README.md

---
configs:
- config_name: exp1_counting
  data_files:
  - split: train
    path: exp1_counting/train-*.parquet
- config_name: exp2_discrimination
  data_files:
  - split: train
    path: exp2_discrimination/train-*.parquet
- config_name: exp3_controlled
  data_files:
  - split: train
    path: exp3_controlled/train-*.parquet
- config_name: exp4_realworld_discrimination
  data_files:
  - split: train
    path: exp4_realworld_discrimination/train-*
- config_name: exp4_realworld_naming
  data_files:
  - split: train
    path: exp4_realworld_naming/train-*.parquet
- config_name: exp5_synthetic_matched
  data_files:
  - split: train
    path: exp5_synthetic_matched/train-*
dataset_info:
- config_name: exp4_realworld_discrimination
  features:
  - name: image
    dtype: image
  - name: pair_num
    dtype: string
  - name: condition
    dtype: string
  - name: left_category
    dtype: string
  - name: right_category
    dtype: string
  - name: left_count
    dtype: string
  - name: right_count
    dtype: string
  - name: num_ratio
    dtype: string
  - name: answer
    dtype: string
  - name: prompt
    dtype: string
  - name: task
    dtype: string
  - name: tag
    dtype: string
  - name: eval_id
    dtype: int64
  - name: correct_answer
    dtype: string
  splits:
  - name: train
    num_bytes: 325752264
    num_examples: 584
  download_size: 325629874
  dataset_size: 325752264
- config_name: exp5_synthetic_matched
  features:
  - name: image
    dtype: image
  - name: pair_num
    dtype: string
  - name: condition
    dtype: string
  - name: shape_type
    dtype: string
  - name: left_category
    dtype: string
  - name: right_category
    dtype: string
  - name: left_count
    dtype: string
  - name: right_count
    dtype: string
  - name: num_ratio
    dtype: string
  - name: answer
    dtype: string
  - name: prompt
    dtype: string
  - name: task
    dtype: string
  - name: tag
    dtype: string
  - name: eval_id
    dtype: int64
  - name: correct_answer
    dtype: string
  splits:
  - name: train
    num_bytes: 41105917
    num_examples: 1134
  download_size: 39706387
  dataset_size: 41105917
---

# ANS Benchmark

A cognitively-grounded benchmark for **numerical cognition in vision-language models**,
covering **exact counting** and **approximate numerosity discrimination (ANS)**.

Each row is a self-contained trial: the stimulus image is embedded inline, and `prompt`
holds the exact question text sent to the model during evaluation.

## Configs (6)

| Config | Task | Rows | Stimuli |
|---|---|---|---|
| `exp1_counting` | Count items in one image | 1,994 | Abstract shapes + real-world (FSC-133), small-n & large-n |
| `exp2_discrimination` | Which side has more? (abstract, random sizes) | 480 | Pre-stitched pairs, 6 ratio conditions |
| `exp3_controlled` | Which side has more? (numerosity decorrelated from area/spacing) | 2,500 | Pre-stitched pairs, 3 shapes × 4 colors |
| `exp4_realworld_naming` | Name the object category | 864 | Single real-world panels |
| `exp4_realworld_discrimination` | Which side has more? (real-world) | 600 | Pre-stitched same/diff-category pairs |
| `exp5_synthetic_matched` | Which side has more? (abstract matched to real-world) | 1,164 | Pre-stitched pairs, counts/coords matched to Exp4 |

Every paired discrimination image is `left | 10 px white divider | right`.

## Common columns (all configs)

| Column | Type | Description |
|---|---|---|
| `image` | `Image` | Stimulus image (embedded bytes, loads as PIL) |
| `prompt` | `string` | Exact question text used in evaluation |
| `task` | `string` | Task type — see values below |
| `tag` | `string` | Analysis tag (`ans`, `ans2`, `ans3`, `ans4`, `ans5`) |
| `eval_id` | `int` | Global sequential trial index within each tag |
| `answer` / `correct_answer` | `string` | Ground-truth label (`left`/`right`/`tie` or integer count or category name) |

**`task` values:**

| Value | Description |
|---|---|
| `counting` | Exact count of objects |
| `discrimination_abstract` | Which side has more? — abstract shapes, unconstrained |
| `discrimination_controlled` | Which side has more? — numerosity decorrelated from surface area |
| `discrimination_realworld` | Which side has more? — real-world object images |
| `discrimination_synthetic` | Which side has more? — synthetic shapes matched to real-world stimuli |
| `naming` | Identify the object category |

## Config-specific columns

**exp1_counting** — `subset`, `stimulus_type` {abstract, realworld}, `n_range` {small_n, large_n}, `shape`, `category`, `count`

**exp2_discrimination** — `pair_id`, `shape` {dots, rectangles}, `anchor_n`, `ratio_condition`, `ratio_value`, `left_count`, `right_count`, `correct_answer`

**exp3_controlled** — `pair_num`, `pair_shape` {dots, ellipse, rectangle}, `pair_color`, `pair_ratio`, `left_numerosity`, `right_numerosity`, `left_TSA`, `right_TSA`, `left_FA`, `right_FA`, `correct_answer`
(TSA = total surface area; FA = field area / convex hull)

**exp4_realworld_naming** — `category`, `count`, `original_image_name`

**exp4_realworld_discrimination** — `pair_num`, `condition` {same_cat, diff_cat}, `left_category`, `right_category`, `left_count`, `right_count`, `num_ratio`, `answer`

**exp5_synthetic_matched** — `pair_num`, `condition`, `shape_type` {dots, rectangles}, `left_category`, `right_category`, `left_count`, `right_count`, `num_ratio`, `answer`

## Prompt templates

**5 semantically-equivalent templates per task**, assigned **one per stimulus** deterministically
(md5 hash of stimulus id). Each image is tested exactly once — prompts rotate across stimuli,
not within.

- **Counting:** `"How many {item} are there in the image? Please answer with an integer directly."`  (+ 4 variants)
- **Discrimination abstract:** `"Two images of {desc} appear side by side. Which image contains more shapes? Respond with 'left' or 'right'."` (+ 4 variants)
- **Discrimination same-category:** `"Look at these two images. Which image has more {cat}? … Answer with 'left' or 'right'."` (+ 2 variants)
- **Discrimination diff-category:** `"Left image contains {lcat}, right image contains {rcat}. Which image has more items? … Answer with 'left' or 'right'."` (+ 2 variants)
- **Naming:** `"What is(are) the object(s) in the image called? Please answer with one object category name directly."` (+ 4 variants)

## Quick start

```python
from datasets import load_dataset

# Load one config
ds = load_dataset("87cc2s/ans-benchmark", "exp1_counting")
row = ds["train"][0]
row["image"]   # PIL Image
row["prompt"]  # "How many dots are there in the image? ..."
row["answer"]  # "1"
row["task"]    # "counting"

# Load discrimination
ds2 = load_dataset("87cc2s/ans-benchmark", "exp2_discrimination")
row2 = ds2["train"][0]
row2["prompt"]          # "Two images of white dots appear side by side ..."
row2["correct_answer"]  # "right"
row2["task"]            # "discrimination_abstract"
```

## Provenance & notes

- Derived from original Experiment1–Experiment4, Experiment1_1, Experiment2_1, Experiment3_1 stimulus sets.
- **Excluded:** Exp1 `random_largen`-in-small-n bucket, real-world `FSC_sampled`/`FSC_sampled_largen`,
  Exp3 `ellipses_white`/`rectangles_white` (rendered incorrectly — replaced by Exp3_1 re-renders).
  36 synthetic pairs with missing source images and 1 exact-duplicate counting row were dropped.
- **License:** Real-world images derive from FSC-133 (Ranjan et al., 2021) / FSC-147. Abstract stimuli
  are procedurally generated and freely usable. Respect upstream FSC licensing.