Deep learning · transfer learning

With the emergence of large-scale pre-trained neural networks, methods to adapt such "foundation" models to data-limited downstream tasks have become a necessity. Fine-tuning, preference optimization, and transfer learning have all been successfully employed for these purposes when the target task closely resembles the source task, but a precise theoretical understanding of ``task similarity'' is still lacking. We adopt a \emph{feature-centric} viewpoint on transfer learning and establish a number of theoretical results that demonstrate that when the target task is well represented by the feature space of the pre-trained model, transfer learning outperforms training from scratch. We study deep linear networks as a minimal model of transfer learning in which we can analytically characterize the transferability phase diagram as a function of the target dataset size and the feature space overlap. For this model, we establish rigorously that when the feature space overlap between the source and target tasks is sufficiently strong, both linear transfer and fine-tuning improve performance, especially in the low data limit. These results build on an emerging understanding of feature learning dynamics in deep linear networks, and we demonstrate numerically that the rigorous results we derive for the linear case also apply to nonlinear networks.

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into one-dimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation.

Efficiently counting Markov equivalent directed acyclic graphs (DAGs) is crucial in graphical causal analysis. Wienöbst et al. (2023) introduced a polynomial-time algorithm, known as the Clique-Picking algorithm, to count the number of Markov equivalent DAGs for a given completed partially directed acyclic graph (CPDAG). This algorithm iteratively selects a root clique, determines fixed orientations with outgoing edges from the clique, and generates the unresolved undirected connected components (UCCGs). In this work, we propose a more efficient approach to UCCG generation by utilizing previously computed results for different root cliques. Our method introduces the concept of super cliques within rooted clique trees, enabling their efficient transfer between trees with different root cliques. The proposed algorithm effectively reduces the computational complexity of the Clique-Picking method, particularly when the number of cliques is substantially smaller than the number of vertices and edges.

Multiple Instance Learning (MIL) is a cornerstone approach in computational pathology for distilling embeddings from gigapixel tissue images into patient-level representations to predict clinical outcomes. However, MIL is frequently challenged by the constraints of working with small, weakly-supervised clinical datasets. Unlike fields such as natural language processing and computer vision, which effectively use transfer learning to improve model quality in data-scarce environments, the transferability of MIL models remains largely unexplored. We conduct the first comprehensive investigation into transfer learning capabilities of pretrained MIL models, evaluating 11 MIL models across 19 pretraining tasks spanning tissue subtyping, cancer grading, and molecular subtype prediction. We observe a substantial performance boost with finetuning pretrained models over training from randomly initialized weights, even with domain differences between pretraining and target tasks. Pretraining on pan-cancer datasets enables consistent generalization across organs and task types compared to single-disease pretraining. Remarkably, this pan-cancer pretraining leads to better transfer than that of a state-of-the-art slide-level foundation model, while using only 6.5\% of the training data. These findings indicate that MIL architectures exhibit robust adaptability, offering insights into the benefits of leveraging pretrained models to enhance performance in computational pathology.

We consider layerwise function-space learning rates, which measure the magnitude of the change in a neural network's output function in response to an update to a parameter tensor. This contrasts with traditional learning rates, which describe the magnitude of changes in parameter space. We develop efficient methods to measure and set function-space learning rates in arbitrary neural networks, requiring only minimal computational overhead through a few additional backward passes that can be performed at the start of, or periodically during, training. We demonstrate two key applications: (1) analysing the dynamics of standard neural network optimisers in function space, rather than parameter space, and (2) introducing FLeRM (Function-space Learning Rate Matching), a novel approach to hyperparameter transfer across model scales. FLeRM records function-space learning rates while training a small, cheap base model, then automatically adjusts parameter-space layerwise learning rates when training larger models to maintain consistent function-space updates. FLeRM gives hyperparameter transfer across model width, depth, initialisation scale, and LoRA rank in various architectures including MLPs with residual connections and transformers with different layer normalisation schemes.

Maximal Update Parameterization ($\mu$P) has shown significant promise in allowing zero-shot hyperparameter transfer across neural network scales, reducing the prohibitive cost of hyperparameter tuning for large models. However, the theoretical foundation behind the observed approximate transferability of hyperparameters remains underexplored. Relying on a width-dominance regime, which ensures that as width grows, certain terms of the learning dynamics dominate, we establish the first fundamental separation of scales in $\mu$P between macro-variables (e.g. loss landscapes) and micro-variables (e.g. individual weights). Our formulation explains why hyperparameter tuning can be effectively performed in early training stages, i.e., \textit{early statistics effectively approximate global hyperparameter optima}, implying the potential to further reduce the training costs required for searching optimal hyperparameters. We further apply our main theory to explain an empirical deep learning phenomenon discovered independently by prior work.

Large language models are pre-trained on ever-growing token budgets under the assumption that better pre-training performance translates to improved downstream models. In this work, we challenge this assumption and show that extended pre-training can make models harder to fine-tune, leading to degraded final performance. We term this phenomenon \textbf{catastrophic overtraining}. For example, the instruction-tuned OLMo-1B model pre-trained on 3T tokens leads to over 2\% worse performance on multiple standard LLM benchmarks than its 2.3T token counterpart. Through controlled experiments and theoretical analysis, we show that catastrophic overtraining arises from a systematic increase in the broad sensitivity of pre-trained parameters to modifications, including but not limited to fine-tuning. Our findings call for a critical reassessment of pre-training design that considers the downstream adaptability of the model.

A central challenge in transfer learning is designing algorithms that can quickly adapt and generalize to new tasks without retraining. Yet, the conditions of when and how algorithms can effectively transfer to new tasks is poorly characterized. We introduce a geometric characterization of transfer in Hilbert spaces and define three types of inductive transfer: interpolation within the convex hull, extrapolation to the linear span, and extrapolation outside the span. We propose a method grounded in the theory of function encoders to achieve all three types of transfer. Specifically, we introduce a novel training scheme for function encoders using least-squares optimization, prove a universal approximation theorem for function encoders, and provide a comprehensive comparison with existing approaches such as transformers and meta-learning on four diverse benchmarks. Our experiments demonstrate that the function encoder outperforms state-of-the-art methods on four benchmark tasks and on all three types of transfer.

Accurate estimation of mutational effects on protein-protein binding energies is an open problem with applications in structural biology and therapeutic design. Several deep learning predictors for this task have been proposed but, presumably due to the scarcity of binding data, these methods under-perform computationally expensive estimates based on empirical force-fields. In response, we propose a transfer-learning approach that leverages advances in protein sequence modeling and folding stability prediction for this task. The key idea is to parameterize the binding energy as the difference between the folding energy of the protein complex and the sum of the folding energies of its binding partners. We show that using a pre-trained inverse-folding model as a proxy for folding energy provides strong zero-shot performance, and can be fine-tuned with (1) copious folding energy measurements and (2) more limited binding energy measurements. The resulting predictor, StaB-ddG, is the first deep learning predictor to match the accuracy of the state-of-the-art empirical force-field method Flex ddG, while offering an over 10,000x speed-up.

Label completion serves as a preprocessing approach to handling the sparse crowdsourced label matrix problem, significantly boosting the effectiveness of the downstream label aggregation. In recent advances, worker modeling has been proved to be a powerful strategy to further improve the performance of label completion. However, in real-world scenarios, workers typically annotate only a few instances, leading to insufficient worker modeling and thus limiting the improvement of label completion. To address this issue, we propose a novel transfer learning-based label completion (TLLC) method. Specifically, we first identify all high-confidence instances from the whole crowdsourced data as a source domain and use it to pretrain a Siamese network. The abundant annotated instances in the source domain provide essential knowledge for worker modeling. Then, we transfer the pretrained network to the target domain with the instances annotated by each worker separately, ensuring worker modeling captures unique characteristics of each worker. Finally, we leverage the new embeddings learned by the transferred network to complete each worker’s missing labels. Extensive experiments on several widely used real-world datasets demonstrate the effectiveness of TLLC. Our codes and datasets are available at https://github.com/jiangliangxiao/TLLC.