update dataset card: N=250 eval sets, Quirke arxiv link, subtraction enrichment, M6 note

README.md

@@ -49,23 +49,40 @@ Small transformers trained on integer addition/subtraction, with
 [SoRL](https://github.com/fangyuan-ksgk/mod_gpt) to externalize carry/borrow circuits
 as explicit abstraction tokens.
 
-Reference: Quirke et al., "Understanding Addition and Subtraction in Transformers" (2024)
+**Reference:** Quirke et al., ["Understanding Addition and Subtraction in Transformers"](https://arxiv.org/abs/2402.02619) (2024).
+Paper: [arXiv:2402.02619](https://arxiv.org/abs/2402.02619) — see Table 8 for complexity classification and Section 3 for sub-task definitions.
 
 ## Dataset Structure
 
 | Subfolder | Operations | Train | Val | Eval (stratified) |
 |---|---|---|---|---|
-| `add_6digit` | addition only | 500K | 10K | ~550 (50 per S0-S6 + 200 random) |
-| `add_sub_6digit` | add + sub | 500K | 10K | ~1100 (50 per S0-S6 + M0-M6 + random) |
+| `add_6digit` | addition only | 500K | 10K | ~2950 (250 per S0-S6, C3-C6 + 200 random) |
+| `add_sub_6digit` | add + sub | 500K | 10K | ~5400 (250 per split + 400 random) |
+| `add_handcrafted` | addition only | — | — | 108 |
+| `sub_handcrafted` | subtraction only | — | — | 68 |
+
+### Eval Splits
+
+All eval sets use seed=42 for reproducibility. Every model is evaluated on identical examples.
+
+| Split Type | Splits | Examples/split | Description |
+|---|---|---|---|
+| Quirke cascades (add) | S0-S6 | 250 | Carry cascade depth 0-6 |
+| Hot carry chains | C3-C6 | 250 | Carry cascades with varied answer digits (not just 0s) |
+| Quirke cascades (sub) | M0-M5 | 250 | Borrow cascade depth 0-5 (M6 is impossible for 6-digit) |
+| Hot borrow chains | B3-B5 | 250 | Borrow cascades with varied answer digits (not just 9s) |
+| Random | add_random, sub_random | 200 | Uniform random |
+
+**Note:** M6 (borrow cascade of length 6) is impossible for 6-digit subtraction — it would require 7 digit positions.
 
 ## Columns
 
 | Column | Type | Description |
 |---|---|---|
-| `tokens` | list[int] | Full sequence (21 tokens for 6-digit) |
-| `labels` | list[str] | Per-answer-digit sub-task label |
+| `tokens` | list[int] | Full sequence (21 tokens for 6-digit, Qwen3 tokenizer) |
+| `labels` | list[str] | Per-answer-digit sub-task label (SA, SC, SS, UC, US for add; MD, MB, ME, UB, UD for sub) |
 | `op` | str | `"add"` or `"sub"` |
-| `complexity` | str | Quirke complexity: `S0`-`S6` (add) or `M0`-`M6` (sub) |
+| `complexity` | str | Quirke complexity: `S0`-`S6` (add) or `M0`-`M5` (sub) |
 | `cascade_depth` | int | Max carry/borrow cascade length |
 | `x_digits` | list[int] | First operand (MSB first) |
 | `y_digits` | list[int] | Second operand (MSB first) |
@@ -73,9 +90,9 @@ Reference: Quirke et al., "Understanding Addition and Subtraction in Transformer
 
 The `eval_stratified` split has an additional `eval_category` column.
 
-## Sub-task Labels (Quirke et al.)
+## Sub-task Labels ([Quirke et al. 2024](https://arxiv.org/abs/2402.02619))
 
-Each answer digit requires a specific arithmetic operation:
+Each answer digit requires a specific arithmetic operation. These labels follow Quirke et al. Section 3.
 
 ### Addition
 | Label | Name | Condition | Role |
@@ -95,7 +112,7 @@ Each answer digit requires a specific arithmetic operation:
 | UB | Use Borrow | borrow_in=1, `Dn != D'n` | Consumes incoming borrow |
 | UD | Use Equal | borrow_in=1, `Dn == D'n` | Cascade: hardest case |
 
-## Complexity Classification (Quirke Table 8)
+## Complexity Classification ([Quirke Table 8](https://arxiv.org/abs/2402.02619))
 
 Complexity = length of longest carry/borrow cascade chain.
 
@@ -114,8 +131,9 @@ S6: cascade of 6          <0.5%
 
 ## Data Enrichment
 
-Following Quirke: 60% of batches have 40% of digit positions forced to sum-to-9,
-increasing cascade frequency so the model sees enough S4-S6 cases.
+**Addition:** Following Quirke et al., 60% of batches have 40% of digit positions forced to sum-to-9, increasing carry cascade frequency so the model sees enough S4-S6 cases.
+
+**Subtraction:** 40% of digit positions are forced equal (`Dn == D'n`), creating borrow propagation cascades (ME/UD). Without this, M3-M5 borrow cascades are extremely rare (M3=0.7%, M4=0.04% in unmodified data). With enrichment: M3=3.0%, M4=0.8%.
 
 ## Usage
 
@@ -130,9 +148,14 @@ print(ds["train"][0])
 # Stratified eval
 eval_ds = load_dataset("thoughtworks/arithmetic-sorl-data",
                        data_dir="add_6digit", data_files="eval_stratified.parquet")
+
+# Addition + subtraction
+ds_mixed = load_dataset("thoughtworks/arithmetic-sorl-data", data_dir="add_sub_6digit")
 ```
 
 ## Related
 
-- Model checkpoints: [thoughtworks/arithmetic-sorl](https://huggingface.co/thoughtworks/arithmetic-sorl)
-- Code: [mod_gpt/arithmetic/](https://github.com/fangyuan-ksgk/mod_gpt/tree/amir/arithmetic/arithmetic)
+- **Reference paper:** Quirke et al., ["Understanding Addition and Subtraction in Transformers"](https://arxiv.org/abs/2402.02619) (2024)
+- **Model checkpoints:** [thoughtworks/arithmetic-sorl](https://huggingface.co/thoughtworks/arithmetic-sorl)
+- **Dashboard:** [thoughtworks/arithmetic-sorl-dashboard](https://huggingface.co/spaces/thoughtworks/arithmetic-sorl-dashboard)
+- **Code:** [mod_gpt/arithmetic/](https://github.com/fangyuan-ksgk/mod_gpt/tree/amir/arithmetic/arithmetic)