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Dan Busbridge

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11 papers

2 author rows

ICML Conference 2025 Conference Paper

Distillation Scaling Laws

Dan Busbridge
Amitis Shidani
Floris Weers
Jason Ramapuram
Etai Littwin
Russell Webb

We propose a distillation scaling law that estimates distilled model performance based on a compute budget and its allocation between the student and teacher. Our findings mitigate the risks associated with large-scale distillation by enabling compute-optimal allocation for both the teacher and student to maximize student performance. We provide compute-optimal distillation recipes for two key scenarios: when a teacher already exists, and when a teacher needs training. In settings involving many students or an existing teacher, distillation outperforms supervised learning up to a compute level that scales predictably with student size. Conversely, if only one student is to be distilled and a teacher also requires training, supervised learning is generally preferable. Additionally, our large-scale study of distillation increases our understanding of the process and helps inform experimental design.

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ICML Conference 2025 Conference Paper

Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for Mixture-of-Experts Language Models

Samira Abnar
Harshay Shah
Dan Busbridge
Alaaeldin El-Nouby
Joshua M. Susskind
Vimal Thilak

Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the compute per example. While scaling typically involves increasing both, the precise interplay between these factors and their combined contribution to overall capacity remains not fully understood. We explore this relationship in the context of sparse Mixture-of-Expert models (MoEs), which allow scaling the number of parameters without proportionally increasing the FLOPs per example. We investigate how varying the sparsity level, i. e. , the ratio of non-active to total parameters, affects model performance in terms of both pretraining and downstream performance. We find that under different constraints (e. g. parameter size and total training compute), there is an optimal level of sparsity that improves both training efficiency and model performance. These results provide a better understanding of the impact of sparsity in scaling laws for MoEs and complement existing works in this area, offering insights for designing more efficient architectures.

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ICML Conference 2025 Conference Paper

Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection

Louis Béthune
David Grangier
Dan Busbridge
Eleonora Gualdoni
Marco Cuturi
Pierre Ablin

A widespread strategy to obtain a language model that performs well on a target domain is to finetune a pretrained model to perform unsupervised next-token prediction on data from that target domain. Finetuning presents two challenges: (i) if the amount of target data is limited, as in most practical applications, the model will quickly overfit, and (ii) the model will drift away from the original model, forgetting the pretraining data and the generic knowledge that comes with it. Our goal is to derive scaling laws that quantify these two phenomena for various target domains, amounts of available target data, and model scales. We measure the efficiency of injecting pretraining data into the finetuning data mixture to avoid forgetting and mitigate overfitting. A key practical takeaway from our study is that injecting as little as $1%$ of pretraining data in the finetuning data mixture prevents the model from forgetting the pretraining set.

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NeurIPS Conference 2025 Conference Paper

Scaling Laws for Optimal Data Mixtures

Mustafa Shukor
Louis Bethune
Dan Busbridge
David Grangier
Enrico Fini
Alaaeldin El-Nouby
Pierre Ablin

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach accurately predicts the loss of a model of size $N$ trained with $D$ tokens and a specific domain weight vector $h$. We validate the universality of these scaling laws by demonstrating their predictive power in three distinct and large-scale settings: large language model (LLM), native multimodal model (NMM), and large vision models (LVM) pretraining. We further show that these scaling laws can extrapolate to new data mixtures and across scales: their parameters can be accurately estimated using a few small-scale training runs, and used to estimate the performance at larger scales and unseen domain weights. The scaling laws allow to derive the optimal domain weights for any target domain under a given training budget ($N$, $D$), providing a principled alternative to costly trial-and-error methods.

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ICLR Conference 2025 Conference Paper

Theory, Analysis, and Best Practices for Sigmoid Self-Attention

Jason Ramapuram
Federico Danieli
Eeshan Gunesh Dhekane
Floris Weers
Dan Busbridge
Pierre Ablin
Tatiana Likhomanenko
Jagrit Digani

Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as the softmax of dot products between keys and queries. Recent work has explored alternatives to softmax attention in transformers, such as ReLU and sigmoid activations. In this work, we revisit sigmoid attention and conduct an in-depth theoretical and empirical analysis. Theoretically, we prove that transformers with sigmoid attention are universal function approximators and benefit from improved regularity compared to softmax attention. Through detailed empirical analysis, we identify stabilization of large initial attention norms during the early stages of training as a crucial factor for the successful training of models with sigmoid attention, outperforming prior attempts. We also introduce FLASHSIGMOID, a hardware-aware and memory-efficient implementation of sigmoid attention yielding a 17% inference kernel speed-up over FLASHATTENTION2 on H100 GPUs. Experiments across language, vision, and speech show that properly normalized sigmoid attention matches the strong performance of softmax attention on a wide range of domains and scales, which previous attempts at sigmoid attention were unable to fully achieve. Our work unifies prior art and establishes best practices for sigmoid attention as a drop-in softmax replacement in transformers.

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ICLR Conference 2024 Conference Paper

Poly-View Contrastive Learning

Amitis Shidani
R. Devon Hjelm
Jason Ramapuram
Russell Webb
Eeshan Gunesh Dhekane
Dan Busbridge

Contrastive learning typically matches pairs of related views among a number of unrelated negative views. Views can be generated (e.g. by augmentations) or be observed. We investigate matching when there are more than two related views which we call poly-view tasks, and derive new representation learning objectives using information maximization and sufficient statistics. We show that with unlimited computation, one should maximize the number of related views, and with a fixed compute budget, it is beneficial to decrease the number of unique samples whilst increasing the number of views of those samples. In particular, poly-view contrastive models trained for 128 epochs with batch size 256 outperform SimCLR trained for 1024 epochs at batch size 4096 on ImageNet1k, challenging the belief that contrastive models require large batch sizes and many training epochs.

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ICML Conference 2023 Conference Paper

DUET: 2D Structured and Approximately Equivariant Representations

Xavier Suau
Federico Danieli
T. Anderson Keller
Arno Blaas
Chen Huang 0001
Jason Ramapuram
Dan Busbridge
Luca Zappella

Multiview Self-Supervised Learning (MSSL) is based on learning invariances with respect to a set of input transformations. However, invariance partially or totally removes transformation-related information from the representations, which might harm performance for specific downstream tasks that require such information. We propose 2D strUctured and EquivarianT representations (coined DUET), which are 2d representations organized in a matrix structure, and equivariant with respect to transformations acting on the input data. DUET representations maintain information about an input transformation, while remaining semantically expressive. Compared to SimCLR (Chen et al. , 2020) (unstructured and invariant) and ESSL (Dangovski et al. , 2022) (unstructured and equivariant), the structured and equivariant nature of DUET representations enables controlled generation with lower reconstruction error, while controllability is not possible with SimCLR or ESSL. DUET also achieves higher accuracy for several discriminative tasks, and improves transfer learning.

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NeurIPS Conference 2023 Conference Paper

How to Scale Your EMA

Dan Busbridge
Jason Ramapuram
Pierre Ablin
Tatiana Likhomanenko
Eeshan Gunesh Dhekane
Xavier Suau Cuadros
Russell Webb

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important machine learning tool is the model EMA, a functional copy of a target model, whose parameters move towards those of its target model according to an Exponential Moving Average (EMA) at a rate parameterized by a momentum hyperparameter. This model EMA can improve the robustness and generalization of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have not considered the optimization of the model EMA when performing scaling, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of a model EMA and demonstrate the rule's validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24, 576 without sacrificing performance, a 6$\times$ wall-clock time reduction under idealized hardware settings.

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ICML Conference 2023 Conference Paper

Stabilizing Transformer Training by Preventing Attention Entropy Collapse

Shuangfei Zhai
Tatiana Likhomanenko
Etai Littwin
Dan Busbridge
Jason Ramapuram
Yizhe Zhang 0002
Jiatao Gu
Joshua M. Susskind

Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each attention head during the course of training, which is a proxy for model sharpness. We identify a common pattern across different architectures and tasks, where low attention entropy is accompanied by high training instability, which can take the form of oscillating loss or divergence. We denote the pathologically low attention entropy, corresponding to highly concentrated attention scores, as $\textit{entropy collapse}$. As a remedy, we propose $\sigma$Reparam, a simple and efficient solution where we reparametrize all linear layers with spectral normalization and an additional learned scalar. We demonstrate that $\sigma$Reparam successfully prevents entropy collapse in the attention layers, promoting more stable training. Additionally, we prove a tight lower bound of the attention entropy, which decreases exponentially fast with the spectral norm of the attention logits, providing additional motivation for our approach. We conduct experiments with $\sigma$Reparam on image classification, image self-supervised learning, machine translation, speech recognition, and language modeling tasks. We show that $\sigma$Reparam provides stability and robustness with respect to the choice of hyperparameters, going so far as enabling training (a) a Vision Transformer to competitive performance without warmup, weight decay, layer normalization or adaptive optimizers; (b) deep architectures in machine translation and (c) speech recognition to competitive performance without warmup and adaptive optimizers. Code is available at https: //github. com/apple/ml-sigma-reparam.

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ICML Conference 2023 Conference Paper

The Role of Entropy and Reconstruction in Multi-View Self-Supervised Learning

Borja Rodríguez Gálvez
Arno Blaas
Pau Rodríguez
Adam Golinski
Xavier Suau
Jason Ramapuram
Dan Busbridge
Luca Zappella

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients.

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ICML Conference 2022 Conference Paper

Position Prediction as an Effective Pretraining Strategy

Shuangfei Zhai
Navdeep Jaitly
Jason Ramapuram
Dan Busbridge
Tatiana Likhomanenko
Joseph Yitan Cheng
Walter Talbott
Chen Huang 0001

Transformers \cite{transformer} have gained increasing popularity in a wide range of applications, including Natural Language Processing (NLP), Computer Vision and Speech Recognition, because of their powerful representational capacity. However, harnessing this representational capacity effectively requires a large amount of data, strong regularization, or both, to mitigate overfitting. Recently, the power of the Transformer has been unlocked by self-supervised pretraining strategies based on masked autoencoders which rely on reconstructing masked inputs, directly, or contrastively from unmasked content. This pretraining strategy which has been used in BERT models in NLP \cite{bert}, Wav2Vec models in Speech \cite{wv2v2} and, recently, in MAE models in Vision \cite{beit, mae}, forces the model to learn about relationships between the content in different parts of the input using autoencoding related objectives. In this paper, we propose a novel, but surprisingly simple alternative to content reconstruction – that of predicting locations from content, without providing positional information for it. Doing so requires the Transformer to understand the positional relationships between different parts of the input, from their content alone. This amounts to an efficient implementation where the pretext task is a classification problem among all possible positions for each input token. We experiment on both Vision and Speech benchmarks, where our approach brings improvements over strong supervised training baselines and is comparable to modern unsupervised/self-supervised pretraining methods. Our method also enables Transformers trained without position embeddings to outperform ones trained with full position information.

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