Dynastic Potential Crossover Operator

An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

NK Hybrid Genetic Algorithm for Clustering

The NK hybrid genetic algorithm for clustering is proposed in this paper. In order to evaluate the solutions, the hybrid algorithm uses the NK clustering validation criterion 2 (NKCV2). NKCV2 uses information about the disposition of $N$ small groups of objects. Each group is composed of $K+1$ objects of the dataset. Experimental results show that density-based regions can be identified by using NKCV2 with fixed small $K$. In NKCV2, the relationship between decision variables is known, which in turn allows us to apply gray box optimization. Mutation operators, a partition crossover, and a local search strategy are proposed, all using information about the relationship between decision variables. In partition crossover, the evaluation function is decomposed into $q$ independent components; partition crossover then deterministically returns the best among $2^q$ possible offspring with computational complexity $O(N)$. The NK hybrid genetic algorithm allows the detection of clusters with arbitrary shapes and the automatic estimation of the number of clusters. In the experiments, the NK hybrid genetic algorithm produced very good results when compared to another genetic algorithm approach and to state-of-art clustering algorithms.

Stochastic Subnetwork Annealing: A Regularization Technique for Fine Tuning Pruned Subnetworks

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

A Parallel Ensemble of Metaheuristic Solvers for the Traveling Salesman Problem

The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study suggests that EAX with restart mechanisms perform well on a wide range of TSP instances. However, this study is limited to 2,000 city problems. We study for problems ranging from 2,000 to 85,900. We see that the performance of the solver varies with the type of the problem. However, combining these solvers in an ensemble setup, we are able to outperform the individual solver's performance. We see the ensemble setup as an efficient way to make use of the abundance of compute resources. In addition to EAX and LKH, we use several versions of the hybrid of EAX and Mixing Genetic Algorithm (MGA). A hybrid of MGA and EAX is known to solve some hard problems. We see that the ensemble of the hybrid version outperforms the state-of-the-art solvers on problems larger than 10,000 cities.

Randomly Initialized Subnetworks with Iterative Weight Recycling

The Multi-Prize Lottery Ticket Hypothesis posits that randomly initialized neural networks contain several subnetworks that achieve comparable accuracy to fully trained models of the same architecture. However, current methods require that the network is sufficiently overparameterized. In this work, we propose a modification to two state-of-the-art algorithms (Edge-Popup and Biprop) that finds high-accuracy subnetworks with no additional storage cost or scaling. The algorithm, Iterative Weight Recycling, identifies subsets of important weights within a randomly initialized network for intra-layer reuse. Empirically we show improvements on smaller network architectures and higher prune rates, finding that model sparsity can be increased through the "recycling" of existing weights. In addition to Iterative Weight Recycling, we complement the Multi-Prize Lottery Ticket Hypothesis with a reciprocal finding: high-accuracy, randomly initialized subnetwork's produce diverse masks, despite being generated with the same hyperparameter's and pruning strategy. We explore the landscapes of these masks, which show high variability.

Sparse Mutation Decompositions: Fine Tuning Deep Neural Networks with Subspace Evolution

Neuroevolution is a promising area of research that combines evolutionary algorithms with neural networks. A popular subclass of neuroevolutionary methods, called evolution strategies, relies on dense noise perturbations to mutate networks, which can be sample inefficient and challenging for large models with millions of parameters. We introduce an approach to alleviating this problem by decomposing dense mutations into low-dimensional subspaces. Restricting mutations in this way can significantly reduce variance as networks can handle stronger perturbations while maintaining performance, which enables a more controlled and targeted evolution of deep networks. This approach is uniquely effective for the task of fine tuning pre-trained models, which is an increasingly valuable area of research as networks continue to scale in size and open source models become more widely available. Furthermore, we show how this work naturally connects to ensemble learning where sparse mutations encourage diversity among children such that their combined predictions can reliably improve performance. We conduct the first large scale exploration of neuroevolutionary fine tuning and ensembling on the notoriously difficult ImageNet dataset, where we see small generalization improvements with only a single evolutionary generation using nearly a dozen different deep neural network architectures.

Interpretable Diversity Analysis: Visualizing Feature Representations In Low-Cost Ensembles

Diversity is an important consideration in the construction of robust neural network ensembles. A collection of well trained models will generalize better if they are diverse in the patterns they respond to and the predictions they make. Diversity is especially important for low-cost ensemble methods because members often share network structure in order to avoid training several independent models from scratch. Diversity is traditionally analyzed by measuring differences between the outputs of models. However, this gives little insight into how knowledge representations differ between ensemble members. This paper introduces several interpretability methods that can be used to qualitatively analyze diversity. We demonstrate these techniques by comparing the diversity of feature representations between child networks using two low-cost ensemble algorithms, Snapshot Ensembles and Prune and Tune Ensembles. We use the same pre-trained parent network as a starting point for both methods which allows us to explore how feature representations evolve over time. This approach to diversity analysis can lead to valuable insights and new perspectives for how we measure and promote diversity in ensemble methods.

Synaptic Stripping: How Pruning Can Bring Dead Neurons Back To Life

Rectified Linear Units (ReLU) are the default choice for activation functions in deep neural networks. While they demonstrate excellent empirical performance, ReLU activations can fall victim to the dead neuron problem. In these cases, the weights feeding into a neuron end up being pushed into a state where the neuron outputs zero for all inputs. Consequently, the gradient is also zero for all inputs, which means that the weights which feed into the neuron cannot update. The neuron is not able to recover from direct back propagation and model capacity is reduced as those parameters can no longer be further optimized. Inspired by a neurological process of the same name, we introduce Synaptic Stripping as a means to combat this dead neuron problem. By automatically removing problematic connections during training, we can regenerate dead neurons and significantly improve model capacity and parametric utilization. Synaptic Stripping is easy to implement and results in sparse networks that are more efficient than the dense networks they are derived from. We conduct several ablation studies to investigate these dynamics as a function of network width and depth and we conduct an exploration of Synaptic Stripping with Vision Transformers on a variety of benchmark datasets.

Prune and Tune Ensembles: Low-Cost Ensemble Learning With Sparse Independent Subnetworks

Ensemble Learning is an effective method for improving generalization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associated with training several independent networks becomes expensive. We introduce a fast, low-cost method for creating diverse ensembles of neural networks without needing to train multiple models from scratch. We do this by first training a single parent network. We then create child networks by cloning the parent and dramatically pruning the parameters of each child to create an ensemble of members with unique and diverse topologies. We then briefly train each child network for a small number of epochs, which now converge significantly faster when compared to training from scratch. We explore various ways to maximize diversity in the child networks, including the use of anti-random pruning and one-cycle tuning. This diversity enables "Prune and Tune" ensembles to achieve results that are competitive with traditional ensembles at a fraction of the training cost. We benchmark our approach against state of the art low-cost ensemble methods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100.