A crucial capability of Machine Learning models in real-world applications is the ability to continuously learn new tasks. This adaptability allows them to respond to potentially inevitable shifts in the data-generating distribution over time. However, in Continual Learning (CL) settings, models often struggle to balance learning new tasks (plasticity) with retaining previous knowledge (memory stability). Consequently, they are susceptible to Catastrophic Forgetting, which degrades performance and undermines the reliability of deployed systems. Variational Continual Learning methods tackle this challenge by employing a learning objective that recursively updates the posterior distribution and enforces it to stay close to the latest posterior estimate. Nonetheless, we argue that these methods may be ineffective due to compounding approximation errors over successive recursions. To mitigate this, we propose new learning objectives that integrate the regularization effects of multiple previous posterior estimations, preventing individual errors from dominating future posterior updates and compounding over time. We reveal insightful connections between these objectives and Temporal-Difference methods, a popular learning mechanism in Reinforcement Learning and Neuroscience. We evaluate the proposed objectives on challenging versions of popular CL benchmarks, demonstrating that they outperform standard Variational CL methods and non-variational baselines, effectively alleviating Catastrophic Forgetting.

Variational continual learning (VCL) is a turn-key learning algorithm that has state-of-the-art performance among the best continual learning models. In our work, we explore an extension of the generalized variational continual learning (GVCL) model, named AutoVCL, which combines task heuristics for informed learning and model optimization. We demonstrate that our model outperforms the standard GVCL with fixed hyperparameters, benefiting from the automatic adjustment of the hyperparameter based on the difficulty and similarity of the incoming task compared to the previous tasks.

Continual learning aims to allow models to learn new tasks without forgetting what has been learned before. This work introduces Elastic Variational Continual Learning with Weight Consolidation (EVCL), a novel hybrid model that integrates the variational posterior approximation mechanism of Variational Continual Learning (VCL) with the regularization-based parameter-protection strategy of Elastic Weight Consolidation (EWC). By combining the strengths of both methods, EVCL effectively mitigates catastrophic forgetting and enables better capture of dependencies between model parameters and task-specific data. Evaluated on five discriminative tasks, EVCL consistently outperforms existing baselines in both domain-incremental and task-incremental learning scenarios for deep discriminative models.

An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory ground. Here, we focus on continual learning in single-layered and multi-layered neural networks of binary weights. A variational Bayesian learning setting is thus proposed, where the neural networks are trained in a field-space, rather than gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and modulates synaptic resources among tasks. From a physics perspective, we translate the variational continual learning into Franz-Parisi thermodynamic potential framework, where previous task knowledge acts as a prior and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multi-layered neural networks, and performs better than the currently available metaplasticity algorithm where binary synapses bear hidden continuous states and the synaptic plasticity is modulated by a heuristic regularization function. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience inspired metaplasticity, providing a theory-grounded method for the real-world multi-task learning with deep networks.

In the continual learning setting, tasks are encountered sequentially. The goal is to learn whilst i) avoiding catastrophic forgetting, ii) efficiently using model capacity, and iii) employing forward and backward transfer learning. In this paper, we explore how the Variational Continual Learning (VCL) framework achieves these desiderata on two benchmarks in continual learning: split MNIST and permuted MNIST. We first report significantly improved results on what was already a competitive approach. The improvements are achieved by establishing a new best practice approach to mean-field variational Bayesian neural networks. We then look at the solutions in detail. This allows us to obtain an understanding of why VCL performs as it does, and we compare the solution to what an `ideal' continual learning solution might be.