Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this contribution, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows to perform optimal learning in polynomial time for a large set of parameters.

The Download: an exclusive chat with Jim O'Neill, and the surprising truth about heists Over the past year, Jim O'Neill has become one of the most powerful people in public health. As the US deputy health secretary, he holds two roles at the top of the country's federal health and science agencies. He oversees a department with a budget of over a trillion dollars. And he signed the decision memorandum on the US's deeply controversial new vaccine schedule. In an exclusive interview with earlier this month, O'Neill described his plans to increase human healthspan through longevity-focused research supported by ARPA-H, a federal agency dedicated to biomedical breakthroughs. Fellow longevity enthusiasts said they hope he will bring attention and funding to their cause.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Wegivethe first efficient algorithms proven to succeed in the correlated Erdös-Rényi model (Pedarsani and Grossglauser, 2011). Specifically, we give apolynomial time algorithm for thegraphsimilarity/hypothesis testingtaskwhich worksforeveryconstant level of correlation between the two graphs that can be arbitrarily close to zero. We also give a quasi-polynomial (nO(logn) time) algorithm for thegraph matching task of recovering the permutation minimizing the symmetric difference in this model.

SSL based on persistent homology (PH), a mathematical tool for modeling topological features of data that persist across multiple scales.

Such biases are known asrepresentation bias [38].