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Zhengyi Zhou

Zhengyi Zhou contributes to research discovery and scholarly infrastructure.

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Published work

9 published item(s)

preprint2026arXiv

SOMA: Efficient Multi-turn LLM Serving via Small Language Model

Large Language Models (LLMs) are increasingly deployed in multi-turn dialogue settings where preserving conversational context across turns is essential. A standard serving practice concatenates the full dialogue history at every turn, which reliably maintains coherence but incurs substantial cost in latency, memory, and API expenditure, especially when queries are routed to large proprietary models. Existing approaches often struggle to balance the trade-off between response quality and efficiency. We propose a framework that exploits the early turns of a session to estimate a local response manifold and then adapt a smaller surrogate model to this local region for the remainder of the conversation. Concretely, we learn soft prompts that maximize semantic divergence between the large and surrogate small language models' responses to surface least-aligned local directions, stabilize training with anti-degeneration control, and distill the mined cases into localized LoRA fine-tuning so the surrogate runs without prompts at inference. A simple gate enables a one-time switch with rollback on drift. We further provide a theoretical analysis for key components in SOMA. Extensive experiments show the effectiveness of SOMA. The source code is provided at: https://github.com/LabRAI/SOMA.

preprint2026arXiv

StackPilot: Autonomous Function Agents for Scalable and Environment-Free Code Execution

Recent advances in large language models (LLMs) have substantially enhanced automated code generation across a wide range of programming languages. Nonetheless, verifying the correctness and executability of LLM-generated code remains a significant challenge, as traditional methods rely on language-specific compilers and environment-dependent runtimes. To overcome these limitations, we introduce StackPilot, an LLM-native, multi-agent framework designed for language-agnostic code verification and execution, which operates independently of conventional toolchains. StackPilot offers three principal innovations: (1) a Function-as-Agents paradigm, in which each function is modeled as an autonomous agent capable of fine-grained reasoning and collaborative verification; (2) an LLM-as-Executor strategy, which enables scalable verification via stack-based scheduling; and (3) a novel snapshot mechanism that preserves complete execution contexts, facilitating deterministic and lossless context switching during verification. Empirical evaluations demonstrate that StackPilot achieves framework reliability rates between 89% and 97%, substantially outperforming baseline approaches. These results indicate that StackPilot can reliably verify and execute a significantly larger proportion of LLM-generated code across diverse programming tasks compared to existing methods.

preprint2022arXiv

Asymptotically holomorphic theory for symplectic orbifolds

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large tensor powers of the prequantizable line bundle such that their zero sets are symplectic suborbifolds. We then derive a Lefschetz hyperplane theorem for these suborbifolds, that computes their real cohomology up to middle dimension. We also get the hard Lefschetz and formality properties for them, when the ambient manifold satisfies those properties.

preprint2022arXiv

Infinite not contact isotopic embeddings in $(S^{2n-1},ξ_{\mathrm{std}})$ for $n\ge 4$

For $n\ge 4$, we show that there are infinitely many formally contact isotopic embeddings of $(ST^*S^{n-1},ξ_{\mathrm{std}})$ to $(S^{2n-1},ξ_{\mathrm{std}})$ that are not contact isotopic. This resolves a conjecture of Casals and Etnyre except for the $n=3$ case. The argument does not appeal to the surgery formula of critical handle attachment for Floer theory/SFT.

preprint2022arXiv

On filings of $\partial(V\times \mathbb{D})$

We show that any symplectically aspherical/Calabi-Yau filling of $Y:=\partial(V\times \mathbb{D})$ has vanishing symplectic cohomology for any Liouville domain $V$. In particular, we make no topological requirement on the filling and $c_1(V)$ can be nonzero. Moreover, we show that for any symplectically aspherical/Calabi-Yau filling $W$ of $Y$, the interior $\mathring{W}$ is diffeomorphic to the interior of $V\times \mathbb{D}$ if $π_1(Y)$ is abelian and $\dim V\ge 4$. And $W$ is diffeomorphic to $V\times \mathbb{D}$ if moreover the Whitehead group of $π_1(Y)$ is trivial.

preprint2022arXiv

On the minimal symplectic area of Lagrangians

We show that the minimal symplectic area of Lagrangian submanifolds are universally bounded in symplectically aspherical domains with vanishing symplectic cohomology. If an exact domain admits a $k$-semi-dilation, then the minimal symplectic area is universally bounded for $K(π,1)$-Lagrangians. As a corollary, we show that Arnol'd chord conjecture holds for the following four cases: (1) $Y$ admits an exact filling with $SH^*(W)=0$ (for some ring coefficient); (2) $Y$ admits a symplectically aspherical filling with $SH^*(W)=0$ and simply connected Legendrians; (3) $Y$ admits an exact filling with a $k$-semi-dilation and the Legendrian is a $K(π,1)$ space; (4) $Y$ is the cosphere bundle $S^*Q$ with $π_2(Q)\to H_2(Q)$ nontrivial and the Legendrian has trivial $π_2$. In addition, we obtain the existence of homoclinic orbits in case (1). We also provide many more examples with $k$-semi-dilations in all dimensions $\ge 4$.

preprint2021arXiv

Symplectic fillings of asymptotically dynamically convex manifolds II--$k$-dilations

We introduce the concept of $k$-(semi)-dilation for Liouville domains, which is a generalization of symplectic dilation defined by Seidel-Solomon. We prove that the existence of $k$-(semi)-dilation is a property independent of fillings for asymptotically dynamically convex (ADC) manifolds. We construct examples with $k$-dilations, but not $k-1$-dilations for all $k\ge 0$. We extract invariants taking value in $\mathbb{N} \cup \{\infty\}$ for Liouville domains and ADC contact manifolds, which are called the order of (semi)-dilation. The order of (semi)-dilation serves as embedding and cobordism obstructions. We determine the order of (semi)-dilation for many Brieskorn varieties and use them to study cobordisms between Brieskorn manifolds.

preprint2019arXiv

Counterexamples in Scale Calculus

We construct counterexamples to classical calculus facts such as the Inverse and Implicit Function Theorems in Scale Calculus -- a generalization of Multivariable Calculus to infinite dimensional vector spaces in which the reparameterization maps relevant to Symplectic Geometry are smooth. Scale Calculus is a cornerstone of Polyfold Theory, which was introduced by Hofer-Wysocki-Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in Polyfold Theory overcomes the lack of Implicit Function Theorems, by formally establishing an often implicitly used fact: The differentials of basic germs -- the local models for scale-Fredholm maps -- vary continuously in the space of bounded operators when the base point changes. We moreover demonstrate that this continuity holds only in specific coordinates, by constructing an example of a scale-diffeomorphism and scale-Fredholm map with discontinuous differentials. This justifies the high technical complexity in the foundations of Polyfold Theory.

preprint2019arXiv

Quotient Theorems in Polyfold Theory and $S^1$-Equivariant Transversality

We introduce group actions on polyfolds and polyfold bundles. We prove quotient theorems for polyfolds, when the group action has finite isotropy. We prove that the sc-Fredholm property is preserved under quotient if the base polyfold is infinite dimensional. The quotient construction is the main technical tool in the construction of equivariant fundamental class in [42]. We also analyze the equivariant transversality near the fixed locus in the polyfold setting. In the case of $S^1$-action with fixed locus, we give a sufficient condition for the existence of equivariant transverse perturbations. We outline the application to Hamiltonian-Floer cohomology and a proof of the weak Arnold conjecture for general symplectic manifolds, assuming the existence of Hamiltonian-Floer cohomology polyfolds.