# Continual Learning with Guarantees via Weight Interval Constraints

arXiv: https://arxiv.org/abs/2206.07996 · HTML: https://mlsanity.com/paper/2206.07996/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 26 of 26)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [Re-evaluating Continual Learning Scenarios: A Categorization and Case for Strong Baselines](https://mlsanity.com/paper/1810.12488/) (2018)
- [Supermasks in Superposition](https://mlsanity.com/paper/2006.14769/) (2020)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [Rotate your Networks: Better Weight Consolidation and Less Catastrophic Forgetting](https://mlsanity.com/paper/1802.02950/) (2018)
- [Avalanche: an End-to-End Library for Continual Learning](https://mlsanity.com/paper/2104.00405/) (2021)
- [Alleviating catastrophic forgetting using context-dependent gating and synaptic stabilization](https://mlsanity.com/paper/1802.01569/) (2018)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [In Defense of the Learning Without Forgetting for Task Incremental Learning](https://mlsanity.com/paper/2107.12304/) (2021)
- [Fast and Stable Interval Bounds Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1906.00628/) (2019)
- [HyperCube: Implicit Field Representations of Voxelized 3D Models](https://mlsanity.com/paper/2110.05770/) (2021)

## Built on by (most cited first, 11 of 11)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Towards Continual Learning Desiderata via HSIC-Bottleneck Orthogonalization and Equiangular Embedding](https://mlsanity.com/paper/2401.09067/) (2024)
- [Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applications](https://mlsanity.com/paper/2410.09218/) (2024)
- [Harnessing Neural Unit Dynamics for Effective and Scalable Class-Incremental Learning](https://mlsanity.com/paper/2406.02428/) (2024)
- [Provably Safe Model Updates](https://mlsanity.com/paper/2512.01899/) (2025)
- [HINT: Hypernetwork Approach to Training Weight Interval Regions in Continual Learning](https://mlsanity.com/paper/2405.15444/) (2024)
- [Class Incremental Learning with Task-Specific Batch Normalization and Out-of-Distribution Detection](https://mlsanity.com/paper/2411.00430/) (2024)
- [InTAct: Interval-based Task Activation Consolidation for Continual Learning](https://mlsanity.com/paper/2511.17439/) (2025)
- [Towards Robust Continual Learning with Bayesian Adaptive Moment Regularization](https://mlsanity.com/paper/2309.08546/) (2023)
- [Complementary Learning Subnetworks for Parameter-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2306.11967/) (2023)
- [Effect of Spherical Parameter Space on Number of Non-Forgetting Tasks and Capacity of Continual Learning](https://mlsanity.com/paper/2610.17453/) (2026)

## Abstract (arXiv)

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.