Previous research on the diagnosis of Bipolar disorder has mainly focused on resting-state functional magnetic resonance imaging. However, their accuracy can not meet the requirements of clinical diagnosis. Efficient multimodal fusion strategies have great potential for applications in multimodal data and can further improve the performance of medical diagnosis models. In this work, we utilize both sMRI and fMRI data and propose a novel multimodal diagnosis model for bipolar disorder. The proposed Patch Pyramid Feature Extraction Module extracts sMRI features, and the spatio-temporal pyramid structure extracts the fMRI features. Finally, they are fused by a fusion module to output diagnosis results with a classifier. Extensive experiments show that our proposed method outperforms others in balanced accuracy from 0.657 to 0.732 on the OpenfMRI dataset, and achieves the state of the art.

Normalization layers are ubiquitous in deep learning, greatly accelerating optimization. However, they also introduce many unexpected phenomena during training, for example, the Fast Equilibrium conjecture proposed by (Li et al.,2020), which states that the scale-invariant normalized network, when trained by SGD with $\eta$ learning rate and $\lambda$ weight decay, mixes to an equilibrium in $\tilde{O}(1/\eta\lambda)$ steps, as opposed to classical $e^{O(\eta^{-1})}$ mixing time. Recent works by Wang & Wang (2022); Li et al. (2022c) proved this conjecture under different sets of assumptions. This paper aims to answer the fast equilibrium conjecture in full generality by removing the non-generic assumptions of Wang & Wang (2022); Li et al. (2022c) that the minima are isolated, that the region near minima forms a unique basin, and that the set of minima is an analytic set. Our main technical contribution is to show that with probability close to 1, in exponential time trajectories will not escape the attracting basin containing its initial position.

We examine both the manifold hypothesis (Bengio et al., 2013) and the union of manifold hypothesis (Brown et al., 2023), and argue that, in contrast to these hypotheses, the local intrinsic dimension varies from point to point even in the same connected component. We propose an alternative CW complex hypothesis that image data is distributed in “manifolds with skeletons". We support the hypothesis through visualization of distributions of image data of random geometric objects, as well as by introducing and testing a criterion on natural image datasets. One motivation of our work is to explain why diffusion models have difficulty generating accurate higher dimensional details such as human hands. Under the CW complex hypothesis and with both theoretical and empirical evidences, we provide an interpretation that the mixture of higher and lower dimensional components in data obstructs diffusion models from efficient learning.

We justify the fast equilibrium conjecture on stochastic gradient descent from (Li et al. 2020) under the assumptions that critical points are non-degenerate and the stochastic noise is a standard Gaussian. In this case, we prove an SGD with constant effective learning rate consists of three stages: descent, diffusion and tunneling, and explicitly identify temporary equilibrium states in the normalized parameter space that can be observed within practical training time. This interprets the gap between the mixing time in the fast equilibrium conjecture and the previously known upper bound. While our assumptions do not represent typical implementations of SGD of neural networks in practice, this is the first description of the three-stage mechanism in any case. The main finding in this mechanism is that a temporary equilibrium of local nature is quickly achieved after polynomial time (in term of the reciprocal of the intrinsic learning rate) and then stabilizes within observable time scales; and that the temporary equilibrium is in general different from the global Gibbs equilibrium, which will only appear after an exponentially long period beyond typical training limits. Our experiments support that this mechanism may extend to the general case.