Yara Shamshoum, Nitzan Hodos, Yuval Sieradzki, Assaf Schuster. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Many recent works use machine learning models to solve various complex algorithmic problems. However, these models attempt to reach a solution without considering the problem’s required computational complexity, which can be detrimental to their ability to solve it correctly. In this work we investigate the effect of computational time and memory on generalization of implicit algorithmic solvers. To do so, we focus on the Differentiable Neural Computer (DNC), a general problem solver that also lets us reason directly about its usage of time and memory. In this work, we argue that the number of planning steps the model is allowed to take, which we call ”planning budget”, is a constraint that can cause the model to generalize poorly and hurt its ability to fully utilize its external memory. We evaluate our method on Graph Shortest Path, Convex Hull, Graph MinCut and Associative Recall, and show how the planning budget can drastically change the behavior of the learned algorithm, in terms of learned time complexity, training time, stability and generalization to inputs larger than those seen during training.

We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a d-dimensional ball to arbitrary accuracy with only 2 layers and O(1) neurons, where a 2-layer deterministic network was shown to require Omega(e^d) neurons, an exponential improvement. We prove a highly non-trivial result, that for almost any classification problem, there exists a trivially simple network that solves it given a sufficiently powerful generator for the network’s weights. Combining these results we conjecture that for most classification problems, there is a CFNN which solves them with higher accuracy or fewer neurons than any deterministic network. Finally, we verify our proofs experimentally using novel CFNN architectures on CIFAR10 and CIFAR100, reaching an improvement of 9.25% from the baseline.