# The Multiple Ticket Hypothesis: Random Sparse Subnetworks Suffice for RLVR

arXiv: https://arxiv.org/abs/2602.01599 · HTML: https://mlsanity.com/paper/2602.01599/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 62 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 46)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)

## Built on by (most cited first, 3 of 3)

- [Preference Tuning as Spectral Update Reorganization](https://mlsanity.com/paper/2607.20438/) (2026)
- [Understanding LLM Parameter Update Sparsity through the Lens of Fisher](https://mlsanity.com/paper/2609.36262/) (2026)
- [Static Gradient Attribution Underperforms a Density-Matched Random Mask on Loss-Based Forgetting Within LoRA B-Matrix](https://mlsanity.com/paper/2610.12744/) (2026)

## Abstract (arXiv)

The Lottery Ticket Hypothesis demonstrated that sparse subnetworks can match full-model performance, suggesting parameter redundancy. Meanwhile, in Reinforcement Learning with Verifiable Rewards (RLVR), recent work has shown that updates concentrate on a sparse subset of parameters, which further lends evidence to this underlying redundancy. We study the simplest possible way to exploit this redundancy: training only a randomly selected subset of parameters at extreme sparsities. Empirically, we find that training just 1% of parameters matches or exceeds full-parameter RLVR finetuning across 3 models and 2 task domains. Moreover, different random masks show minimal overlap (≤ 0.005 Jaccard similarity) and yet all succeed, suggesting pretrained models contain many viable sparse subnetworks rather than one privileged set. We term this the Multiple Ticket Hypothesis. We explain this phenomenon through the implicit per-step KL constraint in RLVR, which restricts updates to a low-dimensional subspace, enabling arbitrary sparse masks to succeed.