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SPICE: Submodular Penalized Information–Conflict Selection for Efficient Large Language Model Training

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Data selection; Submodular; Log-determinant Fisher information; Instruction tuning
Abstract:

Information-based data selection for instruction tuning is compelling: maximizing the log-determinant of the Fisher information yields a monotone submodular objective, enabling greedy algorithms to achieve a (1−1/e)(1-1/e) approximation under a cardinality budget. In practice, however, we identify alleviating gradient conflicts, misalignment between per-sample gradients, is a key factor that slows down the decay of marginal log-determinant information gains, thereby preventing significant loss of information. We formalize this via an ε\varepsilon-decomposition that quantifies the deviation from ideal submodularity as a function of conflict statistics, yielding data-dependent approximation factors that tighten as conflicts diminish. Guided by this analysis, we propose SPICE, a conflict-aware selector that maximizes information while penalizing misalignment, and that supports early stopping and proxy models for efficiency. Empirically, SPICE selects subsets with higher log-determinant information than original criteria, and these informational gains translate into performance improvements: across 8 benchmarks with LLaMA2-7B and Qwen2-7B, SPICE uses only 10% of the data, yet matches or exceeds 6 methods including full-data tuning. This achieves performance improvements with substantially lower training cost. Code is available at https://anonymous.4open.science/r/SPICE-6DF7/README.md.

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Overview

Overall Novelty Assessment

The paper proposes SPICE, a conflict-aware data selector that maximizes Fisher information while penalizing gradient misalignment during instruction tuning. It resides in the 'Gradient-Based Influence and Information Metrics' leaf, which contains five papers total. This leaf sits within the broader 'Model-Intrinsic Quality Assessment' branch, indicating a moderately populated research direction focused on using internal model states to assess data utility. The taxonomy shows this is an active but not overcrowded area, with sibling leaves addressing uncertainty metrics and training trajectory analysis.

The taxonomy reveals neighboring work in 'Uncertainty and Consistency Metrics' (three papers) and 'Training Trajectory and Weight Dynamics' (two papers), both under the same parent branch. The paper's focus on gradient conflicts distinguishes it from uncertainty-based approaches like self-consistency probing, while its information-theoretic framing connects to influence function methods in sibling papers. The broader 'Selection Criteria and Quality Metrics' branch also includes external scoring methods and diversity metrics, suggesting the field balances model-intrinsic signals with heuristic or coverage-based strategies.

Among four candidates examined across three contributions, no clear refutations emerged. The ε-decomposition framework linking conflicts to information decay examined two candidates with no refutable overlap. The SPICE algorithm itself examined zero candidates, and the data-dependent approximation guarantees examined two candidates without finding prior work that directly anticipates this formulation. Given the limited search scope—only four candidates total—these statistics suggest the specific combination of conflict-aware selection and submodularity analysis may be relatively unexplored, though the small sample size precludes strong conclusions about absolute novelty.

Based on top-four semantic matches, the work appears to occupy a distinct niche within gradient-based selection methods. The conflict-aware framing and ε-decomposition analysis do not appear in the examined candidates, though the broader use of Fisher information and influence functions is well-established in the leaf's sibling papers. The analysis covers a narrow slice of the literature; a more exhaustive search might reveal closer precedents in optimization theory or active learning domains outside the instruction tuning context.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
4
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Data selection for efficient instruction tuning of large language models. The field has organized itself around several complementary dimensions. At the highest level, researchers distinguish between Selection Criteria and Quality Metrics (which define what makes an instruction example valuable), Selection Algorithms and Frameworks (which operationalize these criteria at scale), and Specialized Selection Contexts (addressing domain-specific or multimodal settings). Parallel branches examine Robustness and Security in Data Selection (guarding against adversarial or poisoned instructions), Efficient Training Techniques and Optimization (reducing computational overhead), and Evaluation and Benchmarking (measuring the impact of selection strategies). Application-Specific Instruction Tuning captures work tailored to particular downstream tasks or modalities. Within Selection Criteria and Quality Metrics, a dense cluster of methods relies on Model-Intrinsic Quality Assessment, using gradient-based influence and information metrics to score examples by their expected training utility, as seen in works like LESS[17] and In2Core[10]. A particularly active line of research focuses on gradient-based influence and information metrics, where methods estimate how much each instruction contributes to model updates or generalization. SPICE[0] falls squarely within this branch, leveraging influence functions to prioritize high-impact examples during instruction tuning. Nearby works such as LESS[17] and Uncertainty-Aware Influence[33] similarly exploit gradient information but differ in their treatment of uncertainty or approximation strategies. In contrast, SCAR[3] and Balanced Learning Selection[36] emphasize balancing coverage across diverse skills or concepts, highlighting a trade-off between influence-driven selection and representativeness. These gradient-centric approaches must also contend with computational costs and potential vulnerabilities to poisoning attacks, themes explored in the Robustness and Security branch. Overall, SPICE[0] exemplifies the trend toward principled, model-intrinsic scoring mechanisms that aim to distill large instruction pools into compact, high-quality subsets without sacrificing downstream performance.

Claimed Contributions

ε-decomposition framework linking gradient conflicts to marginal information gains decay

The authors introduce a novel theoretical framework that decomposes marginal information gains into a modular baseline and a perturbation term. They prove that the perturbation magnitude, which governs how quickly marginal gains decay, is bounded by gradient inner products, thereby quantitatively connecting gradient conflicts to submodular data selection theory.

2 retrieved papers
SPICE algorithm for conflict-aware data selection

The authors design SPICE (Submodular Penalized Information–Conflict sElection), a conflict-aware greedy selection algorithm that maximizes log-determinant Fisher information while adaptively penalizing gradient conflicts. The method incorporates data-driven early stopping and achieves efficient selection complexity of O(k|D|d).

0 retrieved papers
Data-dependent approximation guarantees via curvature control

The authors establish formal bounds showing that controlling gradient conflicts (via the ε-decomposition) reduces submodular curvature, thereby improving greedy approximation guarantees beyond the standard (1-1/e) factor. This provides tighter, data-dependent approximation factors that improve as conflicts diminish.

2 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

ε-decomposition framework linking gradient conflicts to marginal information gains decay

The authors introduce a novel theoretical framework that decomposes marginal information gains into a modular baseline and a perturbation term. They prove that the perturbation magnitude, which governs how quickly marginal gains decay, is bounded by gradient inner products, thereby quantitatively connecting gradient conflicts to submodular data selection theory.

Contribution

SPICE algorithm for conflict-aware data selection

The authors design SPICE (Submodular Penalized Information–Conflict sElection), a conflict-aware greedy selection algorithm that maximizes log-determinant Fisher information while adaptively penalizing gradient conflicts. The method incorporates data-driven early stopping and achieves efficient selection complexity of O(k|D|d).

Contribution

Data-dependent approximation guarantees via curvature control

The authors establish formal bounds showing that controlling gradient conflicts (via the ε-decomposition) reduces submodular curvature, thereby improving greedy approximation guarantees beyond the standard (1-1/e) factor. This provides tighter, data-dependent approximation factors that improve as conflicts diminish.

Table of Contents