Andrew Gordon Wilson
2025 · arXiv
Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success of overparametrization. We argue that these phenomena are not distinct to neural networks, or particularly mysterious. Moreover, this generalization behaviour can be intuitively understood, and rigorously characterized, using long-standing generalization frameworks such as PAC-Bayes and countable hypothesis bounds. We present soft inductive biases as a key unifying principle in explaining these phenomena: rather than restricting the hypothesis space to avoid overfitting, embrace a flexible hypothesis space, with a soft preference for simpler solutions that are consistent with the data. This principle can be encoded in many model classes, and thus deep learning is not as mysterious or different from other model classes as it might seem. However, we also highlight how deep learning is relatively distinct in other ways, such as its ability for representation learning, phenomena such as mode connectivity, and its relative universality.
Metadata: arXiv. Abstracts retain their original authors’ rights.
Original HN comments, with labels from simple text rules. A label describes the whole comment and may miss context or irony. Read the discussion to make up your own mind. About the labels
4 selected excerpts · 4 total mentions
Check out Andrew Gordon Wilson's excellent paper "Deep Learning is Not so Mysterious or Different" for a discussion of the ways in which existing learning theory does and doesn't work neural nets. https://arxiv.org/pdf/2503.02113
Reminded me strongly of the paper "Deep Learning is Not So Mysterious or Different" from a year ago: https://arxiv.org/abs/2503.02113
Are you asking about open problems? Here are a couple: There are strong arguments that deep learning generalization (and robustness in a slightly different sense) can be successfully explained in terms of PAC-Bayes theory, for example: https://arxiv.org/abs/2503.02113 This requires a strong understanding of the appropriate prior, which effectively quantifies implicit bias in the training setup / architecture setup. Early analyses suggest the bias is that of a minimal gradient norm (https://arxiv.org/pdf/2101.12176) but this is almost certainly not the case, e.g.(https://arxiv.org/abs/2005.06398). There are good empirical arguments that models are trained to achieve…
maximal compression (https://arxiv.org/abs/2211.13609). But we only know this in a vague sense. How are deep learning training procedures and architectures implicitly exhibiting this form of sparsity and compressing information? Why is this more effective for some optimizers/architectures than others? Why would minimum description length circuits be so effective at mimicking human intelligence? How does this form of regularisation induce the exponents in the neural scaling laws (so we can figure out how to best optimize for these exponents)? If we don't know the implicit bias and how it relates to the training procedure, we're just doing alchemy and effectively got lucky. Change the standard approach even slightly and things easily break. We only really know what to do by process of elimination. Then there are the LLM specific questions related to in-context learning (https://arxiv.org/abs/2306.00297), to help explain why next token prediction through transformer designs works so well. Does it implicitly act as an optimization procedure (with bias) relative to the context? What are the biases here? What is the problem being solved? These may sound specific, but they are just examples of some approaches to answer the big question of "why does this standard procedure work so well, and what can we do to make it work better". Without this, we're just following the heuristics of what came before without a guiding framework. Post-hoc, we can do a lot more with interpretability frameworks and linear probes and the like. But without the implicit biases, we are only getting a local picture, which doesn't help us understand what a model is likely to do before we run it. We need global information. These are just a few, and don't include the philosophical and theory of mind questions, and others from neuroscience...
https://arxiv.org/pdf/2503.02113 This paper shows that polynomials show most features of deep neural nets, including double descent and ability to memorize entire dataset. It connects dots there - polynomials there are regularized to be as simple as possible and author argues that hundredths of billions of parameters in modern neural networks work as a regularizers too, they attenuate decisions that "too risky." I really enjoyed that paper, a gem that puts light everywhere.
More from the same topics.
Sébastien Bubeck, Varun Chandrasekaran, Ronen Eldan +11
Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition.
Tom B. Brown, Benjamin Mann, Nick Ryder +28
Recent work has demonstrated substantial gains on many NLP tasks and benchmarks by pre-training on a large corpus of text followed by fine-tuning on a specific task.
Anders Sandberg, Eric Drexler, Toby Ord
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe.
Chiyuan Zhang, Samy Bengio, Moritz Hardt +2
Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance.