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UID:20250910T071033EDT-6277messc8@132.216.98.100
DTSTAMP:20250910T111033Z
DESCRIPTION:“Scaling Effects and Efficiency in Deep Learning Algorithms”\n
 \nAbstract: We are interested in the design of provably-efficient (both st
 atistically and computationally) deep learning algorithms. The cornerstone
  of our approach is to view the neural network output as a stochastic proc
 ess\, i.e.\, a random object evolving over time. In this talk\, I will pre
 sent our recent work on studying the effect of scaling in the statistical 
 behavior (such as bias and variance) of deep neural networks as well as on
  the test accuracy and generalization properties of the given architecture
 . We find that in terms of variance reduction of the neural network’s outp
 ut and increased test accuracy the best choice is to choose the scaling of
  the hidden layers to correspond to the so-called mean-field scaling. We a
 lso find that this is particularly true for the outer layer\, in that the 
 neural network’s behavior is more sensitive to the scaling of the outer la
 yer as opposed to the scaling of the inner layers. The mechanism for the m
 athematical analysis is an asymptotic expansion for the neural network’s o
 utput yielding a clean bias-variance decomposition. An important practical
  consequence of the analysis is that it provides a systematic and mathemat
 ically informed way to choose hyperparameters (such as learning rates) and
  to compare different architectures leading to provably-efficient and stab
 le algorithms. Such choices guarantee that the resulting neural network ar
 chitectures behave in statistically robust ways during training. I will di
 scuss applications of these ideas to the design of deep learning algorithm
 s for scientific problems including solving high dimensional partial diffe
 rential equations (PDEs)\, closure of dynamical systems (like PDEs\, momen
 t equations etc.) and reinforcement learning with applications to financia
 l engineering\, turbulence\, computational biology. I will conclude by pre
 senting an overview of our research program\, aimed at advancing foundatio
 nal understanding to develop efficient and reliable artificial intelligenc
 e.\n\n \n
DTSTART:20250910T143000Z
DTEND:20250910T154500Z
LOCATION:Room 426\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Konstantinos Spiliopoulos (Boston University)
URL:/smerg/channels/event/konstantinos-spiliopoulos-bo
 ston-university-367452
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