A relation between Mirkovic-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE

The irreducible components of the variety of all modules over the preprojective algebra and MV cycles both index bases of the universal enveloping algebra of the positive part of a semisimple Lie algebra canonically. To relate these two objects Baumann and Kamnitzer associate a cycle in the affine Grassmannian to a given module. It is conjectured that the ring of functions of the T-fixed point subscheme of the associated cycle is isomorphic to the cohomology ring of the quiver Grassmannian of the module. I give a proof of part of this conjecture. The relation between this conjecture and the reduceness conjecture is explained at the end

PRSNet: A Masked Self-Supervised Learning Pedestrian Re-Identification Method

In recent years, self-supervised learning has attracted widespread academic debate and addressed many of the key issues of computer vision. The present research focus is on how to construct a good agent task that allows for improved network learning of advanced semantic information on images so that model reasoning is accelerated during pre-training of the current task. In order to solve the problem that existing feature extraction networks are pre-trained on the ImageNet dataset and cannot extract the fine-grained information in pedestrian images well, and the existing pre-task of contrast self-supervised learning may destroy the original properties of pedestrian images, this paper designs a pre-task of mask reconstruction to obtain a pre-training model with strong robustness and uses it for the pedestrian re-identification task. The training optimization of the network is performed by improving the triplet loss based on the centroid, and the mask image is added as an additional sample to the loss calculation, so that the network can better cope with the pedestrian matching in practical applications after the training is completed. This method achieves about 5% higher mAP on Marker1501 and CUHK03 data than existing self-supervised learning pedestrian re-identification methods, and about 1% higher for Rank1, and ablation experiments are conducted to demonstrate the feasibility of this method. Our model code is located at https://github.com/ZJieX/prsnet

Evaluating the Robustness of Text-to-image Diffusion Models against Real-world Attacks

Text-to-image (T2I) diffusion models (DMs) have shown promise in generating high-quality images from textual descriptions. The real-world applications of these models require particular attention to their safety and fidelity, but this has not been sufficiently explored. One fundamental question is whether existing T2I DMs are robust against variations over input texts. To answer it, this work provides the first robustness evaluation of T2I DMs against real-world attacks. Unlike prior studies that focus on malicious attacks involving apocryphal alterations to the input texts, we consider an attack space spanned by realistic errors (e.g., typo, glyph, phonetic) that humans can make, to ensure semantic consistency. Given the inherent randomness of the generation process, we develop novel distribution-based attack objectives to mislead T2I DMs. We perform attacks in a black-box manner without any knowledge of the model. Extensive experiments demonstrate the effectiveness of our method for attacking popular T2I DMs and simultaneously reveal their non-trivial robustness issues. Moreover, we provide an in-depth analysis of our method to show that it is not designed to attack the text encoder in T2I DMs solely

Discovering Predictable Latent Factors for Time Series Forecasting

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex relations between variables and tune the parameters with large-scale data. Many real-world data mining tasks, however, lack sufficient variables for relation reasoning, and therefore these methods may not properly handle such forecasting problems. With insufficient data, time series appear to be affected by many exogenous variables, and thus, the modeling becomes unstable and unpredictable. To tackle this critical issue, in this paper, we develop a novel algorithmic framework for inferring the intrinsic latent factors implied by the observable time series. The inferred factors are used to form multiple independent and predictable signal components that enable not only sparse relation reasoning for long-term efficiency but also reconstructing the future temporal data for accurate prediction. To achieve this, we introduce three characteristics, i.e., predictability, sufficiency, and identifiability, and model these characteristics via the powerful deep latent dynamics models to infer the predictable signal components. Empirical results on multiple real datasets show the efficiency of our method for different kinds of time series forecasting. The statistical analysis validates the predictability of the learned latent factors