In plain words: Networks trained by ordinary gradient descent work almost exactly like a system that stores the training examples and predicts by comparing new inputs to them. So the learned weights are a blend of those examples, with the network's design deciding what counts as similar.
Abstract · Every Model Learned by Gradient Descent Is Approximately a Kernel Machine
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned by the standard gradient descent algorithm are in fact mathematically approximately equivalent to kernel machines, a learning method that simply memorizes the data and uses it directly for prediction via a similarity function (the kernel). This greatly enhances the interpretability of deep network weights, by elucidating that they are effectively a superposition of the training examples. The network architecture incorporates knowledge of the target function into the kernel. This improved understanding should lead to better learning algorithms.
Pedro Domingos
arXiv:2012.00152 · cs.LG, cs.NE, stat.ML · submitted Nov 30, 2020
abstract · pdf · html · 12 pages, 2 figures
Combined with opacity in train/test splits, this suggests a type of data laundering, where the extreme is that much of Sora (for example) is regurgitating things seen in training, which was actually made perhaps by a human using a game engine, or drone video. But it's only news because a model generated it. Of course, I don't have strong evidence for this. But one of the most impressive parts of Sora is the level of detail, much of which is not specified by the text prompt, and still can't fully be accounted for by our knowledge that OAI expands text prompts for image/ video generation behind the scenes. Where is this precise detail coming from exactly? I suggest it's from memorization.