Training deep networks as ordered acquisition of reusable computations
Neural Dynamics as the Composition of Quantized Units
Machine Learning
Summary
Deep learning models are often understood by looking at broad patterns or individual neurons, but it’s unclear how these levels connect. The authors study an intermediate idea where learning is seen as gaining small reusable building blocks called quanta that suddenly start working across many examples. They find that which quanta appear depends on how often they’re needed and how hard they are to learn next. They tested this idea on simple logical tasks and on a Transformer model, showing that these quanta help explain learning order and can improve understanding and generalization.
What this means in practice
- •For machine learning engineers: Use quanta to interpret and trace how neural networks learn discrete reusable computations during training to better debug and optimize models.
- •For natural language processing developers: Improve transformer model generalization on tasks like numeral-to-text mapping by training towards quanta-structured latent computations.
Authors
Jacopo Minniti, Aravinth Kulanthaivelu, Richard Sproat
Abstract
Deep learning is commonly interpreted at two levels: the macroscopic, through aggregate trends in loss summarized by scaling laws, and the microscopic, through neurons, features, and circuits. A central challenge is understanding how these levels connect, so that we can explain how elementary computations compose and collectively shape macroscopic behavior. To this end, we study an intermediate abstraction in which training is described as the ordered acquisition of quanta: reusable computations acquired suddenly and binary-activated across examples to reduce loss. By approximating population-gradient updates, we derive quanta's acquisition dynamics. This yields an acquisition priority governed by demand, how frequently a computation is required across examples, and conditional complexity, how difficult that computation is to acquire given those already available. In a Boolean compositional task, we derive predictions for acquisition order and show how staggered discrete acquisitions can produce smooth aggregate loss and, under certain geometries of quanta composition, give rise to scaling laws. We then train a Transformer to map numerals to English number names and recover candidate quanta from its checkpoint trajectory. From these units, we construct a model that preserves much of the Transformer's behavior while exposing interpretable latent computations and acquisition dynamics consistent with the theory. Separately, the quanta structure can serve as training targets to improve transformer generalization. Together, these results suggest the quanta abstraction can provide useful computational atoms for studying a variety of macroscopic phenomena.