Product Key Memory

Standalone Product Key Memory module for augmenting Transformer models

Install

$ pip install product-key-memory

Usage

Replace the feedforwards in a Transformer with the following

import torch
from product_key_memory import PKM

pkm = PKM(
    dim = 512,
    heads = 4,
    dim_head = 128,       # keep at 128 for best results
    num_keys = 256,       # number of subkeys, # values will be num_keys ^ 2
    topk = 32             # the top number of subkeys to select
)

x = torch.randn(1, 1024, 512)
mask = torch.ones((1, 1024)).bool()
values = pkm(x, input_mask = mask) # (1, 1024, 512)

Learning Rates

To give different learning rates to the value parameters of the product-key-memory network, use the following helper function.

from torch.optim import Adam
from product_key_memory import fetch_pkm_value_parameters

# this helper function, for your root model, finds all the PKM models and the embedding bag weight parameters
pkm_parameters, other_parameters = fetch_pkm_value_parameters(model)

optim = Adam([
    {'params': other_parameters},
    {'params': pkm_parameters, 'lr': 1e-2}
], lr=1e-3)

Or, if product-key-memory parameters are the only other parameters you have a different learning rate for

from torch.optim import Adam
from product_key_memory import fetch_optimizer_parameters

parameters = fetch_optimizer_parameters(model) # automatically creates array of parameter settings with learning rate set at 1e-2 for pkm values
optim = Adam(parameters, lr=1e-3)

Appreciation

Special thanks go to Aran for encouraging me to look into this, and to Madison May for his educational blog post, which helped me understand this better.

Todo

• offer stochasticity with annealed gumbel noise. seen dramatic effects in vector-quantization setting

• offer a way for smaller value dimensions + concat and linear combination of heads (like multi-head attention)

• get caught up on latest literature on product key memories, if any

• instead of additive scores, try multiplicative using coordinate descent routing

Citations

@misc{lample2019large,
    title   = {Large Memory Layers with Product Keys},
    author  = {Guillaume Lample and Alexandre Sablayrolles and Marc'Aurelio Ranzato and Ludovic Denoyer and Hervé Jégou},
    year    = {2019},
    eprint  = {1907.05242},
    archivePrefix = {arXiv}
}

@misc{liu2020evolving,
    title   = {Evolving Normalization-Activation Layers},
    author  = {Hanxiao Liu and Andrew Brock and Karen Simonyan and Quoc V. Le},
    year    = {2020},
    eprint  = {2004.02967},
    archivePrefix = {arXiv}
}

@article{Shen2023ASO,
    title   = {A Study on ReLU and Softmax in Transformer},
    author  = {Kai Shen and Junliang Guo and Xuejiao Tan and Siliang Tang and Rui Wang and Jiang Bian},
    journal = {ArXiv},
    year    = {2023},
    volume  = {abs/2302.06461},
    url     = {https://api.semanticscholar.org/CorpusID:256827573}
}

@article{Csordas2023ApproximatingTF,
    title   = {Approximating Two-Layer Feedforward Networks for Efficient Transformers},
    author  = {R'obert Csord'as and Kazuki Irie and J{\"u}rgen Schmidhuber},
    journal = {ArXiv},
    year    = {2023},
    volume  = {abs/2310.10837},
    url     = {https://api.semanticscholar.org/CorpusID:264172384}
}