We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for $\textit{all}$ geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.

The spread of fake news using out-of-context images has become widespread and is a challenging task in this era of information overload. Since annotating huge amounts of such data requires significant time of domain experts, it is imperative to develop methods which can work in limited annotated data scenarios. In this work, we explore whether out-of-domain data can help to improve out-of-context misinformation detection (termed here as multi-modal fake news detection) of a desired domain, eg. politics, healthcare, etc. Towards this goal, we propose a novel framework termed DPOD (Domain-specific Prompt-tuning using Out-of-Domain data). First, to compute generalizable features, we modify the Vision-Language Model, CLIP to extract features that helps to align the representations of the images and corresponding text captions of both the in-domain and out-of-domain data in a label-aware manner. Further, we propose a domain-specific prompt learning technique which leverages the training samples of all the available domains based on the the extent they can be useful to the desired domain. Extensive experiments on a large-scale benchmark dataset, namely NewsClippings demonstrate that the proposed framework achieves state of-the-art performance, significantly surpassing the existing approaches for this challenging task.

Mixup is a popular data augmentation technique for training deep neural networks where additional samples are generated by linearly interpolating pairs of inputs and their labels. This technique is known to improve the generalization performance in many learning paradigms and applications. In this work, we first analyze Mixup and show that it implicitly regularizes infinitely many directional derivatives of all orders. Based on this new insight, we propose an improved version of Mixup, theoretically justified to deliver better generalization performance than the vanilla Mixup. To demonstrate the effectiveness of the proposed method, we conduct experiments across various domains such as images, tabular data, speech, and graphs. Our results show that the proposed method improves Mixup across multiple datasets using a variety of architectures, for instance, exhibiting an improvement over Mixup by 0.8% in ImageNet top-1 accuracy.

Despite recent success, most contrastive self-supervised learning methods are domain-specific, relying heavily on data augmentation techniques that require knowledge about a particular domain, such as image cropping and rotation. To overcome such limitation, we propose a novel domain-agnostic approach to contrastive learning, named DACL, that is applicable to domains where invariances, and thus, data augmentation techniques, are not readily available. Key to our approach is the use of Mixup noise to create similar and dissimilar examples by mixing data samples differently either at the input or hidden-state levels. To demonstrate the effectiveness of DACL, we conduct experiments across various domains such as tabular data, images, and graphs. Our results show that DACL not only outperforms other domain-agnostic noising methods, such as Gaussian-noise, but also combines well with domain-specific methods, such as SimCLR, to improve self-supervised visual representation learning. Finally, we theoretically analyze our method and show advantages over the Gaussian-noise based contrastive learning approach.

Large capacity deep learning models are often prone to a high generalization gap when trained with a limited amount of labeled training data. A recent class of methods to address this problem uses various ways to construct a new training sample by mixing a pair (or more) of training samples. We propose PatchUp, a hidden state block-level regularization technique for Convolutional Neural Networks (CNNs), that is applied on selected contiguous blocks of feature maps from a random pair of samples. Our approach improves the robustness of CNN models against the manifold intrusion problem that may occur in other state-of-the-art mixing approaches like Mixup and CutMix. Moreover, since we are mixing the contiguous block of features in the hidden space, which has more dimensions than the input space, we obtain more diverse samples for training towards different dimensions. Our experiments on CIFAR-10, CIFAR-100, and SVHN datasets with PreactResnet18, PreactResnet34, and WideResnet-28-10 models show that PatchUp improves upon, or equals, the performance of current state-of-the-art regularizers for CNNs. We also show that PatchUp can provide better generalization to affine transformations of samples and is more robust against adversarial attacks.

We present GraphMix, a regularization technique for Graph Neural Network based semi-supervised object classification, leveraging the recent advances in the regularization of classical deep neural networks. Specifically, we propose a unified approach in which we train a fully-connected network jointly with the graph neural network via parameter sharing, interpolation-based regularization, and self-predicted-targets. Our proposed method is architecture agnostic in the sense that it can be applied to any variant of graph neural networks which applies a parametric transformation to the features of the graph nodes. Despite its simplicity, with GraphMix we can consistently improve results and achieve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets : Cora-Full, Co-author-CS and Co-author-Physics.

In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few steps of gradient-based fine-tuning, become flatter, lower in loss, and further away from the meta-train solution. We also show that those meta-test solutions become flatter even as generalization starts to degrade, thus providing an experimental evidence against the correlation between generalization and flat minima in the paradigm of gradient-based meta-leaning. Furthermore, we provide empirical evidence that generalization to new tasks is correlated with the coherence between their adaptation trajectories in parameter space, measured by the average cosine similarity between task-specific trajectory directions, starting from a same meta-train solution. We also show that coherence of meta-test gradients, measured by the average inner product between the task-specific gradient vectors evaluated at meta-train solution, is also correlated with generalization. Based on these observations, we propose a novel regularizer for MAML and provide experimental evidence for its effectiveness.

Adversarial robustness has become a central goal in deep learning, both in theory and practice. However, successful methods to improve adversarial robustness (such as adversarial training) greatly hurt generalization performance on the clean data. This could have a major impact on how adversarial robustness affects real world systems (i.e. many may opt to forego robustness if it can improve performance on the clean data). We propose Interpolated Adversarial Training, which employs recently proposed interpolation based training methods in the framework of adversarial training. On CIFAR-10, adversarial training increases clean test error from 5.8% to 16.7%, whereas with our Interpolated adversarial training we retain adversarial robustness while achieving a clean test error of only 6.5%. With our technique, the relative error increase for the robust model is reduced from 187.9% to just 12.1%

In this paper, we explore new approaches to combining information encoded within the learned representations of autoencoders. We explore models that are capable of combining the attributes of multiple inputs such that a resynthesised output is trained to fool an adversarial discriminator for real versus synthesised data. Furthermore, we explore the use of such an architecture in the context of semi-supervised learning, where we learn a mixing function whose objective is to produce interpolations of hidden states, or masked combinations of latent representations that are consistent with a conditioned class label. We show quantitative and qualitative evidence that such a formulation is an interesting avenue of research. The autoencoder is a fundamental building block in unsupervised learning. Autoencoders are trained to reconstruct their inputs after being processed by two neural networks: an encoder which encodes the input to a high-level representation or bottleneck, and a decoder which performs the reconstruction using the representation as input.

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points. In classification problems, ICT moves the decision boundary to low-density regions of the data distribution. Our experiments show that ICT achieves state-of-the-art performance when applied to standard neural network architectures on the CIFAR-10 and SVHN benchmark datasets.