Daily Papers

Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception. In contrast, Tversky (1977) proposed an axiomatic theory of similarity based on a representation of objects as sets of features, and their similarity as a function of common and distinctive features. However, this model has not been used in deep learning before, partly due to the challenge of incorporating discrete set operations. We develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive neural network building blocks such as the Tversky projection layer, which unlike the linear projection layer can model non-linear functions such as XOR. Through experiments with image recognition and language modeling, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer, which employs geometric similarity. On the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.5%, and its parameter count by 34.8%. Finally, we propose a unified interpretation of both projection layers as computing similarities of input stimuli to learned prototypes, for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in deep learning, and designing networks that are interpretable under an established theory of psychological similarity.

Deep learning, particularly convolutional neural networks (CNNs) and Transformers, has significantly advanced 3D medical image segmentation. While CNNs are highly effective at capturing local features, their limited receptive fields may hinder performance in complex clinical scenarios. In contrast, Transformers excel at modeling long-range dependencies but are computationally intensive, making them expensive to train and deploy. Recently, the Mamba architecture, based on the State Space Model (SSM), has been proposed to efficiently model long-range dependencies while maintaining linear computational complexity. However, its application in medical image segmentation reveals shortcomings, particularly in capturing critical local features essential for accurate delineation of clinical regions. In this study, we propose MambaClinix, a novel U-shaped architecture for medical image segmentation that integrates a hierarchical gated convolutional network(HGCN) with Mamba in an adaptive stage-wise framework. This design significantly enhances computational efficiency and high-order spatial interactions, enabling the model to effectively capture both proximal and distal relationships in medical images. Specifically, our HGCN is designed to mimic the attention mechanism of Transformers by a purely convolutional structure, facilitating high-order spatial interactions in feature maps while avoiding the computational complexity typically associated with Transformer-based methods. Additionally, we introduce a region-specific Tversky loss, which emphasizes specific pixel regions to improve auto-segmentation performance, thereby optimizing the model's decision-making process. Experimental results on five benchmark datasets demonstrate that the proposed MambaClinix achieves high segmentation accuracy while maintaining low model complexity.