbf{+3.6}$, while reducing forgetting to $\mathbf{1.4\%}$ and $\mathbf{0.6\%}$ in distillation and self-distillation. A two-stage forward-then-reverse KL schedule pushes gains further to $\mathbf{+5.8}$ over standard forward KL on the hardest benchmark.

cs.AI↗