This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system and forward-backward conditions. Our method is efficient, even with a small number of iterations, and is capable of handling up to 300 dimensions with a single layer, which makes it faster than other approaches. In contrast, methods based on Generative Adversarial Networks (GANs) cannot solve MFGs with non-separable Hamiltonians. We demonstrate the effectiveness of our approach by applying it to a traffic flow problem, which was previously solved using the Newton iteration method only in the deterministic case. We compare the results of our method to analytical solutions and previous approaches, showing its efficiency. We also prove the convergence of our neural network approximation with a single hidden layer using the universal approximation theorem.
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We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.
Purpose: Multi-expert deep learning training methods to automatically quantify ischemic brain tissue on Non-Contrast CT Materials and Methods: The data set consisted of 260 Non-Contrast CTs from 233 patients of acute ischemic stroke patients recruited in the DEFUSE 3 trial. A benchmark U-Net was trained on the reference annotations of three experienced neuroradiologists to segment ischemic brain tissue using majority vote and random expert sampling training schemes. We used a one-sided Wilcoxon signed-rank test on a set of segmentation metrics to compare bootstrapped point estimates of the training schemes with the inter-expert agreement and ratio of variance for consistency analysis. We further compare volumes with the 24h-follow-up DWI (final infarct core) in the patient subgroup with full reperfusion and we test volumes for correlation to the clinical outcome (mRS after 30 and 90 days) with the Spearman method. Results: Random expert sampling leads to a model that shows better agreement with experts than experts agree among themselves and better agreement than the agreement between experts and a majority-vote model performance (Surface Dice at Tolerance 5mm improvement of 61% to 0.70 +- 0.03 and Dice improvement of 25% to 0.50 +- 0.04). The model-based predicted volume similarly estimated the final infarct volume and correlated better to the clinical outcome than CT perfusion. Conclusion: A model trained on random expert sampling can identify the presence and location of acute ischemic brain tissue on Non-Contrast CT similar to CT perfusion and with better consistency than experts. This may further secure the selection of patients eligible for endovascular treatment in less specialized hospitals.
This paper proposes a novel approach for detecting objects using mobile robots in the context of the RoboCup Standard Platform League, with a primary focus on detecting the ball. The challenge lies in detecting a dynamic object in varying lighting conditions and blurred images caused by fast movements. To address this challenge, the paper presents a convolutional neural network architecture designed specifically for computationally constrained robotic platforms. The proposed CNN is trained to achieve high precision classification of single objects in image patches and to determine their precise spatial positions. The paper further integrates Early Exits into the existing high-precision CNN architecture to reduce the computational cost of easily rejectable cases in the background class. The training process involves a composite loss function based on confidence and positional losses with dynamic weighting and data augmentation. The proposed approach achieves a precision of 100% on the validation dataset and a recall of almost 87%, while maintaining an execution time of around 170 $\mu$s per hypotheses. By combining the proposed approach with an Early Exit, a runtime optimization of more than 28%, on average, can be achieved compared to the original CNN. Overall, this paper provides an efficient solution for an enhanced detection of objects, especially the ball, in computationally constrained robotic platforms.
This paper presents ContrastWSD, a RoBERTa-based metaphor detection model that integrates the Metaphor Identification Procedure (MIP) and Word Sense Disambiguation (WSD) to extract and contrast the contextual meaning with the basic meaning of a word to determine whether it is used metaphorically in a sentence. By utilizing the word senses derived from a WSD model, our model enhances the metaphor detection process and outperforms other methods that rely solely on contextual embeddings or integrate only the basic definitions and other external knowledge. We evaluate our approach on various benchmark datasets and compare it with strong baselines, indicating the effectiveness in advancing metaphor detection.
We study stochastic Cubic Newton methods for solving general possibly non-convex minimization problems. We propose a new framework, which we call the helper framework, that provides a unified view of the stochastic and variance-reduced second-order algorithms equipped with global complexity guarantees. It can also be applied to learning with auxiliary information. Our helper framework offers the algorithm designer high flexibility for constructing and analyzing the stochastic Cubic Newton methods, allowing arbitrary size batches, and the use of noisy and possibly biased estimates of the gradients and Hessians, incorporating both the variance reduction and the lazy Hessian updates. We recover the best-known complexities for the stochastic and variance-reduced Cubic Newton, under weak assumptions on the noise. A direct consequence of our theory is the new lazy stochastic second-order method, which significantly improves the arithmetic complexity for large dimension problems. We also establish complexity bounds for the classes of gradient-dominated objectives, that include convex and strongly convex problems. For Auxiliary Learning, we show that using a helper (auxiliary function) can outperform training alone if a given similarity measure is small.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.
We introduce a new language representation model called BERT, which stands for Bidirectional Encoder Representations from Transformers. Unlike recent language representation models, BERT is designed to pre-train deep bidirectional representations by jointly conditioning on both left and right context in all layers. As a result, the pre-trained BERT representations can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of tasks, such as question answering and language inference, without substantial task-specific architecture modifications. BERT is conceptually simple and empirically powerful. It obtains new state-of-the-art results on eleven natural language processing tasks, including pushing the GLUE benchmark to 80.4% (7.6% absolute improvement), MultiNLI accuracy to 86.7 (5.6% absolute improvement) and the SQuAD v1.1 question answering Test F1 to 93.2 (1.5% absolute improvement), outperforming human performance by 2.0%.
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