In this work, we introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states.

While optimization-based methods boast gen-eralizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature.

Once closed-form expressions for these Jacobians are derived, it remains to substitute those expressions into (16). The following identity (often termed the "vec" rule) will To depict the spatial topographies of the latent components measured on the EEG and fMRI analyses, the "forward-model" [ The results of the comparison are shown in Fig S1, where it is clear that the signal fidelity of the GCs (right panel) significantly exceeds those yielded by PCA (left) and ICA (middle). GCA is only able to recover sources with temporal dependencies (i.e., s Both the single electrodes and Granger components exhibit two pronounced peaks in the spectra: one near 2 Hz ("delta" Fig S3 shows the corresponding result for the left motor imagery condition. EEG motor imagery dataset described in the main text. For each technique, the first 6 components are presented.

Here the concept of Granger causality is employed to propose a new criterion for unsupervised learning that is appropriate in the case of temporally-dependent source signals. The basic idea is to identify two projections of a multivariate time series such that the Granger causality among the resulting pair of components is maximized.

Generating video stories from text prompts is a complex task. In addition to having high visual quality, videos need to realistically adhere to a sequence of text prompts whilst being consistent throughout the frames.

These works are regarded as passive works for object detection as they take the input image as is. However, convergence to global minima is not guaranteed to be optimal in neural networks; therefore, we argue that the trained weights in the object detector are not optimal. To rectify this problem, we propose a wrapper based on proactive schemes, PrObeD, which enhances the performance of these object detectors by learning a signal. PrObeD consists of an encoder-decoder architecture, where the encoder network generates an image-dependent signal termed templates to encrypt the input images, and the decoder recovers this template from the encrypted images. We propose that learning the optimum template results in an object detector with an improved detection performance. The template acts as a mask to the input images to highlight semantics useful for the object detector. Finetuning the object detector with these encrypted images enhances the detection performance for both generic and camouflaged.

We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number.

To evaluate VLMs' fine-grained understanding, existing benchmarks primarily focus on evaluating VLMs' capability