Often, observational data alone is not enough to uniquely identify a system's causal structure.

Whilestochastic optimization ofAUROChasbeenstudied extensively, principled stochastic optimization of AUPRC has been rarely explored.

Often, observational data alone is not enough to uniquely identify a system's causal structure.

The correspondence principle is proposed to enable a unified representation of the representational principles from PSG, DG, and CG . To that end, the paper first illustrates a series of steps in achieving a unified representation for a discontinuous subordinate clause from Turkish as an illustrative case. This affords a new way of approach ing discontinuity in natural language from a theoretical point of view that unites and integrates the basic tenets of PSG, DG, and CG, with significant consequences for syntactic analysis. The n this paper demonstrates that a unified representation can simplify computational complexity with regards to the neurocognitive representation and processing of both continuous and discontinuous sentences vis - à - vis the basic principles of PSG, DG, and CG. 1 Introduction Discontinuity refers to a case of non - adjacency when a predicate and its argument (s) are not adjacent as per the linear order of the sentence -- predicate structure here may apply to constituents such as verb phrases, noun phrases, adjective phrases, etc. It is typically observed in free word order languages including Australian languages such as W arlpiri, Jiwarli, Turkish (Hale, 1982, 1983; Nordlinger, 2014). Figure 1 depicts a schematic representation of continuity and discontinuity.

We propose Gradient Inversion Transcript (GIT), a novel generative approach for reconstructing training data from leaked gradients. GIT employs a generative attack model, whose architecture is tailored to align with the structure of the leaked model based on theoretical analysis. Once trained offline, GIT can be deployed efficiently and only relies on the leaked gradients to reconstruct the input data, rendering it applicable under various distributed learning environments. When used as a prior for other iterative optimization-based methods, GIT not only accelerates convergence but also enhances the overall reconstruction quality. GIT consistently outperforms existing methods across multiple datasets and demonstrates strong robustness under challenging conditions, including inaccurate gradients, data distribution shifts and discrepancies in model parameters.

Foundation models aim to create general, cross-task, and cross-domain machine learning models by pretraining on large-scale datasets to capture shared patterns or concepts (generalities), such as contours, colors, textures, and edges in images, or tokens, words, and sentences in text. However, discovering generalities across graphs remains challenging, which has hindered the development of graph foundation models. To tackle this challenge, in this paper, we propose a novel approach to learn generalities across graphs via task-trees. Specifically, we first define the basic learning instances in graphs as task-trees and assume that the generalities shared across graphs are, at least partially, preserved in the task-trees of the given graphs. To validate the assumption, we first perform a theoretical analysis of task-trees in terms of stability, transferability, and generalization. We find that if a graph neural network (GNN) model is pretrained on diverse task-trees through a reconstruction task, it can learn sufficient transferable knowledge for downstream tasks using an appropriate set of fine-tuning samples. To empirically validate the assumption, we further instantiate the theorems by developing a cross-task, cross-domain graph foundation model named Graph generality Identifier on task-Trees (GIT). The extensive experiments over 30 graphs from five domains demonstrate the effectiveness of GIT in fine-tuning, in-context learning, and zero-shot learning scenarios. Particularly, the general GIT model pretrained on large-scale datasets can be quickly adapted to specific domains, matching or even surpassing expert models designed for those domains. Our data and code are available at https://github.com/Zehong-Wang/GIT.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in $5\sim 10$ function evaluations.

Inferring causal structure from data is a challenging task of fundamental importance in science. Often, observational data alone is not enough to uniquely identify a system's causal structure. The use of interventional data can address this issue, however, acquiring these samples typically demands a considerable investment of time and physical or financial resources. In this work, we are concerned with the acquisition of interventional data in a targeted manner to minimize the number of required experiments. We propose a novel Gradient-based Intervention Targeting method, abbreviated GIT, that'trusts' the gradient estimator of a gradient-based causal discovery framework to provide signals for the intervention targeting function. We provide extensive experiments in simulated and real-world datasets and demonstrate that GIT performs on par with competitive baselines, surpassing them in the low-data regime.

Deep neural networks tend to make overconfident predictions and often require additional detectors for misclassifications, particularly for safety-critical applications. Existing detection methods usually only focus on adversarial attacks or out-of-distribution samples as reasons for false predictions. However, generalization errors occur due to diverse reasons often related to poorly learning relevant invariances. We therefore propose GIT, a holistic approach for the detection of generalization errors that combines the usage of gradient information and invariance transformations. The invariance transformations are designed to shift misclassified samples back into the generalization area of the neural network, while the gradient information measures the contradiction between the initial prediction and the corresponding inherent computations of the neural network using the transformed sample. Our experiments demonstrate the superior performance of GIT compared to the state-of-the-art on a variety of network architectures, problem setups and perturbation types.