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--- ml:optimization_in_deep_learning [2021/04/01 10:16] – [Backprop Through Discontinuities] jmflanig
+++ ml:optimization_in_deep_learning [2025/03/25 00:49] (current) – [Effects on Optimization] jmflanig
@@ Line 3: / Line 3: @@
 ===== Effects on Optimization =====
   * Batch normalization
-    * Makes the objective function and gradients smoother (more Lipschitz) ([[https://arxiv.org/pdf/1805.11604.pdf|Santurkar 2018 - How Does Batch Normalization Help Optimization?]])
+    * Makes the objective function and gradients smoother (more Lipschitz) ([[https://arxiv.org/pdf/1805.11604.pdf|Santurkar 2018 - How Does Batch Normalization Help Optimization?]]. Another perspective: see section 3 of [[https://arxiv.org/pdf/2002.10444.pdf|De 2020]].)
   * Weight normalization
     * Improves the conditioning of the optimization problem ([[https://arxiv.org/pdf/1602.07868.pdf|Salimans & Kingma 2016]])
+  * Lipschitz Constant
+    * [[https://arxiv.org/pdf/2306.09338|Qi et al 2023 - Understanding Optimization of Deep Learning via Jacobian Matrix and Lipschitz Constant]] Talks about the effect of the Lipschitz constant on optimizing deep neural networks.
 ===== On Global Optimization of Neural Networks =====
+  * [[https://arxiv.org/pdf/1412.0233.pdf|Choromanska et al 2014 - The Loss Surfaces of Multilayer Networks]]
   * [[https://arxiv.org/pdf/1810.02054.pdf|Du et al 2018 - Gradient Descent Provably Optimizes Over-parameterized Neural Networks]] "We show that as long as m is large enough and no two inputs are parallel, randomly initialized gradient descent converges to a globally optimal solution at a linear convergence rate for the quadratic loss function, for an m hidden node shallow neural network with ReLU activation and n training data."
+  * [[https://arxiv.org/pdf/1910.00359.pdf|Goldblum et al 2020 - Truth or Backpropaganda? An Empirical Investigation of Deep Learning Theory]] Examines optimization issues in deep learning and their relation to ML theory
+===== Symmetries and Local Minima =====
+  * [[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.6931&rep=rep1&type=pdf|Sussman 1991 - Uniqueness of the weights for minimal feedforward nets with a given input-output map]] Also points out some discrete symmetries in neural networks: swapping any two neurons in the same layer, negating the input weights and output weights for any neuron (if using tahn activation), etc.
 ===== Properties of Neural Networks =====
@@ Line 23: / Line 30: @@
   * REINFORCE
   * [[https://www.aclweb.org/anthology/P18-1173.pdf|Peng et al 2018 - Backpropagating through Structured Argmax using a SPIGOT]]
+===== Instabilities =====
+==== Instability of Fine-tuning ====
+  * [[https://arxiv.org/pdf/2006.04884.pdf|Mosbach 2020 - ON THE STABILITY OF FINE-TUNING BERT: MISCONCEPTIONS, EXPLANATIONS, AND STRONG BASELINES]] catastrophic forgetting and small size of the fine-tuning datasets fail to explain the fine-tuning instability, which is caused by optimization difficulties and differences in generalization.
+===== Implicit Regularization of SGD =====
+See also Soheil Feizi's lecture [[https://www.youtube.com/watch?v=hGRssrXF-vI&list=PLHgjs9ncvHi80UCSlSvQe-TK_uOyDv_Jf&index=4|The implicit bias of gradient descent]].
+  * [[https://www.jmlr.org/papers/volume19/18-188/18-188.pdf|Soudry et al 2018 - The Implicit Bias of Gradient Descent on Separable Data]]
+  * [[https://arxiv.org/pdf/1806.01796.pdf|Nacson et al 2018 - Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate]]
+===== Miscellaneous Topics =====
+==== Effect of Skip Connections ====
+  * [[https://arxiv.org/pdf/1702.08591.pdf|Balduzzi et al 2017 - The Shattered Gradients Problem: If resnets are the answer, then what is the question?]]
+  * [[https://arxiv.org/pdf/1701.09175.pdf|Orhan & Pitkow 2017 - Skip Connections Eliminate Singularities]]
+===== People =====
+  * [[https://scholar.google.com/citations?user=AEBWEm8AAAAJ&hl=en|Daniel Soudry]]
+===== Related Pages =====
+  * [[Optimization]]