Continual Learning with Guarantees via Weight Interval Constraints

TL;DR

This paper proposes Hyperrectangle Training, a novel continual learning method that uses interval constraints on neural network parameters to guarantee bounded forgetting and improve resilience without storing past data.

Contribution

It introduces a new training paradigm that enforces hyperrectangle constraints on parameters, transforming the continual learning problem into a polynomial-time, forgetting-resilient process.

Findings

The InterContiNet algorithm effectively models parameter regions with interval arithmetic.

The approach provides full resilience against forgetting in continual learning tasks.

Experimental results show competitive performance without storing previous data.

Abstract

We introduce a new training paradigm that enforces interval constraints on neural network parameter space to control forgetting. Contemporary Continual Learning (CL) methods focus on training neural networks efficiently from a stream of data, while reducing the negative impact of catastrophic forgetting, yet they do not provide any firm guarantees that network performance will not deteriorate uncontrollably over time. In this work, we show how to put bounds on forgetting by reformulating continual learning of a model as a continual contraction of its parameter space. To that end, we propose Hyperrectangle Training, a new training methodology where each task is represented by a hyperrectangle in the parameter space, fully contained in the hyperrectangles of the previous tasks. This formulation reduces the NP-hard CL problem back to polynomial time while providing full resilience against forgetting. We validate our claim by developing InterContiNet (Interval Continual Learning) algorithm which leverages interval arithmetic to effectively model parameter regions as hyperrectangles. Through experimental results, we show that our approach performs well in a continual learning setup without storing data from previous tasks.