Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure-- updating one neuron's synaptic weights requires knowledge of synaptic weights or receptive fields of downstream neurons. This limits the use of artificial neural networks as a tool for understanding the biological principles of information processing in the brain. Lillicrap et al. (2016) propose a more biologically plausible "feedback alignment" algorithm that uses random and fixed backpropagation weights, and show promising simulations. In this paper we study the mathematical properties of the feedback alignment procedure by analyzing convergence and alignment for two-layer networks under squared error loss. In the overparameter-ized setting, we prove that the error converges to zero exponentially fast, and also that regularization is necessary in order for the parameters to become aligned with the random backpropagation weights. Simulations are given that are consistent with this analysis and suggest further generalizations. These results contribute to our understanding of how biologically plausible algorithms might carry out weight learning in a manner different from Hebbian learning, with performance that is comparable with the full non-local backpropagation algorithm.

Second-order information, in the form of Hessian-or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems.

In this section, we argue that the GNN architecture looses its advantages in the face of solving multiple MILPs at the same time. GPU such that each GNN is dedicated to solving one MILP . GNNs on Tesla V100 32 GB GPU. Figure 1 shows the inefficient utilization of GPUs when multiple GNNs are packed on a single GPU. Figure 1: Packing several GNNs together on a GPU keeps it underutilized. The work was done during an internship at Mila and CERC. We use the features that were used by Gasse et al.

Because the deep learning models for the classification task always have a normalization operation (e.g., Softmax) to make the final unconstrained These authors contributed equally to the work. Work performed during the internship at MSRA. 36th Conference on Neural Information Processing Systems (NeurIPS 2022). Complexity Measure C will be a positive number in those local minima. Measure C will be 0. The Lemma is proven. C.1 Open Source Code We publish our code in Github (i.e., https://github.