💻 computer science

FRAP: Fisher–Rao Geometric Trajectory Pruning for Class-Aware Dataset Selection

The paper proposes FRAP, a class-aware dataset pruning framework that leverages Fisher–Rao geometry to quantify the predictive trajectory of training samples via an Effective Information-Geometric Displacement score, enabling efficient selection of informative data to reduce computational costs while maintaining classification performance.

Original authors: Bahar Niknam, Hedieh Sajedi

Published 2026-09-28

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CC BY 4.0

Original authors: Bahar Niknam, Hedieh Sajedi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep learning has transformed how machines see and understand the world, powering everything from medical diagnostics to self-driving cars. This progress relies on feeding artificial intelligence systems massive amounts of labeled examples, allowing them to learn patterns by adjusting their internal settings. However, as these datasets have grown to include millions of images, the cost of processing them has become a significant burden, demanding immense computing power and memory. Researchers have long suspected that not every single example in these giant libraries is equally useful; in fact, much of the data may be redundant, offering little new information once the system has learned the basics. The challenge, then, is to identify which specific examples are essential for teaching a model and which can be safely discarded without hurting its performance.

A team of researchers at the University of Tehran has developed a new method called FRAP to solve this problem. Instead of treating data points as static items to be judged by a single score, the researchers watched how the model's understanding of each image changed over time. They trained a model on the full dataset and recorded its predictions at the end of every training session. By tracking the path these predictions took as the model learned, they could see the unique "journey" of every single image. Some images caused the model to swing wildly between different guesses before settling on the right answer, while others were recognized immediately and stayed consistent. The team realized that the shape and length of these prediction paths held the key to identifying the most valuable training data.

To measure these paths, the researchers used a mathematical concept that treats probability as a curved space, allowing them to calculate the true distance between different states of uncertainty. They combined this measurement of movement with a simple check of how confident the model was in the correct answer. This created a dual signal: one part measured how much the model's thinking evolved, and the other measured how difficult the image was for the model to master. Crucially, the method does not just rank all images from easiest to hardest across the entire board. Instead, it first decides how many images to keep from each category, ensuring that rare or difficult groups are not accidentally wiped out. It then selects the best examples from within each group based on their unique learning journeys.

When tested on standard image libraries containing tens of thousands of pictures, this approach consistently outperformed existing methods. On a dataset with ten categories, the new method achieved an accuracy of 95.58 percent when keeping only 30 percent of the data, a result that was higher than any other technique tested. Even on a much larger dataset with one thousand categories, the method maintained the highest accuracy among its competitors, reaching nearly 80 percent accuracy with just half the original data. The researchers found that simply looking at the final prediction of an image was not enough; the history of how the model arrived at that prediction mattered just as much. By preserving the specific mix of easy and hard examples from every category, the system could learn just as well from a fraction of the data.

The study suggests that the most effective way to shrink a dataset is to respect the diversity of the learning process itself. The researchers showed that discarding data based on a single snapshot of performance often leads to a loss of important information, whereas tracking the full evolution of the model's understanding preserves the necessary lessons. While the method requires an initial period of training to map out these learning paths, the resulting smaller datasets allow for faster and more efficient training in the future. This work offers a practical blueprint for making deep learning more sustainable, proving that sometimes, knowing less is only possible if you understand exactly how the learning happened.

Technical Summary: FRAP – Fisher–Rao Geometric Trajectory Pruning for Class-Aware Dataset Selection

1. Problem Statement

The increasing scale of deep learning datasets has introduced substantial computational and memory costs, motivating the need for effective dataset pruning. While additional data can improve generalization, redundancy suggests that a significant portion of training samples offers limited benefit. Existing pruning methods often rely on static properties (e.g., loss, gradients) or scalar uncertainty measures collected at single time points. These approaches fail to capture the full geometric evolution of a sample's predictive distribution over time. Furthermore, many methods employ global ranking strategies that do not explicitly control the distribution of the retention budget across classes, potentially leading to undesirable class imbalances in the pruned subset.

2. Methodology

The authors propose FRAP (Fisher–Rao Geometric Trajectory Pruning), a class-aware framework that characterizes training samples through the trajectories of their predictive distributions across recorded training epochs. The method operates in two coupled levels: trajectory-based scoring and hierarchical class-aware selection.

2.1 Predictive Trajectory Extraction

A reference model is trained on the full dataset for $T$ epochs. At the end of each epoch, the model evaluates the training set to record the predictive probability vector $p^{(t)}_n$ for each sample $n$ . This sequence forms the predictive trajectory $\mathcal{T}_n$ .

2.2 Fisher–Rao Geometric Scoring (EIGD)

To quantify the movement of a sample's predictive distribution, FRAP utilizes the Fisher–Rao geodesic distance on the probability simplex.

Smoothing: Predictive vectors are smoothed to ensure strictly positive components for geometric calculations.
Path Length ( $L_n$ ): The cumulative Fisher–Rao distance between consecutive predictive states across epochs, representing total predictive movement.
Net Displacement ( $G_n$ ): The Fisher–Rao distance between the initial ( $t=1$ ) and final ( $t=T$ ) predictive states.
Trajectory Efficiency ( $E_n$ ): Defined as the ratio of net displacement to cumulative path length ( $G_n / (L_n + \epsilon_d)$ ), measuring how directly a sample moves toward its final state.
EIGD Score ( $Q_n$ ): The Effective Information-Geometric Displacement combines magnitude and efficiency:
$Q_n = G_n E_n = \frac{G_n^2}{L_n + \epsilon_d}$
This score favors samples that undergo substantial predictive change without excessive intermediate oscillation.

2.3 Robustified Label-Aware Difficulty

To complement the trajectory score, a label-aware difficulty signal is computed based on the average confidence in the ground-truth class ( $q^{(t)}_n$ ). The difficulty $H_n$ is defined as $1 - \text{mean}(q^{(t)}_n)$ . To prevent extreme values from dominating, an upper-tail clipping is applied at the $\kappa$ -th percentile to produce $H^{rob}_n$ .

2.4 Hierarchical Class-Aware Selection

FRAP avoids global ranking in favor of a two-stage process:

Class-Level Budget Allocation: Class-level statistics (mean EIGD and mean clipped difficulty) are aggregated and normalized. A class-level priority score $D_c$ is computed as a weighted sum of these normalized statistics. This priority, combined with class size, determines the retention quota $K_c$ for each class, ensuring that the global pruning budget is distributed according to class-specific predictive behaviors.
Within-Class Sample Selection: Within each class, samples are ranked based on a combined score $S_n = (1-\alpha)\tilde{Q}_n + \alpha\tilde{H}^{rob}_n$ , where $\tilde{Q}$ and $\tilde{H}$ are normalized within the class. The top $K_c$ samples are retained.

3. Key Contributions

Fisher–Rao Trajectory Representation: A novel framework representing samples via the evolution of their full predictive distributions rather than scalar statistics, utilizing Fisher–Rao geometry to measure predictive movement.
EIGD Score: The introduction of the Effective Information-Geometric Displacement, which integrates net predictive displacement with the efficiency of the cumulative trajectory.
Class-Aware Hierarchical Mechanism: A selection procedure that explicitly separates class-level budget allocation from within-class sample ranking, addressing class imbalance issues inherent in global ranking methods.
Comprehensive Evaluation: Empirical validation across multiple datasets (CIFAR-10, CIFAR-100, ImageNet-1K, Waterbirds) and pruning ratios, demonstrating superior performance over representative baselines.

4. Experimental Results

The authors evaluated FRAP against methods including Random, Forgetting, EL2N, CCS, MetriQ, Dyn-Unc, TDDS, and InfoBatch.

Performance: FRAP consistently achieved the highest Top-1 accuracy across all datasets and pruning rates tested.
- CIFAR-10: Achieved 95.58% at 30% pruning and 87.86% at 90% pruning.
- CIFAR-100: Achieved 77.78% at 30% pruning and 56.72% at 90% pruning.
- ImageNet-1K: Achieved 79.83% at 25% pruning and 78.58% at 50% pruning.
- Waterbirds: Achieved 96.42% at 30% pruning and 93.18% at 90% pruning.
Ablation Studies:
- Removing the class-level allocation or the difficulty signal resulted in lower accuracy, confirming the necessity of both components.
- Replacing the full EIGD score with simple endpoint displacement ( $G_n$ ) yielded lower performance, validating the importance of trajectory efficiency.
Sensitivity: The mixing coefficient $\alpha$ (balancing trajectory and difficulty) showed optimal performance at $\alpha=0.5$ on CIFAR-100.

5. Significance and Claims

The paper claims that FRAP addresses critical limitations in existing pruning methods by capturing the geometric evolution of predictive distributions and explicitly managing class-level retention budgets. The authors state that their approach effectively balances the information gained from predictive trajectories against the computational cost of collecting them.

The results suggest that representing samples through their full predictive trajectories in the probability simplex, rather than relying on static or scalar metrics, provides a more robust signal for identifying informative data. The hierarchical selection mechanism is presented as a necessary step to ensure that aggressive pruning does not disproportionately harm specific classes. The authors conclude that FRAP sets a new state-of-the-art for dataset pruning under the tested conditions, though they acknowledge future work is needed to reduce the computational overhead associated with extracting full training trajectories.