# Winning the Lottery by Preserving Network Training Dynamics with Concrete Ticket Search

arXiv: https://arxiv.org/abs/2512.07142 · HTML: https://mlsanity.com/paper/2512.07142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Pruning Neural Networks at Initialization: Why are We Missing the Mark?](https://mlsanity.com/paper/2009.08576/) (2020)
- [The Early Phase of Neural Network Training](https://mlsanity.com/paper/2002.10365/) (2020)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models](https://mlsanity.com/paper/1703.07370/) (2017)
- [Gradient Flow in Sparse Neural Networks and How Lottery Tickets Win](https://mlsanity.com/paper/2010.03533/) (2020)
- [Sanity-Checking Pruning Methods: Random Tickets can Win the Jackpot](https://mlsanity.com/paper/2009.11094/) (2020)
- [Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2404.02657/) (2024)
- [Estimating or Propagating Gradients Through Stochastic Neurons](https://mlsanity.com/paper/1305.2982/) (2013)
- [Fast as CHITA: Neural Network Pruning with Combinatorial Optimization](https://mlsanity.com/paper/2302.14623/) (2023)
- [Rare Gems: Finding Lottery Tickets at Initialization](https://mlsanity.com/paper/2202.12002/) (2022)
- [Self-Knowledge Distillation via Dropout](https://mlsanity.com/paper/2208.05642/) (2022)

## Abstract (arXiv)

The Lottery Ticket Hypothesis asserts the existence of highly sparse, trainable subnetworks ('winning tickets') within dense, randomly initialized neural networks. However, state-of-the-art methods of drawing these tickets, like Lottery Ticket Rewinding (LTR), are computationally prohibitive, while more efficient saliency-based Pruning-at-Initialization (PaI) techniques suffer from a significant accuracy-sparsity trade-off and fail basic sanity checks. In this work, we argue that PaI's reliance on first-order saliency metrics, which ignore inter-weight dependencies, contributes substantially to this performance gap, especially in the sparse regime. To address this, we introduce Concrete Ticket Search (CTS), an algorithm that frames subnetwork discovery as a holistic combinatorial optimization problem. By leveraging a Concrete relaxation of the discrete search space and a novel gradient balancing scheme (GRADBALANCE) to control sparsity, CTS efficiently identifies high-performing subnetworks near initialization without requiring sensitive hyperparameter tuning. Motivated by recent works on lottery ticket training dynamics, we further propose a knowledge distillation-inspired family of pruning objectives, finding that minimizing the reverse Kullback-Leibler divergence between sparse and dense network outputs (CTS-KL) is particularly effective. Experiments on varying image classification tasks show that CTS produces subnetworks that robustly pass sanity checks and achieve accuracy comparable to or exceeding LTR, while requiring only a small fraction of the computation. For example, on ResNet-20 on CIFAR10, it reaches 99.3% sparsity with 74.0% accuracy in 7.9 minutes, while LTR attains the same sparsity with 68.3% accuracy in 95.2 minutes. CTS's subnetworks outperform saliency-based methods across all sparsities, but its advantage over LTR is most pronounced in the highly sparse regime.