arXiv subjects

Jiuzhou Zhao

Publications and source records attributed to Jiuzhou Zhao.

5 recordsLinked to original sources

arXiv2026

SkillEvo: Self-Renewing Evolution Gradients from Multi-Turn Interaction Feedback

Agent Skills are today either hand-authored or produced in a single LLM generation pass, and consequently possess no closed loop through which they might improve from the interaction failures they actually cause. Recent work does close this loop, but derives its feedback from single-turn question-answering evaluation. The consequence is a sharp asymmetry: once the first round has patched the gaps that a single exchange can reveal, the evolution gradient decays, the defects that surface only across multiple turns remain invisible, and evolution stalls. Governance in these systems is likewise driven by an end-to-end verification score, a scalar gate that can reject a degraded candidate but can neither localize nor repair its structural cause. We argue that the binding constraint on sustained skill evolution is neither editing capability nor the number of iterations, but whether the evaluation feedback keeps supplying trustworthy evolution gradients. We introduce SkillEvo, in which trustworthy feedback generates the gradient and controllable governance constrains its direction. The first component recasts multi-turn user simulation from an evaluation endpoint into a feedback generator: follow-up questions expose defects layer by layer, so that every round of revision both consumes feedback and produces new feedback. The second replaces the passive rejection of a scalar gate with an independent governance layer that actively repairs factual degradation and structural bloat, preventing the gradient from drifting as degradation accumulates. Across six categories of cloud services, 9 production Skills, and 98 skill-reference files, SkillEvo surpasses self-reflection-based evolution by 23.0 points and single- turn-QA-driven evolution by 15.4 points.

cs.AI↗

arXiv2026

Non-Wieferich property of prime ideals and a conjecture of Erdös

Let $K$ be a number field with ring of integers $\mathcal{O}$ and $α\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $α$-Wieferich property, which implies a nonexistence theorem for higher Wieferich unramified prime ideals. If $β\in\mathcal{O}$ is relatively prime to $α$ and all prime ideal factors of $(β)$ are unramified and have residue degree $1$, we apply our higher $α$-Wieferich property to establish the asymptotic equidistribution of digits in $β$-adic expansions of $α^n$, which is a generalization of the Dupuy-Weirich theorem. When $(β)$ have ramified prime ideal factors, we also obtain a result on the block complexity of $β$-adic expansions of $α^n$.

math.NT↗

arXiv2026

TCAndon-Router: Adaptive Reasoning Router for Multi-Agent Collaboration

Multi-Agent Systems(MAS) have become a powerful paradigm for building high performance intelligent applications. Within these systems, the router responsible for determining which expert agents should handle a given query plays a crucial role in overall performance. Existing routing strategies generally fall into two categories: performance routing, which balances latency and cost across models of different sizes, and task routing, which assigns queries to domain-specific experts to improve accuracy. In real-world enterprise applications, task routing is more suitable; however, most existing approaches rely on static single-label decisions, which introduce two major limitations: (i) difficulty in seamlessly integrating new agents as business domains expand, and (ii) routing conflicts caused by overlapping agent capabilities, ultimately degrading accuracy and robustness.To address these challenges, we propose TCAndon-Router(TCAR): an adaptive reasoning router for multi-agent collaboration. Unlike traditional routers, TCAR supports dynamic agent onboarding and first generates a natural-language reasoning chain before predicting a set of candidate agents capable of handling the query. In addition, we design a collaborative execution pipeline in which selected agents independently produce responses, which are then aggregated and refined into a single high-quality response by a dedicated Refining Agent.Experiments on public datasets and real enterprise data demonstrate that TCAR significantly improves routing accuracy, reduces routing conflicts, and remains robust in ambiguous scenarios. We have released TCAR at https://huggingface.co/tencent/TCAndon-Router to support future research on explainable and collaborative multi-agent routing.

cs.AI↗

arXiv2025

Rational points in Cantor sets in the complex plane

Let $K$ be an imaginary quadratic field and let $\mathcal{O}_K$ be the ring of algebraic integers of $K$. For $α\in \mathcal{O}_K$ with $|α| > 1$, define \[ \mathcal{D}_α= \bigcup_{n=0}^\infty \frac{\mathcal{O}_K}{α^n}. \] For $β\in \mathcal{O}_K$ with $|β|>1$ and a finite subset $A \subset \mathcal{O}_K$, define \[ S_{β,A} = \bigg\{ \sum_{k=1}^{\infty} \frac{a_k}{β^k}: \; a_k \in A \;\forall k \in \mathbb{N} \bigg\}. \] Suppose that $α$ and $β$ are relatively prime. In this paper, we show that if $\dim_{\mathrm{H}} S_{β,A} < 1$, then the intersection $\mathcal{D}_α\cap S_{β,A}$ is a finite set. In general, the threshold for the Hausdorff dimension of $S_{β,A}$ is sharp. If we further assume that $\mathcal{O}_K$ is a unique factorization domain and that $\overlineα$ and $α$ are relatively prime, then we establish the finiteness of the intersection under the weaker condition $\dim_{\mathrm{H}} S_{β,A} < 2$. This extends the previously known results on the real line.

math.NT↗

arXiv2025

On $β$-adic expansions of powers of algebraic integer omitting a digit

Let $α, β$ be two relatively prime algebraic integers in a number field $K$ and $N$ be a positive integer. We show that the number of $n\in\{1,2,\dots,N\}$ such that the $β$-adic expansion of $α^n$ omits a given digit is less than $C_1 N^{σ(β)}$, where $σ(β):=\frac{\log(|N(β)|-1)}{\log|N(β)|}$ and $C_1$ is an absolute constant, if all prime ideal factors of $β$ are unramified and their norms are integer primes.

math.NT↗