Path Integral Optimiser: Global Optimisation via Neural Schrödinger-Föllmer Diffusion

We present an early investigation into the use of neural diffusion processes for global optimisation, focusing on Zhang et al.'s Path Integral Sampler. One can use the Boltzmann distribution to formulate optimization as solving a Schr\"odinger bridge sampling problem, then apply Girsanov's theorem with a simple (single-point) prior to frame it in stochastic control terms, and compute the solution's integral terms via a neural approximation (a Fourier MLP). We provide theoretical bounds for this optimiser, results on toy optimisation tasks, and a summary of the stochastic theory motivating the model. Ultimately, we found the optimiser to display promising per-step performance at optimisation tasks between 2 and 1,247 dimensions, but struggle to explore higher-dimensional spaces when faced with a 15.9k parameter model, indicating a need for work on adaptation in such environments.

Exploring the Performance of Pruning Methods in Neural Networks: An Empirical Study of the Lottery Ticket Hypothesis

In this paper, we explore the performance of different pruning methods in the context of the lottery ticket hypothesis. We compare the performance of L1 unstructured pruning, Fisher pruning, and random pruning on different network architectures and pruning scenarios. The experiments include an evaluation of one-shot and iterative pruning, an examination of weight movement in the network during pruning, a comparison of the pruning methods on networks of varying widths, and an analysis of the performance of the methods when the network becomes very sparse. Additionally, we propose and evaluate a new method for efficient computation of Fisher pruning, known as batched Fisher pruning.