We formulate and solve the fixed horizon linear quadratic covariance steering problem in continuous time with a terminal cost measured in Hilbert-Schmidt (i.e., Frobenius) norm error between the desired and the controlled terminal covariances. For this problem, the necessary conditions of optimality become a coupled matrix ODE two-point boundary value problem. To solve this system of equations, we design a matricial recursive algorithm and prove its convergence. The proposed algorithm and its analysis make use of the linear fractional transforms parameterized by the state transition matrix of the associated Hamiltonian matrix. To illustrate the results, we provide two numerical examples: one with a two dimensional and another with a six dimensional state space.

We introduce the first direct policy search algorithm which provably converges to the globally optimal dynamic filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain an internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of informativity, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a regularizer which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a "reconditioning step" - converges to the globally optimal cost at a O (1 /T) rate.

Transformers, the standard implementation for large language models (LLMs), typically consist of tens to hundreds of discrete layers. While more layers can lead to better performance, this approach has been challenged as far from efficient, especially given the superiority of continuous layers demonstrated by diffusion and flow-based models for image generation. We propose the Latent Flow Transformer (LFT), which replaces a block of layers with a single learned transport operator trained via flow matching, offering significant compression while maintaining compatibility with the original architecture. Additionally, we address the limitations of existing flow-based methods in \textit{preserving coupling} by introducing the Flow Walking (FW) algorithm. On the Pythia-410M model, LFT trained with flow matching compresses 6 of 24 layers and outperforms directly skipping 2 layers (KL Divergence of LM logits at 0.407 vs. 0.529), demonstrating the feasibility of this design. When trained with FW, LFT further distills 12 layers into one while reducing the KL to 0.736 surpassing that from skipping 3 layers (0.932), significantly narrowing the gap between autoregressive and flow-based generation paradigms.

Lane-free traffic (LFT) is a new traffic system that relies on connected and automated vehicles (CAV) to increase road capacity and utilization by removing traditional lane markings using coordinated maneuvering of CAVs in LFT strategies. LFT is based on two main principles: upstream nudging and vehicles moving without adhering to any lane markings. By leveraging CAV capabilities to communicate and exchange information, LFT represents a promising future traffic system. While current research uses LFT simulations in two-dimensional space, driving simulators are necessary to investigate human behavior and perceived safety in LFT. This paper proposes a conceptual framework for LFT driving simulations and describes the assumptions, requirements, and recent technological developments that make it possible to investigate the human perspective and acceptance of LFT. Additionally, we propose a scenario matrix that can act as a test guide to building driving simulation scenarios for the LFT.

We introduce the first direct policy search algorithm which provably converges to the globally optimal $\textit{dynamic}$ filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of $\textit{informativity}$, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a $\textit{regularizer}$ which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a ``reconditioning step'' - converges to the globally optimal cost a $\mathcal{O}(1/T)$ rate. Our analysis relies on several new results which may be of independent interest, including a new framework for analyzing non-convex gradient descent via convex reformulation, and novel bounds on the solution to linear Lyapunov equations in terms of (our quantitative measure of) informativity.

Model-agnostic meta-learning (MAML) effectively meta-learns an initialization of model parameters for few-shot learning where all learning problems share the same format of model parameters -- congruous meta-learning. We extend MAML to incongruous meta-learning where different yet related few-shot learning problems may not share any model parameters. A Learned Fine Tuner (LFT) is used to replace hand-designed optimizers such as SGD for the task-specific fine-tuning. Here, MAML instead meta-learns the parameters of this LFT across incongruous tasks leveraging the learning-to-optimize (L2O) framework such that models fine-tuned with LFT (even from random initializations) adapt quickly to new tasks. As novel contributions, we show that the use of LFT within MAML (i) offers the capability to tackle few-shot learning tasks by meta-learning across incongruous yet related problems (e.g., classification over images of different sizes and model architectures), and (ii) can efficiently work with first-order and derivative-free few-shot learning problems. Theoretically, we quantify the difference between LFT (for MAML) and L2O. Empirically, we demonstrate the effectiveness of LFT through both synthetic and real problems and a novel application of generating universal adversarial attacks across different image sources in the few-shot learning regime.