Pham The Bao

Bao Pham, Gabriel Raya, Matteo Negri et al.

Hopfield networks are associative memory (AM) systems, designed for storing and retrieving patterns as local minima of an energy landscape. In the classical Hopfield model, an interesting phenomenon occurs when the amount of training data reaches its critical memory load $- spurious\,\,states$, or unintended stable points, emerge at the end of the retrieval dynamics, leading to incorrect recall. In this work, we examine diffusion models, commonly used in generative modeling, from the perspective of AMs. The training phase of diffusion model is conceptualized as memory encoding (training data is stored in the memory). The generation phase is viewed as an attempt of memory retrieval. In the small data regime the diffusion model exhibits a strong memorization phase, where the network creates distinct basins of attraction around each sample in the training set, akin to the Hopfield model below the critical memory load. In the large data regime, a different phase appears where an increase in the size of the training set fosters the creation of new attractor states that correspond to manifolds of the generated samples. Spurious states appear at the boundary of this transition and correspond to emergent attractor states, which are absent in the training set, but, at the same time, have distinct basins of attraction around them. Our findings provide: a novel perspective on the memorization-generalization phenomenon in diffusion models via the lens of AMs, theoretical prediction of existence of spurious states, empirical validation of this prediction in commonly-used diffusion models.

Beatrice Achilli, Enrico Ventura, Gianluigi Silvestri et al.

Generative diffusion processes are state-of-the-art machine learning models deeply connected with fundamental concepts in statistical physics. Depending on the dataset size and the capacity of the network, their behavior is known to transition from an associative memory regime to a generalization phase in a phenomenon that has been described as a glassy phase transition. Here, using statistical physics techniques, we extend the theory of memorization in generative diffusion to manifold-supported data. Our theoretical and experimental findings indicate that different tangent subspaces are lost due to memorization effects at different critical times and dataset sizes, which depend on the local variance of the data along their directions. Perhaps counterintuitively, we find that, under some conditions, subspaces of higher variance are lost first due to memorization effects. This leads to a selective loss of dimensionality where some prominent features of the data are memorized without a full collapse on any individual training point. We validate our theory with a comprehensive set of experiments on networks trained both in image datasets and on linear manifolds, which result in a remarkable qualitative agreement with the theoretical predictions.

Duy H. M. Nguyen, Duy M. Nguyen, Mai T. N. Truong et al.

Brain extraction (skull stripping) is a challenging problem in neuroimaging. It is due to the variability in conditions from data acquisition or abnormalities in images, making brain morphology and intensity characteristics changeable and complicated. In this paper, we propose an algorithm for skull stripping in Magnetic Resonance Imaging (MRI) scans, namely ASMCNN, by combining the Active Shape Model (ASM) and Convolutional Neural Network (CNN) for taking full of their advantages to achieve remarkable results. Instead of working with 3D structures, we process 2D image sequences in the sagittal plane. First, we divide images into different groups such that, in each group, shapes and structures of brain boundaries have similar appearances. Second, a modified version of ASM is used to detect brain boundaries by utilizing prior knowledge of each group. Finally, CNN and post-processing methods, including Conditional Random Field (CRF), Gaussian processes, and several special rules are applied to refine the segmentation contours. Experimental results show that our proposed method outperforms current state-of-the-art algorithms by a significant margin in all experiments.

Viet-Hang Duong, Yuan-Shan Lee, Bach-Tung Pham et al.

This work developed novel complex matrix factorization methods for face recognition; the methods were complex matrix factorization (CMF), sparse complex matrix factorization (SpaCMF), and graph complex matrix factorization (GraCMF). After real-valued data are transformed into a complex field, the complex-valued matrix will be decomposed into two matrices of bases and coefficients, which are derived from solutions to an optimization problem in a complex domain. The generated objective function is the real-valued function of the reconstruction error, which produces a parametric description. Factorizing the matrix of complex entries directly transformed the constrained optimization problem into an unconstrained optimization problem. Additionally, a complex vector space with N dimensions can be regarded as a 2N-dimensional real vector space. Accordingly, all real analytic properties can be exploited in the complex field. The ability to exploit these important characteristics motivated the development herein of a simpler framework that can provide better recognition results. The effectiveness of this framework will be clearly elucidated in later sections in this paper.