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Christopher Rasmussen

Publications and source records attributed to Christopher Rasmussen.

13 recordsLinked to original sources

Toward Low-Latency Vision-Language Models with Doubly-Correct Predictions in Egocentric Visual Understanding

The rapid rise of Vision-Language Models (VLMs) in egocentric visual understanding has made low-latency inference in human-robot collaborative (HRC) tasks increasingly critical. Weight pruning techniques developed for VLMs to shrink model size and computation can be readily applied to satisfy the efficiency demands of on-board processing and real-time interactive robotics. Moreover, safe human-robot interaction demands pruning strategies that preserve doubly-correct predictions; outputs must be both accurate and evidentially grounded to mitigate risks and ensure user trust. In this paper, we present a new study of VLM pruning through the lens of doubly-correct prediction. Our experiments surprisingly show that existing pruning methods often preserve the right evidence localization but undermine correct prediction. To address this, we propose a rationale-informed pruning strategy that better aligns evidence with decisions. Benchmark results on egocentric video datasets demonstrate that our method not only achieves the highest prediction accuracy but also outperforms existing approaches in attaining doubly-correct predictions. We aim to stimulate research on efficient and reliable VLMs, ensuring accuracy-driven advances align with the transparency, auditability, and safety required for responsible human-robot interaction and embodied intelligence.

cs.RO

History-Conditioned Spatio-Temporal Visual Token Pruning for Efficient Vision-Language Navigation

Vision-Language Navigation (VLN) enables robots to follow natural-language instructions in visually grounded environments, serving as a key capability for embodied robotic systems. Recent Vision-Language-Action (VLA) models have demonstrated strong navigation performance, but their high computational cost introduces latency that limits real-time deployment. We propose a training-free spatio-temporal vision token pruning framework tailored to VLA-based VLN. We apply spatial token selection to the current view, alongside spatio-temporal compression for historical memories, enabling efficient long-horizon inference while reducing redundant computation. Leveraging attention-based token importance and query-guided spatio-temporal filtering, the proposed approach preserves navigation-relevant information without retraining or modifying pretrained models, allowing plug-and-play integration into existing VLA systems. Through experiments on standard VLN benchmarks, we confirm that our method significantly outperforms existing pruning strategies. It successfully preserves superior navigation accuracy under extreme pruning scenarios, all while maintaining the highly competitive inference efficiency. Real-world deployment on a Unitree Go2 quadruped robot further validates reliable and low-latency instruction-following navigation under practical robotic constraints. We hope this work helps bridge the gap between large-scale multimodal modeling and efficient, real-time embodied deployment in robotic navigation systems. Project Page: https://wqtwjt1996.github.io/publications/2026-vln.html

cs.RO

When One Modality Rules Them All: Backdoor Modality Collapse in Multimodal Diffusion Models

While diffusion models have revolutionized visual content generation, their rapid adoption has underscored the critical need to investigate vulnerabilities, e.g., to backdoor attacks. In multimodal diffusion models, it is natural to expect that attacking multiple modalities simultaneously (e.g., text and image) would yield complementary effects and strengthen the overall backdoor. In this paper, we challenge this assumption by investigating the phenomenon of Backdoor Modality Collapse, a scenario where the backdoor mechanism degenerates to rely predominantly on a subset of modalities, rendering others redundant. To rigorously quantify this behavior, we introduce two novel metrics: Trigger Modality Attribution (TMA) and Cross-Trigger Interaction (CTI). Through extensive experiments across diverse training configurations in multimodal conditional diffusion, we consistently observe a ``winner-takes-all'' dynamic in backdoor behavior. Our results reveal that (1) attacks often collapse into subset-modality dominance, and (2) cross-modal interaction is negligible or even negative, contradicting the intuition of synergistic vulnerability. These findings highlight a critical blind spot in current assessments, suggesting that high attack success rates often mask a fundamental reliance on a subset of modalities. This establishes a principled foundation for mechanistic analysis and future defense development.

cs.LG

Equivalence of conjectures on heavenly elliptic curves

Heavenly abelian varieties are abelian varieties defined over number fields that exhibit constrained $\ell$-adic Galois representations for some rational prime $\ell$. At the ICMS Workshop held in November 2024, we presented evidence for two finiteness conjectures around the distribution of heavenly elliptic curves over quadratic number fields, one in terms of isomorphism classes of curves, and a second in terms of quadratic fields which admit heavenly elliptic curves. We prove these two conjectures are equivalent.

math.NT

Heavenly elliptic curves over quadratic fields

An abelian variety $A/K$ is heavenly at $\ell$ if the extension $K(A[\ell^\infty])/K(\mu_{\ell^{\infty}}\!)$ is both pro-$\ell$ and unramified away from $\ell$. It is known that for a fixed quadratic field $K$, the number of $K$-isomorphism classes of heavenly elliptic curves is finite, even running over all primes $\ell$. We prove a complementary result, that for a fixed prime $\ell\geq 7$, there are only finitely many such classes, even running over all quadratic fields. This naturally raises the question of whether to expect a finiteness result when both $K$ and $\ell$ are allowed to vary. We demonstrate similarities in the behavior of heavenly elliptic curves and elliptic curves with complex multiplication, in terms of their Frobenius traces modulo $\ell$. We determine the complete list of heavenly elliptic curves defined over quadratic fields with complex multiplication and with irrational $j$-invariant (up to isomorphism). We include various extensions of our results to higher degree fields and higher-dimensional abelian varieties where possible.

math.NT

A robust implementation for solving the $S$-unit equation and several applications

Let $K$ be a number field, and $S$ a finite set of places in $K$ containing all infinite places. We present an implementation for solving the $S$-unit equation $x + y = 1$, $x,y \in\mathscr{O}_{K,S}^\times$ in the computer algebra package SageMath. This paper outlines the mathematical basis for the implementation. We discuss and reference the results of extensive computations, including exponent bounds for solutions in many fields of small degree for small sets $S$. As an application, we prove an asymptotic version of Fermat's Last Theorem for totally real cubic number fields with bounded discriminant where 2 is totally ramified. In addition, we use the implementation to find all solutions to some cubic Ramanujan-Nagell equations.

math.NT

Cyclic covers and Ihara's Question

Let $\ell$ be a rational prime and $k$ a number field. Given a superelliptic curve $C/k$ of $\ell$-power degree, we describe the field generated by the $\ell$-power torsion of the Jacobian variety in terms of the branch set and reduction type of $C$ (and hence, in terms of data determined by a suitable affine model of $C$). If the Jacobian is good away from $\ell$ and the branch set is defined over a pro-$\ell$ extension of $k(\mu_{\ell^\infty})$ unramified away from $\ell$, then the $\ell$-power torsion of the Jacobian is rational over the maximal such extension. By decomposing the covering into a chain of successive cyclic $\ell$-coverings, the mod $\ell$ Galois representation attached to the Jacobian is decomposed into a block triangular form. The blocks on the diagonal of this form are further decomposed in terms of the Tate twists of certain subgroups $W_s$ of the quotients of the Jacobians of successive coverings. The result is a natural extension of earlier work by Anderson and Ihara, who demonstrated that a stricter condition on the branch locus guarantees the $\ell$-power torsion of the Jacobian is rational over the fixed field of the kernel of the canonical pro-$\ell$ outer Galois representation attached to an open subset of $\mathbf{P}^1$.

math.AG

Abelian surfaces good away from 2

Fix a number field $k$ and a rational prime $\ell$. We consider abelian varieties whose $\ell$-power torsion generates a pro-$\ell$ extension of $k(μ_{\ell^\infty})$ which is unramified away from $\ell$. It is a necessary, but not generally sufficient, condition that such varieties have good reduction away from $\ell$. In the special case of $\ell = 2$, we demonstrate that for abelian surfaces $A/\mathbb{Q}$, good reduction away from $\ell$ does suffice. The result is extended to elliptic curves and abelian surfaces over certain number fields unramified away from $\{2,\infty\}$. An explicit example is constructed to demonstrate that good reduction is not sufficient, at $\ell = 2$, for abelian varieties of sufficiently high dimension.

math.NT

Picard curves over Q with good reduction away from 3

Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined, and an application to a question of Ihara is discussed.

math.NT

Arithmetic of abelian varieties with constrained torsion

Let $K$ be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over $K$ whose $\ell$-power torsion fields are arithmetically constrained for some rational prime $\ell$. Such arithmetic constraints are related to an unresolved question of Ihara regarding the kernel of the canonical outer Galois representation on the pro-$\ell$ fundamental group of $P^1 - \{0,1,\infty\}$. Under GRH, we demonstrate the set of classes is finite for any fixed $K$ and any fixed dimension. Without GRH, we prove a semistable version of the result. In addition, several unconditional results are obtained when the degree of $K/\Q$ and the dimension of abelian varieties are not too large, through a careful analysis of the special fiber of such abelian varieties. In some cases, the results (viewed as a bound on the possible values of $\ell$) are uniform in the degree of the extension $K/\Q$.

math.NT

Class number formulas via 2-isogenies of elliptic curves

A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of elliptic curves.

math.NT

On the torsion of Jacobians of principal modular curves of level 3^n

We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3^n) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation.

math.NT