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Understanding Multimodal LLMs Under Distribution Shifts: An Information-Theoretic Approach
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Proposes effective mutual information (EMI) and an information-theoretic upper bound on the ID-OOD EMI gap for MLLMs under visual, text, and joint distribution shifts, validated over 61 shift scenarios.
Problem
MLLMs degrade under distribution shifts between instruction-tuning and evaluation data, but no formal framework quantifies this risk; existing evaluations are empirical and rely on costly, black-box LLM judges.
Approach
Define effective mutual information (EMI) as test-time mutual information between query and model response minus ground-truth mutual information, which removes domain-dependent scale; derive an upper bound on the ID-OOD EMI difference (EMID) in terms of JS divergences of visual/text marginals, conditionals, and output distributions, and connect EMI to the Bradley-Terry preference / RP score.
Key results
- EMI correlates strongly with the GPT-4-judged RP score across 61 shift scenarios for LLaVA variants (Spearman rho 0.457 to 0.794, all p<0.05).
- EMID and its upper bound are strongly Pearson-correlated (r=0.746 synthetic, 0.565 natural across all models).
- EMI-based evaluation is about 138x faster per instance than GPT-4o judge-based RP scoring on LLaVA-Bench COCO.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add EMID upper bound regularization term during visual instruction tuning (ablation) | LLaVA v1.5 7B (10% LLaVA-mix-665K) · LLaVA-Bench COCO ID and V/T/J shifts | relative preference score: V +0.5, T +0.3, J +1.2; ID unchanged | Helped |
| use EMI (effective mutual information) instead of RP score for evaluation | LLaVA v1.5, LLaVA NeXT, 7B/13B · Synthetic and natural shifts | Spearman correlation with RP score | Helped |
| EMI estimator choice: CLUB vs InfoNCE, MINE, NWJ with different embeddings (ablation) | EMI estimation · Synthetic shifts, four MLLMs | Spearman rho with RP | Mixed |
| use E5-V joint multimodal embeddings instead of individual CLIP+XLM-R embeddings for EMI (ablation) | CLUB EMI estimator · Synthetic shifts | Spearman rho with RP: e.g. LLaVA v1.5 7B 0.606 -> 0.910 | Helped |
| use partial EMID bound (only visual and text JSD terms, dropping output term) (ablation) | EMID estimation · Synthetic and natural shifts | Pearson correlation with EMID | No clear effect |
| apply EMI-based evaluation with InternVL2.5-7B | InternVL2.5-7B · Synthetic shifts | Spearman rho with RP | Mixed |
Surprising findings
- InternVL2.5-7B shows only weak Spearman correlation (0.375) between EMI and RP score, though still significant at 0.05.
Limitations
- The upper bound is not tight, and no lower bound on EMID is provided.
- EMI captures only input-output relevance and not other quality facets such as helpfulness or safety.
- Shift simulations are simplified and do not cover complex spurious-correlation shifts.
Experimental setup
Datasets: LLaVA-Bench COCO LLaVA-Bench Wild LLaVA-Med LLaVA-mix-665K
Benchmarks: LLaVA-Bench COCO LLaVA-Bench Wild LLaVA-Med
Metrics: relative preference score Spearman correlation Kendall tau Pearson correlation EMI EMID
Baselines: GPT-4 judge relative preference score NWJ MINE InfoNCE MMD
Builds on: CLUB mutual information estimator relative preference score (LLM-as-a-judge) effective robustness visual instruction tuning
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