Compact Example-Based Explanations for Language Models¶

Conference: ACL 2026 arXiv: 2601.03786 Code: None Area: LLM Pretraining Keywords: Training data influence, example-based explanations, selection relevance, gradient reconstruction, redundancy elimination

TL;DR¶

This paper proposes the Selection Relevance Score, a retraining-free metric for evaluating the quality of training sample subsets as example-based explanations. It demonstrates that the commonly used "select top-k by influence" strategy frequently underperforms random selection, and introduces a new strategy that balances influence and representativeness.

Background & Motivation¶

Background: Training data influence estimation methods (e.g., influence functions) can quantify each training document's contribution to model outputs, making them a promising source for example-based explanations. However, humans cannot process thousands of documents, so only a small number of training samples can be selected as explanations in practice.

Limitations of Prior Work: (1) Selecting the top-k highest-influence samples is the current default strategy, but high-influence samples tend to be global outliers (e.g., mislabeled data) and are not necessarily the most relevant to the test instance at hand; (2) top-k samples are often highly redundant, leading to diminishing returns; (3) existing evaluation methods either operate in embedding space (whereas ranking is performed in gradient space), rely on class labels (inapplicable to generative tasks), or require retraining (infeasible for LLMs).

Key Challenge: Influence estimation methods assign independent scores to individual training samples, but effective explanations require consideration of inter-sample complementarity and redundancy — a good explanation set should collectively cover the key aspects of the model's decision.

Goal: (1) Propose a retraining-free metric for evaluating selection quality; (2) expose the shortcomings of common selection strategies; (3) design improved selection strategies.

Key Insight: Framing example-based explanation as a gradient reconstruction task — good explanation samples should enable reconstruction of the test instance's gradient via a linear combination of their own gradients.

Core Idea: Selection relevance = the ability of selected samples' gradients to reconstruct the test instance's gradient; a high-quality explanation set should maximize reconstruction fidelity.

Method¶

Overall Architecture¶

The selection quality evaluation is formalized as a gradient reconstruction problem. Given the loss gradient \(\nabla\mathcal{L}'\) of a test instance and the gradient matrix \(A\) of \(k\) selected training samples, the method computes the optimal linear combination \(\hat{\nabla\mathcal{L}}' = At\) and measures the reconstruction error. The Selection Relevance Score \(\xi^{SR}\) is the ratio of the original gradient norm to the reconstruction error, expressed in dB.

Key Designs¶

Selection Relevance Score:
- Function: Quantifies the overall quality of a selected training sample set as an explanation.
- Mechanism: \(\xi^{SR} = \frac{\mathbb{E}[\|G(\omega)\|^2]}{\mathbb{E}[\|G(\omega) - At_\omega\|^2]}\), i.e., the ratio of the expected squared gradient norm to the expected squared reconstruction error. Values \(> 0\) dB indicate that the selected samples provide useful information; values \(< 0\) dB indicate performance worse than a zero-vector baseline.
- Design Motivation: Reconstruction capability in gradient space directly reflects the explanatory power of training samples over model decisions, and assesses samples as a group rather than scoring them independently.
Constrained Projection:
- Function: Ensures that the linear combination coefficients satisfy explanation semantics.
- Mechanism: A non-negativity constraint is imposed on coefficients \(t\) (preventing irrelevant samples from gaining weight through cancellation) along with a normalization constraint (\(\sum t = 1\), rendering \(t\) interpretable as relative importance). The unconstrained least-squares solution is first computed, then projected onto the unit simplex.
- Design Motivation: Unconstrained least squares may yield negative coefficients, implying that certain "explanation" samples are in fact contradicting the prediction.
Influence-Representativeness Balanced Selection Strategy:
- Function: Replaces the naive "select top-k by influence" strategy.
- Mechanism: The selection process jointly considers influence scores and inter-sample diversity/representativeness to avoid redundant selections and dominance by global outliers.
- Design Motivation: Experiments demonstrate that naive top-k selection frequently underperforms random selection, as global outliers and redundant information degrade explanation quality.

Loss & Training¶

This paper involves no model training. The Selection Relevance Score is computed analytically (least squares + simplex projection) without any gradient updates. Validation experiments use fine-tuning comparisons to confirm the metric's effectiveness.

Key Experimental Results¶

Main Results¶

Selection Relevance Score by Selection Strategy (dB, higher is better)

Selection Strategy	k=1	k=5	k=10	k=25
Random Selection	Baseline	Baseline	Baseline	Baseline
Top-k (Highest Influence)	< Random	< Random	≈ Random	> Random
Balanced Strategy (Ours)	> Random	> Random	> Random	> Random

Ablation Study¶

Influence Estimation Method	Combined with Top-k	Combined with Balanced Strategy
Influence Functions	Poor (many global outliers)	Significant improvement
TracIn	Moderate	Improvement
TRAK	Relatively good	Further improvement

Key Findings¶

The top-k selection strategy frequently underperforms random selection at small budgets (\(k \leq 10\)), primarily due to global outliers and redundancy.
The Selection Relevance Score is highly correlated with fine-tuning validation metrics, confirming its validity as a proxy evaluation measure.
Different influence estimation methods significantly affect selection quality: TRAK is better suited for the selection task than influence functions.
The balanced strategy consistently outperforms both top-k and random selection across all budget sizes and estimation method combinations.

Highlights & Insights¶

The paper reveals an overlooked yet important issue: the quality of example-based explanations depends not only on the accuracy of influence estimation but critically on the selection strategy.
The finding that "top-k underperforms random" challenges a default assumption in the field.
The Selection Relevance Score provides the first retraining-free, task-agnostic tool for evaluating selection quality.

Limitations & Future Work¶

Gradient reconstruction as a proxy for explanation quality may not fully capture users' actual needs.
The constrained projection (non-negativity + normalization) may exclude certain valid reconstruction solutions.
Gradient computation on large-scale LLMs remains computationally expensive.
Validation is conducted only on classification tasks; effectiveness on generative tasks remains to be confirmed.

vs. Bhatt et al. (2021): Their approach reduces redundancy via an additive diversity-plus-influence objective, but may favor outliers; this paper proposes representativeness as an alternative.
vs. Bae et al. (2022): They introduce the concept of prediction-constrained influence; the proposed score is highly compatible with their framework.
vs. Influence Functions: The global outlier problem of influence functions is particularly pronounced in the selection task; this paper quantitatively corroborates this observation.

Rating¶

Novelty: ⭐⭐⭐⭐ The gradient reconstruction perspective and Selection Relevance Score constitute novel evaluation tools.
Experimental Thoroughness: ⭐⭐⭐⭐ Systematic evaluation across multiple influence methods × selection strategies × budget sizes.
Writing Quality: ⭐⭐⭐⭐⭐ Rigorous formalization, clear motivation, and in-depth analysis.
Value: ⭐⭐⭐⭐ Provides important evaluation tools and practical guidance for the example-based explanation community.