[Paper Review] Bayesian Structure Adaptation for Continual Learning

Abhishek Kumar, Sunabha Chatterjee+1 more|arXiv (Cornell University)|Dec 8, 2019

Domain Adaptation and Few-Shot Learning43 references4 citations

TL;DR

This paper proposes a Bayesian nonparametric continual learning framework that dynamically adapts neural network architecture using the Indian Buffet Process (IBP) to enable task-specific sparse weight subsets while sharing structure across tasks. By integrating structure learning with variational Bayesian inference, the model mitigates catastrophic forgetting and achieves state-of-the-art performance on both supervised and unsupervised continual learning benchmarks.

ABSTRACT

Continual Learning is a learning paradigm where learning systems are trained with sequential or streaming tasks. Two notable directions among the recent advances in continual learning with neural networks are ($i$) variational Bayes based regularization by learning priors from previous tasks, and, ($ii$) learning the structure of deep networks to adapt to new tasks. So far, these two approaches have been orthogonal. We present a novel Bayesian approach to continual learning based on learning the structure of deep neural networks, addressing the shortcomings of both these approaches. The proposed model learns the deep structure for each task by learning which weights to be used, and supports inter-task transfer through the overlapping of different sparse subsets of weights learned by different tasks. Experimental results on supervised and unsupervised benchmarks shows that our model performs comparably or better than recent advances in continual learning setting.

Motivation & Objective

• Address catastrophic forgetting in continual learning by enabling dynamic neural network architecture adaptation.
• Integrate Bayesian nonparametric priors (IBP) with variational inference to support incremental model growth and task-specific weight sparsity.
• Enable inter-task transfer through overlapping, task-specific sparse weight subsets while preserving performance on previous tasks.
• Extend the applicability of Bayesian continual learning beyond supervised learning to include unsupervised generative modeling (e.g., VAEs).
• Achieve effective representation learning in shared latent spaces across tasks via task-modulated, masked neural networks.

Proposed method

• Model each hidden layer’s connectivity using the Indian Buffet Process (IBP) prior, allowing infinite potential features and dynamic growth with new tasks.
• Use a structured mean-field variational posterior to approximate the joint posterior over weights, masks, and latent variables, enabling end-to-end training.
• Apply a binary mask matrix $\bm{B}^l$ to sparsely select active connections in each layer, with $\bm{W}^l = \bm{B}^l \odot \bm{V}^l$, where $\bm{V}^l$ are the weight values.
• Leverage amortized inference via neural networks to parameterize posterior distributions over latent variables and model parameters, enabling scalable inference.
• Formulate the evidence lower bound (ELBO) for both discriminative (Bayesian neural networks) and generative (VAEs) models, optimizing it via stochastic gradient descent.
• Support both supervised and unsupervised continual learning by applying the same framework to Bayesian neural networks and variational autoencoders with task-specific masking.

Experimental results

Research questions

• RQ1 Can a Bayesian nonparametric approach dynamically grow neural network structures to accommodate new tasks while retaining performance on previous ones?
• RQ2 How effective is the use of IBP-based sparse weight selection in enabling inter-task transfer and reducing catastrophic forgetting?
• RQ3 Can the proposed method generalize across both supervised and unsupervised continual learning settings with shared architectural and inference mechanisms?
• RQ4 To what extent does the model preserve task-specific representations while enabling shared latent space learning across tasks?
• RQ5 How does the model compare to state-of-the-art methods in terms of forgetting mitigation and representation quality on benchmark datasets?

Key findings

• The model achieves a 3-KNN error of 0.37% on MNIST and 0.08% on notMNIST in unsupervised continual learning, significantly outperforming EwC and VCL.
• On MNIST, the model maintains test likelihoods across tasks with minimal decay, indicating strong resistance to catastrophic forgetting.
• t-SNE visualizations show clearer class separation in the latent space for MNIST than for notMNIST, reflecting better representation learning on more uniform data.
• Generated samples from the final prior after all tasks show high-quality image generation, confirming effective latent space modeling.
• The model’s representation learning via KNN classification on latent codes demonstrates superior performance, with errors an order of magnitude lower than baselines.
• Reconstructed images from both MNIST and notMNIST retain high quality despite model constraints, indicating effective generative capacity and stable training.