J. P. Crutchfield

A. B. Boyd, J. P. Crutchfield, M. Gu

Adaptive systems -- such as a biological organism gaining survival advantage, an autonomous robot executing a functional task, or a motor protein transporting intracellular nutrients -- must model the regularities and stochasticity in their environments to take full advantage of thermodynamic resources. Analogously, but in a purely computational realm, machine learning algorithms estimate models to capture predictable structure and identify irrelevant noise in training data. This happens through optimization of performance metrics, such as model likelihood. If physically implemented, is there a sense in which computational models estimated through machine learning are physically preferred? We introduce the thermodynamic principle that work production is the most relevant performance metric for an adaptive physical agent and compare the results to the maximum-likelihood principle that guides machine learning. Within the class of physical agents that most efficiently harvest energy from their environment, we demonstrate that an efficient agent's model explicitly determines its architecture and how much useful work it harvests from the environment. We then show that selecting the maximum-work agent for given environmental data corresponds to finding the maximum-likelihood model. This establishes an equivalence between nonequilibrium thermodynamics and dynamic learning. In this way, work maximization emerges as an organizing principle that underlies learning in adaptive thermodynamic systems.

S. E. Marzen, J. P. Crutchfield

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network's universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

S. E. Marzen, J. P. Crutchfield

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and their optimal memory-limited predictors are easily computed. Unsurprisingly, LSTMs outperform RCs, which outperform generalized linear models. Surprisingly, each of these methods can fall short of the maximal predictive accuracy by as much as 50% after training and, when optimized, tend to fall short of the maximal predictive accuracy by ~5%, even though previously available methods achieve maximal predictive accuracy with orders-of-magnitude less data. Thus, despite the representational universality of RCs and RNNs, using them can engender a surprising predictive gap for simple stimuli. One concludes that there is an important and underappreciated role for methods that infer "causal states" or "predictive state representations".

S. Loomis, J. R. Mahoney, C. Aghamohammadi et al.

Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate variable is a quantum state. We determine when and how well quantum simulations of classical channels may improve upon the minimal rates of classical simulation. This inverts Holevo's original question of quantifying the capacity of quantum channels with classical resources. We also show that this problem is equivalent to another, involving the local generation of a distribution from common entanglement.

P. M. Riechers, D. P. Varn, J. P. Crutchfield

Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated analytically as explicit functions of model parameters or the expressions may be used as a fast, accurate, and efficient way to obtain numerical values. We present several examples, finding agreement with previous work as well as deriving new relations.