Circuit-Based Intrinsic Methods to Detect Overfitting

Satrajit Chatterjee, Alan Mishchenko

Abstract:

The focus of this paper is on intrinsic methods to
detect overfitting. By intrinsic methods, we mean
methods that rely only on the model and the training data, as opposed to traditional methods (we
call them extrinsic methods) that rely on performance on a test set or on bounds from model complexity. We propose a family of intrinsic methods
called Counterfactual Simulation (CFS) which
analyze the flow of training examples through
the model by identifying and perturbing rare patterns. By applying CFS to logic circuits we get a
method that has no hyper-parameters and works
uniformly across different types of models such
as neural networks, random forests and lookup
tables. Experimentally, CFS can separate models
with different levels of overfit using only their
logic circuit representations without any access
to the high level structure. By comparing lookup
tables, neural networks, and random forests using CFS, we get insight into why neural networks
generalize. In particular, we find that stochastic
gradient descent in neural nets does not lead to
“brute force” memorization, but finds common patterns (whether we train with actual or randomized
labels), and neural networks are not unlike forests
in this regard. Finally, we identify a limitation
with our proposal that makes it unsuitable in an
adversarial setting, but points the way to future
work on robust intrinsic methods.