Engineering flexible machine learning systems by traversing functionally invariant paths in weight space

Deep neural networks achieve human-like performance on a variety of perceptual and decision-making tasks. However, networks perform poorly when confronted with changing tasks or goals, and broadly fail to match the flexibility and robustness of human intelligence. Here, we develop a mathematical and algorithmic framework that enables flexible and continuous training of neural networks on a range of objectives by constructing path connected sets of networks that achieve equivalent functional performance on a given machine learning task. We view the weight space of a neural network as a curved Riemannian manifold and move a network along a functionally invariant path in weight space while searching for networks that satisfy secondary objectives. A path-sampling algorithm trains computer vision and natural language processing networks with millions of weight parameters to learn a series of classification tasks without performance loss while accommodating secondary objectives including network sparsification, incremental task learning, and increased adversarial robustness. Broadly, we conceptualize a neural network as a mathematical object that can be iteratively transformed into distinct configurations by the path-sampling algorithm to define a sub-manifold of networks that can be harnessed to achieve user goals.