The challenge arises from heteroscedasticity, which implies that the covariance is sample dependent and is often unknown. Consequently, recent methods learn the covariance through unsupervised frameworks, which unfortunately yield a trade-off between computational complexity and accuracy. While this trade-off could be alleviated through supervision, obtaining labels for the covariance is non-trivial. Here, we study self-supervised covariance estimation in deep heteroscedastic regression. We address two questions: (1) How should we supervise the covariance assuming ground truth is available? We address (1) by analysing two popular measures: the KL Divergence and the 2-Wasserstein distance. Subsequently, we derive an upper bound on the 2-Wasserstein distance between normal distributions with non-commutative covariances that is stable to optimize. We address (2) through a simple neighborhood based heuristic algorithm which results in surprisingly effective pseudo-labels for the covariance. Our experiments over a wide range of synthetic and real datasets demonstrate that the proposed 2-Wasserstein bound coupled with pseudo-label annotations results in a computationally cheaper yet accurate deep heteroscedastic regression. The target distribution is typically used for downstream tasks such as uncertainty estimation, correlation analysis, sampling, and in bayesian frameworks. The key challenge in deep heteroscedastic regression lies in estimating heteroscedasticity, which implies that the variance of the target is input dependent and variable. Moreover, unlike the mean, the covariance lacks direct supervision and needs to be inferred. The standard approach without the ground-truth covariance relies on optimizing the negative loglikelihood to jointly learn the mean and covariance (Dorta et al., 2018).

Large transformer models are known to produce high-norm tokens. In vision transformers (ViTs), such tokens have been mathematically modeled through the singular vectors of the linear approximations of layers. However, in large language models (LLMs), the underlying causes of high-norm tokens remain largely unexplored, and their different properties from those of ViTs require a new analysis framework. In this paper, we provide both theoretical insights and empirical validation across a range of recent models, leading to the following observations: i) The layer-wise singular direction predicts the abrupt explosion of token norms in LLMs. ii) The negative eigenvalues of a layer explain its sudden decay. iii) The computational pathways leading to high-norm tokens differ between initial and noninitial tokens. iv) High-norm tokens are triggered by the right leading singular vector of the matrix approximating the corresponding modules. We showcase two practical applications of these findings: the improvement of quantization schemes and the design of LLM signatures. Our findings not only advance the understanding of singular defects in LLMs but also open new avenues for their application. We expect that this work will stimulate further research into the internal mechanisms of LLMs and will therefore publicly release our code.

Adversarial training is a popular method to robustify models against adversarial attacks. However, it exhibits much more severe overfitting than training on clean inputs. In this work, we investigate this phenomenon from the perspective of training instances, i.e., training input-target pairs. Based on a quantitative metric measuring the relative difficulty of an instance in the training set, we analyze the model's behavior on training instances of different difficulty levels. This lets us demonstrate that the decay in generalization performance of adversarial training is a result of fitting hard adversarial instances. We theoretically verify our observations for both linear and general nonlinear models, proving that models trained on hard instances have worse generalization performance than ones trained on easy instances, and that this generalization gap increases with the size of the adversarial budget. Finally, we investigate solutions to mitigate adversarial overfitting in several scenarios, including fast adversarial training and fine-tuning a pretrained model with additional data. Our results demonstrate that using training data adaptively improves the model's robustness.

Text-to-image diffusion models have demonstrated remarkable capability in generating realistic images from arbitrary text prompts. However, they often produce inconsistent results for compositional prompts such as "two dogs" or "a penguin on the right of a bowl". Understanding these inconsistencies is crucial for reliable image generation. In this paper, we highlight the significant role of initial noise in these inconsistencies, where certain noise patterns are more reliable for compositional prompts than others. Our analyses reveal that different initial random seeds tend to guide the model to place objects in distinct image areas, potentially adhering to specific patterns of camera angles and image composition associated with the seed. To improve the model's compositional ability, we propose a method for mining these reliable cases, resulting in a curated training set of generated images without requiring any manual annotation. By fine-tuning text-to-image models on these generated images, we significantly enhance their compositional capabilities. For numerical composition, we observe relative increases of 29.3% and 19.5% for Stable Diffusion and PixArt-{\alpha}, respectively. Spatial composition sees even larger gains, with 60.7% for Stable Diffusion and 21.1% for PixArt-{\alpha}.

Domain Generalization (DG) aims to train models that perform well not only on the training (source) domains but also on novel, unseen target data distributions. A key challenge in DG is preventing overfitting to source domains, which can be mitigated by finding flatter minima in the loss landscape. In this work, we propose Quantization-aware Training for Domain Generalization (QT-DoG) and demonstrate that weight quantization effectively leads to flatter minima in the loss landscape, thereby enhancing domain generalization. Unlike traditional quantization methods focused on model compression, QT-DoG exploits quantization as an implicit regularizer by inducing noise in model weights, guiding the optimization process toward flatter minima that are less sensitive to perturbations and overfitting. We provide both theoretical insights and empirical evidence demonstrating that quantization inherently encourages flatter minima, leading to better generalization across domains. Moreover, with the benefit of reducing the model size through quantization, we demonstrate that an ensemble of multiple quantized models further yields superior accuracy than the state-of-the-art DG approaches with no computational or memory overheads. Our extensive experiments demonstrate that QT-DoG generalizes across various datasets, architectures, and quantization algorithms, and can be combined with other DG methods, establishing its versatility and robustness.

We introduce an approach to bias deep generative models, such as GANs and diffusion models, towards generating data with either enhanced fidelity or increased diversity. Our approach involves manipulating the distribution of training and generated data through a novel metric for individual samples, named pseudo density, which is based on the nearest-neighbor information from real samples. Our approach offers three distinct techniques to adjust the fidelity and diversity of deep generative models: 1) Per-sample perturbation, enabling precise adjustments for individual samples towards either more common or more unique characteristics; 2) Importance sampling during model inference to enhance either fidelity or diversity in the generated data; 3) Fine-tuning with importance sampling, which guides the generative model to learn an adjusted distribution, thus controlling fidelity and diversity. Furthermore, our fine-tuning method demonstrates the ability to improve the Frechet Inception Distance (FID) for pre-trained generative models with minimal iterations.

We propose an approach for reconstructing free-moving object from a monocular RGB video. Most existing methods either assume scene prior, hand pose prior, object category pose prior, or rely on local optimization with multiple sequence segments. We propose a method that allows free interaction with the object in front of a moving camera without relying on any prior, and optimizes the sequence globally without any segments. We progressively optimize the object shape and pose simultaneously based on an implicit neural representation. A key aspect of our method is a virtual camera system that reduces the search space of the optimization significantly. We evaluate our method on the standard HO3D dataset and a collection of egocentric RGB sequences captured with a head-mounted device. We demonstrate that our approach outperforms most methods significantly, and is on par with recent techniques that assume prior information.

Current 3D reconstruction techniques struggle to infer unbounded scenes from a few images faithfully. Specifically, existing methods have high computational demands, require detailed pose information, and cannot reconstruct occluded regions reliably. We introduce 6Img-to-3D, an efficient, scalable transformer-based encoder-renderer method for single-shot image to 3D reconstruction. Our method outputs a 3D-consistent parameterized triplane from only six outward-facing input images for large-scale, unbounded outdoor driving scenarios. We take a step towards resolving existing shortcomings by combining contracted custom cross- and self-attention mechanisms for triplane parameterization, differentiable volume rendering, scene contraction, and image feature projection. We showcase that six surround-view vehicle images from a single timestamp without global pose information are enough to reconstruct 360$^{\circ}$ scenes during inference time, taking 395 ms. Our method allows, for example, rendering third-person images and birds-eye views. Our code is available at https://github.com/continental/6Img-to-3D, and more examples can be found at our website here https://6Img-to-3D.GitHub.io/.

In the realm of point cloud scene understanding, particularly in indoor scenes, objects are arranged following human habits, resulting in objects of certain semantics being closely positioned and displaying notable inter-object correlations. This can create a tendency for neural networks to exploit these strong dependencies, bypassing the individual object patterns. To address this challenge, we introduce a novel self-supervised learning (SSL) strategy. Our approach leverages both object patterns and contextual cues to produce robust features. It begins with the formulation of an object-exchanging strategy, where pairs of objects with comparable sizes are exchanged across different scenes, effectively disentangling the strong contextual dependencies. Subsequently, we introduce a context-aware feature learning strategy, which encodes object patterns without relying on their specific context by aggregating object features across various scenes. Our extensive experiments demonstrate the superiority of our method over existing SSL techniques, further showing its better robustness to environmental changes. Moreover, we showcase the applicability of our approach by transferring pre-trained models to diverse point cloud datasets.

Unsupervised Semantic Segmentation (USS) involves segmenting images without relying on predefined labels, aiming to alleviate the burden of extensive human labeling. Existing methods utilize features generated by self-supervised models and specific priors for clustering. However, their clustering objectives are not involved in the optimization of the features during training. Additionally, due to the lack of clear class definitions in USS, the resulting segments may not align well with the clustering objective. In this paper, we introduce a novel approach called Optimally Matched Hierarchy (OMH) to simultaneously address the above issues. The core of our method lies in imposing structured sparsity on the feature space, which allows the features to encode information with different levels of granularity. The structure of this sparsity stems from our hierarchy (OMH). To achieve this, we learn a soft but sparse hierarchy among parallel clusters through Optimal Transport. Our OMH yields better unsupervised segmentation performance compared to existing USS methods. Our extensive experiments demonstrate the benefits of OMH when utilizing our differentiable paradigm. We will make our code publicly available.