Human-Centered Learning Mechanics: A Dynamical Framework for Entropy-Regulated Representation Learning

Background

The paper challenges existing views that treat deep learning as a closed optimization system, arguing that real-world AI models must contend with uncertainty, resource constraints, distribution shifts, decision risks, and human feedback. Traditional methods often fall short due to their focus on loss minimization without adequate consideration of information dynamics.

Key Points

1. Entropy Regularization Limitations: The paper identifies limitations in using entropy regularization, noting that it can produce weak or misaligned gradients if the chosen entropy surrogate does not generate a non-degenerate information force along the optimization trajectory.
2. Effective Entropy Concept: A new concept of "effective entropy" is introduced to formalize this idea. Effective entropy considers how an entropy term affects the overall training dynamics, ensuring that it contributes meaningfully to the learning process.
3. Geometric Entropy Surrogates: The authors propose tractable geometric surrogates for entropy, including variance-based and log-determinant covariance proxies. These are designed to maintain non-degeneracy in the information force, leading to more stable training dynamics.

Significance

1. Formalization of Effective Information Force: HCLM formalizes the concept of effective entropy through the lens of information forces, providing a rigorous mathematical framework for understanding how different entropy terms impact learning dynamics.
2. Convergence and Generalization Results: The paper derives several theoretical results, including convergence properties, entropy-flow behavior, Wasserstein gradient flows, and generalization guarantees under explicit assumptions. These results offer valuable insights into the stability and robustness of training processes.
3. Conditional Dynamical Interpretation: HCLM offers a conditional dynamical interpretation of scaling-law-like behaviors, attributing them to balances between information injection, entropy dissipation, and residual risk. This approach is more pragmatic than attempting an unconditional derivation of empirical neural scaling laws.

Effective Entropy and Geometric Surrogates: Controlled representation-learning experiments demonstrate that geometric entropy surrogates, particularly log-determinant covariance entropy, produce stronger and more stable gradients compared to softmax-normalized entropy. This finding supports the hypothesis that non-degenerate information forces are crucial for effective learning in complex real-world scenarios.

Conclusion

HCLM significantly advances our understanding of open and controlled learning systems by introducing a new framework that addresses critical limitations in traditional optimization theories. Through rigorous formalization and practical experiments, it offers valuable insights into how to achieve more robust and stable training dynamics in dynamic and uncertain environments.