# Spectral Regularization: an Inductive Bias for Sequence Modeling

arXiv: https://arxiv.org/abs/2211.02255 · HTML: https://mlsanity.com/paper/2211.02255/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods](https://mlsanity.com/paper/1306.4032/) (2013)
- [Efficient Optimization of Loops and Limits with Randomized Telescoping Sums](https://mlsanity.com/paper/1905.07006/) (2019)

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

- [Geometry-Aware Normalizing Wasserstein Flows for Optimal Causal Inference](https://mlsanity.com/paper/2311.18826/) (2023)

## Abstract (arXiv)

Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept of simplicity defined in the Chomsky hierarchy. From fundamental connections between Hankel matrices and regular grammars, we propose to use the trace norm of the Hankel matrix, the tightest convex relaxation of its rank, as the spectral regularizer. To cope with the fact that the Hankel matrix is bi-infinite, we propose an unbiased stochastic estimator for its trace norm. Ultimately, we demonstrate experimental results on Tomita grammars, which exhibit the potential benefits of spectral regularization and validate the proposed stochastic estimator.