Language Models Without a Trainable Input Embedding Table: Learning from Fixed Minimal Binary Token Codes

TL;DR

This paper demonstrates that trainable input embedding tables in language models can be replaced with fixed minimal binary token codes without significant loss in performance, reducing parameters.

Contribution

It introduces a method to replace trainable input embeddings with fixed binary codes, showing comparable performance in large language models.

Findings

Fixed minimal binary codes achieve similar perplexity to learned embeddings.

Removing trainable input tables reduces 67.1 million parameters.

Affine-recoded codes perform comparably with slightly shorter training.

Abstract

Trainable input embedding tables are a standard component of modern language models. We ask whether they are actually necessary at the input interface. For a vocabulary of size $V$, exact token identity requires only $K=\lceil \log_2 V\rceil$ bits. We replace the usual trainable $V\times d_{\text{model}}$ input embedding matrix with fixed minimal binary token codes and a zero-parameter lift to model width. In our main setting, $V=65{,}536$, so $K=16$, and tokens are represented by fixed 16-dimensional binary codes tiled to $d_{\text{model}}=1024$. We also evaluate a fully table-free variant in which codes are generated from token IDs on the fly and randomly recoded by an invertible affine transform over $\mathbb{F}_2^K$. Across matched 32-layer decoder-only models trained on approximately 17B tokens and evaluated over three independent training seeds, fixed minimal codes achieve comparable held-out validation perplexity to a standard learned-input baseline while removing 67.1M trainable input parameters. The fixed-code runs have a lower mean validation perplexity in our experiments, 2.36 versus 2.44, but the observed gap is within the measured seed-to-seed variation of 4.8\%; we therefore interpret the result as evidence that the trainable input table is not necessary, rather than as a statistically resolved superiority claim. The table-free affine-recoded variant remains close at 2.39 despite a slightly shorter training run. These results show that, in this regime, a trainable input embedding table is not necessary for useful language modeling. The output projection remains standard and trainable.