Composing Linear Layers from Irreducibles

Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: can we identify/synthesize linear transformations from a minimal set of geometric primitives? Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors -- geometric objects encoding oriented planes -- and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only O(log^2 d) parameters, versus O(d^2) required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, our rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.

A computationally frugal open-source foundation model for thoracic disease detection in lung cancer screening programs

Low-dose computed tomography (LDCT) imaging employed in lung cancer screening (LCS) programs is increasing in uptake worldwide. LCS programs herald a generational opportunity to simultaneously detect cancer and non-cancer-related early-stage lung disease. Yet these efforts are hampered by a shortage of radiologists to interpret scans at scale. Here, we present TANGERINE, a computationally frugal, open-source vision foundation model for volumetric LDCT analysis. Designed for broad accessibility and rapid adaptation, TANGERINE can be fine-tuned off the shelf for a wide range of disease-specific tasks with limited computational resources and training data. Relative to models trained from scratch, TANGERINE demonstrates fast convergence during fine-tuning, thereby requiring significantly fewer GPU hours, and displays strong label efficiency, achieving comparable or superior performance with a fraction of fine-tuning data. Pretrained using self-supervised learning on over 98,000 thoracic LDCTs, including the UK's largest LCS initiative to date and 27 public datasets, TANGERINE achieves state-of-the-art performance across 14 disease classification tasks, including lung cancer and multiple respiratory diseases, while generalising robustly across diverse clinical centres. By extending a masked autoencoder framework to 3D imaging, TANGERINE offers a scalable solution for LDCT analysis, departing from recent closed, resource-intensive models by combining architectural simplicity, public availability, and modest computational requirements. Its accessible, open-source lightweight design lays the foundation for rapid integration into next-generation medical imaging tools that could transform LCS initiatives, allowing them to pivot from a singular focus on lung cancer detection to comprehensive respiratory disease management in high-risk populations.

Adaptive Scoring and Thresholding with Human Feedback for Robust Out-of-Distribution Detection

Machine Learning (ML) models are trained on in-distribution (ID) data but often encounter out-of-distribution (OOD) inputs during deployment -- posing serious risks in safety-critical domains. Recent works have focused on designing scoring functions to quantify OOD uncertainty, with score thresholds typically set based solely on ID data to achieve a target true positive rate (TPR), since OOD data is limited before deployment. However, these TPR-based thresholds leave false positive rates (FPR) uncontrolled, often resulting in high FPRs where OOD points are misclassified as ID. Moreover, fixed scoring functions and thresholds lack the adaptivity needed to handle newly observed, evolving OOD inputs, leading to sub-optimal performance. To address these challenges, we propose a human-in-the-loop framework that \emph{safely updates both scoring functions and thresholds on the fly} based on real-world OOD inputs. Our method maximizes TPR while strictly controlling FPR at all times, even as the system adapts over time. We provide theoretical guarantees for FPR control under stationary conditions and present extensive empirical evaluations on OpenOOD benchmarks to demonstrate that our approach outperforms existing methods by achieving higher TPRs while maintaining FPR control.