nltower-100m-cpt32

A 124M-parameter Llama-style model from the nl_tower study: the base model mid-trained with 32 solver-written reasoning traces in every batch (CPT-32). It is a starting point for reinforcement learning on nl_tower puzzles, not a general-purpose assistant.

This repository is part of the nl_tower (100M) collection on the Hugging Face Hub (5 CPT models, 6 SFT models, the base model and 4 datasets).

nl_tower in brief

nl_tower is a synthetic reasoning task. Each puzzle places 6-12 people on distinct floors (1-40) of a tower. The prompt lists the occupied floors, each person's best friend, and clues that relate the floors of two terms ("greater than", "k floors above", sums, parity, "twice", highest/lowest). Many clues refer to people indirectly, for example "the best friend of the person on the second-highest floor"; such a clue becomes usable only after other clues have pinned part of the answer. Each puzzle has a unique solution that a step-by-step solver reaches without guessing.

The study asks whether reinforcement learning can teach reasoning compositions that the imitation data never shows:

• Covered patterns (shown in the mid-training traces): friend ("Ava's best friend"), friend2 ("the best friend of Ava's best friend"), order ("the person directly above Ava"), rankn ("the person on the second-highest floor"), dfriend_occ ("the best friend of the person on floor 19").
• Held-out patterns (appear only in RL prompts and tests): dfriend_rank ("the best friend of the person on the highest floor"), dfriend_above ("the best friend of the person directly above Ava"), and nested (two-level references).

Test rungs: easy (nltw_e, 6-7 people, covered only), covered mid (nltw_m0, 8-9 people, covered only), held-out mid (nltw_m, 8-9 people, 2-4 held-out steps), size-only hard (nltw_hb, 10-11 people, 2-4 held-out steps) and 12 people (nltw_hb12, test only).

Position in the pipeline

base pretraining (iteration 30,000, before the cooldown) --CPT-N (cooldown + N trace sequences per batch)--> CPT-N models --RL--> policies
base pretraining (iteration 38,147, end of the run) --SFT on the same traces--> SFT models --RL (no demos)--> policies

This model is the CPT-N model with N = 32. RL from it was run in four groups of runs: pure RL with no demonstrations ("no-mix"), RL with demonstration rows in a shared loss ("unified"), RL plus a separately weighted SFT loss on demonstration rows ("separate-loss"), and the shared loss with pretraining text added to every update ("pre-mid-rl"). See sfanm/nltower-results and sfanm/nltower-rl-mixes.

Training (CPT-32)

• Start: sfanm/nltower-100m-base (iteration 30,000 of the base run).
• Continue for the remaining 8,147 iterations (to iteration 38,147), through the same WSD cooldown as the base run.
• Every batch holds 256 web sequences (the base run's 75 % ClimbMix / 25 % Dolmino blend) plus 32 trace sequences from the packed tw1X trace shard: global batch 288 x 2,048 tokens, language-modelling loss on all tokens.
• Trace share of each batch: 11.1 %. Trace tokens seen: 533,921,792 = 1.05 passes over the 509,942,713-token shard.
• Traces: sfanm/nltower-traces-tw1X (config cpt_shard), covering easy and covered-mid puzzles with covered patterns only.

All five CPT models use the same recipe and differ only in N:

N	global batch	trace share	passes over the traces
8	264	3.0 %	0.26
16	272	5.9 %	0.52
32	288	11.1 %	1.05
64	320	20.0 %	2.09
128	384	33.3 %	4.19

Architecture

property	value
architecture	LlamaForCausalLM (decoder-only)
parameters	123,587,328 (embeddings tied with the output layer)
layers / hidden size / heads	12 / 768 / 12 (head dim 64, no grouped-query attention)
MLP	SwiGLU, intermediate size 2,048
normalisation / position	RMSNorm (eps 1e-5) / RoPE (theta 10,000)
tokenizer	GPT-2 BPE (50,257 tokens; embedding padded to 50,304)
special tokens	<|endoftext|> (id 50256) is BOS, EOS and PAD
context length	2,048 tokens
weights	model.safetensors, bfloat16

Prompt format and usage

The prompt is the puzzle text followed by "\n\nAnswer: ". The model writes its reasoning and ends with the full assignment in \boxed{Name=floor, ...}. A completion is correct when every Name=floor pair in the boxed answer matches the solution (order does not matter). The chat template only concatenates message contents (no role markers), so apply_chat_template and the raw prompt give the same tokens.

from transformers import AutoModelForCausalLM, AutoTokenizer
from datasets import load_dataset

repo = "sfanm/nltower-100m-cpt32"
tok = AutoTokenizer.from_pretrained(repo)
model = AutoModelForCausalLM.from_pretrained(repo, torch_dtype="bfloat16")

test = load_dataset("sfanm/nltower-env", "tests", split="nltw_m0")
prompt = test[0]["prompt"]                      # question + "\n\nAnswer: "
ids = tok(prompt, return_tensors="pt").input_ids
out = model.generate(ids, max_new_tokens=1280, do_sample=False, pad_token_id=tok.eos_token_id)
print(tok.decode(out[0, ids.shape[1]:], skip_special_tokens=True))   # ... \boxed{Name=floor, ...}
print("gold:", test[0]["answer"])

Evaluation

Zero-shot screen of this model before any RL. Protocol: 1,024 test questions per rung; 64 samples per question at temperature 1.0 (top-p 1.0) and up to 1,280 new tokens with vLLM in bfloat16; pass@k uses the unbiased estimator 1 - C(n-c, k)/C(n, k) with n = 64; greedy is one temperature-0 sample. Test sets: sfanm/nltower-env, config tests.

test rung	pass@1	pass@64	greedy
easy (nltw_e)	0.388	0.992	0.616
covered mid (nltw_m0)	0.167	0.967	0.366
held-out mid (nltw_m)	0.005	0.178	0.015

RL runs that start from this model and have evaluations in sfanm/nltower-results (filter init == "mixed-534M", the name of this model in the code), by setting (base: 8-9-person prompts, 6,000 updates; extended: 10-11-person prompts added, 12,000 updates) and group:

setting	group	runs
base	unified	10
base	separate-loss	11
base	pre-mid-rl	2
extended	unified	10
extended	separate-loss	20
extended	no-mix	2
extended	pre-mid-rl	4

Intended use and limitations

• Intended for research on how imitation (mid-training on traces) and reinforcement learning interact, especially on compositions that the traces never show.
• The model saw only the five covered reference patterns in its traces. Expect low accuracy on held-out-pattern rungs (held-out mid, size-only hard) before RL.
• 124M parameters and a synthetic task: results may not transfer to larger models or natural tasks. The model is not instruction-tuned or safety-tuned and is not for user-facing use.

Training data

• Pretraining and the web part of CPT: karpathy/climbmix-400b-shuffle, allenai/dolma3_dolmino_mix-100B-1025.
• Traces: sfanm/nltower-traces-tw1X. They are written by a deterministic solver program, not by a language model.
• Tests and RL prompts: sfanm/nltower-env, sfanm/nltower-rl-mixes.

Code

Code: https://github.com/yudasong/unified-training/tree/release (environment generator, solver, data builders, training recipes and evaluator).

License

No license has been chosen for these weights yet, so the metadata says license: other. The base model was pretrained on:

• karpathy/climbmix-400b-shuffle (75 % of tokens): a reshuffled copy of NVIDIA's ClimbMix. The copy is tagged MIT, while the original nvidia/Nemotron-ClimbMix card gives CC BY-NC 4.0 and says it is for research and development only.
• allenai/dolma3_dolmino_mix-100B-1025 (25 % of tokens): ODC-By 1.0, with a note that it is intended for research and educational use.

Use the weights only in ways that the terms of these datasets allow. The nl_tower data used after pretraining is the authors' own synthetic data (Apache-2.0, see the dataset repositories).

Authors and citation

Authors and citation: to be added.

This release (files and this card) was prepared with AI assistance (Claude, an Anthropic model) and is being reviewed by the authors.