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The Z-loss: a shift and scale invariant classification loss belonging to the Spherical Family [article]

Alexandre de Brébisson, Pascal Vincent
2016 arXiv   pre-print
Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with  ...  On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.  ...  The Z-loss can be seen as a function of a single variable z c and is plotted in Figure 1 . The Z-loss clearly belongs to the spherical family described in section 1.2.  ... 
arXiv:1604.08859v2 fatcat:sp2k3l2sa5e2lik6poekf5tvxi

Patterns, predictions, and actions: A story about machine learning [article]

Moritz Hardt, Benjamin Recht
2021 arXiv   pre-print
Self-contained introductions to causality, the practice of causal inference, sequential decision making, and reinforcement learning equip the reader with concepts and tools to reason about actions and  ...  A chapter on datasets as benchmarks examines their histories and scientific bases.  ...  That is, loss( f , z) = loss( f (x), y).  ... 
arXiv:2102.05242v2 fatcat:wy47g4fojnfuxngklyewtjtqdi

Training Deep and Recurrent Networks with Hessian-Free Optimization [chapter]

James Martens, Ilya Sutskever
2012 Lecture Notes in Computer Science  
spherical 2 penalty β θ 2 , Tikhonov damping appears to be a natural choice, and works pretty well in practice.  ...  Indeed, the trust region R is invariant to changes in the scale of the objective 6 , which may make it easier to tune, either manually or by some automatic method.  ... 
doi:10.1007/978-3-642-35289-8_27 fatcat:xhvzvekqhbbj3d6txx72tdh3uu

Semi-supervised and weakly-supervised learning with spatio-temporal priors in medical image segmentation

Gabriele Valvano
Over the last decades, medical imaging techniques have played a crucial role in healthcare, supporting radiologists and facilitating patient diagnosis.  ...  With the advent of faster and higher-quality imaging technologies, the amount of data that is possible to collect for each patient is paving the way toward personalised medicine.  ...  On the contrary, the WPCE loss is invariant to the number of an- notated pixels.  ... 
doi:10.13118/imtlucca/e-theses/344/ fatcat:qru63k6hibed3pwtxemhd523ua