arXiv subjects

Quan Gu

Publications and source records attributed to Quan Gu.

3 recordsLinked to original sources

arXiv2026

GSToken: Geometry-Structured Gaussian Tokens for Compact 3D Medical Image Representation

Effective segmentation of multi-modal MRI is central to improving neural network accuracy in brain tumor recognition. Existing methods typically compress 3D volumes into token sequences via fixed patch encoding or learned attention pooling (e.g., TokenLearner). However, these compression schemes discard explicit spatial shape information; the resulting tokens convey no notion of lesion morphology or spatial extent. Meanwhile, end-to-end evaluation entangles a tokenizer's information retention with the reconstruction capacity of the downstream decoder, and the lack of a unified capacity contract across methods makes performance differences difficult to attribute. In this paper, we introduce Gaussian tokens to multi-modal brain tumor segmentation for the first time: each token carries not only a semantic feature but also a learned 3D center, anisotropic scale, and orientation, endowing the representation with explicit geometric support at negligible parameter cost. We further propose a frozen-token utility evaluation protocol: the trained tokenizer is frozen, its output is cast into a fixed-capacity serialized contract, and a shared lightweight Transformer probe independently measures each tokenizer's retained information under strictly matched conditions. Multi-seed paired statistical testing shows that GSToken consistently and substantially outperforms capacity-matched adaptive baselines under frozen probing, with uniform advantages across all tumor sub-regions, surface, and distance metrics. These results demonstrate that explicitly encoding spatial geometry within tokens significantly improves the information density of volumetric representations, offering a new design principle for compact 3D medical image representation and downstream reading.

cs.CV↗

arXiv2026

Feature Interaction Modeling for Neural Operators

Despite the many variants of DeepONet that have been proposed, query-based operator networks still struggle with shock-dominated and low-viscosity PDEs, whose sharp moving discontinuities and slowly decaying solution spectra challenge finite-dimensional separable representations. In this work, we propose \emph{Feature Interaction Modeling Operator} (FM-Operator), a point-wise query neural operator that explicitly models feature construction and interactions between sensor observations and query coordinates. Our design is motivated by a reinterpretation of the canonical DeepONet aggregation through the lens of multiplicative interactions. Specifically, the branch--trunk inner product admits the equivalent form $\boldsymbol{b}(u)^\top \boldsymbol{\tau}(y)=\boldsymbol{1}^\top \operatorname{diag}(\boldsymbol{b}(u))\,\boldsymbol{\tau}(y)$, revealing that the two representations interact only along corresponding latent dimensions and therefore constitute a diagonally constrained multiplicative interaction. This observation suggests that, beyond improving the individual branch and trunk networks, the structure through which function and query representations interact is itself an important inductive bias in point-wise operator learning. FM-Operator accordingly redesigns both feature construction and feature interaction, enabling structured information exchange beyond the conventional branch--trunk coupling while retaining point-wise query evaluation. Experiments across multiple PDE benchmarks demonstrate that FM-Operator consistently outperforms vanilla DeepONet and achieves clear improvements over the strong Shift-DeepONet baseline. These results suggest that explicitly designing representation construction and interaction provides a promising direction for improving the effectiveness of DeepONet-style query-based neural operators.

cs.LG↗

arXiv2025

Resource analysis of Shor's elliptic curve algorithm with an improved quantum adder on a two-dimensional lattice

Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based cryptanalysis are well established, comparable evaluations for Shor's elliptic curve algorithm under realistic architectural constraints remain limited. In this work, we propose a carry-lookahead quantum adder that achieves Toffoli depth $\log n + \log\log n + O(1)$ with only $O(n)$ ancillas, matching state-of-the-art performance in depth while avoiding the prohibitive $O(n\log n)$ space overhead of existing approaches. Importantly, our design is naturally compatible with the two-dimensional nearest-neighbor architectures and introduce only a constant-factor overhead. Further, we perform a comprehensive resource analysis of Shor's elliptic curve algorithm on two-dimensional lattices using the improved adder. By leveraging dynamic circuit techniques with mid-circuit measurements and classically controlled operations, our construction incorporates the windowed method, Montgomery representation, and quantum tables, and substantially reduces the overhead of long-range gates. For cryptographically relevant parameters, we provide precise resource estimates. In particular, breaking the NIST P-256 curve, which underlies most modern public-key infrastructures and the security of Bitcoin, requires about $4300$ logical qubits and logical Toffoli fidelity about $10^{-9}$. These results establish new benchmarks for efficient quantum arithmetic and provide concrete guidance toward the experimental realization of Shor's elliptic curve algorithm.

quant-ph↗