<story><title>Empiricism and the limits of gradient descent</title><url>http://togelius.blogspot.com/2018/05/empiricism-and-limits-of-gradient.html</url></story><parent_chain></parent_chain><comment><author>simonster</author><text>There are a couple of factual errors here. First, the difference between backprop and evolution is smaller than the author indicates. The error signal used in modern backprop training is stochastic because it is computed on a minibatch (which is why it&amp;#x27;s called stochastic gradient descent). This stochasticity seems important to achieving good results. And the most popular evolutionary algorithm in the deep learning world is Evolution Strategies, which effectively approximates a gradient. Ordinary genetic algorithms are not gradient-based and have recently shown promise in limited domains, but can&amp;#x27;t compete with gradient-based algorithms for supervised learning.&lt;p&gt;The key claim in the article, that gradient descent could not discover physics from equations seems, like it is a statement about neural networks, not gradient descent. Given sufficient training data, a neural network can probably learn to model physics. I sympathize with the concern that it&amp;#x27;s very difficult to translate a neural network&amp;#x27;s knowledge into human concepts, but I see no reason to believe that optimizing the same system with an evolutionary algorithm would make this problem any easier. You could e.g. try to do program induction (which was supposed to be the future of AI many decades ago) instead of modeling the data directly, but choosing to perform program induction does not preclude the use of a neural network. Neural networks trained by gradient descent can generate ASTs (e.g. &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;nlp.cs.berkeley.edu&amp;#x2F;pubs&amp;#x2F;Rabinovich-Stern-Klein_2017_AbstractSyntaxNetworks_paper.pdf&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;nlp.cs.berkeley.edu&amp;#x2F;pubs&amp;#x2F;Rabinovich-Stern-Klein_2017_...&lt;/a&gt;).&lt;p&gt;[Edited to remove reference to universal approximation; as comments point out, even if a neural network can approximate a function, it isn&amp;#x27;t guaranteed to be able to learn it. But I am reasonably confident that a neural network can learn Newton&amp;#x27;s second law.]</text></comment>
<story><title>Empiricism and the limits of gradient descent</title><url>http://togelius.blogspot.com/2018/05/empiricism-and-limits-of-gradient.html</url></story><parent_chain></parent_chain><comment><author>sepranu</author><text>The points the author makes about gradient descent are accurate, in a sense. However, they oversimplify the technique (as it is currently applied today) and the context in which it is used. It seems as if the author, like many others, has a basic understanding of the subject&amp;#x27;s basic mechanisms, but not the context in which experts understand them.&lt;p&gt;The example the author cites regarding evo algorithms learning physical laws is laughable - &amp;quot;It&amp;#x27;s just not in the data - it has to be invented&amp;quot; applies equally to both the backprop and the evolutionary learning algorithms.&lt;p&gt;&amp;quot;In this case, the representation (mathematical expressions represented as trees) is distinctly non-differentiable, so could not even in principle be learned through gradient descent.&amp;quot;&lt;p&gt;This is incorrect, almost like saying NLP data is not differentiable. For instance, set this representation up as the output of a network (or, if you wanted to be fancier, the central component of an autoencoder), and see how well it predicts&amp;#x2F;correlates with the experimental data. This is the error, which is back-propagated through the network&amp;#x27;s nodes.&lt;p&gt;FWIW, many theoreticians believe that the unreasonable effectiveness of neural networks and especially transfer learning &lt;i&gt;is a result&lt;/i&gt; of their well-suitedness to encode laws of physics and Euclidean geometry. The author&amp;#x27;s final points about a nine-year-old survey may be out of date w.r.t. contemporary neural networks, which often have spookily good local minima and do not behave in the way intuition about gradient descent might suggest.</text></comment>