arXiv subjects

Roy Zhao

Publications and source records attributed to Roy Zhao.

10 recordsLinked to original sources

arXiv2026

Runtime-Independent Persistent Agents: Preserving Identity, Memory, and Code Across Models, Harnesses, and Servers

Agent systems are commonly described by the model and harness that currently produce their behavior. That boundary is useful for one execution but underspecifies a long-lived agent that may change models, orchestration harnesses, interaction sessions, and host servers while retaining one identity, memory, and executable code lineage. We present a runtime-independent architecture for persistent agents. A continuity-bearing substrate $P_t=(I_t,M_t,B_t)$ contains an architectural identity representation, private durable memory, and a versioned software body. A replaceable deployment binding comprises an execution substrate $E_t=(R_t,H_t,D_t)$, which supplies a reasoner, harness, and host, and a set of interaction surfaces $S_t$, such as chat, API, or user interface bindings. A deployed execution is $A_t=P_t\triangleright(E_t,S_t)$; changing either replaceable layer is migration, not agent creation, when an authorized protocol preserves attributable lineage and transfers continuation authority within a governed deployment boundary. We define six continuity invariants and a quiesce--checkpoint--validate--bind--rehydrate--resume protocol. Enoch realizes the design as a reusable body plus private installed identity, memory, workflow state, and continuation authority, with infrastructure dependencies behind versioned provider contracts. A clean-room run of the frozen public commit passes 833 core tests and 92 provider and library tests executed separately from the core suite; deployments have exercised reasoner-version, interaction-surface, and host-machine substitutions while retaining continuity-bearing state. This evidence supports mechanical substitutability and authorized system continuity, not behavioral invariance or exhaustive pairwise evaluation. The downstream measurement question is whether an authorized continuation still recalls, composes, and enacts its identity.

cs.SE↗

arXiv2026

Code Is the Body: Agent-Owned Software Bodies for Recursive Evolution and Descent

Personalized AI agents are often configurable without giving users control over the artifacts that determine their future behavior. We present OurArk, an architecture for persistent personal agents centered on an agent-owned software body: an identity-bearing, inspectable, and versioned artifact under human custody. The body contains behavior-defining code, prompts, tools, skills, policies, tests, and evolution mechanisms. Memories and credentials remain private instance state, while model inference is treated as a replaceable external service. OurArk defines governed self-evolution and recursive descent over the same body. Self-evolution produces isolated candidate changes that are validated, reviewed, and merged under human control, enabling human-agent co-development of the agent's software body. Descent creates an independently versioned descendant with a distinct identity, mission, history, and fresh private-state boundary; compatible descendants can themselves source further descent. After divergence, direct-parent changes and peer skills can be inspected for selective local adaptation. We implement the architecture in the open-source Genesis creation engine and Enoch reference agent. A four-agent, three-descent linear lineage and executable regression tests demonstrate recursive creation, inherited validation contracts, isolated body changes, human-controlled review, and failed-update recovery. OurArk provides a concrete substrate for personal agents that people can possess, govern, specialize, and evolve over time.

cs.SE↗

arXiv2026

Towards Verifiable Agentic Data Science: Solving Irregular TSQA Via Tool-Grounded Reasoning

Time series data in real-world deployments is overwhelmingly irregular. Observations are asynchronous, missing values are informative rather than random, and sampling frequencies vary across sensors and operational windows. However, existing Time Series Question Answering (TSQA) benchmarks mostly assume regularly sampled inputs, leaving a fundamental gap in understanding how large language models (LLMs) and AI agents perform under irregular conditions. To bridge this gap, we introduce IRTS-ToolBench, a benchmark of 1,700 questions spanning 10 task types across 13 domains. IRTS-ToolBench is designed to be used independently by any researcher working on LLM-based irregular time series analysis, providing standardized inputs and a reproducible evaluation protocol. Code can be found in https://github.com/SanhornC/IRTS-ToolBench.

cs.AI↗

arXiv2025

Accelerating Multi-modal LLM Gaming Performance via Input Prediction and Mishit Correction

Real-time sequential control agents are often bottlenecked by inference latency. Even modest per-step planning delays can destabilize control and degrade overall performance. We propose a speculation-and-correction framework that adapts the predict-then-verify philosophy of speculative execution to model-based control with TD-MPC2. At each step, a pretrained world model and latent-space MPC planner generate a short-horizon action queue together with predicted latent rollouts, allowing the agent to execute multiple planned actions without immediate replanning. When a new observation arrives, the system measures the mismatch between the encoded real latent state and the queued predicted latent. For small to moderate mismatch, a lightweight learned corrector applies a residual update to the speculative action, distilled offline from a replanning teacher. For large mismatch, the agent safely falls back to full replanning and clears stale action queues. We study both a gated two-tower MLP corrector and a temporal Transformer corrector to address local errors and systematic drift. Experiments on the DMC Humanoid-Walk task show that our method reduces the number of planning inferences from 500 to 282, improves end-to-end step latency by 25 percent, and maintains strong control performance with only a 7.1 percent return reduction. Ablation results demonstrate that speculative execution without correction is unreliable over longer horizons, highlighting the necessity of mismatch-aware correction for robust latency reduction.

cs.AI↗

arXiv2025

Bialgebraic varieties of the Gamma function

We characterize the bialgebraic varieties of the $\Gamma$ function, that is, if $V,W\subseteq\mathbb{C}^n$ are irreducible affine algebraic variety which satisfy $\dim V =\dim W$ and $\Gamma(V)\subseteq W$, then the equations defining $V$ (and hence also $W$) either give an equality between coordinates, or set some coordinates to be constant. We also classify the case where $V$ and $W$ have the same dimension as varieties over the field of algebraic functions.

math.CV↗

arXiv2025

Towards the Colmez Conjecture

We prove a collection of results involving Colmez's periods and the Colmez Conjecture. Using Colmez's theory of periods of CM abelian varieties, we propose a definition for the height of a partial CM-type and prove that the Colmez conjecture follows from an arithmetic period formula for surfaces. We give an explicit conjecture for the form of this period formula, which relates the height of special points on a Shimura surface with special values of $L$-functions. Further, we relate the heights of periods given by Colmez to arithmetic degree of Hermitian line bundles and thus give a formulation of Colmez's full conjecture in geometric terms.

math.NT↗

arXiv2024

Algebraic Independence of Special Points on Shimura Varieties

Given a correspondence $V$ between a connected Shimura variety $S$, a commutative connected algebraic group $G$, and $n \in \mathbb{N}$, we prove that the $V$-images of any $n$ special points on $S$ outside a proper Zariski closed subset are algebraically independent. Our result unifies previous unlikely intersection results on multiplicative independence and linear independence. We prove multiplicative independence of differences of singular moduli, generalizing previous results by Pila-Tsimerman, and Aslanlyan-Eterovi\'c-Fowler. We also give an application to abelian varieties by proving that the special points of $S$ whose $V$-images lie in a finite-rank subgroup of $T$ are contained in a finite union of proper special subvarieties of $S$, only dependent on the rank of the subgroup. In this way, our result is a generalization of the works of Pila-Tsimerman and Buium-Poonen.

math.NT↗

arXiv2023

Heights of Special Points on Quaternionic Shimura Varieties

Let $B/F$ be a quaternion algebra over a totally real number field. We give an explicit formula for heights of special points on the quaternionic Shimura variety associated with $B$ in terms of Faltings heights of CM abelian varieties. Special points correspond to CM fields $E$ and partial CM-types $\phi \subset \mathrm{Hom}(E, \mathbb{C})$. We then show that our height is compatible with the canonical height of a partial CM-type defined by Pila, Shankar, and Tsimerman. This gives another proof that the height of a partial CM-type is bounded subpolynomially in terms of the discriminant of $E$.

math.NT↗

arXiv2021

Algebraic Varieties and Automorphic Functions

Let $(G, X)$ be a Shimura datum, let $\Omega$ be a connected component of $X$, let $\Gamma$ be a congruence subgroup of $G(\mathbb{Q})^{+}$, and consider the quotient map $q: \Omega \to S:=\Gamma \backslash \Omega$. Consider the Harish-Chandra embedding $\Omega\subset\mathbb{C}^{N}$, where $N=\dim X$. We prove two results that give geometric conditions which if satisfied by an algebraic variety $V \subset \mathbb{C}^{N} \times S$, ensure that there is a Zariski dense subset of $V$ of points of the form $(x,q(x))$.

math.AG↗

arXiv2018

A Homological Definition for the Tate--Shafarevich Group of a Pell Conic

Franz Lemmermeyer's previous work laid the framework for a description of the arithmetic of Pell conics, which is analogous to that of elliptic curves. He describes a group law on conics and conjectures the existence of an analogous Tate--Shafarevich group with order the squared ideals of the narrow class group. In this article, we provide a cohomological definition of the Tate--Shafarevich group and show that its order is as Lemmermeyer conjectured.

math.NT↗