Metadata-Version: 2.5
Name: concept-benchmark
Version: 0.4.0
Summary: Synthetic benchmarks for evaluating Concept Bottleneck Models.
Project-URL: Repository, https://github.com/ustunb/concept-benchmark
Project-URL: Datasets, https://huggingface.co/juliannski
Author: Julian Skirzyński, Harry Cheon, Shreyas Kadekodi, Meredith Stewart, Berk Ustun
License-Expression: MIT
License-File: LICENSE
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: MIT License
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: 3.13
Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
Requires-Python: >=3.10
Requires-Dist: colorir>=2.0.0
Requires-Dist: dill>=0.3.8
Requires-Dist: matplotlib>=3.10.3
Requires-Dist: numpy==2.2.6
Requires-Dist: opencv-python-headless>=4.10
Requires-Dist: pandas>=2.3.1
Requires-Dist: pero>=0.18.0
Requires-Dist: pillow>=10.0.0
Requires-Dist: pycairo>=1.28.0
Requires-Dist: pyyaml>=6.0
Requires-Dist: scikit-learn>=1.7.0
Requires-Dist: scipy>=1.15.3
Requires-Dist: torch==2.8.0
Requires-Dist: torchvision==0.23.0
Requires-Dist: tqdm>=4.67.1
Provides-Extra: explore
Requires-Dist: renumics-spotlight>=1.6; extra == 'explore'
Provides-Extra: llm
Requires-Dist: anthropic>=0.30.0; extra == 'llm'
Requires-Dist: google-genai>=1.0.0; extra == 'llm'
Requires-Dist: openai>=1.0.0; extra == 'llm'
Description-Content-Type: text/markdown

# Concept Benchmark

[![python](https://img.shields.io/badge/python-3.10%2B-blue)](https://www.python.org)
[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/logo.svg" width="400" alt="Concept Benchmark logo">
</p>

**Concept Benchmark** is a Python package for generating synthetic datasets to benchmark [concept bottleneck models](https://arxiv.org/abs/2007.04612) (CBMs). It provides datasets with fully-specified ground-truth concept labels, letting you vary concept granularity, annotation quality, and the labeling rule — then measure exactly how each factor affects model performance and the value of interventions.

The package includes two benchmarks:

- **Robot Classification** — a decision-support task where a human corrects concept predictions to improve accuracy. Available as image and text modalities.
- **Sudoku Validation** — an automation task where the model handles routine cases and defers uncertain ones. Demonstrates selective classification and AND-fragility of concepts.

## Table of Contents

1. [Installation](#installation)
2. [Quick Start](#quick-start)
3. [Benchmarks](#benchmarks)
4. [Benchmark Your Own Model](#benchmark-your-own-model)
5. [Interventions and Alignment](#interventions-and-alignment)
6. [Reproducing the Paper](#reproducing-the-paper)
7. [Citation](#citation)

## Installation

The package requires the **cairo** graphics library. Install it first:

```bash
# macOS
brew install cairo pkg-config

# Ubuntu / Debian
sudo apt-get install libcairo2-dev pkg-config python3-dev

# Fedora / RHEL
sudo dnf install cairo-devel pkg-config python3-devel
```

Then install the package:

```bash
pip install concept-benchmark
```

**Dataset generation, metrics, and plots** work out of the box with `pip install`. **Model training and interventions** (`experiments/` package and the pipelines in `scripts/`) require cloning the repo:

```bash
git clone https://github.com/ustunb/concept-benchmark.git
cd concept-benchmark
uv sync
```

Verify the installation:

```bash
python3 -c "import concept_benchmark; print(concept_benchmark.__version__)"
```

The datasets of the paper are also on the Hugging Face Hub ([`robots-true-concepts`](https://huggingface.co/datasets/juliannski/robots-true-concepts), [`robots-human-concepts`](https://huggingface.co/datasets/juliannski/robots-human-concepts), [`sudoku`](https://huggingface.co/datasets/juliannski/sudoku)):

```python
# pip install datasets
from datasets import load_dataset
ds = load_dataset("juliannski/robots-human-concepts")
```

<details>
<summary><b>Optional: CEM, ProbCBM, and ECBM Baselines</b></summary>

The repo supports three additional CBM families beyond the standard CBM/DNN:

- **CEM** — Concept Embedding Model (`--cbm-family cem`)
- **ProbCBM** — Probabilistic Concept Bottleneck Model (`--cbm-family probcbm`)
- **ECBM** — Energy-based Concept Bottleneck Model (`--cbm-family ecbm`)

**ECBM** is included in the repo and works out of the box (it follows the authors' code). **CEM and ProbCBM** require the official [`mateoespinosa/cem`](https://github.com/mateoespinosa/cem) package — install it with:

```bash
./scripts/install_cem_repo.sh
```

If you prefer the manual path:

```bash
git clone https://github.com/mateoespinosa/cem.git third_party/cem
python -m pip install "pytorch-lightning>=1.6,<2.0" "torchmetrics<1.0"
python -m pip install -r third_party/cem/requirements.txt
python -m pip install -e third_party/cem
```

Once installed, use `--cbm-family` to select the model in the robot and sudoku pipelines (the text pipeline trains the CBM only):

```bash
# Train and evaluate a CEM on the robot benchmark
python scripts/robot_pipeline.py --seed 1014 --cbm-family cem

# Train and evaluate a ProbCBM on the robot benchmark
python scripts/robot_pipeline.py --seed 1014 --cbm-family probcbm

# Train and evaluate an ECBM on the robot benchmark
python scripts/robot_pipeline.py --seed 1014 --cbm-family ecbm

# Any family on sudoku
python scripts/sudoku_pipeline.py --seed 171 --cbm-family cem
python scripts/sudoku_pipeline.py --seed 171 --cbm-family ecbm
```

Key configuration options (fields of the config dataclass):

| Parameter | Default | Description |
|---|---|---|
| `cem_emb_size` | 16 | Concept embedding dimension for CEM |
| `cem_training_intervention_prob` | 0.25 | Intervention probability during CEM training |
| `training_mode` | `independent` | How the concept and label parts are trained: `independent`, `sequential` or `joint` (CLI: `--training-mode`) |
| `probcbm_n_samples_inference` | 50 | Monte Carlo samples during ProbCBM inference |

Notes:

- Existing CBM / DNN / conceptual-safeguards paths do not require these packages.
- Every family runs on the robot and sudoku benchmarks.
- Alignment remains on the original `cbm` path.

</details>

## Quick Start

A concept bottleneck model (CBM) first predicts interpretable *concepts* from inputs (e.g., "has pointy feet"), then uses those concepts to predict the final label. This two-stage design lets users inspect and correct the model's reasoning at test time — an operation called an *intervention*. This package gives you synthetic datasets where the ground-truth concepts are known, so you can measure exactly how much interventions help under different conditions.

**Robot** — classify fictional robots (**Glorps** vs. **Drents**) from body features:

```python
from concept_benchmark.robots import DatasetGenerator

dataset = DatasetGenerator(
    seed=1014,
    concept_preset="foot_subtypes",  # expand foot_shape into subtypes (default: "ground_truth")
    render_images=True,              # set False to skip rendering for quick exploration
).generate_splits()                  # the train/val/test split of the paper

print(dataset.train.C.shape)   # (3800, 12) — concept annotations
print(dataset.train.concepts)
# ['head_shape', 'body_shape', 'has_knees', 'has_antennae', 'ears_shape',
#  'mouth_type', 'foot_shape_flat_trapezoid', 'foot_shape_flat_square',
#  'foot_shape_flat_5sided', 'foot_shape_pointy_rounded',
#  'foot_shape_pointy_square', 'foot_shape_pointy_4sided']
```

`generate()` returns the unsplit dataset with every concept, for you to drop concepts and split as you choose (see [Post-processing](#post-processing)).

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/robot_samples.png" width="600" alt="Sample Glorps and Drents with concept annotations">
</p>

**Sudoku** — determine whether a 9×9 board is valid. 27 concepts capture row, column, and block validity:

```python
from concept_benchmark.sudoku import DatasetGenerator

dataset = DatasetGenerator(
    seed=171,             # reproducibility
    n_boards=1000,        # number of boards
    max_cell_swaps=9,     # corruptions applied to each invalid board, 1 to 9 (each swaps or duplicates digits)
    valid_board_ratio=0.5,  # fraction of valid boards
    render_images=False,  # set True to generate board images (slower)
).generate_splits()       # 60/20/20, stratified on the label

print(dataset.train.C.shape)   # (600, 27) — 27 concept annotations
print(dataset.train.concepts)  # ['row_valid_1', 'row_valid_2', ..., 'block_valid_9']
```

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/sudoku_samples.png" width="600" alt="Sample Sudoku boards generated by the benchmark">
</p>

For complete walkthroughs including training and evaluation, see [`examples/robot_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/robot_pipeline_example.py) and [`examples/sudoku_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/sudoku_pipeline_example.py).

## Benchmarks

### Robot Classification

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/robot_concepts.png" width="400" alt="Robot with annotated concepts">
</p>

#### Parameters

All parameters below can be passed to `DatasetGenerator(...)` (imported from `concept_benchmark.robots`). Common parameters apply to both image and text modalities; scope-specific parameters are ignored when the other modality is selected.

```python
from concept_benchmark.robots import DatasetGenerator, LabelFormula, F

dataset = DatasetGenerator(
    # ── Common (image + text) ──
    seed=1014,                       # random seed (default: 1014; the text pipeline uses 1337)
    data_type="image",               # "image" (default) or "text"
    concepts={                           # 9 features (default: ROBOT_CONCEPTS)
        "head_shape": ["square", "round"],
        "body_shape": ["square", "round"],
        "has_knees": ["false", "true"],
        "has_elbows": ["false", "true"],
        "has_antennae": ["false", "true"],
        "ears_shape": ["square", "triangle"],
        "mouth_type": ["closed", "open"],
        # the two shapes list their subtypes; each becomes one binary concept (round/edgy, flat/pointy)
        # unless it is named in expand_concepts
        "hand_shape": ["round_circle", "round_oval", "round_oval2",
                       "edgy_triangle", "edgy_square", "edgy_trapezoid"],
        "foot_shape": ["flat_trapezoid", "flat_rounded", "flat_square", "flat_5sided", "flat_lshaped",
                       "pointy_trapezoid", "pointy_rounded", "pointy_square", "pointy_3sided", "pointy_4sided"],
    },
    label_rule="balanced",           # "balanced" (default) or "sparse"; see Labeling rules below
    label_formula=None,              # or your own LabelFormula (see below), which replaces the rule's formula
    concept_preset="foot_subtypes",  # "ground_truth" or "foot_subtypes" (expands foot_shape into subtypes)
    renders_per_robot=4,             # samples per unique robot config (image: 4, text: 1)
    expand_concepts=["foot_shape"],                 # which features expand into subconcepts
    # ── Image-only (data_type="image") ──
    image_size="medium",             # "small" (8px), "medium" (32px), or "large" (600px)
    color_mode="color",              # "color" or "grayscale"
    render_images=True,              # set False to skip rendering PNGs (faster)
    # ── Text-only (data_type="text") ──
    template_complexity="high",      # template complexity level
).generate()
```

#### Labeling rules

A robot is a Glorp with probability `σ(4.2 × score)`, where the score comes from one of two rules:

| Rule | Score | What it models |
|------|-------|----------------|
| **balanced** (default) | `6·[mouth closed] + 6·[body round] + 6·[head round] + 6·[antennae] + 6·[ears triangle] + 8·[foot pointy] − 3·[knees] − 2·[elbows] − 16.5` | No single concept decides the label and both classes are equally likely. `has_elbows` drives the label but is not a concept, so it cannot be intervened on; its dot is drawn on every robot below 120 px, so it cannot be read from the 32 px images either. |
| **sparse** | `5·[mouth closed] + 8·[foot pointy] − 5·[knees] + 2` | Three concepts decide the label and 87.5% of robots are Glorps. Models a task where the class of interest is rare. |

Each rule also sets which foot subtypes the training split of `generate_splits()` holds: six of the ten subtypes, at 30%/10% shares under the balanced rule and 49%/0.5% under the sparse rule (`concept_benchmark.config.ROBOT_LABEL_RULES`). To use your own rule, pass a `LabelFormula`:

```python
from concept_benchmark.robots import DatasetGenerator, LabelFormula, F

dataset = DatasetGenerator(
    seed=1014,
    label_formula=LabelFormula(
        score=4 * F("mouth_type").closed + 6 * F("body_shape").round - 3 * F("has_knees").true - 2,
        temperature=4.2,              # P(Glorp) = σ(4.2 × score)
        stochastic=True,
    ),
).generate()
```

#### Inspecting the data

```python
dataset.train.to_dataframe().head(2)
#    head_shape  body_shape  has_knees  ...  foot_shape_pointy_4sided  label  class
# 0           0           0          0  ...                         0      1  glorp
# 1           0           0          0  ...                         0      1  glorp
```

For interactive browsing with [Renumics Spotlight](https://github.com/Renumics/spotlight) (`pip install concept-benchmark[explore]`):

```python
dataset.train.explore()  # opens in the browser
```

#### Post-processing

After generating, you can drop concepts and split into train/val/test:

```python
from concept_benchmark.transforms import ConceptDropGenerator

# Remove concepts from the concept set
dataset = ConceptDropGenerator(dataset, ["has_elbows", "hand_shape"]).generate()

# Split into train/val/test
dataset.sample(test_size=10000, val_size=0.2, train_size=3800, seed=1014)
```

`generate_splits()` does both steps for the paper's setup. Its split requires a minimum share of each training foot subtype through `sampling_constraints`, which you can also pass yourself:

```python
from concept_benchmark.config import PRESET_EXCLUDED_CONCEPTS

dataset = DatasetGenerator(seed=1014, concept_preset="foot_subtypes").generate()
dataset.sample(
    test_size=10000, val_size=0.2, train_size=3800, seed=1014,
    sampling_constraints=[
        {"concepts": {"foot_shape_pointy_4sided": 1}, "min_fraction": 0.30},
    ],
)
# split first: the constraints name subtypes that the preset drops
dataset.drop_concepts(PRESET_EXCLUDED_CONCEPTS["foot_subtypes"])
```

#### Pipeline

```bash
python scripts/robot_pipeline.py --seed 1014 --concept-preset foot_subtypes
python scripts/robot_pipeline.py --seed 1014 --concept-preset foot_subtypes --cbm-family cem
python scripts/robot_pipeline.py --seed 1014 --concept-preset foot_subtypes --cbm-family probcbm

# The rare-class rule
python scripts/robot_pipeline.py --seed 1014 --label-rule sparse

# Add plot to generate figures from results
python scripts/robot_pipeline.py --seed 1014 --stages setup cbm dnn intervene align collect plot
```

| Option | Description |
|--------|-------------|
| `--concept-preset` | `ground_truth` (7 true concepts) or `foot_subtypes` (12 human concepts) |
| `--label-rule` | `balanced` (default) or `sparse` |
| `--cbm-family` | `cbm`, `cem`, `probcbm` or `ecbm` |
| `--concept-sources` | Who annotates the concepts: `ground_truth`, `human_concepts`, `noisy_human_concepts`, `machine_annotation`, `llm_concepts`, `clip_concepts` |
| `--intervention-sources` | Who answers at test time: `perfect`, `expert`, `llm`, or `self` (the model's own predictions) |
| `--budgets` | Intervention budgets, e.g. `1 3 max` |
| `--intervention-encoding` | What a label-free CBM reads after an intervention: `binary` (default), `percentile` or `binary_revealed` |
| `--dump-interventions DIR` | Save what was asked and answered for each budget (input to `plot_concept_report`) |

Run `python scripts/robot_pipeline.py --help` for the full list of options (including training and LLM parameters).

#### Training and evaluation

Quickstart: one command trains the paper's models for one seed and draws the figure below into `results/figures/`:

```bash
python scripts/robot_pipeline.py --seed 1014 --concept-preset ground_truth --stages setup cbm dnn intervene collect plot
```

The same in code (requires cloning the repo); each call is a block the pipelines are built from, so swap in your own model or your own results:

```python
import pandas as pd
from concept_benchmark.robots import DatasetGenerator
from concept_benchmark.evaluation import accuracy, plot_intervention_curve
from experiments.evaluate import intervention_table, predict_labels, train_cbm, train_dnn
from experiments.models import RobotClassifierCNN

tables = []
for preset, name in (("ground_truth", "CBM, true_concepts"), ("foot_subtypes", "CBM, human_concepts")):
    dataset = DatasetGenerator(seed=1014, concept_preset=preset).generate_splits()
    cbm = train_cbm(dataset.train, dataset.val, seed=1014)
    tables.append(intervention_table(cbm, dataset.test, budgets=(1, 3, "max"), seed=1014).assign(model=name))
results = pd.concat(tables)
print(results.pivot(index="model", columns="budget", values="accuracy").round(3))

dnn = train_dnn(lambda: RobotClassifierCNN(input_size=32), dataset.train, dataset.val, seed=1014)  # image -> label
dnn_accuracy = accuracy(predict_labels(dnn, dataset.test), dataset.test.y)

fig, ax = plot_intervention_curve(results, group="model", baseline_accuracy=dnn_accuracy)
fig.savefig("robot_example.png", dpi=150, bbox_inches="tight")
```

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/robot_example.png" width="480" alt="Accuracy against the intervention budget for a CBM with true and with human concepts, and the DNN, one run">
</p>

One run, about ten minutes on a laptop. Over the 10 seeds of the paper the CBM reaches 84.5% (true concepts) and
77.6% (human concepts) before interventions, 92.0% and 85.7% after, and the DNN 88.0%.

For a complete walkthrough including interventions and alignment, see [`examples/robot_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/robot_pipeline_example.py).

### Sudoku Validation

This benchmark targets automation settings where the system handles routine cases and defers uncertain ones to a human. The task is to determine whether a 9×9 Sudoku board is valid, i.e., contains the digits 1–9 exactly once in each row, column, and block. The 27 concepts correspond to the validity of each row, column, and 3×3 block. A board is valid if and only if all 27 concepts are true (AND structure), so a single violated concept is enough to invalidate the board. When the model abstains, a human can verify specific concepts (e.g., "is row 5 valid?") to resolve the uncertainty.

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/sudoku_handwritten.png" width="400" alt="Sudoku board with handwritten digits and concept annotations">
</p>

#### Parameters

```python
from concept_benchmark.sudoku import DatasetGenerator

dataset = DatasetGenerator(
    seed=171,                  # random seed
    data_type="image",         # "image" (renders board PNGs) or "tabular" (digit vectors)
    render_images=True,        # set False to skip rendering PNGs (faster, image only)
    block_size=3,              # block size (3 = standard 9×9 board)
    n_boards=1000,             # number of boards to generate
    max_cell_swaps=9,          # corruptions applied to each invalid board, 1 to 9 (each swaps or duplicates digits)
    valid_board_ratio=0.5,     # fraction of valid boards
    # ── Rendering (image only) ──
    font_style="handwritten",  # "handwritten" or "printed"
    font_size=25,              # printed-digit font size at 50 px per cell; every size is this board scaled
    cell_px=50,                # cell size in pixels
    cell_margin_px=2,          # cell margin in pixels
    gridline_px=2,             # grid line width in pixels
    block_border_px=5,         # block border width in pixels
).generate()
```

#### Inspecting the data

```python
df = dataset.train.to_dataframe()
show_cols = list(dataset.train.concepts[:5]) + ["label"]
print(df[show_cols])
#      row_valid_1  row_valid_2  row_valid_3  row_valid_4  row_valid_5  label
# 0              1            1            1            1            1      1
# ..           ...          ...          ...          ...          ...    ...
# 301            1            0            0            1            1      0
```

#### Pipeline

```bash
python scripts/sudoku_pipeline.py --seed 171
python scripts/sudoku_pipeline.py --seed 171 --cbm-family cem

# Harder concept detection: 10 pixels per cell instead of 50
python scripts/sudoku_pipeline.py --seed 171 --cell-px 10

# Save each model's confidence for plot_confidence (optional stage)
python scripts/sudoku_pipeline.py --seed 171 --stages cs intervene selective diagnose plot
```

| Option | Description |
|--------|-------------|
| `--cbm-family` | `cbm`, `cem`, `probcbm` or `ecbm` |
| `--cell-px` | Pixels per cell (50 by default; at 10 the recognizer misreads a digit on half the boards) |
| `--target-accuracy` | Selective accuracy that kept predictions must reach (0.90 by default; the paper uses 0.95) |
| `--stages` | `setup ocr cs dnn intervene selective align collect plot`, plus the optional `diagnose` |

Run `python scripts/sudoku_pipeline.py --help` for the full list of options (including training, intervention, and evaluation parameters).

#### Training and evaluation

Quickstart: one command trains the paper's models on the handwritten boards of one seed (10 px per cell, where the recognizer misreads a digit on half the boards) and draws the figure below:

```bash
python scripts/sudoku_pipeline.py --seed 171 --cell-px 10 --target-accuracy 0.95 --stages setup ocr cs dnn intervene selective collect plot
```

The same in code, on the digits of each board instead of its image (requires cloning the repo); the blocks are the ones the pipeline is built from:

```python
from concept_benchmark.sudoku import DatasetGenerator
from concept_benchmark.evaluation import plot_automation
from experiments.evaluate import automation_table, coverage_at_target, train_cbm, train_dnn
from experiments.models import GroupPoolingConceptSudokuCNN, SudokuValidatorCNN

dataset = DatasetGenerator(
    seed=171, n_boards=1000, max_cell_swaps=9, data_type="tabular",  # the digits of each board, not its image
).generate_splits()

# CBM: board -> 27 validity concepts -> valid; DNN: board -> valid
cbm = train_cbm(dataset.train, dataset.val, detector=GroupPoolingConceptSudokuCNN,
                epochs=100, patience=20, seed=171, should_propagate=True)
dnn = train_dnn(SudokuValidatorCNN, dataset.train, dataset.val, seed=171)

# both abstain until they are right on 95% of the boards they keep; a human checks up to k concepts of a board the CBM would defer
results = automation_table(cbm, dataset.val, dataset.test, budgets=(1, 3, "max"), target_accuracy=0.95, seed=171)
_, dnn_coverage = coverage_at_target(dnn, dataset.val, dataset.test, target_accuracy=0.95)
print(results[["budget", "coverage_after", "total_concept_checks"]], f"\nDNN coverage: {dnn_coverage:.3f}")

fig, ax = plot_automation(results, n_instances=dataset.test.n, n_concepts=27,
                          baseline_coverage=dnn_coverage, target_accuracy=0.95)
fig.savefig("sudoku_example.png", dpi=150, bbox_inches="tight")
```

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/sudoku_example.png" width="480" alt="Coverage and net work automated against the intervention budget for the CBM and the DNN, one run">
</p>

One run of the pipeline command. At 10 px per cell the recognizer misreads a digit on about half the boards, so the
CBM answers 64% of the boards on its own (the DNN 7%). Checking up to 3 concepts on the boards it defers raises the
boards answered to 77% and the net work automated to 73%; checking all 27 raises the boards answered to 95% but costs
more work than it recovers, and the net work automated falls to 59%. The abstention threshold is fitted on the
validation boards; on the test boards of this run the answered predictions are 95% correct without checks and 94%
with all 27, since a misread digit makes the model confidently wrong on a few boards that it never defers. With the
digits instead of the images, as in the code block, the CBM keeps every board.

For a complete walkthrough including selective classification and interventions, see [`examples/sudoku_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/sudoku_pipeline_example.py).

<details>
<summary><h2 style="display:inline">Benchmark Your Own Model</h2></summary>

This guide shows how to evaluate your own concept bottleneck model on the benchmarks provided by this package. All examples below use the robot benchmark, but the same approach works for sudoku.

> **Prerequisite:** You need the full repository (not just `pip install concept-benchmark`) to run the pipeline scripts and examples.

### Getting data for your model

Generate a dataset as shown in the [Quick Start](#quick-start), then access the splits:

```python
train, val, test = dataset.train, dataset.val, dataset.test
```

Each split is a `ConceptDatasetSample` with these attributes:

| Attribute | Type | Description |
|-----------|------|-------------|
| `X` | `np.ndarray` | Input features (images or tabular) |
| `C` | `np.ndarray` | Concept labels `(N, n_concepts)` |
| `y` | `np.ndarray` | Target labels `(N,)` |
| `concepts` | `list[str]` | Concept names |
| `n_concepts` | `int` | Number of concepts |
| `classes` | `list[str]` | Class names |
| `n` | `int` | Number of samples |

Access formats:

```python
# NumPy arrays; X (also .inputs) holds the image file names, the texts or the feature rows
X_train, C_train, y_train = train.X, train.C, train.y

# PyTorch DataLoader
loader = train.loader(batch_size=64, shuffle=True)
for x_batch, c_batch, y_batch in loader:
    ...

# Pandas DataFrame
df = train.to_dataframe()
```

#### Splitting

`sample()` splits the dataset into train/val/test. Sizes can be absolute counts or fractions:

```python
# Absolute counts
dataset.sample(test_size=10000, val_size=1000, train_size=3800, seed=42)

# Fractions (of total dataset size)
dataset.sample(test_size=0.2, val_size=0.2, seed=42)

# Stratified — preserves class proportions in each split
dataset.sample(test_size=0.2, val_size=0.2, stratify=dataset.y, seed=42)

# Group-based — no group appears in multiple splits (group_ids: one id per row, e.g. the robot's identity)
dataset.sample(test_size=0.2, val_size=0.2, groups=group_ids, seed=42)

# Skewed training set — ensure min-fraction of specific concept patterns
dataset.sample(
    test_size=10000, val_size=0.2, train_size=3800,
    sampling_constraints=[{"concepts": {"my_concept": 1}, "min_fraction": 0.3}],
    seed=42,
)
```

You can re-split at any time by calling `sample()` again.

#### Concept missingness

Simulate missing concept annotations (e.g., incomplete labels from crowdsourcing). Use the generator transforms to produce a new dataset with missingness applied:

```python
from concept_benchmark.transforms import ConceptMissingnessGenerator

dataset.sample(test_size=0.2, val_size=0.2, seed=42)

# MCAR: each concept label independently missing with probability p
dataset = ConceptMissingnessGenerator(dataset, p=0.2, mechanism="mcar", seed=99).generate()

# MNAR: missingness depends on concept value (present concepts more likely observed)
dataset = ConceptMissingnessGenerator(
    dataset, p=0.2, mechanism="mnar", seed=99,
    mnar_config={"present_prob": 0.8, "absent_prob": 0.1},
).generate()
```

Similarly, `ConceptNoiseGenerator` adds symmetric or asymmetric label flips, and `LabelNoiseGenerator` corrupts target labels:

```python
from concept_benchmark.transforms import ConceptNoiseGenerator, LabelNoiseGenerator

dataset = ConceptNoiseGenerator(dataset, p=0.1, seed=99).generate()
dataset = LabelNoiseGenerator(dataset, p=0.05, seed=99).generate()
```

### Wrapping your concept detector

The intervention runner requires a `ConceptDetector` subclass. Wrap your model:

```python
from experiments.models import ConceptDetector

class MyConceptDetector(ConceptDetector):
    def __init__(self, my_model):
        super().__init__()
        self._my_model = my_model

    def predict_proba(self, dataset, **kwargs):
        """Must return (N, n_concepts) float array in [0, 1]."""
        return self._my_model.predict_concept_probs(dataset.X)
```

**Key point:** Override `predict_proba()` — it receives a `ConceptDatasetSample`, not raw arrays. Access inputs via `dataset.X`. The base class `predict()` calls `predict_proba()` and thresholds at 0.5 automatically.

#### Using a PyTorch module directly

If your model is already a PyTorch `nn.Module`, you can pass it directly instead of subclassing. Your module's `forward()` must:

- Accept a batched input tensor (e.g. `(B, 3, 32, 32)` for images)
- Return `(B, n_concepts)` **raw logits** (pre-sigmoid) — sigmoid is applied internally by `predict()`

The return value can also be a tuple (first element is used) or a dict with a `"logits"` key.

```python
cd = ConceptDetector(model=my_pytorch_module)
cd.fit(train, val, fit_params={"epochs": 50, "lr": 1e-3})
```

You can also split your model into a backbone + concept head using the `embedding_model` parameter. The detector will probe the backbone's output shape and attach an MLP head automatically:

```python
cd = ConceptDetector(embedding_model=my_backbone)
cd.fit(train, val, fit_params={"epochs": 50, "lr": 1e-3})
```

### Wrapping your label predictor

Subclass `FrontEndModel` and override `predict()` and `predict_proba()`:

```python
from experiments.models import FrontEndModel

class MyFrontEnd(FrontEndModel):
    def __init__(self, my_classifier):
        super().__init__()
        self._clf = my_classifier

    def predict(self, C):
        """C is (N, n_concepts) binary 0/1. Returns (N,) int labels."""
        return self._clf.predict(C)

    def predict_proba(self, C):
        """C is (N, n_concepts) binary 0/1. Returns (N, n_classes) probs."""
        return self._clf.predict_proba(C)
```

**Key point:** `C` is already binarized at 0.5 — binary 0/1 values, not probabilities.

For a simple logistic regression baseline, the built-in `FrontEndModel()` works out of the box:

```python
fe = FrontEndModel()
fe.fit(train.C, train.y)
```

### Assembling and evaluating

Combine your concept detector and label predictor into a `ConceptBasedModel`:

```python
import numpy as np
from experiments.models import ConceptBasedModel

cbm = ConceptBasedModel(
    concept_detector=MyConceptDetector(my_concept_model),
    label_predictor=MyFrontEnd(my_classifier),
)

predictions = cbm.predict(test)
accuracy = np.mean(predictions == test.y)
print(f"CBM accuracy: {accuracy:.4f}")
```

For running interventions and alignment on your model, see the [Interventions and Alignment](#interventions-and-alignment) section and [`examples/robot_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/robot_pipeline_example.py).

### Metrics and Plots

The `concept_benchmark.evaluation` module provides standalone metric functions and plotting utilities for evaluating CBMs:

```python
from concept_benchmark.evaluation import (
    accuracy, gain, selective_accuracy, coverage,
    plot_intervention_curve, plot_intervention_heatmap, plot_concept_report,
)
```

**Metrics:**

| Function | Description |
|----------|-------------|
| `accuracy(y_pred, y_true)` | Fraction of correct predictions |
| `delta_accuracy(y_after, y_before, y_true)` | Improvement in accuracy from interventions |
| `gain(y_pred, y_true, baseline_accuracy)` | Accuracy gain over a baseline model (e.g. DNN) |
| `selective_accuracy(y_pred, y_true, confidence, threshold)` | Accuracy on non-abstained samples |
| `coverage(confidence, threshold)` | Fraction of samples where the model does not abstain |
| `PlattScaling().fit(prob_positive, y_true)` | Calibrates a label probability on validation predictions, as the abstention rule requires |
| `abstention_threshold(y_true, prob_positive, target_accuracy)` | The paper's abstention rule: the threshold at which the kept predictions reach a target accuracy, and their coverage; fit it on validation predictions |
| `selective_at(y_true, prob_positive, abstention_threshold, 0.5)` | Selective accuracy and coverage under that threshold |
| `intervention_metrics(mask, concepts_before, concepts_after, y_prob_before, y_prob_after, y_true, accuracy_before)` | What an intervention did: accuracy, gain, predictions and concepts touched |
| `net_work_automated(confidence, threshold, n_interventions, n_concepts)` | Net fraction of work automated after intervention cost |

**Blocks that need a model** live in `experiments.evaluate` (requires cloning the repo); the pipelines are built from them:

| Function | Returns |
|----------|---------|
| `train_cbm(train, validation, seed=..., detector=...)` | The paper's CBM: concept detector plus logistic label predictor |
| `train_dnn(model, train, validation, seed=...)` | A binary classifier trained with early stopping |
| `intervention_table(cbm, test, budgets=(1, 3, "max"), seed=...)` | Accuracy at each budget of corrected concepts (the decision-support table) |
| `automation_table(cbm, validation, test, budgets=(1, 3, "max"), target_accuracy=0.95, seed=171)` | Coverage and checks at each budget under the paper's abstention protocol, label probability calibrated on validation (the automation table) |
| `coverage_at_target(model, validation, test, target_accuracy)` | Selective accuracy and coverage of any model at a target |
| `predict_labels(model, dataset)`, `predict_proba_positive(model, dataset)` | Predictions of a DNN or a CBM |

**Plots** take the results tables that the pipelines write (or your own, with the same columns). Rows from several runs are averaged and drawn with a standard-error band, so pass the concatenated results of all your seeds.

Outcome plots show *what* happens:

| Function | Shows |
|----------|-------|
| `plot_intervention_curve(results, group=..., baseline_accuracy=...)` | The paper's decision-support panel: accuracy against the intervention budget *k*, one line per model or concept set, with the DNN as a dashed line |
| `plot_intervention_heatmap(results)` | Change in accuracy from interventions for each model, concept set and intervention source |
| `plot_alignment_comparison(results)` | Constrained against unconstrained model, before and after interventions |
| `plot_automation(results, n_instances, n_concepts, baseline_coverage=..., target_accuracy=...)` | The paper's automation panel: Coverage and NetWorkAutomated against the intervention budget, with the DNN's coverage and the target in the title |
| `plot_selective_classification(dnn_metrics, cbm_metrics)` | DNN against CBM on selective accuracy and coverage |
| `plot_concept_discovery(ideal_df, subconcept_df, dnn_accuracy)` | True against human concepts at each budget |
| `plot_model_comparison(results, dnn_accuracy)` | Models × concept sets at each budget |

Diagnostic plots show *why*:

| Function | Shows | Read it as |
|----------|-------|------------|
| `plot_concept_report(mask, concept_proba, concept_answers, concepts_true, concept_names)` | Per concept: detector accuracy, share of interventions, intervener accuracy | An intervener helps only if it is accurate on the concepts the model asks about |
| `plot_answer_reliance(results)` | Change in accuracy when interventions supply the model's own answers against the true values | Similar bars mean the model does not rely on its concept values |
| `plot_confidence(prob_positive, y_true, abstention_threshold)` | Predicted probabilities by class, with the band where the model abstains | Instances inside the band are deferred no matter how many concepts are checked |

```python
import pandas as pd
from concept_benchmark.evaluation import plot_intervention_curve, plot_intervention_heatmap

# one results file per seed, as written by scripts/robot_pipeline.py
results = pd.concat(
    # results_by_seed: {seed: path to a pipeline's results CSV}; dnn_accuracies: one DNN accuracy per seed
    pd.read_csv(path).assign(seed=seed) for seed, path in results_by_seed.items()
)
fig, ax = plot_intervention_curve(results, group="model_family", baseline_accuracy=dnn_accuracies)
fig, ax = plot_intervention_heatmap(results)
```

All plot functions return `(fig, ax)`. The pipelines' `plot` stage draws the ones that apply to a run. The examples below use the 10-seed results of the paper ([`scripts/paper/make_readme_figures.py`](https://github.com/ustunb/concept-benchmark/blob/main/scripts/paper/make_readme_figures.py)).

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/intervention_heatmap.png" width="800" alt="Change in accuracy from interventions per model, concept set and intervention source">
</p>

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/concept_report.png" width="420" alt="Per-concept detector accuracy, share of interventions and intervener accuracy">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/answer_reliance.png" width="380" alt="Change in accuracy with the model's own answers against the true values">
</p>

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/automation.png" width="400" alt="Coverage and net work automated against concept checks">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/confidence.png" width="400" alt="Predicted probability of a valid board with the abstention band">
</p>

</details>

<details>
<summary><h2 style="display:inline">Interventions and Alignment</h2></summary>

### Interventions

Interventions are the core benefit of concept bottleneck models: at test time, a user (or automated system) can inspect and correct the model's concept predictions before the final label is determined.

#### Oracle interventions (manual approach)

The simplest way to run interventions is to directly manipulate concept predictions. After training a `ConceptDetector` and `FrontEndModel`, the workflow is:

1. Get concept probabilities from the detector
2. Identify the most uncertain concepts per sample
3. Replace them with ground-truth values
4. Re-predict with the label model

```python
import numpy as np
from experiments.models import ConceptDetector, FrontEndModel

# cd and fe are a trained concept detector and label predictor, e.g. cbm.concept_detector and
# cbm.label_predictor of a CBM from experiments.evaluate.train_cbm

# Step 1: Get concept probabilities
concept_probs = cd.predict_proba(test)

# Step 2-3: For each sample, replace the k most uncertain concepts
# with ground-truth values
for k in [1, 3]:
    C_intervened = concept_probs.copy()
    uncertainty = np.abs(concept_probs - 0.5)  # distance from decision boundary
    for i in range(len(test)):
        most_uncertain = np.argsort(uncertainty[i])[:k]
        C_intervened[i, most_uncertain] = test.C[i, most_uncertain]

    # Step 4: Threshold to binary and predict
    preds = fe.predict((C_intervened > 0.5).astype(np.float32))
    acc = np.mean(preds == test.y)
    print(f"k={k}: accuracy={acc:.4f}")
```

#### Using the intervention API

For more complex intervention scenarios (budgets, strategies, batched evaluation), use the `ConceptInterventionRunner`:

```python
import numpy as np
from experiments.models import ConceptBasedModel
from experiments.intervention import ConceptInterventionRunner, InterventionConfig
from experiments.kflip import KFlipInterventionStrategy

# Combine detector and label predictor into a CBM
cbm = ConceptBasedModel(concept_detector=cd, label_predictor=fe)

# Configure the intervention
config = InterventionConfig(
    per_instance_budget=3,  # correct up to 3 concepts per sample
    score_threshold=0.2,          # intervene when the label would change
                                  # with probability 0.2 or more
)

# Run interventions
runner = ConceptInterventionRunner(model=cbm)
strategy = KFlipInterventionStrategy()
result = runner.run(strategy, config, test)

# InterventionResult contains y_prob_before/after and y_pred_after
acc_before = np.mean(np.argmax(result.y_prob_before, axis=1) == test.y)
acc_after = np.mean(result.y_pred_after == test.y)
print(f"Accuracy before: {acc_before:.4f}")
print(f"Accuracy after:  {acc_after:.4f}")
print(f"Concepts corrected: {result.mask.sum()}")
```

##### Key classes

- **`InterventionConfig`** — controls intervention budgets, thresholds, and per-instance caps
- **`KFlipInterventionStrategy`** — the default strategy: evaluates all subsets of up to *k* concepts per sample and selects the intervention that maximizes predicted confidence
- **`ConceptInterventionRunner`** — coordinates intervention execution and before/after evaluation

#### Writing a custom strategy

You can implement your own intervention strategy by subclassing `InterventionStrategy` and implementing the `propose()` method.

##### The intervention flow

When `ConceptInterventionRunner.run()` is called, it:

1. Builds an `InterventionBatch` from the dataset (concept predictions + ground truth)
2. Calls `strategy.propose(model, batch, config)` → returns a `StrategyProposal`
3. Applies the proposal's `mask` to replace predicted concepts with ground truth
4. Re-predicts labels with the corrected concepts
5. Returns an `InterventionResult` with before/after predictions

##### Key data classes

**`InterventionBatch`** — the input your strategy receives:

| Field | Type | Description |
|-------|------|-------------|
| `C_pred` | `(N, C) float` | Predicted concept probabilities |
| `C_true` | `(N, C) float` | Ground-truth concept values |
| `y_true` | `(N,) int` or `None` | True labels (optional) |
| `n_samples` | `int` | Number of samples |
| `n_concepts` | `int` | Number of concepts |

**`StrategyProposal`** — what your strategy returns:

| Field | Type | Description |
|-------|------|-------------|
| `mask` | `(N, C) bool` | `True` = replace prediction with ground truth |
| `ordering_used` | array or `None` | Concept order applied (optional) |
| `selected_instances` | array or `None` | Instance indices that received interventions |
| `details` | `dict` | Additional metadata |

##### Minimal example

Here's a strategy that intervenes on concepts closest to the 0.5 decision boundary:

```python
import numpy as np
from experiments.intervention import InterventionStrategy, StrategyProposal

class UncertaintyStrategy(InterventionStrategy):
    def __init__(self):
        super().__init__(name="uncertainty")

    def propose(self, model, batch, config):
        k = int(min(config.per_instance_limit(batch.n_concepts), batch.n_concepts))
        mask = np.zeros((batch.n_samples, batch.n_concepts), dtype=bool)

        # Rank concepts by uncertainty (closeness to 0.5)
        uncertainty = 0.5 - np.abs(batch.C_pred - 0.5)
        for i in range(batch.n_samples):
            top_k = np.argsort(uncertainty[i])[-k:]
            mask[i, top_k] = True

        return StrategyProposal(mask=mask)
```

Use it with the runner:

```python
result = runner.run(
    strategy=UncertaintyStrategy(),
    config=InterventionConfig(per_instance_budget=3, score_threshold=0.2),
    dataset=test,
)
```

##### The `prepare()` hook

Override `prepare()` if your strategy needs a validation pass before inference — for example, to precompute a global concept ordering:

```python
class MyStrategy(InterventionStrategy):
    def __init__(self):
        super().__init__(name="my_strategy")

    def prepare(self, model, batch, config):
        """Called once on the validation set before run()."""
        # Compute concept importance from validation data
        self._state["concept_order"] = compute_importance(model, batch)

    def propose(self, model, batch, config):
        order = self._state["concept_order"]
        # ... use precomputed order
```

Call `runner.prepare()` before `runner.run()` to trigger the hook:

```python
runner.prepare(strategy, config, validation_dataset=val)
result = runner.run(strategy, config, dataset=test)
```

#### Concept sources and intervention sources

The robot pipeline varies two things independently: who annotates the concepts a model is trained on, and who answers when the model asks about a concept at test time.

| Concept source | Concepts |
|----------------|----------|
| **ground_truth** | The 7 true concepts |
| **human_concepts** | 12 concepts as a human annotator would list them (six foot subtypes) |
| **noisy_human_concepts** | The same concepts, annotated with 20% label noise (annotators who disagree) |
| **machine_annotation** | The human concepts, scored by CLIP (label-free CBM) |
| **llm_concepts** | Concepts written by an LLM, scored by CLIP |
| **clip_concepts** | Single words chosen by CLIP, scored by CLIP |

| Intervention source | Answers |
|---------------------|---------|
| **perfect** | The true concept values — the upper bound |
| **expert** | A simulated expert, correct 80% of the time on every concept |
| **llm** | An LLM that answers each concept from the image (Gemini by default) |
| **self** | The model's own thresholded predictions — changes no value, so it isolates the effect of the intervention mechanism |

```bash
python scripts/robot_pipeline.py --seed 1014 --concept-preset foot_subtypes \
    --concept-sources human_concepts machine_annotation \
    --intervention-sources perfect expert self --budgets 1 3 max
```

LLM interventions need an API key (`--llm-api-key` or `GEMINI_API_KEY`); `--llm-cache-only` reuses saved answers.

#### Regimes

A regime names one pairing of concept source and intervention source, as in the first version of the benchmark:

| Regime | Concepts from | Corrected by | Description |
|--------|--------------|-------------|-------------|
| **baseline** | Human annotation | True values | Upper bound on the benefit of interventions |
| **expert** | Human annotation | Expert (80% accurate) | Realistic human annotator |
| **subjective** | Human annotation with 20% label noise | Expert (80% accurate) | Annotators who disagree on the concepts |
| **machine** | CLIP scores of the human concepts | Expert (80% accurate) | Automated annotation |
| **llm** | Concepts written by an LLM | LLM | Fully automated with an LLM |
| **clip** | Single words chosen by CLIP | LLM | Fully automated with CLIP |

Both robot pipelines accept `--regimes` as shorthand for the matching sources:

```bash
python scripts/robot_pipeline.py --seed 1014 --concept-preset foot_subtypes --regimes baseline expert subjective
python scripts/robot_text_pipeline.py --seed 1337 --regimes baseline expert subjective
```

For a complete end-to-end example with training, interventions (through the `intervention_table` block, which runs `ConceptInterventionRunner` with the paper's policy) and alignment, see [`examples/robot_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/robot_pipeline_example.py).

### Alignment

Alignment constraints force the label predictor's concept weights to match a user's prior expectations about concept-label relationships. For example, if a domain expert knows that "has knees" should positively predict the Glorp class, alignment constrains that weight to be positive during retraining.

#### Why alignment matters

In standard CBM training, the label predictor (logistic regression on concept activations) learns weights freely from data. This can produce **counterintuitive** weights — e.g., `has_knees` getting a *negative* weight even when knees truly indicate Glorp — because the model exploits correlations among imperfect concept predictions.

The paper shows that an alignment constraint can:

- **Raise** accuracy before interventions — the constrained model no longer relies on a concept its detector reads at chance.
- **Remove** the benefit of interventions — after every concept is corrected, the unconstrained model is the more accurate one.

The constraint closes the pathway through which a corrected concept reaches the label.

#### Usage

After training a `ConceptBasedModel`, use `run_alignment()` to retrain the frontend with sign constraints and compare:

```python
from experiments.utils import run_alignment

results = run_alignment(
    concept_based_model=cbm,
    train_dataset=train,
    test_dataset=test,
    monotonicity_constraints={"has_knees": 1},  # require a non-negative weight
)

print(f"Original accuracy: {results['original_accuracy']:.4f}")
print(f"Aligned accuracy:  {results['aligned_accuracy']:.4f}")
print(f"Accuracy change:   {results['accuracy_change']:+.4f}")
```

The `monotonicity_constraints` dict maps concept names to their required sign: `+1` for positive weight, `-1` for negative.

#### Expected results

Mean accuracy over the 10 seeds of the paper (balanced rule):

| Concepts | CBM (k=0) | Constrained (k=0) | CBM (k=max) | Constrained (k=max) |
|----------|-----------|-------------------|-------------|---------------------|
| true (7 concepts) | 84.5% | 89.8% | 92.0% | 90.7% |
| human (12 concepts) | 77.6% | 81.0% | 85.7% | 83.2% |

<p align="center">
  <img src="https://raw.githubusercontent.com/ustunb/concept-benchmark/main/docs/assets/alignment.png" width="700" alt="Constrained against unconstrained CBM before and after interventions">
</p>

For a complete end-to-end example with training, interventions, and alignment, see [`examples/robot_pipeline_example.py`](https://github.com/ustunb/concept-benchmark/blob/main/examples/robot_pipeline_example.py).

</details>

## Reproducing the Paper

[`EXPERIMENTS.md`](https://github.com/ustunb/concept-benchmark/blob/main/EXPERIMENTS.md) lists the commands behind each experiment, and [`scripts/paper/README.md`](https://github.com/ustunb/concept-benchmark/blob/main/scripts/paper/README.md) maps every table, figure and test of the paper to the script that produces it.

The paper's results (`paper-results.zip`, 14 MB) are attached to the [v0.4.0 release](https://github.com/ustunb/concept-benchmark/releases/tag/v0.4.0); unpack them and pass the folder to any paper script as `--results-root`.

## Citation

If you use this package in your research, please cite:

```bibtex
@inproceedings{skirzynski2026measuring,
  title={Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models},
  author={Skirzy{\'n}ski, Julian and Cheon, Harry and Kadekodi, Shreyas and Stewart, Meredith and Ustun, Berk},
  booktitle={Advances in Neural Information Processing Systems},
  year={2026},
}
```
