Bayesian Flow Networks (BFNs) link iterative denoising diffusion and recursive estimation of distribution parameters.

In my new post, I constrast autoregressive generative modeling (prevalent in language) and recursive Bayesian estimation of all parameters jointly.

https://proger.github.io/posts/bfn/normal.html

Excited to see the first book on differentiable programming. It explicitly talks about how to encode regular programs into structures that have gradient flow. https://arxiv.org/abs/2403.14606

Discrete Bayesian Flow Networks teaser

I stumbled on this paper on Efficient Backprop from LeCun et al when discussing the differences between internal covariate shift and input whitening.

This work provides a comprehensive overview of tricks that are necessary succeessfully train deep models — why and how to initialize weights, choose nonlinearities (to some extent), how to choose and preprocess training data, how to choose learning rates, what is the basic optimization dynamics behavior and how to use the Hessian to diagnose it: https://cseweb.ucsd.edu/classes/wi08/cse253/Handouts/lecun-98b.pdf

Balancing sequence lengths in your dataset is the best augmentation you can do to successfully train a Transformer

https://aclanthology.org/2021.emnlp-main.650/

The same principle (sequence length distribution needs to be uniform) actually applies to RNNs too. I trained a SHA-RNN on byte-level ukpron (grapheme to phoneme task) and making sequence lengths uniform was key to get the model to work: https://huggingface.co/darkproger/ukpron

When we were already training uk4b, Karpathy posted a note that padding the number of rows in the tied input-output embedding table to a multiple of 8 (from 50257 to 50304) gave a significant training speedup. This thread from Horace He characterizes the space of phenomena that are related to this https://twitter.com/cHHillee/status/1630274804795445248

In short, GEMM kernels access memory in tile blocks, and when the blocks are aligned to the cache line the SM spends the least amount of memory access operations to feed the kernel.

In Accelerated Scan (it is my high performance training kernel for linear RNNs — it's responsible for computing the recurrence for all tokens when training the network or reading the prompt at inference), the backward kernel would read the memory in reverse. Alex Nichol found that loading the memory in reverse in chunks of 4 would make the access aligned — and speed up the loads!

That change in turn allowed fusing the reverse scan with a few other kernels, resulting in 30-50% training speedups. Coming in Accelerated Scan 0.2.

Continuing the saga of sequence length being a data domain: even modern transformers with RoPE, Alibi, Transformer XL-like relative positional encodings non-robustly generalize over sequence length and depend on the format of training data.

Recent work has been using index hints when formatting inputs — in NLP a common instance of an index hint could be punctuation (e.g. finishing sentences with a dot). In practice, we've seen that models often refuse to perform the task if you forget punctuation.

https://arxiv.org/abs/2402.09371

https://app.suno.ai/song/f44b528c-0bce-45fe-b5b6-bca579f97ed2

Hi Pedro, you tweeted:

This is outrageously wrong, Attention was invented at U. Montreal by Bahdanau, Cho and Bengio. Transformers were just an extension. This is the paper
that really invented modern AI.

THIS IS OUTRAGEOUSLY WRONG.

The first Transformer variant was published over 30 years ago.

It is now called "unnormalized linear Transformer".

THIS IS OUTRAGEOUSLY WRONG.

See my eye see em ell paper. Attention terminology was introduced in ninety three.


Back in the day, compute costs were high,
A million times more, oh my, oh my!
Transformers unnormalized, they'd fly,
Linear, efficient, no cry.

No quadratic woes, just linear stride,
Scaling with input, ain't no need to RAG.
Compute constraints, they pushed the tide,
In Transformer's journey, they'd confide.

So listen up, in the computational spree,
Efficiency's the key, it's plain to see.
Sequence length scalability, that's the decree,
In the Transformer world, we're wild and free!

THIS IS OUTRAGEOUSLY WRONG.

Vaswani did not cite this.

THIS IS OUTRAGEOUSLY WRONG.

Here is a well-known tweet on this

THIS IS OUTRAGEOUSLY WRONG.

Quadratic ChatGPT

THIS IS OUTRAGEOUSLY WRONG.

THIS IS OUTRAGEOUSLY WRONG.

MACHINE LEARNING IS THE SCIENCE OF CREDIT ASSIGNMENT

ETH has an Engineering-focused course on Category Theory, checking out its notes: https://applied-compositional-thinking.engineering/resources/

Wow — time to get your kids into writing NeurIPS papers

Parameter-shared state expansion is the next frontier in efficient RNNs. It's a bit cumbersome concept that has been explored in linear transformers but really became popular with Mamba.

Now, HGRN2 has introduced an elegant implementation of the most simple expansion rule — the outer product. An outer product is an operation that multiplies two vectors of shape Nx1 and 1xN making an NxN matrix — a quadratic number of pairwise multiplicative interactions.

Outer products work well with Accelerated Scan and are already supported in the mqar branch of Hippogriff

https://twitter.com/SonglinYang4/status/1778897457159758010

Outer product state expansion learns *really fast*

Wrote a small summary of Transformers, RNNs and Fast Weight Programmers using the language of transformers.
https://twitter.com/darkproger/status/1779123166561890357

Emergent property

Discovered this probability result by Fisher-Darmois-Koopman-Pitman (F-D-K-P theorem):

an i.i.d stream of data of arbitrary size can be summarized into a finite fixed number of sufficient statistics (= hidden state can be of fixed size and no information will be lost) iff the data is from an exponential family of distributions.

Normal, Bernoulli and MRFs are exponential, but uniform distribution is not. Weirdly enough, a lot of LM diagnostic tasks sample from uniform distributions.

The attached paper generalized the result to random processes summarizable by Kalman filters, so it translates to single-layer linear RNNs.

Meta is in the RNN game https://arxiv.org/abs/2404.08801

https://arxiv.org/abs/2404.08819

A paper precisely demonstrating the difference between input-dependent forget gate vectors and input-dependent recurrence matrices — my intuition from Dyck-1 synthetic tasks suggested there is no difference between recurrence matrices and gated vectors, however there is one (I am super pissed I arrived at the wrong conclusion)!

A linear RNN with a non-diagonal recurrence matrix can simulate DFAs (solve word problems that involve state permutation) and stay linear — strictly better than a transformer!