arXiv subjects

Yichi Xu

Publications and source records attributed to Yichi Xu.

5 recordsLinked to original sources

arXiv2026

Laziness of Quantum Walks on Graphs

The trace of the average mixing matrix of a quantum walk measures the "laziness" of the walk: the higher the trace, the more likely that the walker returns home in the long run. In this paper, we develop tools to study this graph invariant arising from Laplacian quantum walks. It is known that the complete graph $K_n$ is the laziest connected graph on $n$ vertices. Using our machinery, we show that the star $S_n$ is the second laziest connected graph on $n$ vertices (and hence the laziest tree on $n$ vertices), the complete multipartite graph $K_{n-2,1,1}$ is the third laziest connected graph on $n$ vertices, and the double star $DS(n-3,1)$ is the second laziest tree on $n$ vertices. We also show that on the same number of vertices, more unbalanced double stars are lazier.

math.CO↗

arXiv2025

Subspace State Transfer in Coined Quantum Walks

We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer using the spectral properties of a Hermitian weighted digraph obtained from the underlying graph. We then provide a polynomial-time algorithm that tests whether pointwise perfect subspace state transfer occurs at an integer step, given that the subspace and coins are rational. Finally, we construct several infinite families of examples that admit pointwise perfect $d$-dimensional subspace state transfer where $d\ge 2$.

math.CO↗

arXiv2025

A Coq Formalization of Unification Modulo Exclusive-Or

Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory contains an operator with the properties Associativity, Commutativity, Nilpotency, and the presence of an identity. In the proof assistant Coq, we implement an algorithm that solves XOR unification problems, whose design was inspired by Liu and Lynch, and prove it sound, complete, and terminating. Using Coq's code extraction capability we obtain an implementation in the programming language OCaml.

cs.LO↗

arXiv2024

TrainMover: An Interruption-Resilient Runtime for ML Training

Large-scale ML training jobs are frequently interrupted by hardware and software anomalies, failures, and management events. Existing solutions like checkpoint-restart or runtime reconfiguration suffer from long downtimes and degraded performance. We present TrainMover, a resilient LLM training runtime that leverages elastic and standby machines to handle interruptions with minimal downtime and zero memory overhead. To achieve these goals, TrainMover introduces three key techniques: two-phase, delta-based communication group setup; communication-free sandboxed warmup; and general standby design that enables failure recovery from any role. Our evaluation shows that TrainMover consistently achieves around 20 seconds of downtime when handling various interruptions at the 1024-GPU scale. TrainMover is projected to reduce wasted GPU hours by 55% compared to the best alternative, saving 1.4 million GPU-hours per week at the 64K-GPU scale.

cs.DC↗

arXiv2018

Deep Reinforcement Learning of Cell Movement in the Early Stage of C. elegans Embryogenesis

Cell movement in the early phase of C. elegans development is regulated by a highly complex process in which a set of rules and connections are formulated at distinct scales. Previous efforts have shown that agent-based, multi-scale modeling systems can integrate physical and biological rules and provide new avenues to study developmental systems. However, the application of these systems to model cell movement is still challenging and requires a comprehensive understanding of regulation networks at the right scales. Recent developments in deep learning and reinforcement learning provide an unprecedented opportunity to explore cell movement using 3D time-lapse images. We present a deep reinforcement learning approach within an ABM system to characterize cell movement in C. elegans embryogenesis. Our modeling system captures the complexity of cell movement patterns in the embryo and overcomes the local optimization problem encountered by traditional rule-based, ABM that uses greedy algorithms. We tested our model with two real developmental processes: the anterior movement of the Cpaaa cell via intercalation and the rearrangement of the left-right asymmetry. In the first case, model results showed that Cpaaa's intercalation is an active directional cell movement caused by the continuous effects from a longer distance, as opposed to a passive movement caused by neighbor cell movements. This is because the learning-based simulation found that a passive movement model could not lead Cpaaa to the predefined destination. In the second case, a leader-follower mechanism well explained the collective cell movement pattern. These results showed that our approach to introduce deep reinforcement learning into ABM can test regulatory mechanisms by exploring cell migration paths in a reverse engineering perspective. This model opens new doors to explore large datasets generated by live imaging.

q-bio.QM↗