# The impact of allocation strategies in subset learning on the expressive power of neural networks

arXiv: https://arxiv.org/abs/2502.06300 · HTML: https://mlsanity.com/paper/2502.06300/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Supermasks in Superposition](https://mlsanity.com/paper/2006.14769/) (2020)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Adversarial Reprogramming of Neural Networks](https://mlsanity.com/paper/1806.11146/) (2018)
- [The Expressive Power of Low-Rank Adaptation](https://mlsanity.com/paper/2310.17513/) (2023)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Expressive power of recurrent neural networks](https://mlsanity.com/paper/1711.00811/) (2017)
- [Capacity and Trainability in Recurrent Neural Networks](https://mlsanity.com/paper/1611.09913/) (2016)
- [SPDF: Sparse Pre-training and Dense Fine-tuning for Large Language Models](https://mlsanity.com/paper/2303.10464/) (2023)
- [An Analytical Theory of Curriculum Learning in Teacher-Student Networks](https://mlsanity.com/paper/2106.08068/) (2021)
- [The Expressive Power of Tuning Only the Normalization Layers](https://mlsanity.com/paper/2302.07937/) (2023)

## Abstract (arXiv)

In traditional machine learning, models are defined by a set of parameters, which are optimized to perform specific tasks. In neural networks, these parameters correspond to the synaptic weights. However, in reality, it is often infeasible to control or update all weights. This challenge is not limited to artificial networks but extends to biological networks, such as the brain, where the extent of distributed synaptic weight modification during learning remains unclear. Motivated by these insights, we theoretically investigate how different allocations of a fixed number of learnable weights influence the capacity of neural networks. Using a teacher-student setup, we introduce a benchmark to quantify the expressivity associated with each allocation. We establish conditions under which allocations have maximal or minimal expressive power in linear recurrent neural networks and linear multi-layer feedforward networks. For suboptimal allocations, we propose heuristic principles to estimate their expressivity. These principles extend to shallow ReLU networks as well. Finally, we validate our theoretical findings with empirical experiments. Our results emphasize the critical role of strategically distributing learnable weights across the network, showing that a more widespread allocation generally enhances the network's expressive power.