# Pruning as a Game: Equilibrium-Driven Sparsification of Neural Networks

arXiv: https://arxiv.org/abs/2512.22106 · HTML: https://mlsanity.com/paper/2512.22106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [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)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Soft Filter Pruning for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.06866/) (2018)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Gradient Flow in Sparse Neural Networks and How Lottery Tickets Win](https://mlsanity.com/paper/2010.03533/) (2020)
- [Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks](https://mlsanity.com/paper/2110.05667/) (2021)

## Abstract (arXiv)

Neural network pruning is widely used to reduce model size and computational cost. Yet, most existing methods treat sparsity as an externally imposed constraint, enforced through heuristic importance scores or training-time regularization. In this work, we propose a fundamentally different perspective: pruning as an equilibrium outcome of strategic interaction among model components. We model parameter groups such as weights, neurons, or filters as players in a continuous non-cooperative game, where each player selects its level of participation in the network to balance contribution against redundancy and competition. Within this formulation, sparsity emerges naturally when continued participation becomes a dominated strategy at equilibrium. We analyze the resulting game and show that dominated players collapse to zero participation under mild conditions, providing a principled explanation for pruning behavior. Building on this insight, we derive a simple equilibrium-driven pruning algorithm that jointly updates network parameters and participation variables without relying on explicit importance scores. This work focuses on establishing a principled formulation and empirical validation of pruning as an equilibrium phenomenon, rather than exhaustive architectural or large-scale benchmarking. Experiments on standard benchmarks demonstrate that the proposed approach achieves competitive sparsity-accuracy trade-offs while offering an interpretable, theory-grounded alternative to existing pruning methods.