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When Partition Crossover is used to recombine two parents which are local optima, the ospring are all local optima in the smallest hyperplane subspace that contains the two parents. The ospring can also be organized into a non-planar hypercube "lattice." Fur- thermore, all of the ospring can be evaluated using a simple linear equation. When a child of Partition Crossover is a local optimum in the full search space, the linear equation exactly determines its evaluation. When a child of Partition Crossover can be improved by local search, the linear equation is an upper bound on the evaluation of the associated local optimum when minimizing. This theoret- ical result holds for all k-bounded Pseudo-Boolean optimization problems, including MAX-kSAT, QUBO problems, as well as ran- dom and adjacent NK landscapes. These linear equations provide a stronger explanation as to why the "Big Valley" distribution of local optima exists. 

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. This approach to diversity analysis can lead to valuable insights for how we measure and promote diversity in ensemble methods. 

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. 

Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse 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 net- work 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” ensem- bles 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 meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100. 

Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse 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 net- work 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” ensem- bles 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 meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100.