Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms
Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
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Keywords: differentiable, differentiable algorithms, second-order, newton, algorithmic losses, sorting, ranking, differentiable sorting, differentiable ranking, sort, rank, shortest-path, dijkstra
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Abstract: In many supervised learning problems, model predictions are compared to ground truth labels using simple convex losses such as softmax cross-entropy and squared error. In weakly-supervised learning, more complex losses involving problem-specific algorithmic procedures and knowledge, e.g., differentiable shortest-path computations or sorting algorithms, are common. These losses can be hard to optimize as they are non-convex in the model output and may exhibit vanishing and exploding gradients. To alleviate this issue, we present Newton Losses, a method for boosting the performance of non-convex and hard to optimize losses by locally approximating an existing loss function with a quadratic (incorporating second-order information). As Newton Losses only replaces the loss function, the method allows training the neural network with gradient descent and is computationally efficient. We apply Newton Losses to eight differentiable algorithm methods for the multi-digit MNIST sorting benchmark and the Warcraft shortest-path benchmark.
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Submission Number: 555
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