# Logit Distillation on Manifolds: Mapping by Learning

arXiv: https://arxiv.org/abs/2606.00771 · HTML: https://mlsanity.com/paper/2606.00771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 24 of 24)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [MLS: A Large-Scale Multilingual Dataset for Speech Research](https://mlsanity.com/paper/2012.03411/) (2020)
- [Boosting Continual Learning of Vision-Language Models via Mixture-of-Experts Adapters](https://mlsanity.com/paper/2403.11549/) (2024)
- [Logit Standardization in Knowledge Distillation](https://mlsanity.com/paper/2403.01427/) (2024)
- [A Comprehensive Survey of Mixture-of-Experts: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2503.07137/) (2025)
- [Distil-Whisper: Robust Knowledge Distillation via Large-Scale Pseudo Labelling](https://mlsanity.com/paper/2311.00430/) (2023)
- [nGPT: Normalized Transformer with Representation Learning on the Hypersphere](https://mlsanity.com/paper/2410.01131/) (2024)
- [Tabular Benchmarks for Joint Architecture and Hyperparameter Optimization](https://mlsanity.com/paper/1905.04970/) (2019)
- [Meta-DMoE: Adapting to Domain Shift by Meta-Distillation from Mixture-of-Experts](https://mlsanity.com/paper/2210.03885/) (2022)
- [Decoupled Networks](https://mlsanity.com/paper/1804.08071/) (2018)
- [TAID: Temporally Adaptive Interpolated Distillation for Efficient Knowledge Transfer in Language Models](https://mlsanity.com/paper/2501.16937/) (2025)
- [Teacher-Student Compression with Generative Adversarial Networks](https://mlsanity.com/paper/1812.02271/) (2018)

## Abstract (arXiv)

A simple way to improve the performance of almost any machine learning model is not to train a single but several models with diverse algorithms which will make slightly distinct kinds of predictions and errors on the same data, and thus improve the average predictions and robustness. However, making predictions using a whole ensemble of models is cumbersome and computationally too expensive to allow deployment to a large number of users, especially if the models are large neural nets. In response to this, we introduce a layer and point wise projection mapping, which maps student and teacher representations into an aligned high-dimensional embedding space during training process. The proposed approach combined with LoRA injection reduces the student model trainable parameters to less than 1% of the teacher model, while significantly improving word error rate (WER) compared to other distillation methods, as demonstrated in ablation studies. Unlike a mixture of experts, our method can be trained rapidly and in parallel.