# S3: Structured Sparsity Specification

arXiv: https://arxiv.org/abs/2604.11315 · HTML: https://mlsanity.com/paper/2604.11315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [Structured Pruning for Deep Convolutional Neural Networks: A survey](https://mlsanity.com/paper/2303.00566/) (2023)

## Abstract (arXiv)

We introduce the Structured Sparsity Specification (S3), an algebraic framework for defining, composing, and implementing structured sparse patterns. S3 specifies sparsity through three components: a View that reshapes the tensor via layout composition, a Block specification that defines the atomic pruning unit, and the sparsity decision Scope. Both Block and Scope support Coupling across tensors for coordinated sparsification. S3 enables precise specification of diverse sparsity structures, from fine-grained N:M patterns to coarse channel pruning, and integrates seamlessly with Optimal Brain Damage (OBD) and Surgeon (OBS). We formalize the framework mathematically, demonstrate its expressiveness on canonical patterns, and validate it experimentally via structured OBS and OBD implementations built entirely on S3, which surpasses well-established second order heuristics on output reconstruction across common configurations.