arXiv subjects

Yihang Sun

Publications and source records attributed to Yihang Sun.

At least 19 recordsLinked to original sources

arXiv2026

Improved Local Leakage Resilience of Shamir Secret Sharing and Worst-Case Optimal Polynomial Intersection

We study two problems: Local Leakage Resilience (LLR) for Shamir secret sharing, and worst-case Optimal Polynomial Intersection (OPI), over a prime field $\mathbb{F}_p$. For a polynomial $Q(X)$ of degree less than $k$, LLR for Shamir secret sharing asks what a few leaked bits from each of the $n$ shares $Q(α_1), \ldots, Q(α_n)$ reveal about $Q(0)$. Given (worst-case) input lists $S_1, \ldots, S_n \subset \mathbb{F}_p$, OPI seeks a polynomial $Q(X)$ so that $Q(α_i) \in S_i$ for as many $i$ as possible. Leveraging recent connections between these two problems due to (Sun, Wootters 2026), we improve the state-of-the-art for both problems. For LLR, we show that there is some constant $δ> 0$ so that Shamir secret-sharing is one-bit LLR (only a negligible amount about $Q(0)$ is learned) whenever $R := k/n \geq 1/2 - δ$. This is the first result to break the so-called ``one-half barrier'' for LLR, and improves over the previous best known result, requiring $R \geq 0.668$ (Kasser, 2025). For OPI, we give a quantum algorithm that finds a polynomial $Q(X)$ that agrees with at least a $\mathsf{SCL}_ρ(R)-\varepsilon$ fraction of the lists, for every fixed $\varepsilon>0$, where $\mathsf{SCL}_ρ$ is the \emph{semicircle law} of (Jordan et al., 2025). This improves previous algorithmic (and existential) results of (Jo, 2026) and (Horinaga, Yamakawa, 2026). We also give further improved existential results for all OPI instances; and when the evaluation points $α_i$ are chosen at random, for every rate $R > 0$ we show that, with high probability, for worst-case $S_i$ there exists \emph{perfect} solution. Finally, we adapt the hardness result of (Yamakawa, Zhandry, 2024) to apply to OPI (rather than a folded version); this gives an unconditional separation between the quantum and classical hardness of OPI relative to a membership oracle.

quant-ph↗

arXiv2026

Resolving Representation Ambiguity in Feedforward Novel View Synthesis Transformer via Semantic-Spatial Decoupling

Transformer-based models have advanced feedforward novel view synthesis (NVS). Current architectures such as GS-LRM and LVSM mix semantic information (e.g., RGB) and spatial information (e.g., Plücker rays) into a shared feature space. Since Plücker rays naturally carry lattice-like spatial structure, these designs can make the spatial bias interfere with appearance representation and degrade rendering fidelity. To this end, we propose to decouple the representation of feedforward NVS transformers into separate semantic and spatial tokens. The decoupled design keeps semantic and spatial information explicit in their branches while preserving cross-branch interaction through shared attention routing. Built on this design, we introduce optional categorized supervision and bidirectional modulation: the former provides branch-specific training signals, while the latter improves interaction between the two branches. Notably, the base decoupled design introduces virtually zero additional inference latency due to its architectural design. The proposed designs achieve consistent improvements, demonstrating effectiveness across decoder-only and encoder-decoder feedforward NVS models.

cs.CV↗

arXiv2026

Improved LCL Equivalences and Curve Decoding Alphabet Sizes

Local Coordinate-wise Linear (LCL) properties, introduced by Levi, Mosheiff, and Shagrithaya (2025), capture coding-theoretic properties such as list decoding and list recovery. They showed that every LCL property has the same rate threshold for random linear codes (RLC) and random Reed--Solomon codes (RRS). Brakensiek, Chen, Dhar, and Zhang (2025) extended this to random additive codes. Thus any property of all subspace design codes holds for RLCs and RRS at the same rate. In this work, we improve the probabilistic guarantees in the RRS local equivalence theorem and extend the equivalence to all known subspace design constructions individually. Each such construction, including folded Reed--Solomon codes, has the same LCL threshold as RLC and RRS codes. We apply these results to alphabet-size bounds for curve decoding. Curve decoding, introduced by Goyal and Guruswami (2025) and Carmon et al. (2026), is a row-span-constrained LCL property implying proximity gaps (PG), correlated agreement (CA), and mutual correlated agreement (MCA), relevant to IOPs and SNARKs. Informally, a rate-$R$ code $C \subset \mathbb{F}^n$ is $(\ell,δ,a,b)$-curve decodable if any degree-$\ell$ curve $u:\mathbb{F}\to\mathbb{F}^n$ that is $δ$-close to $C$ on at least $a$ points has at least $b\leq a$ nearby codewords lying on a degree-$\ell$ curve in $C$. Goyal and Guruswami (2025) and Goyal, Guruswami, Sun, and Wootters (2026) established curve decodability for RLC and RRS codes at radius $δ$ approaching $1-R$, but with large alphabets in $\ell$ and $η:=1-R-δ$. Using our improved LCL equivalence and rank-sensitive counting inspired by Goyal and Guruswami (2026), we exponentially improve alphabet requirements while matching the best known values of $(a,b)$. For $\ell=O(1)$, our alphabet-size bounds match the best known for list decoding, and improves results for PG, CA, and MCA.

cs.IT↗

arXiv2026

MemT-1.0: Towards Memory-Native Evolution

Memory-native evolution requires making memory an intrinsic capability of foundation models, enabling them to continuously accumulate and utilize information. To this end, we introduce MemT-1.0, a new architecture of memory foundation models that internalize memory as part of model computation. Building on Metis, MemT-1.0 employs Gated DeltaNet-2 with a stable token-level memory update mechanism within each turn. We further introduce Mixture-of-Storage to scale native memory capacity. Following a deliberate backbone preparation, we develop a two-stage training pipeline consisting of continued pre-training and post-training, supported by 34B tokens of training data and efficient training and inference infrastructure. We release a model family comprising MemT-1.0-Nano and MemT-1.0-Flash, and conduct a comprehensive evaluation of memory and general capabilities. The results show that they outperform the parametric memory baselines on average and remain competitive with retrieval-augmented methods, while largely preserving general capabilities. At a history length of 128K tokens, MemT-1.0-Nano achieves approximately $1.86\times$ end-to-end inference speedup and a $66\times$ reduction in persistent storage relative to full context KV cache. By internalizing retrieved procedural experience, MemT-1.0 improves task success on agentic tasks, providing a practical step toward memory-native evolution.

cs.CL↗

arXiv2026

Learning from Teacher Continuations at Student States

We present OLIVE (OnLine InterVEntion). At each iteration, the evolving student policy generates a new prefix, the teacher continues it autoregressively, and the student is updated using cross-entropy computed on the teacher-generated tokens. Each design choice targets a corresponding limitation of existing distillation methods: (1) sequential covariate shift in offline supervised fine-tuning (SFT) on fixed teacher trajectories, (2) fragmented supervision under prefix failure in token-level on-policy distillation (OPD), and (3) the need for access to teacher token probabilities in distribution-matching distillation. OLIVE achieves higher reasoning performance than OPD (with a top-16 KL approximation) at comparable GPU-hour cost. Our asynchronous implementation further reduces OLIVE's total training time by 23.8\%. We evaluate OLIVE on both hard reasoning tasks and agentic tasks which reflects modern post-training scenarios, and it consistently outperforms existing distillation methods under the same training budget. By regenerating prefixes from the evolving student, OLIVE continues improving after offline distillation plateaus while better preserving the general capabilities and plasticity of the student. Using only text from GPT-5.4-mini, continuously training with OLIVE outperforms offline SFT from the same teacher by 13\% on ScienceWorld. These results support OLIVE as an effective and efficient approach to online language-model distillation.

cs.CL↗

arXiv2026

Optimal Quantum Speedups for Repeatedly Nested Expectation Estimation

We study the estimation of repeatedly nested expectations (RNEs) with a constant horizon (number of nestings) using quantum computing. We propose a quantum algorithm that achieves $\varepsilon$-error with cost $\tilde O(\varepsilon^{-1})$, up to logarithmic factors. Standard lower bounds show this scaling is essentially optimal, yielding an almost quadratic speedup over the best classical algorithm. Our results extend prior quantum speedups for single nested expectations to repeated nesting, and therefore cover a broader range of applications, including optimal stopping. This extension requires a new derandomized variant of the classical randomized Multilevel Monte Carlo (rMLMC) algorithm. Careful de-randomization is key to overcoming a variable-time issue that typically increases quantized versions of classical randomized algorithms.

quant-ph↗

arXiv2026

Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent

We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation in a tractable model where the barrier-crossing mechanism can be computed explicitly. For one-dimensional double-well objectives in the under-guessing regime, we compute the expected dynamical hitting times from a local minimum to the global minimum. We prove that both sECD and qECD exhibit exponential improvements in continuous hitting time relative to their respective gradient-based baselines, stochastic gradient descent (SGD) and quantum tunneling walk (QTW). For objectives with tall barriers, qECD admits a further hitting time improvement over sECD. Mechanistically, ECD sidesteps the exponential cost associated with rare-escape events of SGD from local minima by moving from dissipative to energy-conserving dynamics.

quant-ph↗

arXiv2026

From Gradients to Capabilities: Understanding Multi-Teacher On-Policy Distillation

Multi-teacher on-policy distillation (MOPD) aims to combine the strengths of RL-trained teachers in a single student, but how teacher signals affect parameter changes remains underexplored. We study Qwen3-1.7B with four domain teachers trained with RL from the same initialization as the student, comparing gradients, optimizer updates, and task learning curves, with additional SmolLM3-3B diagnostics. We find that several factors influence teacher signals. First, loss averaging implicitly weights responses: token averaging favors longer responses, and equalizing domain contributions retains this weighting within domains. Second, Adam's first moment reduces differences in parameter updates: the cosine similarity is 0.83 between teachers and 0.96 between averaging rules, despite differences in raw gradients. Third, BF16 rounding hides small changes: about 97\% of FP32 master weights differ from initialization, but only 7--11\% of BF16 weights do. Finally, the top-64 intersection KL gradient closely matches Qwen's full-vocabulary gradient, but the effect on task performance depends on averaging: mathematics accuracy is 2.6 points higher than with sampled-token policy-gradient (PG) under response averaging and 2.1 points lower under global token averaging.

cs.LG↗

arXiv2026

Determinant maximization subject to a partition matroid constraint via stable distributions

Given vectors $v_i \in {\mathbb R}^d$, we consider the problem of choosing a set $I$ independent in a partition matroid in order to maximize the determinant $\det (\sum_{i \in I} v_i v_i^T)$. Our main result is a polynomial-time approximation algorithm that finds a solution of value $det ( \sum_{i \in I} v_{i} v_{i}^T) \geq e^{-O(d)} OPT$, where $OPT = \max_{I^*} det ( \sum_{i \in I^*} v_{i} v_{i}^T)$. For partition matroids of rank $m \leq d$, we give a similar result for approximating the $m$-dimensional volume spanned by the chosen vectors, within a factor of $e^{O(m)}$. This matches earlier known algorithms that estimate the optimal value but do not find the corresponding solution, up to a constant in the exponent. Similar to these estimation algorithms, our algorithm is based on the saddle-point relaxation proposed by Nikolov and Singh. A new ingredient is a randomized transformation based on $1/2$-stable distributions, which converts the saddle-point relaxation into a more convenient multilinear relaxation.

cs.DS↗

arXiv2026

GMTRouter: Personalized LLM Router over Multi-turn User Interactions

Large Language Model (LLM) routing has demonstrated strong capability in balancing response quality with computational cost. As users exhibit diverse preferences, personalization has attracted increasing attention in LLM routing, since even identical queries may require different models to generate responses tailored to individual needs. However, existing approaches are not fully personalized and often fail to faithfully capture the complex interactions between users and LLMs. Moreover, user preference data is typically scarce and inconsistent in format, which limits the effectiveness of methods that directly leverage user-specific data. To address these challenges, we propose GMTRouter, which represents multi-turn user-LLM interactions as a heterogeneous graph with five node types: user, LLM, query, response and turn, thereby maximally preserving the rich relational structure of the interaction. Through a lightweight inductive graph learning framework combined with a tailored user-conditioned graph sampling mechanism, GMTRouter learns to capture user preferences from few-shot data, enabling effective personalization. Extensive experiments demonstrate that GMTRouter outperforms the strongest baselines, achieving up to a 0.108 absolute improvement in accuracy and a 0.124 improvement in AUC. More importantly, we further demonstrate that GMTRouter can adapt to new users using only few-shot data, without extensive fine-tuning. The code for GMTRouter is publicly available at https://github.com/ulab-uiuc/GMTRouter.

cs.CL↗

arXiv2026

HyGRAIL: Cost-Aware and Evidence-Grounded Scientific Hypothesis Discovery over Knowledge Graphs

Scientific knowledge graphs organize entities and relations extracted from scientific literature, but they remain inherently incomplete. Missing typed links in such graphs can therefore represent plausible scientific hypotheses, such as unexplored associations between materials and applications. However, scientific hypothesis discovery is challenging because true discoveries are extremely sparse among typed candidate pairs: graph neural networks (GNNs) are efficient but unreliable for ambiguous cases, while large language models (LLMs) are knowledgeable but too costly to apply exhaustively and are not naturally grounded in graph structures. We propose HyGRAIL, a cost-aware and evidence-grounded framework that combines heterogeneous GNN triage with LLM-based hypothesis review. HyGRAIL first uses a GNN to score candidate hypotheses and identify a validation-calibrated ambiguous region, routing only graph-uncertain cases to LLM review. For each routed hypothesis, HyGRAIL retrieves node-level associations and multi-hop relational paths from the knowledge graph (KG), then converts this structured evidence into natural language through template-based or LLM-based naturalization. An LLM review agent finally judges each hard hypothesis using the naturalized evidence and validation-selected decision criteria. On MatKG, HyGRAIL achieves the best F1 score of 0.429, improving over the strongest prior baseline by 0.242 F1 points and over the GNN-only baseline by 0.322. Meanwhile, GNN triage reduces the LLM call rate by 54.36% on average. Ablation studies further show that retrieved graph evidence is crucial for reliable hypothesis verification and that compact, two-sided evidence is more effective than simply increasing retrieval quantity.

cs.CL↗

arXiv2026

Useful Memories Become Faulty When Continuously Updated by LLMs

Learning from past experience benefits from two complementary forms of memory: episodic traces -- raw trajectories of what happened -- and consolidated abstractions distilled across many episodes into reusable, schema-like lessons. Recent agentic-memory systems pursue the consolidated form: an LLM rewrites past trajectories into a textual memory bank that it continuously updates with new interactions, promising self-improving agents without parameter updates. Yet we find that such consolidated memories produced by today's LLMs are often faulty even when derived from useful experiences. As consolidation proceeds, memory utility first rises, then degrades, and can fall below the no-memory baseline. More surprisingly, even when consolidating from ground-truth solutions, GPT-5.4 fails on 54% of a set of ARC-AGI problems it had previously solved without memory. We trace the regression to the consolidation step rather than the underlying experience: the same trajectories yield qualitatively different memories under different update schedules, and an episodic-only control that simply retains those trajectories remains competitive with the consolidators we test. In a controlled ARC-AGI Stream environment that exposes Retain, Delete, and Consolidate actions, agents preserve raw episodes by default and double the accuracy of their forced-consolidation counterparts; disabling consolidation entirely (episodic management only) matches this auto regime. Practically, robust agent memory should treat raw episodes as first-class evidence and gate consolidation explicitly rather than firing it after every interaction. Looking forward, reliable agentic memory will require LLMs that can consolidate without overwriting the evidence they depend on.

cs.AI↗

arXiv2026

Resonant Untrapping of Active Polymers in Breathing Lattices

In crowded environments, active polymers can trap themselves by winding into long-lived conformations. We show that fluctuations of the surrounding confinement can resonantly accelerate escape from these self-generated traps. Brownian dynamics simulations of a driven semiflexible chain in a breathing obstacle lattice reveal intermittent switching between a compact rotating spiral and an extended translating state. Long-time diffusion increases by up to two orders of magnitude when the environmental fluctuation rate becomes comparable to the spiral's intrinsic relaxation rate. The enhancement persists under stochastic fluctuations, showing that coherent periodic forcing is not required. Activity creates a second optimum: it promotes escape once favorable conformations form, yet at strong drive stabilizes the spiral and suppresses their formation. Resonant untrapping thus provides a general mechanism by which fluctuating environments regulate transport through barriers generated by internal conformational dynamics.

cond-mat.soft↗

arXiv2026

Metis: Memory Foundation Model

Recent advances in AI agents have increasingly internalized native capabilities into their underlying foundation models, giving rise to multimodal foundation models and large reasoning models. However, agent memory is still primarily implemented through external modules, leaving the native memory capability largely unexplored. In this paper, we take a first step toward this direction by introducing memory foundation models, which empower foundation models with native memory capabilities. We formalize native memory from two perspectives: a persistent and dynamically evolving memory state within the backbone, and native memory procedures that autonomously store and utilize information through model computation. We show that native memory offers advantages in architecture, end-to-end optimization, and efficiency. Based on this formulation, we propose Metis, the first prototype of memory foundation models. Metis introduces a new architecture that equips a foundation model with a native memory state, allowing historical information to be compressed into the model and accessed through memory attention. We construct large-scale memory-specific training data and introduce multiple optimization objectives to acquire these native memory procedures through mid-training. The online memory maintenance of Metis is gradient-free, and the memory update requires only a forward pass. At inference time, all learned model weights remain frozen, while the native memory states are autonomously transformed through standard forward computation. Through extensive experiments, we show that Metis exhibits native memory capabilities and further provide a detailed analysis of its strengths, limitations, and behaviors. To facilitate future research on memory foundation models, we release our project and model checkpoints.

cs.CL↗

arXiv2026

MemOps: Benchmarking Lifecycle Memory Operations in Long-Horizon Conversations

Long-term memory has become a foundational capability for LLM-based agents that accompany users across extended, multi-session interactions. Existing benchmarks, however, evaluate such memory almost exclusively through downstream question answering, scoring only the correctness of a final answer. This black-box formulation conflates the heterogeneous causes of memory failure, such as missing the introduction of a relevant fact, binding an operation to the wrong target, or relying on stale values after a correction. As a result, it can credit correct answers despite their reliance on inconsistent or unsafe memory states. In this paper, we argue that, in dynamic long-horizon interactions, memory is not a static collection of facts but a lifecycle of explicit operations, including remembering, forgetting, updating, reflecting, and their compositions. We introduce MemOps, a benchmark that reformulates conversational memory as a sequence of lifecycle operations and represents each memory event with a structured trace specifying its trigger, target, scope, state transition, and supporting evidence. A controllable generation pipeline embeds these operations into long, task-oriented conversations and produces gold operation traces together with six categories of operation-level probes, evaluated under both adjacent-evidence and long-context settings. Across long-context, retrieval-based, parametric and managed-memory systems, MemOps disentangles failure modes that final-answer accuracy alone conceals, revealing that current systems remain far from uniformly reliable. For instance, session-level retrieval outperforms turn-level retrieval, and long-context models remain notably weak at reconstructing ordered memory-state trajectories. These results move long-term memory evaluation from final-answer scoring toward interpretable, operation-level diagnosis.

cs.AI↗

arXiv2026

Locality of Curve-Decoding and Improved Proximity Gaps

Proximity gaps are a property of error correcting codes that arise in the study of Interactive Oracle Proofs (IOPs) and Succinct Non-interactive Arguments of Zero Knowledge (SNARKs). Recent work of Goyal and Guruswami has established near-optimal proximity gaps for many families of codes, including subspace design codes, as well as random ensembles like random linear codes, Reed-Solomon codes with random evaluation points, and Gallager's ensemble of LDPC codes (Goyal & Guruswami, 2025). However, the parameters for these latter randomized ensembles are worse than the parameters for subspace design codes, and degrade as the degree ell increases. In this work, we obtain improved proximity gaps for random ensembles of codes, including random linear codes, Reed-Solomon codes with random evaluation points, and Gallager's ensemble. Quantitatively, our results for these random ensembles match the results that Goyal and Guruswami attained for subspace design codes. In fact, our techniques are a black-box transference from subspace design codes: any progress on subspace design codes will automatically lead to analogous progress for these random ensembles. To obtain our results, we extend the Local Coordinate-wise Linear (LCL) property framework developed by Levi, Mosheiff, and Shagrithaya and by Brakensiek, Chen, Dhar, and Zhang to a \textit{row-span constrained} version (Levi, Mosheiff & Shagrithaya, 2025; Brakensiek, Chen, Dhar & Zhang, 2025). This allows us to cast \textit{curve-decodability} -- a property that implies proximity gaps -- directly as a row-span constrained LCL property, and make use of that machinery. In contrast, because curve-decodability is not obviously a vanilla LCL property, prior work had worked with a proxy property instead, leading to the aforementioned parameter losses.

cs.IT↗

arXiv2026

$Ψ$-Bench: Evaluating Persona-Sensitive Influencing in Persuasive Dialogues

Personalization is a crucial capability of modern language agents. However, current research primarily positions personalized agents as passive responders to user preferences, limiting their ability to interact with users and provide suggestions or guidance proactively. To systematically evaluate such proactive personalization in realistic interactions, we propose $Ψ$-Bench, a benchmark for assessing LLMs' ability to influence realistic users through conversation. We design three real-world interaction scenarios that involve persuasion in $Ψ$-Bench, and endow simulated clients with personal characteristics through explicit user profiles derived from dialogue histories. We evaluate 10 frontier LLMs on $Ψ$-Bench and find that while most models can produce coherent and reasonable arguments, even state-of-the-art models still leave considerable room for improvement in persuasion. We also find that providing access to client profiles yields an average performance gain of 18.24\%, highlighting the importance of user-specific information for effective persuasion. Overall, our work highlights persona-sensitive influencing as a challenging yet practical direction for evaluating and developing more proactive personalized LLM agents. Codes are available at: https://github.com/Hanpx20/Psi-Bench.

cs.LG↗

arXiv2026

On Worst-Case Optimal Polynomial Intersection

The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in \mathbb{F}[x]$ of degree less than $n$ so that $Q(a_i) \in S_i$ for as many $i \in \{1, 2, \ldots, m\}$ as possible. Decoded Quantum Interferometry (DQI) is a quantum algorithm that efficiently returns good solutions to the problem, even on worst-case instances (Jordan et. al., 2025). The quality of the solutions returned follows a semicircle law, which outperforms known efficient classical algorithms. But does DQI obtain the best possible solutions? That is, are there solutions better than the semicircle law for worst-case OPI instances? Surprisingly, before this work, the best existential results coincide with (and follow from) the best algorithmic results. In this work, we show that there are better solutions for worst-case OPI instances over prime fields. In particular, DQI and the semicircle law are not optimal. For example, when the lists $S_i$ have size $ρp$ for $ρ\sim 1/2$, our results imply the existence of a solution that asymptotically beats the semicircle law whenever $n/m \geq 0.6225$, and we show that an asymptotically perfect solution exists whenever $n/m \geq 0.7496$. Our results generalize to Max-LINSAT problems derived from any Maximum Distance Separable (MDS) code, and to any $ρ\in (0,1)$. The key insight to our improvement is a connection to local leakage resilience of secret sharing schemes. Along the way, we recover several re-proofs of the existence of solutions achieving the semicircle law.

cs.DM↗