Vikas Verma

Yingtian Zou, Vikas Verma, Sarthak Mittal et al. · cmu, deepmind

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.

Amartya Bhattacharya, Debarshi Brahma, Suraj Nagaje Mahadev et al.

Spread of fake news using out-of-context images and captions has become widespread in this era of information overload. Since fake news can belong to different domains like politics, sports, etc. with their unique characteristics, inference on a test image-caption pair is contingent on how well the model has been trained on similar data. Since training individual models for each domain is not practical, we propose a novel framework termed DPOD (Domain-specific Prompt tuning using Out-of-domain data), which can exploit out-of-domain data during training to improve fake news detection of all desired domains simultaneously. 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 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 training samples of all the available domains based on the extent they can be useful to the desired domain. Extensive experiments on the large-scale NewsCLIPpings and VERITE benchmarks demonstrate that DPOD achieves state of-the-art performance for this challenging task. Code: https://github.com/scviab/DPOD.

Alexia Jolicoeur-Martineau, Alex Lamb, Vikas Verma et al. · mila

We propose a novel regularizer for supervised learning called Conditioning on Noisy Targets (CNT). This approach consists in conditioning the model on a noisy version of the target(s) (e.g., actions in imitation learning or labels in classification) at a random noise level (from small to large noise). At inference time, since we do not know the target, we run the network with only noise in place of the noisy target. CNT provides hints through the noisy label (with less noise, we can more easily infer the true target). This give two main benefits: 1) the top-down feedback allows the model to focus on simpler and more digestible sub-problems and 2) rather than learning to solve the task from scratch, the model will first learn to master easy examples (with less noise), while slowly progressing toward harder examples (with more noise).

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Yuri Chervonyi, Trieu H. Trinh, Miroslav Olšák et al.

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 support for non-constructive problems, 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 enables effective communication between 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.

Vikas Verma, Minh-Thang Luong, Kenji Kawaguchi et al.

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.

Mojtaba Faramarzi, Mohammad Amini, Akilesh Badrinaaraayanan et al.

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. 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 CIFAR10/100, SVHN, Tiny-ImageNet, and ImageNet using ResNet architectures including PreActResnet18/34, WRN-28-10, ResNet101/152 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 a better generalization to deformed samples and is more robust against adversarial attacks.

Jisoo Jeong, Vikas Verma, Minsung Hyun et al.

Despite the data labeling cost for the object detection tasks being substantially more than that of the classification tasks, semi-supervised learning methods for object detection have not been studied much. In this paper, we propose an Interpolation-based Semi-supervised learning method for object Detection (ISD), which considers and solves the problems caused by applying conventional Interpolation Regularization (IR) directly to object detection. We divide the output of the model into two types according to the objectness scores of both original patches that are mixed in IR. Then, we apply a separate loss suitable for each type in an unsupervised manner. The proposed losses dramatically improve the performance of semi-supervised learning as well as supervised learning. In the supervised learning setting, our method improves the baseline methods by a significant margin. In the semi-supervised learning setting, our algorithm improves the performance on a benchmark dataset (PASCAL VOC and MSCOCO) in a benchmark architecture (SSD).

Alex Lamb, Sherjil Ozair, Vikas Verma et al.

Deep networks have achieved excellent results in perceptual tasks, yet their ability to generalize to variations not seen during training has come under increasing scrutiny. In this work we focus on their ability to have invariance towards the presence or absence of details. For example, humans are able to watch cartoons, which are missing many visual details, without being explicitly trained to do so. As another example, 3D rendering software is a relatively recent development, yet people are able to understand such rendered scenes even though they are missing details (consider a film like Toy Story). The failure of machine learning algorithms to do this indicates a significant gap in generalization between human abilities and the abilities of deep networks. We propose a dataset that will make it easier to study the detail-invariance problem concretely. We produce a concrete task for this: SketchTransfer, and we show that state-of-the-art domain transfer algorithms still struggle with this task. The state-of-the-art technique which achieves over 95\% on MNIST $\xrightarrow{}$ SVHN transfer only achieves 59\% accuracy on the SketchTransfer task, which is much better than random (11\% accuracy) but falls short of the 87\% accuracy of a classifier trained directly on labeled sketches. This indicates that this task is approachable with today's best methods but has substantial room for improvement.

Vikas Verma, Meng Qu, Kenji Kawaguchi et al.

We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to train a fully-connected network jointly with the graph neural network via parameter sharing and interpolation-based regularization. Further, we provide a theoretical analysis of how GraphMix improves the generalization bounds of the underlying graph neural network, without making any assumptions about the "aggregation" layer or the depth of the graph neural networks. We experimentally validate this analysis by applying GraphMix to various architectures such as Graph Convolutional Networks, Graph Attention Networks and Graph-U-Net. Despite its simplicity, we demonstrate that GraphMix can consistently improve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets: Cora-Full, Co-author-CS and Co-author-Physics.

Fan-Yun Sun, Jordan Hoffmann, Vikas Verma et al.

This paper studies learning the representations of whole graphs in both unsupervised and semi-supervised scenarios. Graph-level representations are critical in a variety of real-world applications such as predicting the properties of molecules and community analysis in social networks. Traditional graph kernel based methods are simple, yet effective for obtaining fixed-length representations for graphs but they suffer from poor generalization due to hand-crafted designs. There are also some recent methods based on language models (e.g. graph2vec) but they tend to only consider certain substructures (e.g. subtrees) as graph representatives. Inspired by recent progress of unsupervised representation learning, in this paper we proposed a novel method called InfoGraph for learning graph-level representations. We maximize the mutual information between the graph-level representation and the representations of substructures of different scales (e.g., nodes, edges, triangles). By doing so, the graph-level representations encode aspects of the data that are shared across different scales of substructures. Furthermore, we further propose InfoGraph*, an extension of InfoGraph for semi-supervised scenarios. InfoGraph* maximizes the mutual information between unsupervised graph representations learned by InfoGraph and the representations learned by existing supervised methods. As a result, the supervised encoder learns from unlabeled data while preserving the latent semantic space favored by the current supervised task. Experimental results on the tasks of graph classification and molecular property prediction show that InfoGraph is superior to state-of-the-art baselines and InfoGraph* can achieve performance competitive with state-of-the-art semi-supervised models.

Simon Guiroy, Vikas Verma, Christopher Pal

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.

Alex Lamb, Vikas Verma, Kenji Kawaguchi et al.

Adversarial robustness has become a central goal in deep learning, both in the theory and the practice. However, successful methods to improve the adversarial robustness (such as adversarial training) greatly hurt generalization performance on the unperturbed data. This could have a major impact on how the adversarial robustness affects real world systems (i.e. many may opt to forego robustness if it can improve accuracy on the unperturbed 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 the standard test error (when there is no adversary) from 4.43% to 12.32%, whereas with our Interpolated adversarial training we retain the adversarial robustness while achieving a standard test error of only 6.45%. With our technique, the relative increase in the standard error for the robust model is reduced from 178.1% to just 45.5%. Moreover, we provide mathematical analysis of Interpolated Adversarial Training to confirm its efficiencies and demonstrate its advantages in terms of robustness and generalization.

Vikas Verma, Kenji Kawaguchi, Alex Lamb et al.

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. Our theoretical analysis shows that ICT corresponds to a certain type of data-adaptive regularization with unlabeled points which reduces overfitting to labeled points under high confidence values.

Christopher Beckham, Sina Honari, Vikas Verma et al.

In this paper, we explore new approaches to combining information encoded within the learned representations of auto-encoders. 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.

Jason Jo, Vikas Verma, Yoshua Bengio

We focus on two supervised visual reasoning tasks whose labels encode a semantic relational rule between two or more objects in an image: the MNIST Parity task and the colorized Pentomino task. The objects in the images undergo random translation, scaling, rotation and coloring transformations. Thus these tasks involve invariant relational reasoning. We report uneven performance of various deep CNN models on these two tasks. For the MNIST Parity task, we report that the VGG19 model soundly outperforms a family of ResNet models. Moreover, the family of ResNet models exhibits a general sensitivity to random initialization for the MNIST Parity task. For the colorized Pentomino task, now both the VGG19 and ResNet models exhibit sluggish optimization and very poor test generalization, hovering around 30% test error. The CNN we tested all learn hierarchies of fully distributed features and thus encode the distributed representation prior. We are motivated by a hypothesis from cognitive neuroscience which posits that the human visual cortex is modularized, and this allows the visual cortex to learn higher order invariances. To this end, we consider a modularized variant of the ResNet model, referred to as a Residual Mixture Network (ResMixNet) which employs a mixture-of-experts architecture to interleave distributed representations with more specialized, modular representations. We show that very shallow ResMixNets are capable of learning each of the two tasks well, attaining less than 2% and 1% test error on the MNIST Parity and the colorized Pentomino tasks respectively. Most importantly, the ResMixNet models are extremely parameter efficient: generalizing better than various non-modular CNNs that have over 10x the number of parameters. These experimental results support the hypothesis that modularity is a robust prior for learning invariant relational reasoning.

Vikas Verma, Alex Lamb, Christopher Beckham et al.

Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly different test examples. This includes distribution shifts, outliers, and adversarial examples. To address these issues, we propose Manifold Mixup, a simple regularizer that encourages neural networks to predict less confidently on interpolations of hidden representations. Manifold Mixup leverages semantic interpolations as additional training signal, obtaining neural networks with smoother decision boundaries at multiple levels of representation. As a result, neural networks trained with Manifold Mixup learn class-representations with fewer directions of variance. We prove theory on why this flattening happens under ideal conditions, validate it on practical situations, and connect it to previous works on information theory and generalization. In spite of incurring no significant computation and being implemented in a few lines of code, Manifold Mixup improves strong baselines in supervised learning, robustness to single-step adversarial attacks, and test log-likelihood.

Kenji Kawaguchi, Yoshua Bengio, Vikas Verma et al.

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.

Stanisław Jastrzębski, Devansh Arpit, Nicolas Ballas et al.

Residual networks (Resnets) have become a prominent architecture in deep learning. However, a comprehensive understanding of Resnets is still a topic of ongoing research. A recent view argues that Resnets perform iterative refinement of features. We attempt to further expose properties of this aspect. To this end, we study Resnets both analytically and empirically. We formalize the notion of iterative refinement in Resnets by showing that residual connections naturally encourage features of residual blocks to move along the negative gradient of loss as we go from one block to the next. In addition, our empirical analysis suggests that Resnets are able to perform both representation learning and iterative refinement. In general, a Resnet block tends to concentrate representation learning behavior in the first few layers while higher layers perform iterative refinement of features. Finally we observe that sharing residual layers naively leads to representation explosion and counterintuitively, overfitting, and we show that simple existing strategies can help alleviating this problem.

Kenji Kawaguchi, Bo Xie, Vikas Verma et al.

We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the model classes contain an arbitrarily good function as the width increases (universality), and despite non-convexity, we can find such a good function (optimization theory) that generalizes to unseen new data (generalization bound). For deep models, with no unrealistic assumptions, we prove universal approximation ability, a lower bound on approximation error, a partial optimization guarantee, and a generalization bound. Depending on the problems, the generalization bound of deep semi-random features can be exponentially better than the known bounds of deep ReLU nets; our generalization error bound can be independent of the depth, the number of trainable weights as well as the input dimensionality. In experiments, we show that semi-random features can match the performance of neural networks by using slightly more units, and it outperforms random features by using significantly fewer units. Moreover, we introduce a new implicit ensemble method by using semi-random features.

Vikas Verma

Content Based Image Retrieval(CBIR) is one of the important subfield in the field of Information Retrieval. The goal of a CBIR algorithm is to retrieve semantically similar images in response to a query image submitted by the end user. CBIR is a hard problem because of the phenomenon known as $\textit {semantic gap}$. In this thesis, we aim at analyzing the performance of a CBIR system build using local feature vectors and Intermediate Matching Kernel. We also propose a Two-Step Matching process for reducing the response time of the CBIR systems. Further, we develop a Meta-Learning framework for improving the retrieval performance of these systems. Our results show that the Two-Step Matching process significantly reduces response time and the Meta-Learning Framework improves the retrieval performance by more than two fold. We also analyze the performance of various image classification systems that use different image representations constructed from the local feature vectors.