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Calibrated Language Models and How to Find Them with Label Smoothing

ICML 2025 · Large language models › Instruction and fine-tuning · approach: Calibration and knowledge in LLM tuning · 0 citations (OpenAlex)

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Shows SFT degrades LLM calibration, that label smoothing restores it except for large-vocabulary small-hidden-size models, and provides a memory-efficient Triton cross-entropy kernel supporting label smoothing.

Problem

Instruction tuning (SFT) of LLMs degrades confidence calibration, and label smoothing, which could fix this, becomes ineffective for large-vocabulary models and cannot be computed memory-efficiently in standard fused cross-entropy kernels.

Approach

Argues via entropy bounds that the LM head's minimum entropy grows with vocabulary size and shrinks with hidden size, explaining when label smoothing fails to help, and designs a fused Triton kernel that computes the label-smoothed cross-entropy without materializing the full logit matrix.

Key results

• With label smoothing (beta=0.1) on Tulu3Mixture, Gemma2-2B MMLU ECE drops from 0.341 to 0.020 with accuracy roughly unchanged.
• The proposed kernel uses about 1.1 MB forward memory versus 24000 MB for the PyTorch baseline on a Gemma2-2B batch of 8192 tokens, with forward+backward 72.9 ms vs 104.9 ms.
• Label smoothing gives smaller calibration gains for LLaMA3 1B and 3B than for 8B, consistent with the entropy bound on large-vocabulary small-hidden-size LM heads.

Measured effects reported in the paper

Surprising findings

• Label smoothing has diminishing effectiveness for smaller large-vocabulary LLMs, because their LM head cannot reach low entropy, so smoothing only penalizes overconfidence that is absent.
• Temperature scaling with T>1 and logit softcapping can change the entropy bound and enable overconfidence in small models, which lets label smoothing work again.

Limitations

• Theoretical entropy bound relies on assumptions (norm constraints on logits) and is motivated rather than fully validated.
• Kernel does not beat torch.compile on time, and label smoothing adds slight overhead in the fused version.
• Experiments are limited to a few model families and MMLU/HellaSwag/Arc-easy with 5-shot evaluation.

Experimental setup

Datasets: Alpaca Tulu3Mixture OpenHermes-2.5

Benchmarks: MMLU HellaSwag Arc-easy

Metrics: accuracy expected calibration error root mean square calibration error peak GPU memory wall-clock time

Baselines: torch.compile torch.nn.CrossEntropyLoss Cut-Cross-Entropy Liger Kernels Chunked Cross Entropy (torchtune)

Builds on: label smoothing Cut-Cross-Entropy Liger Kernels open-instruct

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