# PHI-S: Distribution Balancing for Label-Free Multi-Teacher Distillation

arXiv: https://arxiv.org/abs/2410.01680 · HTML: https://mlsanity.com/paper/2410.01680/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [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)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [LLaVA-NeXT-Interleave: Tackling Multi-image, Video, and 3D in Large Multimodal Models](https://mlsanity.com/paper/2407.07895/) (2024)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [A Comprehensive Overhaul of Feature Distillation](https://mlsanity.com/paper/1904.01866/) (2019)
- [Variational Information Distillation for Knowledge Transfer](https://mlsanity.com/paper/1904.05835/) (2019)
- [Paraphrasing Complex Network: Network Compression via Factor Transfer](https://mlsanity.com/paper/1802.04977/) (2018)
- [Knowledge distillation: A good teacher is patient and consistent](https://mlsanity.com/paper/2106.05237/) (2021)
- [Knowledge Distillation by On-the-Fly Native Ensemble](https://mlsanity.com/paper/1806.04606/) (2018)
- [Probing the 3D Awareness of Visual Foundation Models](https://mlsanity.com/paper/2404.08636/) (2024)
- [AM-RADIO: Agglomerative Vision Foundation Model -- Reduce All Domains Into One](https://mlsanity.com/paper/2312.06709/) (2023)
- [Stabilizing Transformer Training by Preventing Attention Entropy Collapse](https://mlsanity.com/paper/2303.06296/) (2023)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Contrastive Learning Rivals Masked Image Modeling in Fine-tuning via Feature Distillation](https://mlsanity.com/paper/2205.14141/) (2022)
- [Adaptive Multi-Teacher Multi-level Knowledge Distillation](https://mlsanity.com/paper/2103.04062/) (2021)
- [Reinforced Multi-Teacher Selection for Knowledge Distillation](https://mlsanity.com/paper/2012.06048/) (2020)
- [Theia: Distilling Diverse Vision Foundation Models for Robot Learning](https://mlsanity.com/paper/2407.20179/) (2024)
- [Ensemble Knowledge Distillation for Learning Improved and Efficient Networks](https://mlsanity.com/paper/1909.08097/) (2019)
- [Model Compression with Two-stage Multi-teacher Knowledge Distillation for Web Question Answering System](https://mlsanity.com/paper/1910.08381/) (2019)

## Built on by (most cited first, 21 of 21)

- [RADIOv2.5: Improved Baselines for Agglomerative Vision Foundation Models](https://mlsanity.com/paper/2412.07679/) (2024)
- [DUNE: Distilling a Universal Encoder from Heterogeneous 2D and 3D Teachers](https://mlsanity.com/paper/2503.14405/) (2025)
- [UniUGG: Unified 3D Understanding and Generation via Geometric-Semantic Encoding](https://mlsanity.com/paper/2508.11952/) (2025)
- [Chorus: Multi-Teacher Pretraining for Holistic 3D Gaussian Scene Encoding](https://mlsanity.com/paper/2512.17817/) (2025)
- [Swiss Army Knife: Synergizing Biases in Knowledge from Vision Foundation Models for Multi-Task Learning](https://mlsanity.com/paper/2410.14633/) (2024)
- [FeatSharp: Your Vision Model Features, Sharper](https://mlsanity.com/paper/2502.16025/) (2025)
- [Pathryoshka: Compressing Pathology Foundation Models via Multi-Teacher Knowledge Distillation with Nested Embeddings](https://mlsanity.com/paper/2511.23204/) (2025)
- [Agglomerating Large Vision Encoders via Distillation for VFSS Segmentation](https://mlsanity.com/paper/2504.02351/) (2025)
- [SigLino: Efficient Multi-Teacher Distillation for Agglomerative Vision Foundation Models](https://mlsanity.com/paper/2512.20157/) (2025)
- [DriveZero: End-to-End Driving Beyond Human Demonstrations](https://mlsanity.com/paper/2609.06055/) (2026)
- [TwinTURBO: Semi-Supervised Fine-Tuning of Foundation Models via Mutual Information Decompositions for Downstream Task and Latent Spaces](https://mlsanity.com/paper/2503.07851/) (2025)
- [Seeing Further on the Shoulders of Giants: Knowledge Inheritance for Vision Foundation Models](https://mlsanity.com/paper/2508.14707/) (2025)
- [EoS-FM: Can an Ensemble of Specialist Models act as a Generalist Feature Extractor?](https://mlsanity.com/paper/2511.21523/) (2025)
- [FreqKD: Frequency-Decoupled Cross-Modal Knowledge Distillation for Infrared Object Detection](https://mlsanity.com/paper/2606.11572/) (2026)
- [LoFi RADIO: A Distilled In-Domain Backbone Applied for Artifact-Severity Grading of Ultra-Low-Field Neonatal Brain MR](https://mlsanity.com/paper/2609.02676/) (2026)
- [PL-SCEA: Reconfiguring Pretrained Attention for Few-Shot Industrial Anomaly Detection](https://mlsanity.com/paper/2609.03655/) (2026)
- [MIND the Gap: A Geographic Implicit Neural Representation with Adjustable Spatial Scale](https://mlsanity.com/paper/2609.25454/) (2026)
- [The Devil is in the Spectrum Bias: Spectrum-Balanced Feature Matching for Robust Representation Distillation](https://mlsanity.com/paper/2609.34106/) (2026)
- [GRAFT: Growing Agglomerative Foundation Models via Continual Teacher Distillation](https://mlsanity.com/paper/2610.02597/) (2026)
- [ViTok: Improving Dense Semantics in AM-RADIO-Style Multi-Teacher Distillation with PHI-S and Masked Image Modelling](https://mlsanity.com/paper/2610.02903/) (2026)
- [Scaling Multi-Teacher Distillation for Digital Pathology](https://mlsanity.com/paper/2610.12574/) (2026)

## Abstract (arXiv)

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.