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From Few to Many: Self-Improving Many-Shot Reasoners Through Iterative Optimization and Generation
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Proposes BRIDGE, a Bayesian-optimization loop that alternates selecting an influential subset of many-shot demonstrations (optimize) and regenerating model rationales from that subset (generate) to improve many-shot reasoning ICL.
Problem
Many-shot in-context learning yields unstable, redundant gains: performance depends heavily on which examples are included, and naively scaling the number of demonstrations can plateau or degrade, while wasting long-context cost.
Approach
Treat demonstration selection as black-box combinatorial Bayesian optimization with a GP surrogate, random Tchebyshev scalarization to trade off validation accuracy against subset sparsity, and alternate it with regenerating rationales using the selected subset as seeds, so that generated examples can be re-expanded into the many-shot regime.
Key results
- On Gemini 1.5 Pro BBH, BRIDGE 2g averages 87.13% test accuracy versus 79.61% for reinforced ICL (about 7.5 points gain).
- On MATH and GSM-Hard with Gemini 1.5 Pro, the best BRIDGE variant reaches 64.65% and 73.32% versus 63.75% and 69.88% for reinforced ICL.
- On BIRD with Gemini 1.5 Pro, BRIDGE rounds raise execution accuracy from 59.1 (round 0) to 62.0 (round 2), while LoRA with 256 samples reaches 58.2.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BRIDGE's optimize-and-generate iterations instead of reinforced ICL | Gemini 1.5 Pro · BBH (16 tasks; average) | accuracy: 79.61 -> 87.13 | Helped |
| Use BRIDGE's optimize-and-generate iterations instead of reinforced ICL | Gemini 1.5 Flash · BBH (16 tasks; average) | accuracy: 80.25 -> 83.79 | Helped |
| Use BRIDGE's optimize-and-generate iterations instead of reinforced ICL | Mistral NeMo · BBH (16 tasks; average) | accuracy: 60.30 -> 70.05 | Helped |
| Use BRIDGE's optimize-and-generate iterations instead of reinforced ICL | Gemini 1.5 Pro · GSM-Hard | accuracy: 69.88 -> 73.32 | Helped |
| Use BRIDGE's optimize-and-generate iterations instead of the CHASE prompt | Gemini 1.5 Pro · BIRD dev | execution accuracy: 60.1 -> 62.0 | Helped |
| Replace Bayesian optimization with random search (ablation) | BRIDGE · BBH tasks | accuracy | Mixed |
| Stop after the second generate milestone rather than taking another optimize step (ablation) | BRIDGE on Gemini 1.5 Pro · BBH (16 tasks; average) | accuracy: 87.13 -> 86.33 | Helped |
Surprising findings
- Naive many-shot scaling is often outperformed by reinforced ICL with fewer examples, and performance can decline as more examples are added.
- Random search is a strong baseline for subset selection, though Bayesian optimization still outperforms it consistently.
Limitations
- Mainly restricted to black-box LLM setting; white-box optimization efficiency left open.
- Focused on reinforced ICL setting for reasoning tasks; other task types only preliminarily explored.
- Selected examples are static at test time; no sample-dependent ICL.
Experimental setup
Datasets: BIG-Bench Hard MATH GSM-Hard GSM-8K BIRD
Benchmarks: BIG-Bench Hard MATH GSM-Hard BIRD GSM-8K
Metrics: accuracy execution accuracy
Baselines: Direct many-shot CoT many-shot Infill Reinforced ICL Iterative reinforced ICL CHASE prompt LoRA PEFT random search variant of BRIDGE
Builds on: reinforced ICL many-shot ICL Gaussian process regression Bayesian optimization STaR
Closest papers by meaning
- Many-Shot In-Context Learning (NeurIPS 2024 · similarity 0.95)
- MIR-Bench: Can Your LLM Recognize Complicated Patterns via Many-Shot In-Context Reasoning? (NeurIPS 2025 · similarity 0.91)
- MAPLE: Many-Shot Adaptive Pseudo-Labeling for In-Context Learning (ICML 2025 · similarity 0.90)
- Many-Shot CoT-ICL: Making In-Context Learning Truly Learn (ICML 2026 · similarity 0.90)
- The Surprising Effectiveness of Test-Time Training for Few-Shot Learning (ICML 2025 · similarity 0.89)
- What Makes In-context Learning Effective for Mathematical Reasoning (ICML 2025 · similarity 0.88)
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