Bochkov/llm-fix-min-affine-recoded-minimal-code-table-free

Affine-Recoded Minimal Code Table-Free Model

Research checkpoint for the paper:

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

Model variant

This repository contains the fully table-free affine-recoded minimal binary-code model.

The model does not use an input embedding table. Instead, token codes are computed directly from token IDs.

For each token ID t, the model computes:

c(t) = bin_16(t)

and then applies a fixed invertible affine recoding over GF(2):

c_tilde(t) = A c(t) xor b

where:

• A is an invertible binary matrix in GL(16, 2)
• b is a fixed binary shift vector

The resulting 16-dimensional binary code is tiled to model width 1024.

The model uses:

0 trainable input-embedding parameters
0 input embedding table

The output projection remains standard and trainable.

Architecture

• decoder-only Transformer
• vocabulary size: 65,536
• model width: 1024
• number of layers: 32
• number of attention heads: 32
• context length: 1024
• rotary positional embeddings
• GELU activations
• untied trainable output projection

Loading example

import torch
from transformers import AutoTokenizer, AutoModelForCausalLM

repo_id = "Bochkov/llm-fix-min-affine-recoded-minimal-code-table-free"

tokenizer = AutoTokenizer.from_pretrained(repo_id, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(repo_id, trust_remote_code=True)
model.eval()

prompt = "Question: What is the capital of UK?\nAnswer:"
input_ids = torch.tensor([tokenizer.encode(prompt)], dtype=torch.long)

with torch.no_grad():
    output_ids = model.generate(input_ids, max_new_tokens=3, do_sample=False)

print(tokenizer.decode(output_ids[0].tolist()))

Intended use

This checkpoint is provided for reproducibility. It demonstrates that the fixed minimal-code input interface remains viable even when the canonical token-ID binary code is randomly recoded by an invertible affine transform.

Limitations

This model is a research checkpoint. It is not intended for deployment. It may produce incorrect, biased, unsafe, or nonsensical outputs.

Training data

The model was trained on the same FineWeb-Edu + Cosmopedia mixture used for the matched comparisons in the paper. Dataset terms and licenses are those of the original datasets.

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🧑‍🔬 Citation & Concept

If you use this model or the underlying concepts in your research, please cite our work:

@misc{bochkov2026languagemodelstrainableinput,
      title={Language Models Without a Trainable Input Embedding Table: Learning from Fixed Minimal Binary Token Codes}, 
      author={A. Bochkov},
      year={2026},
      eprint={2605.09751},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2605.09751}, 
}