Beyond Post-Hoc Temperature Scaling: Bilevel Optimization for LLM Calibration

• URL: http://arxiv.org/abs/2608.07419v1
• Date: Fri, 07 Aug 2026 17:05:10 GMT
• Title: Beyond Post-Hoc Temperature Scaling: Bilevel Optimization for LLM Calibration
• Abstract summary: Preference alignment often makes large language models (LLMs) overconfident and poorly calibrated.<n>We propose maximizing the entropy of predictive distributions as the calibration objective.<n>Our method yields well-calibrated LLMs with particular advantages in out-of-domain generalization.
• Score: 8.906593271577266
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Preference alignment often makes large language models (LLMs) overconfident and poorly calibrated. Traditional post-hoc temperature scaling is inherently domain-dependent: a temperature fitted on one domain does not generalize across domains. This motivates us to modify model parameters during training to improve calibration. We propose maximizing the entropy of predictive distributions as the calibration objective, which directly targets overconfidence by discouraging overly concentrated predictions. Inspired by temperature scaling, we realize this through a bilevel optimization formulation, where the lower level trains the model under a parametric loss and the upper level selects loss hyperparameters to maximize entropy. To make the framework practical at LLM scale, we adopt an efficient first-order approximation that avoids explicit second-order computation. Across both multiple-choice and open-ended generative question answering, experiments demonstrate that our method yields well-calibrated LLMs with particular advantages in out-of-domain generalization.

Related papers

• Scalable Variational Bayesian Fine-Tuning of LLMs via Orthogonalized Low-Rank Adapters [13.718993776070434]
  Uncertainty quantification (UQ) is of utmost importance to self-assess the reliability of large language models (LLMs)<n>We build on the Bayesian last layer (BLL) model, where the LLM-based deterministic feature extractor is followed by random last layer parameters for uncertainty reasoning.<n>We leverage the variational (V) inference framework to put forth a scalable Bayesian fine-tuning approach.
  arXiv  Detail & Related papers  (2026-04-03T18:42:04Z)
• Curvature-Guided LoRA: Steering in the pretrained NTK subspace [60.35296431630704]
  We introduce the prediction alignment problem, aiming to match the predictor obtained via PEFT to that of full fine-tuning at the level of outputs.<n>We show that this objective naturally leads to a curvature-aware, second-order formulation, where optimal low-rank updates correspond to a Newton-like, curvature-whitened gradient.<n>Based on this insight, we propose Curvature-Guided LoRA (CG-LoRA), which selects and scales adaptation directions using local curvature information.
  arXiv  Detail & Related papers  (2026-03-31T14:46:39Z)
• Mitigating Forgetting in Low Rank Adaptation [17.859306837144732]
  We present LaLoRA, a weight-space regularization technique that applies a Laplace approximation to Low-Rank Adaptation.<n>Our approach estimates the model's confidence in each parameter and constrains updates in high-curvature directions.<n>We evaluate LaLoRA by fine-tuning a Llama model for mathematical reasoning and demonstrate an improved learning-forgetting trade-off.
  arXiv  Detail & Related papers  (2025-12-19T15:54:36Z)
• Low-Rank Curvature for Zeroth-Order Optimization in LLM Fine-Tuning [8.349781300731225]
  We introduce LOREN, a curvature-aware zeroth-order (ZO) optimization method for fine-tuning large language models (LLMs)<n>Existing ZO methods, which estimate gradients via finite differences using random perturbations, often suffer from high variance and suboptimal search directions.<n>Our approach addresses these challenges by: (i) adaptively estimating an anisotropic perturbation distribution for gradient estimation, (ii) capturing curvature through a low-rank block diagonal preconditioner, and (iii) applying a REINFORCE leave-one-out (RLOO) gradient estimator to reduce variance.
  arXiv  Detail & Related papers  (2025-11-11T08:34:09Z)
• From Noisy Traces to Stable Gradients: Bias-Variance Optimized Preference Optimization for Aligning Large Reasoning Models [90.45197506653341]
  Large reasoning models generate intermediate reasoning traces before producing final answers.<n> aligning LRMs with human preferences, a crucial prerequisite for model deployment, remains underexplored.<n>A common workaround optimized a single sampled trajectory, which introduces substantial gradient variance from trace sampling.
  arXiv  Detail & Related papers  (2025-10-06T17:58:01Z)
• Zeroth-Order Fine-Tuning of LLMs in Random Subspaces [63.10833446782114]
  As language models grow in size, memory demands for backpropagation increase.<n>Zeroth-order (ZO) optimization methods offer a memory-efficient alternative.<n>In this paper, we propose Subspace Zero-order optimization to address the challenges posed by posed by high dimensionality perturbations.
  arXiv  Detail & Related papers  (2024-10-11T17:01:43Z)
• Calibrating Language Models with Adaptive Temperature Scaling [58.056023173579625]
  We introduce Adaptive Temperature Scaling (ATS), a post-hoc calibration method that predicts a temperature scaling parameter for each token prediction. ATS improves calibration by over 10-50% across three downstream natural language evaluation benchmarks compared to prior calibration methods.
  arXiv  Detail & Related papers  (2024-09-29T22:54:31Z)
• Sample-dependent Adaptive Temperature Scaling for Improved Calibration [95.7477042886242]
  Post-hoc approach to compensate for neural networks being wrong is to perform temperature scaling. We propose to predict a different temperature value for each input, allowing us to adjust the mismatch between confidence and accuracy. We test our method on the ResNet50 and WideResNet28-10 architectures using the CIFAR10/100 and Tiny-ImageNet datasets.
  arXiv  Detail & Related papers  (2022-07-13T14:13:49Z)
• Laplace Matching for fast Approximate Inference in Generalized Linear Models [27.70274403550477]
  We propose an approximate inference framework primarily designed to be computationally cheap while still achieving high approximation quality. The concept, which we call emphLaplace Matching, involves closed-form, approximate, bi-directional transformations between the parameter spaces of exponential families. This effectively turns inference in GLMs into conjugate inference (with small approximation errors)
  arXiv  Detail & Related papers  (2021-05-07T08:25:17Z)
• Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration [57.568461777747515]
  We introduce a novel calibration method, Parametrized Temperature Scaling (PTS) We demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.
  arXiv  Detail & Related papers  (2021-02-24T10:18:30Z)
• Self-Tuning Stochastic Optimization with Curvature-Aware Gradient Filtering [53.523517926927894]
  We explore the use of exact per-sample Hessian-vector products and gradients to construct self-tuning quadratics. We prove that our model-based procedure converges in noisy gradient setting. This is an interesting step for constructing self-tuning quadratics.
  arXiv  Detail & Related papers  (2020-11-09T22:07:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.