We develop a theory of transfer learning in infinitely wide neural networks where both the pretraining (source) and downstream (target) task can operate in a feature learning regime. We analyze both the Bayesian framework, where learning is described by a posterior distribution over the weights, and gradient flow training of randomly initialized networks trained with weight decay. Both settings track how representations evolve in both source and target tasks. The summary statistics of these theories are adapted feature kernels which, after transfer learning, depend on data and labels from both source and target tasks. Reuse of features during transfer learning is controlled by an elastic weight coupling which controls the reliance of the network on features learned during training on the source task. We apply our theory to linear and polynomial regression tasks as well as real datasets. Our theory and experiments reveal interesting interplays between elastic weight coupling, feature learning strength, dataset size, and source and target task alignment on the utility of transfer learning.

Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random variables. This inherent variability must be accounted for in reliability analysis. While Monte Carlo methods can handle this, their high computational cost is often prohibitive. To address this, stochastic emulators have emerged as efficient surrogate models capable of capturing the random response of simulators at reduced cost. Although promising, current methods still require large training sets to produce accurate reliability estimates, which limits their practicality for expensive simulations. This work introduces an active learning framework to further reduce the computational burden of reliability analysis using stochastic emulators. We focus on stochastic polynomial chaos expansions (SPCE) and propose a novel learning function that targets regions of high predictive uncertainty relevant to failure probability estimation. To quantify this uncertainty, we exploit the asymptotic normality of the maximum likelihood estimator. The resulting method, named active learning stochastic polynomial chaos expansions (AL-SPCE), is applied to three test cases. Results demonstrate that AL-SPCE maintains high accuracy in reliability estimates while significantly improving efficiency compared to conventional surrogate-based methods and direct Monte Carlo simulation. This confirms the potential of active learning in enhancing the practicality of stochastic reliability analysis for complex, computationally expensive models.

In designing generative models, it is commonly believed that in order to learn useful latent structure, we face a fundamental tension between expressivity and structure. In this paper we challenge this view by proposing a new approach to training arbitrarily expressive generative models that simultaneously learn disentangled latent structure. This is accomplished by adding a simple decoder-only module to the head of an existing decoder block that can be arbitrarily complex. The module learns to process concept information by implicitly inverting linear representations from an encoder. Inspired by the notion of intervention in causal graphical models, our module selectively modifies its architecture during training, allowing it to learn a compact joint model over different contexts. We show how adding this module leads to disentangled representations that can be composed for out-of-distribution generation. To further validate our proposed approach, we prove a new identifiability result that extends existing work on identifying structured representations in nonlinear models.

Accurately estimating parameters of physiological models is essential to achieving reliable digital twins. For Type 1 Diabetes, this is particularly challenging due to the complexity of glucose-insulin interactions. Traditional methods based on Markov Chain Monte Carlo struggle with high-dimensional parameter spaces and fit parameters from scratch at inference time, making them slow and computationally expensive. In this study, we propose a Simulation-Based Inference approach based on Neural Posterior Estimation to efficiently capture the complex relationships between meal intake, insulin, and glucose level, providing faster, amortized inference. Our experiments demonstrate that SBI not only outperforms traditional methods in parameter estimation but also generalizes better to unseen conditions, offering real-time posterior inference with reliable uncertainty quantification.

We present a reinforcement learning method for training neuro-fuzzy controllers using Proximal Policy Optimization (PPO). Unlike prior approaches that used Deep Q-Networks (DQN) with Adaptive Neuro-Fuzzy Inference Systems (ANFIS), our PPO-based framework leverages a stable on-policy actor-critic setup. Evaluated on the CartPole-v1 environment across multiple seeds, PPO-trained fuzzy agents consistently achieved the maximum return of 500 with zero variance after 20, 000 updates, outperforming ANFIS-DQN baselines in both stability and convergence speed. This highlights PPO's potential for training explainable neuro-fuzzy agents in reinforcement learning tasks.

Large language models are thought to have potential to aid in medical decision making. We investigate this here. We start with the treatment problem, the patient's core medical decision-making task, which is solved in collaboration with a healthcare provider. We discuss approaches to solving the treatment problem, including -- within evidence-based medicine -- trials and observational data. We then discuss the chat problem, and how this differs from the treatment problem -- in particular as it relates to imitation. We then discuss how a large language model might be used to solve the treatment problem and highlight some of the challenges that emerge. We finally discuss how these challenges relate to evidence-based medicine, and how this might inform next steps.

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.

Neurosymbolic AI (NSAI) has recently emerged to mitigate limitations associated with deep learning (DL) models, e.g. quantifying their uncertainty or reason with explicit rules. Hence, TinyML hardware will need to support these symbolic models to bring NSAI to embedded scenarios. Yet, although symbolic models are typically compact, their sparsity and computation resolution contrasts with low-resolution and dense neuro models, which is a challenge on resource-constrained TinyML hardware severely limiting the size of symbolic models that can be computed. In this work, we remove this bottleneck leveraging a tight hardware/software integration to present a complete framework to compute NSAI with TinyML hardware. We focus on symbolic models realized with tractable probabilistic circuits (PCs), a popular subclass of probabilistic models for hardware integration. This framework: (1) trains a specific class of hardware-efficient \emph{deterministic} PCs, chosen for the symbolic task; (2) \emph{compresses} this PC until it can be computed on TinyML hardware with minimal accuracy degradation, using our $n^{th}$-root compression technique, and (3) \emph{deploys} the complete NSAI model on TinyML hardware. Compared to a 64b precision baseline necessary for the PC without compression, our workflow leads to significant hardware reduction on FPGA (up to 82.3\% in FF, 52.6\% in LUTs, and 18.0\% in Flash usage) and an average inference speedup of 4.67x on ESP32 microcontroller.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

In denoising diffusion probabilistic models (DDPMs), the learned noise predictor $ ε_θ ( {\bf x}_t , t)$ is trained to approximate the forward-process noise $ε_t$. The equality $\nabla_{{\bf x}_t} \log q({\bf x}_t) = -\frac 1 {\sqrt {1- {\bar α}_t} } ε_θ ( {\bf x}_t , t)$ plays a fundamental role in both theoretical analyses and algorithmic design, and thus is frequently employed across diffusion-based generative models. In this paper, an explicit formulation of $ ε_θ ( {\bf x}_t , t)$ in terms of the forward-process noise $ε_t$ is derived. This result show how the forward-process noise $ε_t$ contributes to the learned predictor $ ε_θ ( {\bf x}_t , t)$. Furthermore, based on this formulation, we present a novel and mathematically rigorous proof of the fundamental equality above, clarifying its origin and providing new theoretical insight into the structure of diffusion models.