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A Bayesian Approach to Data Point Selection
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Proposes BADS, a Bayesian data point selection method that infers the joint posterior of a main network and instance-wise weights (via a weight network) using SGLD, avoiding bi-level optimisation.
Problem
Data point selection (reweighting or filtering uncurated training data using a small in-domain meta set) is dominated by bi-level optimisation methods that are memory- and compute-heavy and lack convergence guarantees with minibatches.
Approach
Treat DPS as posterior inference in a Bayesian model where the backbone is conditioned on weighted train data and the meta data is the likelihood; sample backbone and instance weights jointly with stochastic gradient Langevin dynamics, giving an SGD-like update with minibatch convergence guarantees.
Key results
- On CIFAR-10 with 80% label noise, BADS exceeds BLO and non-DPS approaches by about 15% and 20% in accuracy.
- On WebNLG, BADS achieves a 2 BLEU advantage over the second-best system (Duplicate_Meta) and more than 5 BLEU over the rest.
- BADS uses about 1.5x the GPU memory of the base training, versus about 2.5x for BLO, and matches base training time (61.03 s vs 61.2 s per 100 steps).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BADS instead of the strongest listed non-BADS baseline | OpenLLaMA 3B instruction fine-tuning · MMLU | accuracy: 26.59 vs 25.62 | Helped |
| Use BADS instead of AskLLM-O | OpenLLaMA 3B instruction fine-tuning · ARC-challenge | accuracy: 34.39 vs 35.15 | Hurt |
| Use BADS instead of ClassAct | OpenLLaMA 3B instruction fine-tuning · ARC-easy | accuracy: 67.00 vs 67.34 | Hurt |
| Use BADS instead of AskLLM-O | OpenLLaMA 3B instruction fine-tuning · HellaSwag | accuracy: 52.91 vs 53.71 | Hurt |
| Replace the BADS weight network with individual scalar weights (ablation) | BADS on CIFAR-10 denoising · CIFAR-10 | accuracy | Helped |
| Reduce the weight-prior impact constant σ (ablation) | BADS across the three proof-of-concept scenarios · MNIST, CIFAR, WebNLG | performance | No clear effect |
| Increase sparsity level β in the WebNLG and MNIST settings (ablation) | BADS · WebNLG and MNIST | performance | Hurt |
| Decrease sparsity level β in the CIFAR denoising setting (ablation) | BADS · CIFAR | performance | Mixed |
| Use σ = 0.5 rather than a sufficiently low σ (ablation) | BADS on CIFAR-10 with 50% noisy data · CIFAR-10 | clean-example weighting | Hurt |
| Use σ = 0.05 rather than a sufficiently low σ (ablation) | BADS on CIFAR-10 with 50% noisy data · CIFAR-10 | clean-example weighting | No clear effect |
| Set σ to ≤ 5 × 10^{-5} (ablation) | BADS on CIFAR-10 with 50% noisy data · CIFAR-10 | clean-example weighting | Helped |
| Decrease β from 0.8 to 0.05 (ablation) | BADS trained on WebNLG City and Artist domains · WebNLG | Artist-domain weighting | Helped |
Surprising findings
- Most individual weights tend to collapse to zero under plain sparsity priors, so the paper needed a prior that enforces a target non-zero selection level.
- Unsupervised AskLLM-O and ClassAct-style methods did not consistently beat standard mixing on LLM instruction tuning, while BADS did on most tasks.
Limitations
- Many hyperparameters (sparsity level beta, impact constants rho, sigma, learning rates) need careful tuning.
- GPU memory footprint is higher than non-DPS methods because the weight network or all weights are kept in memory.
- Theoretical convergence guarantee relies on adjusted assumptions from prior SGLD analysis and the paper has no formal proof of the posterior approximation beyond that.
Experimental setup
Datasets: MNIST CIFAR-10 WebNLG 2020 FLAN V2 CoT Dolly Open Assistant 1 MMLU ARC-challenge ARC-easy HellaSwag
Benchmarks: MNIST CIFAR-10 WebNLG 2020 MMLU ARC-challenge ARC-easy HellaSwag
Metrics: accuracy BLEU GPU memory (MB) training time (s)
Baselines: Mixing Meta_Only Random_Select Duplicate_Meta BLO CDS ClassAct AskLLM-O
Builds on: bi-level optimisation (learning to reweight) stochastic gradient Langevin dynamics contrastive data selection ClassAct
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