arXiv subjects

Susie Lu

Publications and source records attributed to Susie Lu.

7 recordsLinked to original sources

arXiv2026

DriftWorld: Fast World Modeling through Drifting

Predictive world models enable robots to plan by imagining the outcomes of their actions, but their value for control hinges on generating many rollouts quickly. This creates a bottleneck for diffusion-based world models: multistep sampling makes each rollout expensive, limiting large-scale action search at inference time. We introduce DriftWorld, an action-conditioned world model based on drifting generative models. Rather than denoising iteratively at inference, DriftWorld learns an action-conditioned drift during training, allowing it to generate future frames from the current observation and a candidate action sequence in a single forward pass at 30+ fps, which is 17x faster on average than diffusion based baselines. We evaluate DriftWorld on standard vision-based robotic manipulation benchmarks, including Bridge-V2, RT-1, Language Table, Push-T, and Robomimic. By producing rollouts that are both accurate and fast, DriftWorld achieves state-of-the-art decision-making performance with far less inference time than diffusion-based world model baselines. Beyond online control, DriftWorld can also serve as an offline simulator for ranking real-world robot policies, with rollout-based scores correlating with ground truth at up to 0.99. These results show that drifting models are a strong fit for robot world modeling, where fast, high-quality imagination directly supports planning and policy evaluation.

cs.RO↗

arXiv2026

One-step Latent-free Image Generation with Pixel Mean Flows

Modern diffusion/flow-based models for image generation typically exhibit two core characteristics: (i) using multi-step sampling, and (ii) operating in a latent space. Recent advances have made encouraging progress on each aspect individually, paving the way toward one-step diffusion/flow without latents. In this work, we take a further step towards this goal and propose "pixel MeanFlow" (pMF). Our core guideline is to formulate the network output space and the loss space separately. The network target is designed to be on a presumed low-dimensional image manifold (i.e., x-prediction), while the loss is defined via MeanFlow in the velocity space. We introduce a simple transformation between the image manifold and the average velocity field. In experiments, pMF achieves strong results for one-step latent-free generation on ImageNet at 256x256 resolution (2.22 FID) and 512x512 resolution (2.48 FID), filling a key missing piece in this regime. We hope that our study will further advance the boundaries of diffusion/flow-based generative models.

cs.CV↗

arXiv2025

On the Maximum Spread of Non-Negative Matrices

Given a directed graph $G$, the spread of $G$ is the largest distance between any two eigenvalues of its adjacency matrix. In 2022, Breen, Riasanovsky, Tait, and Urschel asked what $n$-vertex directed graph maximizes spread, and whether this graph is undirected. We prove the more general result that the spread of any $n \times n$ non-negative matrix $A$ with $\|A\|_{\max} \le 1$ is at most $2n/\sqrt{3}$, which is tight up to an additive factor and exact when $n$ is a multiple of three. Furthermore, our results show that the matrix with maximum spread is always symmetric.

math.CO↗

arXiv2025

Fast Consensus over Almost Regular Directed Graphs

This paper studies an open consensus network design problem: identifying the optimal simple directed graphs, given a fixed number of vertices and arcs, that maximize the second smallest real part of all Laplacian eigenvalues, referred to as algebraic connectivity. For sparse and dense graphs, the class of all optimal directed graphs that maximize algebraic connectivity is theoretically identified, leading to the fastest consensus. For general graphs, a computationally efficient sequence of almost regular directed graphs is proposed to achieve fast consensus, with algebraic connectivity close to the optimal value.

math.OC↗

arXiv2025

A Class of Optimal Directed Graphs for Network Synchronization

In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Through simulations, and without theoretical validation, it is conjectured that among all simple directed graphs with a fixed number of vertices and arcs, the optimal value of this quantity is achieved if the Laplacian spectrum satisfies a specific pattern. This paper proves this conjecture and further shows that the conjectured spectral condition is not only sufficient but also necessary. Moreover, the paper proves that the optimal Laplacian spectrum is always achievable by a class of almost regular directed graphs, which can be constructed through an inductive algorithm.

math.OC↗

arXiv2024

On primality and atomicity of numerical power monoids

In the first part of this paper, we establish a variation of a recent result by Bienvenu and Geroldinger on the (almost) non-existence of absolute irreducibles in (restricted) power monoids of numerical monoids: we argue the (almost) non-existence of primal elements in the same class of power monoids. The second part of this paper, devoted to the study of the atomic density of $\mathcal{P}_{\text{fin}, 0}(\mathbb{N}_0)$, is motivated by work of Shitov, a recent paper by Bienvenu and Geroldinger, and some questions pointed out by Geroldinger and Tringali. In the same, we study atomic density through the lens of the natural partition $\{ \mathcal{A}_{n,k} : k \in \mathbb{N}_0\}$ of $\mathcal{A}_n$, the set of atoms of $\mathcal{P}_{\text{fin}, 0}(\mathbb{N}_0)$ with maximum at most $n$: \[ \mathcal{A}_{n,k} = \{A \in \mathcal{A} : \max A \le n \text{ and } |A| = k\} \] for all $n,k \in \mathbb{N}$, where $\mathcal{A}$ is the set of atoms of $\mathcal{P}_{\text{fin}, 0}(\mathbb{N}_0)$. We pay special attention to the sequence $(\alpha_{n,k})_{n,k \ge 1}$, where $\alpha_{n,k}$ denote the size of the block $\mathcal{A}_{n,k}$. First, we establish some bounds and provide some asymptotic results for $(\alpha_{n,k})_{n,k \ge 1}$. Then, we take some probabilistic approach to argue that, for each $n \in \mathbb{N}$, the sequence $(\alpha_{n,k})_{k \ge 1}$ is almost unimodal. Finally, for each $n \in \mathbb{N}$, we consider the random variable $X_n : \mathcal{A}_n \to \mathbb{N}_0$ defined by the assignments $X_n : A \mapsto |A|$, whose probability mass function is $\mathbb{P}(X_n=k) = \alpha_{n,k}/| \mathcal{A}_n|$. We conclude proving that, for each $m \in \mathbb{N}$, the sequence of moments $(\mathbb{E}(X_n^m))_{n \ge 1}$ behaves asymptotically as that of a sequence $(\mathbb{E}(Y_n^m))_{n \ge 1}$, where $Y_n$ is a binomially distributed random variable with parameters $n$ and $\frac12$.

math.CO↗

arXiv2024

Fast Consensus Topology Design via Minimizing Laplacian Energy

This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These constructed graphs possess maximum vertex and edge connectivity, and more importantly, exhibit large algebraic connectivity of an optimal order provided they are not sparse. These properties guarantee fast and resilient consensus processes over these graphs.

math.OC↗