# KASAM: Spline Additive Models for Function Approximation

arXiv: https://arxiv.org/abs/2205.06376 · HTML: https://mlsanity.com/paper/2205.06376/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 12 May 2022.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Neural Network Approximation: Three Hidden Layers Are Enough](https://mlsanity.com/paper/2010.14075/) (2020)
- [Understanding Catastrophic Forgetting and Remembering in Continual Learning with Optimal Relevance Mapping](https://mlsanity.com/paper/2102.11343/) (2021)
- [Universal approximations of permutation invariant/equivariant functions by deep neural networks](https://mlsanity.com/paper/1903.01939/) (2019)
- [Approximation capability of two hidden layer feedforward neural networks with fixed weights](https://mlsanity.com/paper/2101.09181/) (2021)
- [Learning activation functions from data using cubic spline interpolation](https://mlsanity.com/paper/1605.05509/) (2016)

## Built on by (most cited first, 5 of 5)

- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [Multivariate quantile regression via Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2609.23906/) (2026)
- [Evaluating the Effectiveness of SechKAN on 1D Data](https://mlsanity.com/paper/2609.25876/) (2026)
- [Kolmogorov-Arnold Networks for Personal Context Recognition on ExtraSensory](https://mlsanity.com/paper/2610.05250/) (2026)

## Abstract (arXiv)

Neural networks have been criticised for their inability to perform continual learning due to catastrophic forgetting and rapid unlearning of a past concept when a new concept is introduced. Catastrophic forgetting can be alleviated by specifically designed models and training techniques. This paper outlines a novel Spline Additive Model (SAM). SAM exhibits intrinsic memory retention with sufficient expressive power for many practical tasks, but is not a universal function approximator. SAM is extended with the Kolmogorov-Arnold representation theorem to a novel universal function approximator, called the Kolmogorov-Arnold Spline Additive Model - KASAM. The memory retention, expressive power and limitations of SAM and KASAM are illustrated analytically and empirically. SAM exhibited robust but imperfect memory retention, with small regions of overlapping interference in sequential learning tasks. KASAM exhibited greater susceptibility to catastrophic forgetting. KASAM in combination with pseudo-rehearsal training techniques exhibited superior performance in regression tasks and memory retention.