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RT @beenwrekt: The NeurIPS paper checklist corroborates the bureaucratic theory of statistics.

For a more in-depth discussion of the approach and results (and more!):

Finally, we test the manifold hypothesis: what is the local dimensionality around an image? We find that this depends both on the image and the size of the local neighborhood, and there exists images with both large full-dimensional and small low-dimensional neighborhoods.

High probability ≠ typicality: very high-probability images are rare. This is not a contradiction: frequency = probability density *multiplied by volume*, and volume is weird in high dimensions! Also, the log probabilities are Gumbel-distributed, and we don't know why!

These are the highest and lowest probability images in ImageNet64. An interpretation is that -log2 p(x) is the size in bits of the optimal compression of x: higher probability images are more compressible. Also, the probability ratio between these is 10^14,000! 🤯

But how do we know our probability model is accurate on real data?.In addition to computing cross-entropy/NLL, we show *strong* generalization: models trained on *disjoint* subsets of the data predict the *same* probabilities if the training set is large enough!

We call this approach "dual score matching". The time derivative constrains the learned energy to satisfy the diffusion equation, which enables recovery of accurate and *normalized* log probability values, even in high-dimensional multimodal distributions.

We also propose a simple procedure to obtain good network architectures for the energy U: choose any pre-existing score network s and simply take the inner product with the input image y! We show that this preserves the inductive biases of the base score network: grad_y U ≈ s.

How do we train an energy model?.Inspired by diffusion models, we learn the energy of both clean and noisy images along a diffusion. It is optimized via a sum of two score matching objectives, which constrain its derivatives with both the image (space) and the noise level (time).

What is the probability of an image? What do the highest and lowest probability images look like? Do natural images lie on a low-dimensional manifold?.In a new preprint with @ZKadkhodaie @EeroSimoncelli, we develop a novel energy-based model in order to answer these questions: 🧵

RT @EeroSimoncelli: @jpillowtime Tweedie’s formula wasn’t published by Tweedie (AFAIK). It was published by Miyasawa in 1961:. Miyasawa, K….

🌈 I'll be presenting our JMLR paper "A rainbow in deep network black boxes" today at 3pm at #ICLR25! Come to poster #334 if you're interested, I'll be happy to chat.More details in the quoted thread (two levels deep).

RT @docmilanfar: When x and y are independent random variables, their joint cumulative dist function (CDF) is the product of the individual….

RT @EeroSimoncelli: Graduate students and advanced undergraduates: .Interested in a 3-month summer research internship in Computational Neu….

RT @scifordl: Poster session still going on in West meeting rooms 205-207! Come say hi and check your favorite posters (also there is deca….

RT @scifordl: Can LLMs plan? The answer might be in @HanieSedghi's talk. Only one way to know, join us in West meeting rooms 205-207 https:….