# Load model directly
from transformers import AutoTokenizer, AutoModelForCausalLM
tokenizer = AutoTokenizer.from_pretrained("itsusony/LFM2.5-1.2B-Zhusuan")
model = AutoModelForCausalLM.from_pretrained("itsusony/LFM2.5-1.2B-Zhusuan", device_map="auto")
messages = [
{"role": "user", "content": "Who are you?"},
]
inputs = tokenizer.apply_chat_template(
messages,
add_generation_prompt=True,
tokenize=True,
return_dict=True,
return_tensors="pt",
).to(model.device)
outputs = model.generate(**inputs, max_new_tokens=40)
print(tokenizer.decode(outputs[0][inputs["input_ids"].shape[-1]:]))LFM2.5-1.2B-Zhusuan
LoRA-SFT (merged) of LiquidAI/LFM2.5-1.2B-Thinking for abacus-style mental arithmetic (珠算 / 珠心算). Still 1.2B — runs locally.
English
Why this model
Much more accurate integer arithmetic, with a stable expr=result final line. Still 1.2B — no tool calls, pure model.
Headline (hardest head-to-head): same 100 big-integer problems (test_100.py --hard --seed 628488977, greedy, max_new_tokens=3072):
| Op | Base (LFM2.5-1.2B-Thinking) | Zhusuan R5b | Δ |
|---|---|---|---|
| + | 29.2% | 100% | +70.8 |
| − | 63.0% | 92.6% | +29.6 |
| × | 0.0% | 100% | +100 |
| ÷ | 42.9% | 100% | +57.1 |
| Overall | 33.0% | 98.0% | +65.0 |
Base collapses on multi-digit multiplication (often copies an operand or invents digits). R5b runs full abacus-style traces (base-1000 chunked mult for ≥10-digit products) and finishes with a parseable expr=result line. Head-to-head numbers above are the R4 release suite (same seed); stratified R5b below is stronger on hard / hard_div / xl.
Stratified suite (greedy, seed=123, eval_math.py; Base from the same harness as our earlier deploy report):
| Suite | Base | Zhusuan R5b | Δ |
|---|---|---|---|
| easy (n=100) | 96.0% | 99.0% | +3.0 |
| medium (n=100) | 90.0% | 98.0% | +8.0 |
| hard (n=80) | 63.7% | 100% | +36.3 |
| hard — multiplication only | 54.8% (23/42) | 100% (40/40) | +45.2 |
| hard — division only | 83.3% (10/12) | 100% (13/13) | +16.7 |
| hard_div (large divisors, n=40) | — | 97.5% | new stress set |
| xl_fixed (n=30) | 83.3% | 100% | +16.7 |
| plain_easy (n=50) | — | 98.0% | no abacus cue |
| Overall (easy+med+hard+xl, n=310) | 84.5% | 99.0% | +14.5 |
Base tends to slip digits on long multiplication, contradict itself, and emit hard-to-parse final lines — real outputs in Demo. Eval is synthetic abacus-style arithmetic (code in sft/); competition word problems are not the target. Repo weight is R5b (chunked big-mult; init R5a → R5b).
Quick start
No system prompt needed — the bundled chat template injects a zhusuan one by default. Ask in any language (用珠算思路算 73×19, Calculate 73×19 …). Use greedy decoding and max_new_tokens ≥ 3072 (long-multiplication traces are long). The answer is the last line after </think>.
from transformers import AutoModelForCausalLM, AutoTokenizer
import torch
repo = "itsusony/LFM2.5-1.2B-Zhusuan"
tok = AutoTokenizer.from_pretrained(repo, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(
repo, torch_dtype=torch.bfloat16, device_map="auto", trust_remote_code=True)
messages = [{"role": "user", "content": "用珠算思路算 73×19"}]
prompt = tok.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)
inputs = tok(prompt, return_tensors="pt").to(model.device)
out = model.generate(**inputs, max_new_tokens=3072, do_sample=False, pad_token_id=tok.eos_token_id)
print(tok.decode(out[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True))
Quick test (ground truth computed in plain Python, compared with the model's answer):
python3 test_chat.py # interactive chat
python3 test_100.py # random 100 problems -> accuracy report (--seed 42, --hard for big numbers)
License
LFM Open License v1.0 (see LICENSE). Commercial use by entities with annual revenue ≥ USD 10M is not licensed.
中文
为什么用这个模型
整数四则明显更准，末行固定为 式=答。仍是 1.2B，不靠外挂计算器。
同题硬核对比（test_100.py --hard --seed 628488977，greedy，max_new_tokens=3072）：
| 运算 | 底座 Base | 本模型 R5b | Δ |
|---|---|---|---|
| + | 29.2% | 100% | +70.8 |
| − | 63.0% | 92.6% | +29.6 |
| × | 0.0% | 100% | +100 |
| ÷ | 42.9% | 100% | +57.1 |
| 总计 | 33.0% | 98.0% | +65.0 |
底座在大数乘法上几乎全军覆没；R5b 用珠算分步轨迹（≥10 位积走千位分节），大乘/大除都拉到满分档。上表同题硬核为 R4 发布套件；下方分层为 R5b。
分层评测（seed=123，eval_math.py）：
| 套件 | 底座 | 本模型 R5b | Δ |
|---|---|---|---|
| easy (n=100) | 96.0% | 99.0% | +3.0 |
| medium (n=100) | 90.0% | 98.0% | +8.0 |
| hard (n=80) | 63.7% | 100% | +36.3 |
| hard 仅乘法 | 54.8% | 100% (40/40) | +45.2 |
| hard 仅除法 | 83.3% | 100% | +16.7 |
| hard_div（大除数 n=40） | — | 97.5% | 压测 |
| xl_fixed (n=30) | 83.3% | 100% | +16.7 |
| plain_easy (n=50) | — | 98.0% | 不提珠算 |
| 总计 (easy+med+hard+xl, n=310) | 84.5% | 99.0% | +14.5 |
底座常见问题：长乘法串位、末行自相矛盾、答案格式难解析——见 Demo。评测为合成珠算四则（sft/），竞赛应用题不是目标。当前仓库权重为 R5b。
怎么用
- 无需 system prompt：chat template 已内置珠算 system，任意语言提问均可（如
用珠算思路算 73×19） - 用 greedy 解码，
max_new_tokens ≥ 3072（大乘法轨迹很长）；答案在</think>后的最后一行 - 随机测试：
python3 test_100.py（Python 真值比对并输出正确率；--hard大数难度，--seed可复现） - 代码示例见英文 Quick start
许可证
LFM Open License v1.0（见 LICENSE）；年收入 ≥ 1000 万美元的商业使用不在许可范围内。
日本語
このモデルを選ぶ理由
整数の四則演算が大幅に正確になり、最終行は常に 式=答。パラメータは 1.2B のまま（ツール不使用）。
同一 100 問ハード比較（test_100.py --hard --seed 628488977）:
| 演算 | ベース | 本モデル R5b | Δ |
|---|---|---|---|
| + | 29.2% | 100% | +70.8 |
| − | 63.0% | 92.6% | +29.6 |
| × | 0.0% | 100% | +100 |
| ÷ | 42.9% | 100% | +57.1 |
| 全体 | 33.0% | 98.0% | +65.0 |
ベースは大きな掛け算でほぼ全滅。R5b は珠算トレース（10 桁以上の積は 1000 進チャンク）で乗除を安定化。上表は R4 公開スイート；下の層別は R5b。
層別評価（seed=123）:
| スイート | ベース | 本モデル R5b | Δ |
|---|---|---|---|
| easy (n=100) | 96.0% | 99.0% | +3.0 |
| medium (n=100) | 90.0% | 98.0% | +8.0 |
| hard (n=80) | 63.7% | 100% | +36.3 |
| hard 乗算のみ | 54.8% | 100% (40/40) | +45.2 |
| hard 除算のみ | 83.3% | 100% | +16.7 |
| hard_div（大除数 n=40） | — | 97.5% | ストレステスト |
| xl_fixed (n=30) | 83.3% | 100% | +16.7 |
| plain_easy (n=50) | — | 98.0% | 珠算ヒントなし |
| 合計 (easy+med+hard+xl, n=310) | 84.5% | 99.0% | +14.5 |
ベースの典型的な失敗は桁ずれ・自己矛盾・パース困難な最終行（Demo）。評価は合成の珠算四則（sft/）。リポジトリの現行重みは R5b。
使い方
- system プロンプト不要：chat template がデフォルトの珠算 system を自動挿入します。どの言語でも質問できます（例：
珠算の考え方で 73×19 を計算してください。） - greedy デコード、
max_new_tokens ≥ 3072を推奨（長い乗算の思考は長文になります）。答えは</think>の後の最終行です - ランダムテスト：
python3 test_100.py（Python の真値と照合して正答率を表示。--hardで大きな数、--seedで再現可能） - コード例は英語の Quick start を参照
ライセンス
LFM Open License v1.0（LICENSE 参照）。年間売上 1,000 万米ドル以上の主体による商用利用は本契約では許諾されません。
Demo / 示例 / デモ
Real greedy generations. Note: the model always thinks in its trained Chinese abacus trace, even for English/Japanese prompts.（模型无论用什么语言提问，都用中文珠算轨迹思考。どの言語で聞いても中国語の珠算トレースで考えます。）
Calculate 73×19 using abacus-style (珠算) reasoning. — full output
<think>
乘法：逐位取乘数一档，用九九得部分积，再按档错位累加（每步写进位）。
被乘数=73，乘数=19。
— 乘数第1位（权10^0）= 9 —
【一位乘】73×9（从个位向高位，九九口诀+进位）:
第1档: 3×9=27，加进位0 → 27，写7，进2
第2档: 7×9=63，加进位2 → 65，写5，进6
最高进位写6
得 73×9=657
左移0档，部分积=657
【档位加】累加第1个部分积: 0+657（从个位向高位）
第1档: 0+7+进0=7 → 写7，进0
第2档: 0+5+进0=5 → 写5，进0
第3档: 0+6+进0=6 → 写6，进0
得 0+657=657
— 乘数第2位（权10^1）= 1 —
【一位乘】73×1（从个位向高位，九九口诀+进位）:
第1档: 3×1=3，加进位0 → 3，写3，进0
第2档: 7×1=7，加进位0 → 7，写7，进0
得 73×1=73
左移1档（×10^1）: 73 → 730
【档位加】累加第2个部分积: 657+730（从个位向高位）
第1档: 7+0+进0=7 → 写7，进0
第2档: 5+3+进0=8 → 写8，进0
第3档: 6+7+进0=13 → 写3，进1
最高进位写1
得 657+730=1387
验算: 73×19=1387
</think>
73×19=1387。
English translation of the trace (human translation for readability — the model itself always thinks in Chinese)
<think>
Multiplication: take one multiplier digit at a time, build partial products
from the times table, accumulate with digit shifts (record every carry).
Multiplicand=73, multiplier=19.
— Multiplier digit 1 (weight 10^0) = 9 —
[1-digit multiply] 73×9 (units → high, times table + carry):
Rod 1: 3×9=27, +carry 0 → 27, write 7, carry 2
Rod 2: 7×9=63, +carry 2 → 65, write 5, carry 6
Top carry 6
→ 73×9=657
Shift 0 rods, partial product = 657
[Rod addition] Accumulate 1st partial: 0+657 (units → high)
Rod 1: 0+7+carry0=7 → write 7, carry 0
Rod 2: 0+5+carry0=5 → write 5, carry 0
Rod 3: 0+6+carry0=6 → write 6, carry 0
→ 0+657=657
— Multiplier digit 2 (weight 10^1) = 1 —
[1-digit multiply] 73×1:
Rod 1: 3×1=3, +carry 0 → 3, write 3, carry 0
Rod 2: 7×1=7, +carry 0 → 7, write 7, carry 0
→ 73×1=73
Shift 1 rod (×10^1): 73 → 730
[Rod addition] Accumulate 2nd partial: 657+730
Rod 1: 7+0+carry0=7 → write 7, carry 0
Rod 2: 5+3+carry0=8 → write 8, carry 0
Rod 3: 6+7+carry0=13 → write 3, carry 1
Top carry 1
→ 657+730=1387
Check: 73×19=1387
</think>
73×19=1387.
日本語訳（読みやすさのための人間による翻訳。モデル自体は常に中国語で思考します）
<think>
乗法：乗数を1桁ずつ取り、九九で部分積を作り、桁ずらしで累加する（各ステップで繰り上がりを記録）。
被乗数=73、乗数=19。
— 乗数の1桁目（重み10^0）= 9 —
【一桁乗算】73×9（一の位から上位へ、九九＋繰り上がり）:
第1桁: 3×9=27、繰上0を加算 → 27、7を書き、2を繰上
第2桁: 7×9=63、繰上2を加算 → 65、5を書き、6を繰上
最上位の繰上6を書く
→ 73×9=657
0桁シフト、部分積=657
【桁加算】1つ目の部分積を累加: 0+657（一の位から上位へ）
第1桁: 0+7+繰上0=7 → 7を書き、繰上0
第2桁: 0+5+繰上0=5 → 5を書き、繰上0
第3桁: 0+6+繰上0=6 → 6を書き、繰上0
→ 0+657=657
— 乗数の2桁目（重み10^1）= 1 —
【一桁乗算】73×1:
第1桁: 3×1=3、繰上0 → 3、3を書き、繰上0
第2桁: 7×1=7、繰上0 → 7、7を書き、繰上0
→ 73×1=73
1桁シフト（×10^1）: 73 → 730
【桁加算】2つ目の部分積を累加: 657+730
第1桁: 7+0+繰上0=7 → 7、繰上0
第2桁: 5+3+繰上0=8 → 8、繰上0
第3桁: 6+7+繰上0=13 → 3を書き、1を繰上
最上位の繰上1を書く
→ 657+730=1387
検算: 73×19=1387
</think>
73×19=1387。
Calculate 35937×1774 using abacus-style (珠算) reasoning. — base vs this model
Base burns its thinking budget guessing what 珠算 means, then slips a digit → wrong:
<think> Okay, let's tackle this problem ... Hmm, first, I need to recall what
abacus-style calculation involves. Since the user mentioned using the abacus
and pearls (珠算), which I think refers to the traditional Chinese counting
method ... </think>
... After precise computation, the result is **63,753,238**.
\boxed{63753238} ← digit slip, WRONG (correct: 63752238)
(Japanese prompt, same story: base calls it the "Jewel Box Suanpan method" and answers 63,753,238.)
This model (EN or JA prompt — identical output) runs the full partial-product trace (abridged) → correct:
<think>
被乘数=35937，乘数=1774。
【一位乘】35937×4=143748 →【档位加】0+143748=143748
【一位乘】35937×7=251559，左移1档 →【档位加】累加=2659338
…（第3、4位同理，逐档进位累加）…
验算: 35937×1774=63752238
</think>
35937×1774=63752238。 ← CORRECT
More real base failures from the same eval run (prompts carried the 用珠算思路算 … wording):
| Prompt | Correct | Base answered | What went wrong |
|---|---|---|---|
19884×19 |
377796 | (unparseable) | Right math, but final line = 19884 × (20−1) = … hid the answer |
999×999 |
998001 | 1000 | Truncated mid-\boxed{…; wrong earlier number picked up |
64÷8 |
8 | 64 | Rambled about the "pearl method", never gave a clean answer |
Training
- Base:
LiquidAI/LFM2.5-1.2B-Thinking→ LoRA SFT (r=16,alpha=32), merged - Data: synthetic zhusuan Q&A with
<think>traces; R3 round adds 19,666 hard-mined pairs (long ×/÷) - Checkpoint: R3 fine, 2.5 epochs, train_loss 0.027 — overall 79.4% → 93.0% vs base; training/eval code in
sft/
Citation
Please also cite the base model:
LiquidAI/LFM2.5-1.2B-Thinking
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# Use a pipeline as a high-level helper from transformers import pipeline pipe = pipeline("text-generation", model="itsusony/LFM2.5-1.2B-Zhusuan") messages = [ {"role": "user", "content": "Who are you?"}, ] pipe(messages)