In DeltaProduct (Siems et al., 2025), they propose to improve DeltaNet (Yang et al., 2025) by updating the online memory with $n_h$ KVs for each token, which can be seen as performing multiple steps of gradient descent per token. I will explain how this method is almost the same as multi-KV DeltaNet and reveal a potential flaw in the design of DeltaProduct.

This blog post is part 1 of a series that describes my attempt in implementing the Test-Time Training (TTT) model proposed by Sun et al. (2024), and Titans, proposed by Behrouz et al., (2024). At the time of writing, these two are two strong recurrent language models, but they have not yet open-sourced their implementation (TTT has only open-sourced the Jax implementation).