A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising weight-space models that are equivariant to the permutation symmetries of simple feedforward networks. However, they are not applicable to general architectures, since the permutation symmetries of a weight space can be complicated by recurrence or residual connections. This work proposes an algorithm that automatically constructs permutation equivariant models, which we refer to as universal neural functionals (UNFs), for any weight space. Among other applications, we demonstrate how UNFs can be substituted into existing learned optimizer designs, and find promising improvements over prior methods when optimizing small image classifiers and language models. Our results suggest that learned optimizers can benefit from considering the (symmetry) structure of the weight space they optimize.

We present a new technique for the learning of continuous energy functions that we refer to as Wibergian Learning. One common approach to inverse problems is to cast them as an energy minimisation problem, where the minimum cost solution found is used as an estimator of hidden parameters. Our new approach formally characterises the dependency between weights that control the shape of the energy function, and the location of minima, by describing minima as fixed points of optimisation methods. This allows for the use of gradient-based end-toend training to integrate deep-learning and the classical inverse problem methods. We show how our approach can be applied to obtain state-of-the-art results in the diverse applications of tracker fusion and multiview 3D reconstruction.

We thank the reviewers for their extensive comments. Where is the novelty (R2+R4) / What is the point of the new proofs (R2)? However, our primary result is to show why it works. Newton's method with a more stable trust-region based method gave rise to a more stable fixed-point (line 131), and Given this, partial derivatives and full derivatives coincide. This mischaracterisation by R6 is our fault; we had intended to cite Fitzgibbon's later We emphasise that we're modifying a baseline [24] that was published independently All issues raised by the reviewers will be clarified. 'network' instead of'parameters of the energy function' in the pose experiment; we agree the name should be changed.

Monocular depth estimation (MDE) is fundamental for deriving 3D scene structures from 2D images. While state-of-the-art monocular relative depth estimation (MRDE) excels in estimating relative depths for in-the-wild images, current monocular metric depth estimation (MMDE) approaches still face challenges in handling unseen scenes. Since MMDE can be viewed as the composition of MRDE and metric scale recovery, we attribute this difficulty to scene dependency, where MMDE models rely on scenes observed during supervised training for predicting scene scales during inference. To address this issue, we propose to use humans as landmarks for distilling scene-independent metric scale priors from generative painting models.

Satellite-based remote sensing has revolutionised the way we address global challenges in a rapidly evolving world. Huge quantities of Earth Observation (EO) data are generated by satellite sensors daily, but processing these large datasets for use in ML pipelines is technically and computationally challenging. Specifically, different types of EO data are often hosted on a variety of platforms, with differing degrees of availability for Python preprocessing tools. In addition, spatial alignment across data sources and data tiling for easier handling can present significant technical hurdles for novice users. While some preprocessed Earth observation datasets exist, their content is often limited to optical or near-optical wavelength data, which is ineffective at night or in adverse weather conditions. Synthetic Aperture Radar (SAR), an active sensing technique based on microwave length radiation, offers a viable alternative. However, the application of machine learning to SAR has been limited due to a lack of ML-ready data and pipelines, particularly for the full diversity of SAR data, including polarimetry, coherence and interferometry. In this work, we introduce M3LEO, a multi-modal, multi-label Earth observation dataset that includes polarimetric, interferometric, and coherence SAR data derived from Sentinel-1, alongside multispectral Sentinel-2 imagery and a suite of auxiliary data describing terrain properties such as land use.

Learning the probability distribution of high-dimensional data is a challenging problem. To solve this problem, we formulate a deep energy adversarial network (DEAN), which casts the energy model learned from real data into an optimization of a goodness-of-fit (GOF) test statistic. DEAN can be interpreted as a GOF game between two generative networks, where one explicit generative network learns an energy-based distribution that fits the real data, and the other implicit generative network is trained by minimizing a GOF test statistic between the energy-based distribution and the generated data, such that the underlying distribution of the generated data is close to the energy-based distribution. We design a two-level alternative optimization procedure to train the explicit and implicit generative networks, such that the hyper-parameters can also be automatically learned. Experimental results show that DEAN achieves high quality generations compared to the state-of-the-art approaches.

We would like to thank all three reviewers for acknowledging our contributions and providing valuable feedback. Thank you for the positive comments on the novelty of our idea and insightful questions for further improvement. We first characterize the solutions of DEAN. Other choices for the energy objective will be left to future works. (Figure 1).

Achieving robustness to distributional shift is a longstanding and challenging goal of computer vision. Data augmentation is a commonly used approach for improving robustness, however robustness gains are typically not uniform across corruption types. Indeed increasing performance in the presence of random noise is often met with reduced performance on other corruptions such as contrast change. Understanding when and why these sorts of trade-offs occur is a crucial step towards mitigating them. Towards this end, we investigate recently observed tradeoffs caused by Gaussian data augmentation and adversarial training. We find that both methods improve robustness to corruptions that are concentrated in the high frequency domain while reducing robustness to corruptions that are concentrated in the low frequency domain. This suggests that one way to mitigate these trade-offs via data augmentation is to use a more diverse set of augmentations. Towards this end we observe that AutoAugment [6], a recently proposed data augmentation policy optimized for clean accuracy, achieves state-of-the-art robustness on the CIFAR-10-C [17] benchmark.

R2: "Section 4.2 needs more clarity. It's not clear if the Fog noise model is a good model for fog corruption..."

In this work we investigate the generalization performance of random feature ridge regression (RFRR). Our main contribution is a general deterministic equivalent for the test error of RFRR. Specifically, under a certain concentration property, we show that the test error is well approximated by a closed-form expression that only depends on the feature map eigenvalues. Notably, our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension-- allowing for infinite-dimensional features. We expect this deterministic equivalent to hold broadly beyond our theoretical analysis, and we empirically validate its predictions on various real and synthetic datasets. As an application, we derive sharp excess error rates under standard power-law assumptions of the spectrum and target decay. In particular, we provide a tight result for the smallest number of features achieving optimal minimax error rate.