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Dawei Chen

Publications and source records attributed to Dawei Chen.

At least 19 recordsLinked to original sources
arXiv2026

How Do Prompt Variations Affect Energy Consumption in On-Device LLMs?

Large language models (LLMs) are increasingly deployed on mobile devices, making energy efficiency a key deployment constraint, yet the energy impact of prompt design remains underexplored. This paper aims to understand how two prompt properties, cognitive load and phrasing pattern, shape the energy behavior of on-device LLM inference. We conduct a broad empirical study covering prompt properties, datasets, models, and devices, with phase-level profiling that separates prefill and decode energy. We find that cognitive load primarily affects the energy cost per token, while phrasing pattern affects energy largely through token usage. Our energy-quality analysis further shows that prompt design reshapes the attainable frontier differently across models, highlighting the need for model-aware prompt design in energy-efficient on-device LLM inference. Code, datasets, and scripts are available at https://amai-gsu.github.io/PromptProperty/.

cs.CL↗
arXiv2026

Non-asphericity of strata of genus-one differentials and stability spaces

We show that when the number of zeros or poles is at least four, every connected component of the strata of differentials in genus one with prescribed zero and pole orders is not an orbifold $K(\pi,1)$. For quadratic differentials, this provides infinitely many counterexamples to a conjecture attributed to Kontsevich, as well as to a folklore conjecture concerning the contractibility of spaces of Bridgeland stability conditions.

math.GT↗
arXiv2026

Independence of tautological classes and cohomological stability for strata of differentials

The tautological rings of strata of differentials are known to be generated by divisor classes. In this paper, we give lower bounds on the degrees of relations among them, depending on the genus $g$ and the number of simple zeros. For strata with more than $4g/3$ simple zeros, our results show that there are no relations in degrees less than $\lfloor g/3 \rfloor + 1$. Moreover, we conjecture that, outside of a few exceptions, there is always a non-trivial relation in degree $\lfloor g/3 \rfloor + 1$, and prove the conjecture for all strata of holomorphic abelian differentials with $g \leq 30$. We also prove that the cohomology rings of strata of holomorphic differentials with sufficiently many simple zeros stabilize to the free algebra on the tautological divisor class. Finally, we show that for a large class of holomorphic abelian strata, containing hyperelliptic differentials, the tautological ring is non-trivial for sufficiently large $g$.

math.AG↗
arXiv2026

A tale of two volumes of moduli spaces: Weil-Petersson and Masur-Veech

Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable developments in combinatorial enumeration, intersection theory, and recursion relations. In this survey, we review key results, methods, open problems, as well as interesting parallels that emerge in the approaches to computing both types of volumes.

math.GT↗
arXiv2026

Parity of $k$-differentials in genus zero and one

Here we completely determine the spin parity of $k$-differentials with prescribed zero and pole orders on Riemann surfaces of genus zero and one. This result was previously obtained conditionally by the first author and Quentin Gendron assuming the truth of a number-theoretic hypothesis Conjecture A.10. We prove this hypothesis by reformulating it in terms of Jacobi symbols, reducing the proof to a combinatorial identity and standard facts about Jacobi symbols. The proof was obtained by AxiomProver and the system formalized the proof of the combinatorial identity in Lean/Mathlib (see the Appendix).

math.NT↗
arXiv2026

An algebro-geometric perspective on the topology of moduli spaces of differentials

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials to appear in various guises across many areas, including algebraic geometry, dynamical systems, combinatorial enumeration, and mathematical physics. Over the past few decades, remarkable progress has been made in computing invariants of these moduli spaces, classifying linear subvarieties, understanding degenerations and compactifications, and developing intersection theory on these spaces. Despite these advances, our understanding of the topology of moduli spaces of differentials remains limited, and many fundamental questions are still open. In this survey, we aim to present, from an algebro-geometric perspective, the known results and open problems concerning the topology of moduli spaces of differentials, as well as their connections to other aspects of the field, with the hope of inspiring further developments in the coming decade.

math.AG↗
arXiv2025

Complete subvarieties in the projectivized strata of meromorphic differentials

Here we give an explicit construction of a globally defined strictly plurisubharmonic function on projectivized strata of strictly meromorphic differentials with prescribed orders of zeros and poles. In particular, this yields a flat-geometric proof that these strata do not contain positive-dimensional complete subvarieties.

math.AG↗
arXiv2025

PlatformX: An End-to-End Transferable Platform for Energy-Efficient Neural Architecture Search

Hardware-Aware Neural Architecture Search (HW-NAS) has emerged as a powerful tool for designing efficient deep neural networks (DNNs) tailored to edge devices. However, existing methods remain largely impractical for real-world deployment due to their high time cost, extensive manual profiling, and poor scalability across diverse hardware platforms with complex, device-specific energy behavior. In this paper, we present PlatformX, a fully automated and transferable HW-NAS framework designed to overcome these limitations. PlatformX integrates four key components: (i) an energy-driven search space that expands conventional NAS design by incorporating energy-critical configurations, enabling exploration of high-efficiency architectures; (ii) a transferable kernel-level energy predictor across devices and incrementally refined with minimal on-device samples; (iii) a Pareto-based multi-objective search algorithm that balances energy and accuracy to identify optimal trade-offs; and (iv) a high-resolution runtime energy profiling system that automates on-device power measurement using external monitors without human intervention. We evaluate PlatformX across multiple mobile platforms, showing that it significantly reduces search overhead while preserving accuracy and energy fidelity. It identifies models with up to 0.94 accuracy or as little as 0.16 mJ per inference, both outperforming MobileNet-V2 in accuracy and efficiency. Code and tutorials are available at github.com/amai-gsu/PlatformX.

cs.LG↗
arXiv2025

lm-Meter: Unveiling Runtime Inference Latency for On-Device Language Models

Large Language Models (LLMs) are increasingly integrated into everyday applications, but their prevalent cloud-based deployment raises growing concerns around data privacy and long-term sustainability. Running LLMs locally on mobile and edge devices (on-device LLMs) offers the promise of enhanced privacy, reliability, and reduced communication costs. However, realizing this vision remains challenging due to substantial memory and compute demands, as well as limited visibility into performance-efficiency trade-offs on resource-constrained hardware. We propose lm-Meter, the first lightweight, online latency profiler tailored for on-device LLM inference. lm-Meter captures fine-grained, real-time latency at both phase (e.g., embedding, prefill, decode, softmax, sampling) and kernel levels without auxiliary devices. We implement lm-Meter on commercial mobile platforms and demonstrate its high profiling accuracy with minimal system overhead, e.g., only 2.58% throughput reduction in prefill and 0.99% in decode under the most constrained Powersave governor. Leveraging lm-Meter, we conduct comprehensive empirical studies revealing phase- and kernel-level bottlenecks in on-device LLM inference, quantifying accuracy-efficiency trade-offs, and identifying systematic optimization opportunities. lm-Meter provides unprecedented visibility into the runtime behavior of LLMs on constrained platforms, laying the foundation for informed optimization and accelerating the democratization of on-device LLM systems. Code and tutorials are available at https://github.com/amai-gsu/LM-Meter.

cs.LG↗
arXiv2025

Finite isoresidual covers in strata of $k$-differentials

Consider the strata of primitive $k$-differentials on the Riemann sphere whose singularities, except for two, are poles of order divisible by $k$. The map that assigns to each $k$-differential the $k$-residues at these poles is a ramified cover of its image. Generalizing results known in the case of abelian differentials, we describe the ramification locus of this cover and provide a formula, involving the $k$-factorial function, for the cardinality of each fiber. We prove this formula using intersection calculations on the multi-scale compactification of the strata of $k$-differentials. In special cases, we also give alternative proofs using flat geometry. Finally, we present an application to cone spherical metrics with dihedral monodromy.

math.AG↗
arXiv2025

Gorenstein singularities with $\mathbb{G}_m$-action and moduli spaces of holomorphic differentials

Given a holomorphic differential on a smooth complex algebraic curve, we associate to it a Gorenstein curve singularity with $\mathbb G_m$-action via a test configuration. This construction decomposes the strata of holomorphic differentials with prescribed orders of zeros into negatively graded miniversal deformation spaces of such singularities. Additionally, it provides a natural description for the singular curves that appear in the boundary of the miniversal deformation spaces. Our approach leads to a number of applications. We classify the unique Gorenstein singularity with $\mathbb G_m$-action for each nonvarying stratum of holomorphic differentials and study when these nonvarying strata can be compactified by weighted projective spaces. Moreover, extending the classical results about $ADE$ singularities, we establish the $K(\pi,1)$-property for non-hypersurface complete intersection singularities of type $U_7$, $U_8$, $U_9$, and $S_{k}$. We also study singularities with bounded $\alpha$-invariants in the log minimal model program for $\overline{\mathcal M}_g$ and utilize them to bound the slopes of effective divisors in $\overline{\mathcal M}_g$. Finally, we show that the loci of subcanonical points with fixed semigroups have trivial tautological rings and provide a criterion to determine whether they are affine varieties.

math.AG↗
arXiv2025

New highly efficient and accurate numerical scheme for the Cahn-Hilliard-Brinkman system

In this paper, based on a generalized scalar auxiliary variable approach with relaxation (R-GSAV), we construct a class of high-order backward differentiation formula (BDF) schemes with variable time steps for the Cahn-Hilliard-Brinkman(CHB) system. In theory, it is strictly proved that the designed schemes are unconditionally energy-stable. With the delicate treatment of adaptive strategies, we propose several adaptive time-step algorithms to enhance the robustness of the schemes. More importantly, a novel hybrid-order adaptive time steps algorithm performs outstanding for the coupled system. The hybrid-order algorithm inherits the advantages of some traditional high-order BDF adaptive strategies. A comprehensive comparison with some adaptive time-step algorithms is given, and the advantages of the new adaptive time-step algorithms are emphasized. Finally, the effectiveness and accuracy of the new methods are validated through a series of numerical experiments.

math.NA↗
arXiv2025

Connectedness of the boundaries of the strata of differentials

Let $\mathcal{P}(\mu)^{\circ}$ be a connected component of the projectivized stratum of differentials on smooth complex curves, where the zero and pole orders of the differentials are specified by $\mu$. When the complex dimension of $\mathcal{P}(\mu)^{\circ}$ is at least two, Dozier--Grushevsky--Lee, through explicit degeneration techniques, showed that the boundary of $\mathcal{P}(\mu)^{\circ}$ is connected in the multi-scale compactification constructed by Bainbridge--Chen--Gendron--Grushevsky--M\"oller. A natural question is whether the connectedness of the boundary of $\mathcal{P}(\mu)^{\circ}$ is determined by its intrinsic properties. In the case of meromorphic differentials, we provide a concise explanation that the boundary of $\mathcal{P}(\mu)^{\circ}$ is always connected in any complete algebraic compactification, based on the fact that the strata of meromorphic differentials are affine varieties. We also observe that the same result holds for linear subvarieties of meromorphic differentials, as well as for the strata of $k$-differentials with a pole of order at least $k$. In the case of holomorphic differentials, using properties of Teichm\"uller curves, we provide an alternative argument showing that the horizontal boundary of $\mathcal{P}(\mu)^{\circ}$ and every irreducible component of its vertical boundary intersect non-trivially in the multi-scale compactification.

math.AG↗
arXiv2025

Area Siegel--Veech constants for affine invariant submanifolds of REL zero

We describe the principal boundary of an arbitrary affine invariant submanifold of REL zero in terms of level graphs of the multi-scale compactification of strata of Abelian differentials with prescribed orders of zeros. We show that the area Siegel--Veech constant of the affine invariant submanifold can be obtained by using volumes of the principal boundary strata. As an application, we prove the conjectural formula in [CMS23a] that computes the area Siegel--Veech constant via intersection theory in the case of REL zero. In particular, the formula holds for strata of quadratic differentials with odd orders of zeros and for the gothic locus. We also explicitly describe the principal boundary components of the gothic locus and their individual contributions to the area Siegel--Veech constant

math.GT↗
arXiv2025

GreenAuto: An Automated Platform for Sustainable AI Model Design on Edge Devices

We present GreenAuto, an end-to-end automated platform designed for sustainable AI model exploration, generation, deployment, and evaluation. GreenAuto employs a Pareto front-based search method within an expanded neural architecture search (NAS) space, guided by gradient descent to optimize model exploration. Pre-trained kernel-level energy predictors estimate energy consumption across all models, providing a global view that directs the search toward more sustainable solutions. By automating performance measurements and iteratively refining the search process, GreenAuto demonstrates the efficient identification of sustainable AI models without the need for human intervention.

cs.LG↗
arXiv2024

Isoresidual curves

Given a partition $\mu$ of $-2$, the stratum $\mathcal{H}(\mu)$ parametrizes meromorphic differential one-forms on the Riemann sphere $\mathbb{CP}^{1}$ with~$n$ zeros and $p$ poles of orders prescribed by $\mu$. The isoresidual fibration is defined by assigning to each differential in $\mathcal{H}(\mu)$ its configuration of residues at the poles. In the case of differentials with $n=2$ zeros, generic isoresidual fibers are complex curves endowed with a canonical translation structure, which we describe extensively in this paper. Quantitative characteristics of the translation structure on isoresidual fiber curves, including the orders of the singularities and a period central charge encapsulating the linear dependence of periods on the underlying configuration of residues, provide rich discrete invariants for these fibers. We also determine the Euler characteristic of generic isoresidual fiber curves from intersection-theoretic computations, relying on the multi-scale compactification of strata of differentials. In particular, we describe a wall and chamber structure for the Euler characteristic of generic isoresidual fiber curves in terms of the partition $\mu$. Additionally, we classify the connected components of generic isoresidual fibers for strata in genus zero with an arbitrary number of zeros.

math.AG↗