A Fast Learning Algorithm for Deep Belief Nets

TLDR

Digits lie on low‑dimensional manifolds modeled as long ravines in the free‑energy landscape of the top‑level associative memory, which can be explored via directed connections. The study demonstrates how complementary priors can eliminate explaining‑away effects in densely connected belief nets with many hidden layers. A fast, greedy algorithm using complementary priors learns deep directed belief networks layer‑by‑layer when the top two layers form an undirected associative memory, and it initializes a slower contrastive wake‑sleep fine‑tuning procedure. After fine‑tuning, a three‑hidden‑layer network becomes a strong generative model of handwritten digits and their labels, achieving better classification than the best discriminative algorithms.

Abstract

We show how to use “complementary priors” to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.