# Distal Interference: Exploring the Limits of Model-Based Continual Learning

arXiv: https://arxiv.org/abs/2402.08255 · HTML: https://mlsanity.com/paper/2402.08255/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations](https://mlsanity.com/paper/1708.02691/) (2017)
- [Understanding Catastrophic Forgetting and Remembering in Continual Learning with Optimal Relevance Mapping](https://mlsanity.com/paper/2102.11343/) (2021)
- [Continuous online sequence learning with an unsupervised neural network model](https://mlsanity.com/paper/1512.05463/) (2015)
- [Learning activation functions from data using cubic spline interpolation](https://mlsanity.com/paper/1605.05509/) (2016)

## Built on by (most cited first, 1 of 1)

- [Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony](https://mlsanity.com/paper/2506.03302/) (2025)

## Abstract (arXiv)

Continual learning is the sequential learning of different tasks by a machine learning model. Continual learning is known to be hindered by catastrophic interference or forgetting, i.e. rapid unlearning of earlier learned tasks when new tasks are learned. Despite their practical success, artificial neural networks (ANNs) are prone to catastrophic interference. This study analyses how gradient descent and overlapping representations between distant input points lead to distal interference and catastrophic interference. Distal interference refers to the phenomenon where training a model on a subset of the domain leads to non-local changes on other subsets of the domain. This study shows that uniformly trainable models without distal interference must be exponentially large. A novel antisymmetric bounded exponential layer B-spline ANN architecture named ABEL-Spline is proposed that can approximate any continuous function, is uniformly trainable, has polynomial computational complexity, and provides some guarantees for distal interference. Experiments are presented to demonstrate the theoretical properties of ABEL-Splines. ABEL-Splines are also evaluated on benchmark regression problems. It is concluded that the weaker distal interference guarantees in ABEL-Splines are insufficient for model-only continual learning. It is conjectured that continual learning with polynomial complexity models requires augmentation of the training data or algorithm.