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Numerical models of electromyographic (EMG) signals have provided a huge contribution to our fundamental understanding of human neurophysiology and remain a central pillar of motor neuroscience and the development of human-machine interfaces. However, whilst modern biophysical simulations based on finite element methods are highly accurate, they are extremely computationally expensive and thus are generally limited to modelling static systems such as isometrically contracting limbs. As a solution to this problem, we propose a transfer learning approach, in which a conditional generative model is trained to mimic the output of an advanced numerical model. To this end, we present BioMime, a conditional generative neural network trained adversarially to generate motor unit activation potential waveforms under a wide variety of volume conductor parameters. We demonstrate the ability of such a model to predictively interpolate between a much smaller number of numerical model's outputs with a high accuracy. Consequently, the computational load is dramatically reduced, which allows the rapid simulation of EMG signals during truly dynamic and naturalistic movements.

In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG), defined in terms of a matrix with values in subsets of the real line P(R). We leverage semi-ring properties of P(R) to model multi-hop communication in a TVG using matrix multiplication and a truncated Kleene star. This leads to novel statistics on the communication capacity of TVGs called lifetime curves, which we generate for large samples of randomly chosen STARLINK satellites, whose connectivity is modeled over day-long simulations. Determining when a large subsample of STARLINK is temporally strongly connected is further analyzed using novel metrics introduced here that are inspired by topological data analysis (TDA). To better model networking scenarios between the Earth and Mars, we introduce various semi-rings capable of modeling propagation delay as well as protocols common to Delay Tolerant Networking (DTN), such as store-and-forward. Finally, we illustrate the applicability of zigzag persistence for featurizing different space networks and demonstrate the efficacy of K-Nearest Neighbors (KNN) classification for distinguishing Earth-Mars and Earth-Moon satellite systems using time-varying topology alone.

In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against over-fitting. We establish the convergence rates depending on the regularity condition of the slope function and the decay rate of the eigenvalues of the operator composition of covariance and kernel operator. Our convergence rates match the minimax rate available from the literature.

Tsetlin Machines (TMs) have garnered increasing interest for their ability to learn concepts via propositional formulas and their proven efficiency across various application domains. Despite this, the convergence proof for the TMs, particularly for the AND operator (\emph{conjunction} of literals), in the generalized case (inputs greater than two bits) remains an open problem. This paper aims to fill this gap by presenting a comprehensive convergence analysis of Tsetlin automaton-based Machine Learning algorithms. We introduce a novel framework, referred to as Probabilistic Concept Learning (PCL), which simplifies the TM structure while incorporating dedicated feedback mechanisms and dedicated inclusion/exclusion probabilities for literals. Given $n$ features, PCL aims to learn a set of conjunction clauses $C_i$ each associated with a distinct inclusion probability $p_i$. Most importantly, we establish a theoretical proof confirming that, for any clause $C_k$, PCL converges to a conjunction of literals when $0.5<p_k<1$. This result serves as a stepping stone for future research on the convergence properties of Tsetlin automaton-based learning algorithms. Our findings not only contribute to the theoretical understanding of Tsetlin Machines but also have implications for their practical application, potentially leading to more robust and interpretable machine learning models.

Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued fields. In particular, we prove that the unit ball with respect to a discrete valuation on a field is a discrete valuation ring and, conversely, that the adic valuation on the field of fractions of a discrete valuation ring is discrete. We define finite extensions of valuations and of discrete valuation rings, and prove some global-to-local results. Building on this general theory, we formalize the abstract definition and some fundamental properties of local fields. As an application, we show that finite extensions of the field $\mathbb{Q}_p$ of $p$-adic numbers and of the field $\mathbb{F}_p(\!(X)\!)$ of Laurent series over $\mathbb{F}_p$ are local fields.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where $M^* \in \mathbb{R}^{n \times n}$ is a positive semi-definite unknown matrix of rank $r \ll n$, and one uses a symmetric parameterization $XX^\top$ to learn $M^*$. Here $X \in \mathbb{R}^{n \times k}$ with $k > r$ is the factor matrix. We give a novel $\Omega (1/T^2)$ lower bound of randomly initialized GD for the over-parameterized case ($k >r$) where $T$ is the number of iterations. This is in stark contrast to the exact-parameterization scenario ($k=r$) where the convergence rate is $\exp (-\Omega (T))$. Next, we study asymmetric setting where $M^* \in \mathbb{R}^{n_1 \times n_2}$ is the unknown matrix of rank $r \ll \min\{n_1,n_2\}$, and one uses an asymmetric parameterization $FG^\top$ to learn $M^*$ where $F \in \mathbb{R}^{n_1 \times k}$ and $G \in \mathbb{R}^{n_2 \times k}$. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case ($k=r$) with an $\exp (-\Omega(T))$ rate. Furthermore, we give the first global exact convergence result for the over-parameterization case ($k>r$) with an $\exp(-\Omega(\alpha^2 T))$ rate where $\alpha$ is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from $\Omega (1/T^2)$ to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of $\alpha$, recovering the rate in the exact-parameterization case.

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this logic are used in blocks, each block consisting only of existential quantifiers or only of universal quantifiers. In this paper we consider the possibility of mixing quantifiers in blocks. We identify a non-trivial variation of the logic with mixed blocks of quantifiers which retains some good properties of the two-variable fragment and of the uniform one-dimensional fragment: it has the finite (exponential) model property and hence decidable, NExpTime-complete satisfiability problem.

We show that it is possible to learn an open-loop policy in simulation for the dynamic manipulation of a deformable linear object (DLO) -- e.g., a rope, wire, or cable -- that can be executed by a real robot without additional training. Our method is enabled by integrating an existing state-of-the-art DLO model (Discrete Elastic Rods) with MuJoCo, a robot simulator. We describe how this integration was done, check that validation results produced in simulation match what we expect from analysis of the physics, and apply policy optimization to train an open-loop policy from data collected only in simulation that uses a robot arm to fling a wire precisely between two obstacles. This policy achieves a success rate of 76.7% when executed by a real robot in hardware experiments without additional training on the real task.

To maintain a reliable grid we need fast decision-making algorithms for complex problems like Dynamic Reconfiguration (DyR). DyR optimizes distribution grid switch settings in real-time to minimize grid losses and dispatches resources to supply loads with available generation. DyR is a mixed-integer problem and can be computationally intractable to solve for large grids and at fast timescales. We propose GraPhyR, a Physics-Informed Graph Neural Network (GNNs) framework tailored for DyR. We incorporate essential operational and connectivity constraints directly within the GNN framework and train it end-to-end. Our results show that GraPhyR is able to learn to optimize the DyR task.

As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.