SIS (Sufficient Input Subsets)

Sufficient Input Subsets (SIS) finds minimal subsets of embedding dimensions whose values alone suffice for a black-box predictor to make the same prediction, even when all other dimensions are masked (Carter et al. 2019).

For shortcut detection, small mean SIS size indicates the model may rely on few dimensions to predict—a potential shortcut. If those dimensions overlap with group-discriminative dimensions, the shortcut signal is stronger.

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How It Works

SIS uses instance-wise backward selection:

1. Train a probe (LogisticRegression) on embeddings → labels
2. For each test sample: start with full embedding; iteratively mask (zero-out) dimensions in order of least importance (ascending |coef|)
3. Predict on masked input; if prediction unchanged, keep dimension removed
4. Report minimal sufficient subset (SIS) per sample

flowchart TB
    subgraph inputs [Inputs]
        E[embeddings]
        L[labels]
        G[group_labels optional]
    end

    subgraph sis [SISDetector]
        P[Train probe on train split]
        B[Backward selection per sample]
        A[Analyze SIS overlap with group]
    end

    E --> P
    L --> P
    P --> B
    E --> B
    L --> B
    B --> A
    G --> A

Shortcut signal: Small mean SIS size (e.g., < 15% of dimensions) or high overlap between SIS dimensions and group-discriminative dimensions.

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Basic Usage

Via the Unified API (Recommended)

from shortcut_detect import ShortcutDetector
import numpy as np

embeddings = np.load("embeddings.npy")
labels = np.load("labels.npy")
group_labels = np.load("groups.npy")  # optional, for group-SIS overlap

detector = ShortcutDetector(methods=["sis"])
detector.fit(embeddings, labels, group_labels=group_labels)

print(detector.summary())
print(detector.results_["sis"]["metrics"]["mean_sis_size"])

Standalone Usage

from shortcut_detect.xai import SISDetector

detector = SISDetector(
    mask_value=0.0,           # value for masked dimensions
    max_samples=200,         # cap samples for SIS computation
    test_size=0.2,           # train/test split
    shortcut_threshold=0.15,  # frac_dim <= this → shortcut signal
    seed=42,
)
detector.fit(embeddings, labels, group_labels=groups)

metrics = detector.results_["metrics"]
print(metrics["mean_sis_size"], metrics["frac_dimensions"])
print(detector.sis_sizes_)  # per-sample SIS sizes

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Parameters

Parameter	Default	Description
mask_value	0.0	Value used when ablating a dimension
max_samples	200	Max test samples for SIS (for performance)
test_size	0.2	Fraction for train/test split
shortcut_threshold	0.15	If frac_dimensions ≤ this → shortcut signal
seed	42	Random seed

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Interpretation

Metric	Interpretation
Mean SIS size	Average number of dimensions sufficient for prediction (smaller = fewer dims used)
Fraction of dimensions	Mean SIS / n_dim (small = potential shortcut)
Group-SIS overlap	If group_labels provided: fraction of SIS dims that are group-discriminative (high = shortcut correlates with group)

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Reference

Carter, B., Mueller, J., Jain, S., & Gifford, D. (2019). What made you do this? Understanding black-box decisions with sufficient input subsets. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 89:567–576.