Achieving a Better Stability-Plasticity Trade-off via Auxiliary Networks in Continual Learning

In contrast to the natural capabilities of humans to learn new tasks in a sequential fashion, neural networks are known to suffer from catastrophic forgetting, where the model's performances on old tasks drop dramatically after being optimized for a new task. Since then, the continual learning (CL) community has proposed several solutions aiming to equip the neural network with the ability to learn the current task (plasticity) while still achieving high accuracy on the previous tasks (stability). Despite remarkable improvements, the plasticity-stability trade-off is still far from being solved and its underlying mechanism is poorly understood. In this work, we propose Auxiliary Network Continual Learning (ANCL), a novel method that applies an additional auxiliary network which promotes plasticity to the continually learned model which mainly focuses on stability. More concretely, the proposed framework materializes in a regularizer that naturally interpolates between plasticity and stability, surpassing strong baselines on task incremental and class incremental scenarios. Through extensive analyses on ANCL solutions, we identify some essential principles beneath the stability-plasticity trade-off.Comment: CVPR 202

On the Theoretical Properties of Noise Correlation in Stochastic Optimization

Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that the noise of stochastic gradient descent improves optimization by overcoming undesirable obstacles in the landscape. Moreover, injecting artificial Gaussian noise has become a popular idea to quickly escape saddle points. Indeed, in the absence of reliable gradient information, the noise is used to explore the landscape, but it is unclear what type of noise is optimal in terms of exploration ability. In order to narrow this gap in our knowledge, we study a general type of continuous-time non-Markovian process, based on fractional Brownian motion, that allows for the increments of the process to be correlated. This generalizes processes based on Brownian motion, such as the Ornstein-Uhlenbeck process. We demonstrate how to discretize such processes which gives rise to the new algorithm fPGD. This method is a generalization of the known algorithms PGD and Anti-PGD. We study the properties of fPGD both theoretically and empirically, demonstrating that it possesses exploration abilities that, in some cases, are favorable over PGD and Anti-PGD. These results open the field to novel ways to exploit noise for training machine learning models

On the Universality of Linear Recurrences Followed by Nonlinear Projections

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.Comment: Accepted at HLD 2023: 1st Workshop on High-dimensional Learning Dynamic

On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics

Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory and leverages the so-called Signature Transform. This algorithm enjoys strong theoretical guarantees but is hard to scale to high-dimensional data. In this paper, we study a recently derived random projection variant called Randomized Signature, obtained using the Johnson-Lindenstrauss Lemma. We provide an in-depth experimental evaluation of the effectiveness of the Randomized Signature approach, in an attempt to showcase the advantages of this reservoir to the community. Specifically, we find that this method is preferable to the truncated Signature approach and alternative deep learning techniques in terms of model complexity, training time, accuracy, robustness, and data hungriness.Comment: Accepted for IEEE IJCNN 202

An SDE for Modeling SAM: Theory and Insights

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation of continuous-time models (in the form of SDEs) for SAM and two of its variants, both for the full-batch and mini-batch settings. We demonstrate that these SDEs are rigorous approximations of the real discrete-time algorithms (in a weak sense, scaling linearly with the learning rate). Using these models, we then offer an explanation of why SAM prefers flat minima over sharp ones~--~by showing that it minimizes an implicitly regularized loss with a Hessian-dependent noise structure. Finally, we prove that SAM is attracted to saddle points under some realistic conditions. Our theoretical results are supported by detailed experiments.Comment: Accepted at ICML 2023 (Poster