Gated Differential Linear Attention: A Linear-Time Decoder for High-Fidelity Medical Segmentation

Medical image segmentation requires models that preserve fine anatomical boundaries while remaining efficient for clinical deployment. While transformers capture long-range dependencies, they suffer from quadratic attention cost and large data requirements, whereas CNNs are compute-friendly yet struggle with global reasoning. Linear attention offers $\mathcal{O}(N)$ scaling, but often exhibits training instability and attention dilution, yielding diffuse maps. We introduce PVT-GDLA, a decoder-centric Transformer that restores sharp, long-range dependencies at linear time. Its core, Gated Differential Linear Attention (GDLA), computes two kernelized attention paths on complementary query/key subspaces and subtracts them with a learnable, channel-wise scale to cancel common-mode noise and amplify relevant context. A lightweight, head-specific gate injects nonlinearity and input-adaptive sparsity, mitigating attention sink, and a parallel local token-mixing branch with depthwise convolution strengthens neighboring-token interactions, improving boundary fidelity, all while retaining $\mathcal{O}(N)$ complexity and low parameter overhead. Coupled with a pretrained Pyramid Vision Transformer (PVT) encoder, PVT-GDLA achieves state-of-the-art accuracy across CT, MRI, ultrasound, and dermoscopy benchmarks under equal training budgets, with comparable parameters but lower FLOPs than CNN-, Transformer-, hybrid-, and linear-attention baselines. PVT-GDLA provides a practical path to fast, scalable, high-fidelity medical segmentation in clinical environments and other resource-constrained settings.

E-Gen: Leveraging E-Graphs to Improve Continuous Representations of Symbolic Expressions

As vector representations have been pivotal in advancing natural language processing (NLP), some prior research has concentrated on creating embedding techniques for mathematical expressions by leveraging mathematically equivalent expressions. While effective, these methods are limited by the training data. In this work, we propose augmenting prior algorithms with larger synthetic dataset, using a novel e-graph-based generation scheme. This new mathematical dataset generation scheme, E-Gen, improves upon prior dataset-generation schemes that are limited in size and operator types. We use this dataset to compare embedding models trained with two methods: (1) training the model to generate mathematically equivalent expressions, and (2) training the model using contrastive learning to group mathematically equivalent expressions explicitly. We evaluate the embeddings generated by these methods against prior work on both in-distribution and out-of-distribution language processing tasks. Finally, we compare the performance of our embedding scheme against state-of-the-art large language models and demonstrate that embedding-based language processing methods perform better than LLMs on several tasks, demonstrating the necessity of optimizing embedding methods for the mathematical data modality.