# Contrastive Linearized Laplace: Loss Geometry, Valid Repairs, and Reliable Cores

arXiv: https://arxiv.org/abs/2610.14875 · HTML: https://mlsanity.com/paper/2610.14875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Probabilistic Embeddings for Cross-Modal Retrieval](https://mlsanity.com/paper/2101.05068/) (2021)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [Going Deeper through the Gleason Scoring Scale: An Automatic end-to-end System for Histology Prostate Grading and Cribriform Pattern Detection](https://mlsanity.com/paper/2105.10490/) (2021)
- [Probabilistic Representations for Video Contrastive Learning](https://mlsanity.com/paper/2204.03946/) (2022)
- [Bayesian Triplet Loss: Uncertainty Quantification in Image Retrieval](https://mlsanity.com/paper/2011.12663/) (2020)
- [Probabilistic Contrastive Learning Recovers the Correct Aleatoric Uncertainty of Ambiguous Inputs](https://mlsanity.com/paper/2302.02865/) (2023)
- [Accelerated Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2210.12642/) (2022)
- [Variational Linearized Laplace Approximation for Bayesian Deep Learning](https://mlsanity.com/paper/2302.12565/) (2023)
- [Riemannian Laplace approximations for Bayesian neural networks](https://mlsanity.com/paper/2306.07158/) (2023)
- [Bayesian Metric Learning for Uncertainty Quantification in Image Retrieval](https://mlsanity.com/paper/2302.01332/) (2023)
- [Revisiting K-mer Profile for Effective and Scalable Genome Representation Learning](https://mlsanity.com/paper/2411.02125/) (2024)
- [Richer Bayesian Last Layers with Subsampled NTK Features](https://mlsanity.com/paper/2602.01279/) (2026)
- [Risk Controlled Image Retrieval](https://mlsanity.com/paper/2307.07336/) (2023)
- [Scalable Linearized Laplace Approximation via Surrogate Neural Kernel](https://mlsanity.com/paper/2601.21835/) (2026)
- [Uncertainty Estimation and Generalization Bounds for Modern Deep Learning](https://mlsanity.com/paper/2606.13818/) (2026)
- [UncertainGen: Uncertainty-Aware Representations of DNA Sequences for Metagenomic Binning](https://mlsanity.com/paper/2509.26116/) (2025)
- [Tubular Riemannian Laplace Approximations for Bayesian Neural Networks](https://mlsanity.com/paper/2512.24381/) (2025)
- [Improving the Linearized Laplace Approximation via Quadratic Approximations](https://mlsanity.com/paper/2602.03394/) (2026)

## Abstract (arXiv)

While contrastive learning is widely used to learn deterministic representations, it does not inherently provide estimates of uncertainty. Post-hoc uncertainty estimation methods, such as the Linearized Laplace approximation (LLA), offer a way to quantify uncertainty without retraining the encoder. However, we show that directly using the LLA induced distribution over the contrastive embedding does not yield reliable pointwise uncertainty estimates for downstream tasks: embedding variance alone does not reflect whether decisions such as nearest-neighbor retrieval or cluster assignment are stable. To address this limitation, we develop a post-hoc framework based on LLA that propagates encoder uncertainty through the downstream task. We characterize the curvature of contrastive objectives and introduce positive-semidefinite repairs where needed to obtain valid local Gaussian approximations without retraining the encoder. We test the proposed approach in metagenomic binning and image classification tasks. For metagenomic binning, posterior coassignment probabilities support consensus partitions and the selection of reliable cores, leading to improvements over existing baselines. Additional image classification experiments show calibration improvements on standard benchmarks and real histopathology datasets.