Q-164M

A 164.6M-parameter ternary text model with exact tool calls

This is a research release, not a product. It is small and often factually wrong outside its trained tool-calling domain. See Results below and the blog post before using it for anything beyond experimentation.

Model summary

Q-164M is a 164,648,648-parameter decoder-only model. Its weights are ternary ({-1, 0, +1}, quantization-aware from step one of training), and instead of a trained embedding table it uses a frozen 512-bit fingerprint per token plus a small learned correction, covering the whole 32,832-token vocabulary. A fixed circuit intercepts <CALC>expr<EQ> spans during generation and force-decodes the exact result from a deterministic evaluator — the model's job is only ever to decide when and which tool to call (arithmetic, dates, unit conversion, sort, compare, gcd/lcm, primality, and 12 other kinds), never to compute the answer itself. Pretrained from scratch on a single 16GB V100, no cluster: 200,000 steps, ~92.4 hours, 13.1B tokens, zero NaNs over the whole run.

An instruction-tuned version, Q-U-164M, is available as its own repo — chat-SFT then RL, fine-tuned specifically for dialogue. Code for both is at github.com/Q-Project-LM/Q-164M.

Results (final checkpoint, step 200,000)

capability	result	verdict
validation perplexity (held-out mix)	16.98	steadily improving to the end
FineWeb holdout perplexity (plain text, no tool rows)	25.61	generalizes past its own tool-call rows
fixed 8-task tool-calling probe	7/8	—
— the one failure: sort:	never converged	the model calls a wrong tool for this one task family

Usage

from transformers import AutoModelForCausalLM, AutoTokenizer
tok = AutoTokenizer.from_pretrained("q-project/Q-164M")
model = AutoModelForCausalLM.from_pretrained("q-project/Q-164M", trust_remote_code=True)
ids = tok("Once upon a time,", return_tensors="pt").input_ids
print(tok.decode(model.generate(ids, max_new_tokens=60, do_sample=True, top_k=40,
    suppress_tokens=list(range(32768, model.config.vocab_size)))[0], skip_special_tokens=True))

For exact tool calls, build [<bos>, <USER>, *question_ids, <EOT>, <MODEL>] and generate with circuits.CircuitLogitsProcessor(tokenizer):

from circuits import USER, MODEL, EOT, CircuitLogitsProcessor
ids = [1, USER] + tok.encode("What is 91 divided by 7?").ids + [EOT, MODEL]
out = model.generate(torch.tensor([ids]), max_new_tokens=60,
                      logits_processor=[CircuitLogitsProcessor(tok)])

Architecture

• 10 layers, hidden 1280, 20 query / 4 KV heads (head dim 64), plain 2-matrix SiLU MLP 1280→3520→1280, per-head QK-norm, per-head sigmoid output gate on attention, RoPE (θ=1e5), context 4096 (trained at 2048).
• Ternary weights from step 1: every attention/MLP projection is re-quantized to {-1,0,+1}·α (per-row absmean α) at each forward pass with a straight-through estimator.
• Frozen fingerprint vocabulary: each token is a fixed ±1 code of 512 bits instead of a trained embedding. Input = C[id]·W_in; readout = (h·W_out)·Cᵀ/√512 + frozen unigram log-prior. Every id carries its own untied delta_in/delta_out correction on top of the frozen code.
• Exact circuits (circuits.py): the model writes <CALC>expr<EQ>; CircuitLogitsProcessor forces the exact result and <ECALC> — arithmetic, dates, weekday, duration, unit conversion, comparison, sorting, filtering, counting, mean/max/min/sum, gcd/lcm, primality, string reversal, factorial, square root, percent change, and word counts.

Token layout

ids	content
0–32767	text BPE (32k); 0 <pad>, 1 <bos>, 2 <eos>
32768–32831	control: <USER> <MODEL> <EOT> <THINK> <ETHINK> <CALC> <EQ> <ECALC> <NEED> <QUOTE> and reserved ids

How it compares to other small models

Measured with QBench — see the leaderboard for the live table and methodology. See the Q-U-164M model card for the instruct variant's numbers, which is what QBench actually targets (this base model is a plain-text continuation model, not instruction-tuned for chat).

Limitations

• Facts are frequently wrong; thin general knowledge; repetitive under greedy decoding; weak creative writing. No safety tuning.
• Sorting lists (sort:) never converged during pretraining — the model reliably calls the wrong tool for this one task family.
• Ternary weights at this size are a research setting; do not expect competitive benchmark scores from a single-V100, 164M-parameter model.

License and data terms

Code and weights: Apache-2.0 (see LICENSE). Training data keeps its own terms — check before commercial use: FineWeb / FineWeb-Edu and the SmolLM corpus (ODC-By 1.0 / Apache-2.0).