Disease progression models infer group-level temporal trajectories of change in patients' features as a chronic degenerative condition plays out. They provide unique insight into disease biology and staging systems with individual-level clinical utility. Discrete models consider disease progression as a latent permutation of events, where each event corresponds to a feature becoming measurably abnormal. However, permutation inference using traditional maximum likelihood approaches becomes prohibitive due to combinatoric explosion, severely limiting model dimensionality and utility. Here we leverage ideas from optimal transport to model disease progression as a latent permutation matrix of events belonging to the Birkhoff polytope, facilitating fast inference via optimisation of the variational lower bound. This enables a factor of 1000 times faster inference than the current state of the art and, correspondingly, supports models with several orders of magnitude more features than the current state of the art can consider. Experiments demonstrate the increase in speed, accuracy and robustness to noise in simulation. Further experiments with real-world imaging data from two separate datasets, one from Alzheimer's disease patients, the other age-related macular degeneration, showcase, for the first time, pixel-level disease progression events in the brain and eye, respectively. Our method is low compute, interpretable and applicable to any progressive condition and data modality, giving it broad potential clinical utility.

Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase estimation and hybrid quantum-classical optimizers involving parameterized quantum circuits, the latter falling under the umbrella of the variational quantum eigensolver. Here, we analyze the performance of quantum Boltzmann machines for this task, which is a less explored ansatz based on parameterized thermal states and which is not known to suffer from the barren-plateau problem. We delineate a hybrid quantum-classical algorithm for this task and rigorously prove that it converges to an $\varepsilon$-approximate stationary point of the energy function optimized over parameter space, while using a number of parameterized-thermal-state samples that is polynomial in $\varepsilon^{-1}$, the number of parameters, and the norm of the Hamiltonian being optimized. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction that combines classical sampling, Hamiltonian simulation, and the Hadamard test, thus overcoming a key obstacle to quantum Boltzmann machine learning that has been left open since [Amin et al., Phys. Rev. X 8, 021050 (2018)]. Additionally supporting our main claims are calculations of the gradient and Hessian of the energy function, as well as an upper bound on the matrix elements of the latter that is used in the convergence analysis.

Integrating symbolic techniques with statistical ones is a long-standing problem in artificial intelligence. The motivation is that the strengths of either area match the weaknesses of the other, and $\unicode{x2013}$ by combining the two $\unicode{x2013}$ the weaknesses of either method can be limited. Neuro-symbolic AI focuses on this integration where the statistical methods are in particular neural networks. In recent years, there has been significant progress in this research field, where neuro-symbolic systems outperformed logical or neural models alone. Yet, neuro-symbolic AI is, comparatively speaking, still in its infancy and has not been widely adopted by machine learning practitioners. In this survey, we present the first mapping of neuro-symbolic techniques into families of frameworks based on their architectures, with several benefits: Firstly, it allows us to link different strengths of frameworks to their respective architectures. Secondly, it allows us to illustrate how engineers can augment their neural networks while treating the symbolic methods as black-boxes. Thirdly, it allows us to map most of the field so that future researchers can identify closely related frameworks.

As reinforcement learning agents become increasingly deployed in real-world scenarios, predicting future agent actions and events during deployment is important for facilitating better human-agent interaction and preventing catastrophic outcomes. This paper experimentally evaluates and compares the effectiveness of future action and event prediction for three types of RL agents: explicitly planning, implicitly planning, and non-planning. We employ two approaches: the inner state approach, which involves predicting based on the inner computations of the agents (e.g., plans or neuron activations), and a simulation-based approach, which involves unrolling the agent in a learned world model. Our results show that the plans of explicitly planning agents are significantly more informative for prediction than the neuron activations of the other types. Furthermore, using internal plans proves more robust to model quality compared to simulation-based approaches when predicting actions, while the results for event prediction are more mixed. These findings highlight the benefits of leveraging inner states and simulations to predict future agent actions and events, thereby improving interaction and safety in real-world deployments.

Large Language Models (LLMs) have demonstrated remarkable abilities in reasoning and planning by breaking down complex problems into sequential steps. This paper revisits LLM reasoning from an optimal control perspective, proposing a novel method, Predictive-Decoding, that leverages Model Predictive Control to enhance planning accuracy. By reweighting LLM distributions based on foresight trajectories, Predictive-Decoding aims to mitigate early errors and promote non-myopic planning. Our experiments show significant improvements across a wide range of tasks in math, coding, and agent-based scenarios. Furthermore, Predictive-Decoding demonstrates computational efficiency, outperforming search baselines while utilizing inference compute more effectively. This study provides insights into optimizing LLM planning capabilities. Code is available at this repo. Large Language Models (LLMs) are extensively pretrained on large corpus to predict the next tokens.

In a groundbreaking work, Schmidt-Hieber (2020) proved the minimax optimality of deep neural networks with ReLu activation for least-square regression estimation over a large class of functions defined by composition. In this paper, we extend these results in many directions. First, we remove the i.i.d. assumption on the observations, to allow some time dependence. The observations are assumed to be a Markov chain with a non-null pseudo-spectral gap. Then, we study a more general class of machine learning problems, which includes least-square and logistic regression as special cases. Leveraging on PAC-Bayes oracle inequalities and a version of Bernstein inequality due to Paulin (2015), we derive upper bounds on the estimation risk for a generalized Bayesian estimator. In the case of least-square regression, this bound matches (up to a logarithmic factor) the lower bound of Schmidt-Hieber (2020). We establish a similar lower bound for classification with the logistic loss, and prove that the proposed DNN estimator is optimal in the minimax sense.

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant for applications that require joint compression and retrieval, and in scenarios involving distributional shifts due to processing. We show that the proposed formulation extends the classical minimum entropy coupling framework by integrating a bottleneck, allowing for a controlled degree of stochasticity in the coupling. We explore the decomposition of the Minimum Entropy Coupling with Bottleneck (MEC-B) into two distinct optimization problems: Entropy-Bounded Information Maximization (EBIM) for the encoder, and Minimum Entropy Coupling (MEC) for the decoder. Through extensive analysis, we provide a greedy algorithm for EBIM with guaranteed performance, and characterize the optimal solution near functional mappings, yielding significant theoretical insights into the structural complexity of this problem. Furthermore, we illustrate the practical application of MEC-B through experiments in Markov Coding Games (MCGs) under rate limits. These games simulate a communication scenario within a Markov Decision Process, where an agent must transmit a compressed message from a sender to a receiver through its actions. Our experiments highlight the trade-offs between MDP rewards and receiver accuracy across various compression rates, showcasing the efficacy of our method compared to conventional compression baseline.

Many real-world sequential repair problems can be effectively modeled using monotonic Markov Decision Processes (MDPs), where the system state stochastically decreases and can only be increased by performing a restorative action. This work addresses the problem of solving multi-component monotonic MDPs with both budget and capacity constraints. The budget constraint limits the total number of restorative actions and the capacity constraint limits the number of restorative actions that can be performed simultaneously. While prior methods dealt with budget constraints, including capacity constraints in prior methods leads to an exponential increase in computational complexity as the number of components in the MDP grows. We propose a two-step planning approach to address this challenge. First, we partition the components of the multi-component MDP into groups, where the number of groups is determined by the capacity constraint. We achieve this partitioning by solving a Linear Sum Assignment Problem (LSAP). Each group is then allocated a fraction of the total budget proportional to its size. This partitioning effectively decouples the large multi-component MDP into smaller subproblems, which are computationally feasible because the capacity constraint is simplified and the budget constraint can be addressed using existing methods. Subsequently, we use a meta-trained PPO agent to obtain an approximately optimal policy for each group. To validate our approach, we apply it to the problem of scheduling repairs for a large group of industrial robots, constrained by a limited number of repair technicians and a total repair budget. Our results demonstrate that the proposed method outperforms baseline approaches in terms of maximizing the average uptime of the robot swarm, particularly for large swarm sizes.

Experience goods such as sporting and artistic events, songs, videos, news stories, podcasts, and television series, are often packaged and consumed in bundles. Many such bundles are ordered in the sense that the individual items are consumed sequentially, one at a time. We examine if an individual's decision to consume the next item in an ordered bundle can be predicted based on his/her consumption pattern for the preceding items. We evaluate several predictive models, including two custom Transformers using decoder-only and encoder-decoder architectures, fine-tuned GPT-3, a custom LSTM model, a reinforcement learning model, two Markov models, and a zero-order model. Using data from Spotify, we find that the custom Transformer with a decoder-only architecture provides the most accurate predictions, both for individual choices and aggregate demand. This model captures a general form of state dependence. Analysis of Transformer attention weights suggests that the consumption of the next item in a bundle is based on approximately equal weighting of all preceding choices. Our results indicate that the Transformer can assist in queuing the next item that an individual is likely to consume from an ordered bundle, predicting the demand for individual items, and personalizing promotions to increase demand.

Traditionally, model-based reinforcement learning (MBRL) methods exploit neural networks as flexible function approximators to represent $\textit{a priori}$ unknown environment dynamics. However, training data are typically scarce in practice, and these black-box models often fail to generalize. Modeling architectures that leverage known physics can substantially reduce the complexity of system-identification, but break down in the face of complex phenomena such as contact. We introduce a novel framework for learning semi-structured dynamics models for contact-rich systems which seamlessly integrates structured first principles modeling techniques with black-box auto-regressive models. Specifically, we develop an ensemble of probabilistic models to estimate external forces, conditioned on historical observations and actions, and integrate these predictions using known Lagrangian dynamics. With this semi-structured approach, we can make accurate long-horizon predictions with substantially less data than prior methods. We leverage this capability and propose Semi-Structured Reinforcement Learning ($\texttt{SSRL}$) a simple model-based learning framework which pushes the sample complexity boundary for real-world learning. We validate our approach on a real-world Unitree Go1 quadruped robot, learning dynamic gaits -- from scratch -- on both hard and soft surfaces with just a few minutes of real-world data. Video and code are available at: https://sites.google.com/utexas.edu/ssrl