Thermodynamic Overfitting and Generalization: Energetic Limits on Predictive Complexity (2402.16995v1)

Abstract: Efficiently harvesting thermodynamic resources requires a precise understanding of their structure. This becomes explicit through the lens of information engines -- thermodynamic engines that use information as fuel. Maximizing the work harvested using available information is a form of physically-instantiated machine learning that drives information engines to develop complex predictive memory to store an environment's temporal correlations. We show that an information engine's complex predictive memory poses both energetic benefits and risks. While increasing memory facilitates detection of hidden patterns in an environment, it also opens the possibility of thermodynamic overfitting, where the engine dissipates additional energy in testing. To address overfitting, we introduce thermodynamic regularizers that incur a cost to engine complexity in training due to the physical constraints on the information engine. We demonstrate that regularized thermodynamic machine learning generalizes effectively. In particular, the physical constraints from which regularizers are derived improve the performance of learned predictive models. This suggests that the laws of physics jointly create the conditions for emergent complexity and predictive intelligence.

• The paper demonstrates that maximizing thermodynamic work extraction is equivalent to maximum likelihood estimation over ε-machines, quantifying overfitting via asymptotic work metrics.
• It introduces two regularization techniques—autocorrection and engine initialization—to penalize excessive model complexity and reduce energy dissipation.
• Empirical simulations reveal that energy-efficient constraints prevent negative work output, thereby bolstering model generalization in dynamic environments.

Thermodynamic Overfitting and Generalization: Energetic Limits on Predictive Complexity

The paper "Thermodynamic Overfitting and Generalization: Energetic Limits on Predictive Complexity" by Boyd et al. explores a novel paradigm wherein thermodynamic principles guide the development and refinement of predictive models used by information engines—physical systems that convert information into work. By treating the problem of work extraction akin to a machine learning task, the authors draw intriguing connections between maximizing energy efficiency and conventional techniques like Maximum Likelihood Estimation (MLE). In doing so, the paper explores the dual energy dynamics of overfitting and regularization, offering new insights into the role of physical constraints on learning.

Overview of the Approach

The authors adopt a framework where an information engine learns to extract maximal work from a correlated but noisy environment. This learning process is modeled using $\epsilon$-machines, minimal predictive models that encapsulate hidden Markov processes. The informational complexity of these machines is captured by measures such as statistical complexity. A noteworthy assertion of the paper is the equivalence of thermodynamic work maximization and maximum likelihood over $\epsilon$-machines, providing a physical basis for structural inference akin to MLE.

The Problem of Thermodynamic Overfitting

Contrary to classical thermodynamic systems traditionally modeled as demonstrating equilibrium states, information engines must cope with dynamic, nonequilibrium environments. Overfitting emerges as a computational and physical pitfall when an engine maintains a memory or model complexity that exceeds the predictive requirements justified by data. Such an overfit engine, although improving work output during training, fails to generalize, leading to increased dissipation when tested on new data. This paper quantifies this failure rate using an asymptotic work production metric, revealing the costs of thermodynamic "over-commitment" to complexity.

Thermodynamic Regularization Techniques

Boyd et al. propose two complementary regularization strategies to counteract overfitting:

1. Autocorrection Regularization: This strategy penalizes an engine for starting in a non-synchronized state with respect to the source causal states. The dissipative cost of synchronizing correlates positively with complexity, thereby naturally limiting the intricacy of the memory model.
2. Engine Initialization Cost: Regularization rooted in the thermodynamics of initializing memory states suggests Bayesian updates to model parameters, aligned with principles like Laplace's rule of succession. The energy dissipated in preparing a model reflects the precision cost of incorrect predictive state distributions.

Empirical Results and Insights

By simulating these thermodynamic learning processes, the authors showcase diverse scenarios with differing model complexities. They demonstrate that regularization through autocorrection and Bayesian parameter updates allows for thermodynamic learning that is as effective in testing as it is in training. Particularly, engines trained with these constraints typically avoid the peril of negative work production—a signifier of unproductive thermodynamic overfit.

Implications and Future Directions

This framework converges on a phenomenon where complexity in terms of both information and energy cost establishes natural barriers against the inefficiencies seen in traditional numerical overfit models. It presents a promising front in embodied intelligence—situating adaptive learning and computational mechanics within the larger discourse on sustainable energy-efficient technologies.

The work holds profound implications for future artificial intelligence research, particularly in improving autonomous systems that must adapt to uncharted environments while maintaining efficiency. It beckons experimental validation, inviting physicists and computer scientists alike to ponder fundamental questions at the intersection of prediction, computation, and thermodynamics. The suggested regularization techniques propose a novel outlook for systems that need to adaptively strike a balance between energy efficiency and computational efficacy, opening up broader discussions on the nature of intelligence itself.