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We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. Although mixing can be arbitrarily slow, we show that if the Markov chain has a $k$th order spectral gap, initialization from a set of $\tilde O(k/\varepsilon^2)$ samples from the stationary distribution will, with high probability over the samples, efficiently generate a sample whose conditional law is $\varepsilon$-close in TV distance to the stationary measure. In particular, this applies to mixtures of $k$ distributions satisfying a Poincar\'e inequality, with faster convergence when they satisfy a log-Sobolev inequality. Our bounds are stable to perturbations to the Markov chain, and in particular work for Langevin diffusion over $\mathbb R^d$ with score estimation error, as well as Glauber dynamics combined with approximation error from pseudolikelihood estimation. This justifies the success of data-based initialization for score matching methods despite slow mixing for the data distribution, and improves and generalizes the results of Koehler and Vuong (2023) to have linear, rather than exponential, dependence on $k$ and apply to arbitrary semigroups. As a consequence of our results, we show for the first time that a natural class of low-complexity Ising measures can be efficiently learned from samples.

We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly integrated differentiable simulation framework employing efficient pseudo-spectral methods, enabling 46 distinct PDEs across 1D, 2D, and 3D. Facilitating systematic analysis and comparison of learned emulators, we propose a novel taxonomy for unrolled training and introduce a unique identifier for PDE dynamics that directly relates to the stability criteria of classical numerical methods. APEBench enables the evaluation of diverse neural architectures, and unlike existing benchmarks, its tight integration of the solver enables support for differentiable physics training and neural-hybrid emulators. Moreover, APEBench emphasizes rollout metrics to understand temporal generalization, providing insights into the long-term behavior of emulating PDE dynamics. In several experiments, we highlight the similarities between neural emulators and numerical simulators., Comment: Accepted at Neurips 2024. The code is available at https://github.com/tum-pbs/apebench and APEBench can be installed via "pip install apebench"

What representation do deep neural networks learn? How similar are images to each other for neural networks? Despite the overwhelming success of deep learning methods key questions about their internal workings still remain largely unanswered, due to their internal high dimensionality and complexity. To address this, one approach is to measure the similarity of activation responses to various inputs. Representational Similarity Matrices (RSMs) distill this similarity into scalar values for each input pair. These matrices encapsulate the entire similarity structure of a system, indicating which input leads to similar responses. While the similarity between images is ambiguous, we argue that the spatial location of semantic objects does neither influence human perception nor deep learning classifiers. Thus this should be reflected in the definition of similarity between image responses for computer vision systems. Revisiting the established similarity calculations for RSMs we expose their sensitivity to spatial alignment. In this paper, we propose to solve this through semantic RSMs, which are invariant to spatial permutation. We measure semantic similarity between input responses by formulating it as a set-matching problem. Further, we quantify the superiority of semantic RSMs over spatio-semantic RSMs through image retrieval and by comparing the similarity between representations to the similarity between predicted class probabilities., Comment: Accepted at NeurIPS2024

The rise of Large Language Models (LLMs) has revolutionized natural language processing across numerous languages and tasks. However, evaluating LLM performance in a consistent and meaningful way across multiple European languages remains challenging, especially due to the scarcity of language-parallel multilingual benchmarks. We introduce a multilingual evaluation approach tailored for European languages. We employ translated versions of five widely-used benchmarks to assess the capabilities of 40 LLMs across 21 European languages. Our contributions include examining the effectiveness of translated benchmarks, assessing the impact of different translation services, and offering a multilingual evaluation framework for LLMs that includes newly created datasets: EU20-MMLU, EU20-HellaSwag, EU20-ARC, EU20-TruthfulQA, and EU20-GSM8K. The benchmarks and results are made publicly available to encourage further research in multilingual LLM evaluation.

We present two multilingual LLMs designed to embrace Europe's linguistic diversity by supporting all 24 official languages of the European Union. Trained on a dataset comprising around 60% non-English data and utilizing a custom multilingual tokenizer, our models address the limitations of existing LLMs that predominantly focus on English or a few high-resource languages. We detail the models' development principles, i.e., data composition, tokenizer optimization, and training methodologies. The models demonstrate competitive performance across multilingual benchmarks, as evidenced by their performance on European versions of ARC, HellaSwag, MMLU, and TruthfulQA.

In the realm of industrial manufacturing, Artificial Intelligence (AI) is playing an increasing role, from automating existing processes to aiding in the development of new materials and techniques. However, a significant challenge arises in smaller, experimental processes characterized by limited training data availability, questioning the possibility to train AI models in such small data contexts. In this work, we explore the potential of Transfer Learning to address this challenge, specifically investigating the minimum amount of data required to develop a functional AI model. For this purpose, we consider the use case of quality control of Carbon Fiber Reinforced Polymer (CFRP) tape laying in aerospace manufacturing using optical sensors. We investigate the behavior of different open-source computer vision models with a continuous reduction of the training data. Our results show that the amount of data required to successfully train an AI model can be drastically reduced, and the use of smaller models does not necessarily lead to a loss of performance.

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples., Comment: to be published in 63rd IEEE Conference on Decision and Control (CDC 2024)

Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy, but in practice this extraction is often technically difficult and computationally impractical. Here, we consider the electron density as a central observable in quantum chemistry and introduce a novel method to obtain accurate densities from real-space many-electron wave functions by representing the density with a neural network that captures known asymptotic properties and is trained from the wave function by score matching and noise-contrastive estimation. We use variational quantum Monte Carlo with deep-learning ans\"atze (deep QMC) to obtain highly accurate wave functions free of basis set errors, and from them, using our novel method, correspondingly accurate electron densities, which we demonstrate by calculating dipole moments, nuclear forces, contact densities, and other density-based properties., Comment: 12 pages, 9 figures in the main text

With the rise of neural networks in various domains, multi-task learning (MTL) gained significant relevance. A key challenge in MTL is balancing individual task losses during neural network training to improve performance and efficiency through knowledge sharing across tasks. To address these challenges, we propose a novel task-weighting method by building on the most prevalent approach of Uncertainty Weighting and computing analytically optimal uncertainty-based weights, normalized by a softmax function with tunable temperature. Our approach yields comparable results to the combinatorially prohibitive, brute-force approach of Scalarization while offering a more cost-effective yet high-performing alternative. We conduct an extensive benchmark on various datasets and architectures. Our method consistently outperforms six other common weighting methods. Furthermore, we report noteworthy experimental findings for the practical application of MTL. For example, larger networks diminish the influence of weighting methods, and tuning the weight decay has a low impact compared to the learning rate.

Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability problem has been hindering the use of ML in fields like medicine, ecology and insurance, where an understanding of the inner workings of the model is paramount to ensure user acceptance and fairness. The need for interpretable ML models has boosted research in the field of interpretable machine learning (IML). Here we propose a novel approach for the functional decomposition of black-box predictions, which is considered a core concept of IML. The idea of our method is to replace the prediction function by a surrogate model consisting of simpler subfunctions. Similar to additive regression models, these functions provide insights into the direction and strength of the main feature contributions and their interactions. Our method is based on a novel concept termed stacked orthogonality, which ensures that the main effects capture as much functional behavior as possible and do not contain information explained by higher-order interactions. Unlike earlier functional IML approaches, it is neither affected by extrapolation nor by hidden feature interactions. To compute the subfunctions, we propose an algorithm based on neural additive modeling and an efficient post-hoc orthogonalization procedure.

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn's algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF's parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions., Comment: Conference version available from https://proceedings.mlr.press/v235/chang24b.html

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient alternatives like Best Subset Selection. Due to a large conjectured computational-statistical tradeoff in the problem of sparse linear regression, it may be impossible to close this gap in general. In this work, we propose a natural sparse linear regression setting where strong correlations between covariates arise from unobserved latent variables. In this setting, we analyze the problem caused by strong correlations and design a surprisingly simple fix. While Lasso with standard normalization of covariates fails, there exists a heterogeneous scaling of the covariates with which Lasso will suddenly obtain strong provable guarantees for estimation. Moreover, we design a simple, efficient procedure for computing such a "smart scaling." The sample complexity of the resulting "rescaled Lasso" algorithm incurs (in the worst case) quadratic dependence on the sparsity of the underlying signal. While this dependence is not information-theoretically necessary, we give evidence that it is optimal among the class of polynomial-time algorithms, via the method of low-degree polynomials. This argument reveals a new connection between sparse linear regression and a special version of sparse PCA with a near-critical negative spike. The latter problem can be thought of as a real-valued analogue of learning a sparse parity. Using it, we also establish the first computational-statistical gap for the closely related problem of learning a Gaussian Graphical Model.

Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. Based on this framework we propose an efficient algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC improves efficiency by incorporating three techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.

Neural vocoders model the raw audio waveform and synthesize high-quality audio, but even the highly efficient ones, like MB-MelGAN and LPCNet, fail to run real-time on a low-end device like a smartglass. A pure digital signal processing (DSP) based vocoder can be implemented via lightweight fast Fourier transforms (FFT), and therefore, is a magnitude faster than any neural vocoder. A DSP vocoder often gets a lower audio quality due to consuming over-smoothed acoustic model predictions of approximate representations for the vocal tract. In this paper, we propose an ultra-lightweight differential DSP (DDSP) vocoder that uses a jointly optimized acoustic model with a DSP vocoder, and learns without an extracted spectral feature for the vocal tract. The model achieves audio quality comparable to neural vocoders with a high average MOS of 4.36 while being efficient as a DSP vocoder. Our C++ implementation, without any hardware-specific optimization, is at 15 MFLOPS, surpasses MB-MelGAN by 340 times in terms of FLOPS, and achieves a vocoder-only RTF of 0.003 and overall RTF of 0.044 while running single-threaded on a 2GHz Intel Xeon CPU., Comment: Accepted for ICASSP 2024

Safety guarantees are vital in many control applications, such as robotics. Model predictive control (MPC) provides a constructive framework for controlling safety-critical systems, but is limited by its computational complexity. We address this problem by presenting a novel algorithm that automatically computes an explicit approximation to nonlinear MPC schemes while retaining closed-loop guarantees. Specifically, the problem can be reduced to a function approximation problem, which we then tackle by proposing ALKIA-X, the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm. ALKIA-X is a non-iterative algorithm that ensures numerically well-conditioned computations, a fast-to-evaluate approximating function, and the guaranteed satisfaction of any desired bound on the approximation error. Hence, ALKIA-X automatically computes an explicit function that approximates the MPC, yielding a controller suitable for safety-critical systems and high sampling rates. We apply ALKIA-X to approximate two nonlinear MPC schemes, demonstrating reduced computational demand and applicability to realistic problems., Comment: Submitted to IEEE Transactions on Automatic Control. Compared to the previously uploaded version, this version contains an additional numerical example

Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while insufficient for others. To address this, we present Constrained Parameter Regularization (CPR) as an alternative to traditional weight decay. Unlike the uniform application of a single penalty, CPR enforces an upper bound on a statistical measure, such as the L2-norm, of individual parameter matrices. Consequently, learning becomes a constraint optimization problem, which we tackle using an adaptation of the augmented Lagrangian method. CPR introduces only a minor runtime overhead and only requires setting an upper bound. We propose simple yet efficient mechanisms for initializing this bound, making CPR rely on no hyperparameter or one, akin to weight decay. Our empirical studies on computer vision and language modeling tasks demonstrate CPR's effectiveness. The results show that CPR can outperform traditional weight decay and increase performance in pre-training and fine-tuning., Comment: In Proceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS 2024), 35 pages

While multi-task learning (MTL) has gained significant attention in recent years, its underlying mechanisms remain poorly understood. Recent methods did not yield consistent performance improvements over single task learning (STL) baselines, underscoring the importance of gaining more profound insights about challenges specific to MTL. In our study, we investigate paradigms in MTL in the context of STL: First, the impact of the choice of optimizer has only been mildly investigated in MTL. We show the pivotal role of common STL tools such as the Adam optimizer in MTL empirically in various experiments. To further investigate Adam's effectiveness, we theoretical derive a partial loss-scale invariance under mild assumptions. Second, the notion of gradient conflicts has often been phrased as a specific problem in MTL. We delve into the role of gradient conflicts in MTL and compare it to STL. For angular gradient alignment we find no evidence that this is a unique problem in MTL. We emphasize differences in gradient magnitude as the main distinguishing factor. Overall, we find surprising similarities between STL and MTL suggesting to consider methods from both fields in a broader context., Comment: Accepted for publication in German Conference for Pattern Recognition (GCPR), 2024

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Handling entirely unknown data is a challenge for any deployed classifier. Classification models are typically trained on a static pre-defined dataset and are kept in the dark for the open unassigned feature space. As a result, they struggle to deal with out-of-distribution data during inference. Addressing this task on the class-level is termed open-set recognition (OSR). However, most OSR methods are inherently limited, as they train closed-set classifiers and only adapt the downstream predictions to OSR. This work presents LORD, a framework to Leverage Open-set Recognition by exploiting unknown Data. LORD explicitly models open space during classifier training and provides a systematic evaluation for such approaches. We identify three model-agnostic training strategies that exploit background data and applied them to well-established classifiers. Due to LORD's extensive evaluation protocol, we consistently demonstrate improved recognition of unknown data. The benchmarks facilitate in-depth analysis across various requirement levels. To mitigate dependency on extensive and costly background datasets, we explore mixup as an off-the-shelf data generation technique. Our experiments highlight mixup's effectiveness as a substitute for background datasets. Lightweight constraints on mixup synthesis further improve OSR performance., Comment: Accepted at ICCV 2023 Workshop (Out-Of-Distribution Generalization in Computer Vision)

Having precise perception of the environment is crucial for ensuring the secure and reliable functioning of autonomous driving systems. Radar object detection networks are one fundamental part of such systems. CNN-based object detectors showed good performance in this context, but they require large compute resources. This paper investigates sparse convolutional object detection networks, which combine powerful grid-based detection with low compute resources. We investigate radar specific challenges and propose sparse kernel point pillars (SKPP) and dual voxel point convolutions (DVPC) as remedies for the grid rendering and sparse backbone architectures. We evaluate our SKPP-DPVCN architecture on nuScenes, which outperforms the baseline by 5.89% and the previous state of the art by 4.19% in Car AP4.0. Moreover, SKPP-DPVCN reduces the average scale error (ASE) by 21.41% over the baseline.

As collaborative robots (cobots) continue to gain popularity in industrial manufacturing, effective human-robot collaboration becomes crucial. Cobots should be able to recognize human actions to assist with assembly tasks and act autonomously. To achieve this, skeleton-based approaches are often used due to their ability to generalize across various people and environments. Although body skeleton approaches are widely used for action recognition, they may not be accurate enough for assembly actions where the worker's fingers and hands play a significant role. To address this limitation, we propose a method in which less detailed body skeletons are combined with highly detailed hand skeletons. We investigate CNNs and transformers, the latter of which are particularly adept at extracting and combining important information from both skeleton types using attention. This paper demonstrates the effectiveness of our proposed approach in enhancing action recognition in assembly scenarios., Comment: International Conference on Artificial Neural Networks (ICANN) 2023

Independently trained machine learning models tend to learn similar features. Given an ensemble of independently trained models, this results in correlated predictions and common failure modes. Previous attempts focusing on decorrelation of output predictions or logits yielded mixed results, particularly due to their reduction in model accuracy caused by conflicting optimization objectives. In this paper, we propose the novel idea of utilizing methods of the representational similarity field to promote dissimilarity during training instead of measuring similarity of trained models. To this end, we promote intermediate representations to be dissimilar at different depths between architectures, with the goal of learning robust ensembles with disjoint failure modes. We show that highly dissimilar intermediate representations result in less correlated output predictions and slightly lower error consistency, resulting in higher ensemble accuracy. With this, we shine first light on the connection between intermediate representations and their impact on the output predictions., Comment: The Second Workshop on Spurious Correlations, Invariance and Stability at ICML 2023

We establish generic uniform convergence guarantees for Gaussian data in terms of the Rademacher complexity of the hypothesis class and the Lipschitz constant of the square root of the scalar loss function. We show how these guarantees substantially generalize previous results based on smoothness (Lipschitz constant of the derivative), and allow us to handle the broader class of square-root-Lipschitz losses, which includes also non-smooth loss functions appropriate for studying phase retrieval and ReLU regression, as well as rederive and better understand "optimistic rate" and interpolation learning guarantees.

As the use of collaborative robots (cobots) in industrial manufacturing continues to grow, human action recognition for effective human-robot collaboration becomes increasingly important. This ability is crucial for cobots to act autonomously and assist in assembly tasks. Recently, skeleton-based approaches are often used as they tend to generalize better to different people and environments. However, when processing skeletons alone, information about the objects a human interacts with is lost. Therefore, we present a novel approach of integrating object information into skeleton-based action recognition. We enhance two state-of-the-art methods by treating object centers as further skeleton joints. Our experiments on the assembly dataset IKEA ASM show that our approach improves the performance of these state-of-the-art methods to a large extent when combining skeleton joints with objects predicted by a state-of-the-art instance segmentation model. Our research sheds light on the benefits of combining skeleton joints with object information for human action recognition in assembly tasks. We analyze the effect of the object detector on the combination for action classification and discuss the important factors that must be taken into account., Comment: IEEE International Joint Conference on Neural Networks (IJCNN) 2023

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small excess risk. If the true signal is $t$-sparse, information-theoretically, it is possible to achieve strong recovery guarantees with only $O(t\log n)$ samples. However, computationally efficient algorithms have sample complexity linear in (some variant of) the condition number of $\Sigma$. Classical algorithms such as the Lasso can require significantly more samples than necessary even if there is only a single sparse approximate dependency among the covariates. We provide a polynomial-time algorithm that, given $\Sigma$, automatically adapts the Lasso to tolerate a small number of approximate dependencies. In particular, we achieve near-optimal sample complexity for constant sparsity and if $\Sigma$ has few ``outlier'' eigenvalues. Our algorithm fits into a broader framework of feature adaptation for sparse linear regression with ill-conditioned covariates. With this framework, we additionally provide the first polynomial-factor improvement over brute-force search for constant sparsity $t$ and arbitrary covariance $\Sigma$.

Architectures that first convert point clouds to a grid representation and then apply convolutional neural networks achieve good performance for radar-based object detection. However, the transfer from irregular point cloud data to a dense grid structure is often associated with a loss of information, due to the discretization and aggregation of points. In this paper, we propose a novel architecture, multi-scale KPPillarsBEV, that aims to mitigate the negative effects of grid rendering. Specifically, we propose a novel grid rendering method, KPBEV, which leverages the descriptive power of kernel point convolutions to improve the encoding of local point cloud contexts during grid rendering. In addition, we propose a general multi-scale grid rendering formulation to incorporate multi-scale feature maps into convolutional backbones of detection networks with arbitrary grid rendering methods. We perform extensive experiments on the nuScenes dataset and evaluate the methods in terms of detection performance and computational complexity. The proposed multi-scale KPPillarsBEV architecture outperforms the baseline by 5.37% and the previous state of the art by 2.88% in Car AP4.0 (average precision for a matching threshold of 4 meters) on the nuScenes validation set. Moreover, the proposed single-scale KPBEV grid rendering improves the Car AP4.0 by 2.90% over the baseline while maintaining the same inference speed., Comment: (c) 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Kernel-based regularized risk minimizers, also called support vector machines (SVMs), are known to possess many desirable properties but suffer from their super-linear computational requirements when dealing with large data sets. This problem can be tackled by using localized SVMs instead, which also offer the additional advantage of being able to apply different hyperparameters to different regions of the input space. In this paper, localized SVMs are analyzed with regards to their consistency. It is proven that they inherit $L_p$- as well as risk consistency from global SVMs under very weak conditions and even if the regions underlying the localized SVMs are allowed to change as the size of the training data set increases., Comment: 29 pages, 1 figure

Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated using two numerical non-linear MPC benchmarks of different complexity, demonstrating computational speedups that are orders of magnitude higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where a naive NN implementation fails.

Foundation models have taken over natural language processing and image generation domains due to the flexibility of prompting. With the recent introduction of the Segment Anything Model (SAM), this prompt-driven paradigm has entered image segmentation with a hitherto unexplored abundance of capabilities. The purpose of this paper is to conduct an initial evaluation of the out-of-the-box zero-shot capabilities of SAM for medical image segmentation, by evaluating its performance on an abdominal CT organ segmentation task, via point or bounding box based prompting. We show that SAM generalizes well to CT data, making it a potential catalyst for the advancement of semi-automatic segmentation tools for clinicians. We believe that this foundation model, while not reaching state-of-the-art segmentation performance in our investigations, can serve as a highly potent starting point for further adaptations of such models to the intricacies of the medical domain. Keywords: medical image segmentation, SAM, foundation models, zero-shot learning, Comment: 3 Pages, 1 Figure, Short paper under review for MIDL 2023

As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and $L_p$-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same extent as it does for many other results. The results are applied to regularized kernel methods such as support vector machines., Comment: 33 pages, 1 figure

There has been exploding interest in embracing Transformer-based architectures for medical image segmentation. However, the lack of large-scale annotated medical datasets make achieving performances equivalent to those in natural images challenging. Convolutional networks, in contrast, have higher inductive biases and consequently, are easily trainable to high performance. Recently, the ConvNeXt architecture attempted to modernize the standard ConvNet by mirroring Transformer blocks. In this work, we improve upon this to design a modernized and scalable convolutional architecture customized to challenges of data-scarce medical settings. We introduce MedNeXt, a Transformer-inspired large kernel segmentation network which introduces - 1) A fully ConvNeXt 3D Encoder-Decoder Network for medical image segmentation, 2) Residual ConvNeXt up and downsampling blocks to preserve semantic richness across scales, 3) A novel technique to iteratively increase kernel sizes by upsampling small kernel networks, to prevent performance saturation on limited medical data, 4) Compound scaling at multiple levels (depth, width, kernel size) of MedNeXt. This leads to state-of-the-art performance on 4 tasks on CT and MRI modalities and varying dataset sizes, representing a modernized deep architecture for medical image segmentation. Our code is made publicly available at: https://github.com/MIC-DKFZ/MedNeXt., Comment: Accepted at MICCAI 2023

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules., Comment: International Conference on Machine Learning, 2023

We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau envelopes of the loss $\ell$. We use our finite-sample bound to directly recover the "optimistic rate" of Zhou et al. (2021) for linear regression with the square loss, which is known to be tight for minimal $\ell_2$-norm interpolation, but we also handle more general settings where the label is generated by a potentially misspecified multi-index model. The same argument can analyze noisy interpolation of max-margin classifiers through the squared hinge loss, and establishes consistency results in spiked-covariance settings. More generally, when the loss is only assumed to be Lipschitz, our bound effectively improves Talagrand's well-known contraction lemma by a factor of two, and we prove uniform convergence of interpolators (Koehler et al. 2021) for all smooth, non-negative losses. Finally, we show that application of our generalization bound using localized Gaussian width will generally be sharp for empirical risk minimizers, establishing a non-asymptotic Moreau envelope theory for generalization that applies outside of proportional scaling regimes, handles model misspecification, and complements existing asymptotic Moreau envelope theories for M-estimation., Comment: As published at NeurIPS 2022

Deep generative models parametrized up to a normalizing constant (e.g. energy-based models) are difficult to train by maximizing the likelihood of the data because the likelihood and/or gradients thereof cannot be explicitly or efficiently written down. Score matching is a training method, whereby instead of fitting the likelihood $\log p(x)$ for the training data, we instead fit the score function $\nabla_x \log p(x)$ -- obviating the need to evaluate the partition function. Though this estimator is known to be consistent, its unclear whether (and when) its statistical efficiency is comparable to that of maximum likelihood -- which is known to be (asymptotically) optimal. We initiate this line of inquiry in this paper, and show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated -- i.e. the Poincar\'e, log-Sobolev and isoperimetric constant -- quantities which govern the mixing time of Markov processes like Langevin dynamics. Roughly, we show that the score matching estimator is statistically comparable to the maximum likelihood when the distribution has a small isoperimetric constant. Conversely, if the distribution has a large isoperimetric constant -- even for simple families of distributions like exponential families with rich enough sufficient statistics -- score matching will be substantially less efficient than maximum likelihood. We suitably formalize these results both in the finite sample regime, and in the asymptotic regime. Finally, we identify a direct parallel in the discrete setting, where we connect the statistical properties of pseudolikelihood estimation with approximate tensorization of entropy and the Glauber dynamics.

Semantic scene understanding is essential for mobile agents acting in various environments. Although semantic segmentation already provides a lot of information, details about individual objects as well as the general scene are missing but required for many real-world applications. However, solving multiple tasks separately is expensive and cannot be accomplished in real time given limited computing and battery capabilities on a mobile platform. In this paper, we propose an efficient multi-task approach for RGB-D scene analysis~(EMSANet) that simultaneously performs semantic and instance segmentation~(panoptic segmentation), instance orientation estimation, and scene classification. We show that all tasks can be accomplished using a single neural network in real time on a mobile platform without diminishing performance - by contrast, the individual tasks are able to benefit from each other. In order to evaluate our multi-task approach, we extend the annotations of the common RGB-D indoor datasets NYUv2 and SUNRGB-D for instance segmentation and orientation estimation. To the best of our knowledge, we are the first to provide results in such a comprehensive multi-task setting for indoor scene analysis on NYUv2 and SUNRGB-D., Comment: To be published in IEEE International Joint Conference on Neural Networks (IJCNN) 2022

This paper presents a method to learn the Cartesian velocity of objects using an object detection network on automotive radar data. The proposed method is self-supervised in terms of generating its own training signal for the velocities. Labels are only required for single-frame, oriented bounding boxes (OBBs). Labels for the Cartesian velocities or contiguous sequences, which are expensive to obtain, are not required. The general idea is to pre-train an object detection network without velocities using single-frame OBB labels, and then exploit the network's OBB predictions on unlabelled data for velocity training. In detail, the network's OBB predictions of the unlabelled frames are updated to the timestamp of a labelled frame using the predicted velocities and the distances between the updated OBBs of the unlabelled frame and the OBB predictions of the labelled frame are used to generate a self-supervised training signal for the velocities. The detection network architecture is extended by a module to account for the temporal relation of multiple scans and a module to represent the radars' radial velocity measurements explicitly. A two-step approach of first training only OBB detection, followed by training OBB detection and velocities is used. Further, a pre-training with pseudo-labels generated from radar radial velocity measurements bootstraps the self-supervised method of this paper. Experiments on the publicly available nuScenes dataset show that the proposed method almost reaches the velocity estimation performance of a fully supervised training, but does not require expensive velocity labels. Furthermore, we outperform a baseline method which uses only radial velocity measurements as labels., Comment: Accepted for presentation at the 2022 33rd IEEE Intelligent Vehicles Symposium (IV) (IV 2022), June 5-9, 2022, in Aachen, Germany

Dynamic environments require adaptive applications. One particular machine learning problem in dynamic environments is open world recognition. It characterizes a continuously changing domain where only some classes are seen in one batch of the training data and such batches can only be learned incrementally. Open world recognition is a demanding task that is, to the best of our knowledge, addressed by only a few methods. This work introduces a modification of the widely known Extreme Value Machine (EVM) to enable open world recognition. Our proposed method extends the EVM with a partial model fitting function by neglecting unaffected space during an update. This reduces the training time by a factor of 28. In addition, we provide a modified model reduction using weighted maximum K-set cover to strictly bound the model complexity and reduce the computational effort by a factor of 3.5 from 2.1 s to 0.6 s. In our experiments, we rigorously evaluate openness with two novel evaluation protocols. The proposed method achieves superior accuracy of about 12 % and computational efficiency in the tasks of image classification and face recognition., Comment: Accepted at ICPR 2022

Deep learning based computed tomography (CT) reconstruction has demonstrated outstanding performance on simulated 2D low-dose CT data. This applies in particular to domain adapted neural networks, which incorporate a handcrafted physics model for CT imaging. Empirical evidence shows that employing such architectures reduces the demand for training data and improves upon generalisation. However, their training requires large computational resources that quickly become prohibitive in 3D helical CT, which is the most common acquisition geometry used for medical imaging. Furthermore, clinical data also comes with other challenges not accounted for in simulations, like errors in flux measurement, resolution mismatch and, most importantly, the absence of the real ground truth. The necessity to have a computationally feasible training combined with the need to address these issues has made it difficult to evaluate deep learning based reconstruction on clinical 3D helical CT. This paper modifies a domain adapted neural network architecture, the Learned Primal-Dual (LPD), so that it can be trained and applied to reconstruction in this setting. We achieve this by splitting the helical trajectory into sections and applying the unrolled LPD iterations to those sections sequentially. To the best of our knowledge, this work is the first to apply an unrolled deep learning architecture for reconstruction on full-sized clinical data, like those in the Low dose CT image and projection data set (LDCT). Moreover, training and testing is done on a single GPU card with 24GB of memory.

This paper presents novel hybrid architectures that combine grid- and point-based processing to improve the detection performance and orientation estimation of radar-based object detection networks. Purely grid-based detection models operate on a bird's-eye-view (BEV) projection of the input point cloud. These approaches suffer from a loss of detailed information through the discrete grid resolution. This applies in particular to radar object detection, where relatively coarse grid resolutions are commonly used to account for the sparsity of radar point clouds. In contrast, point-based models are not affected by this problem as they process point clouds without discretization. However, they generally exhibit worse detection performances than grid-based methods. We show that a point-based model can extract neighborhood features, leveraging the exact relative positions of points, before grid rendering. This has significant benefits for a subsequent grid-based convolutional detection backbone. In experiments on the public nuScenes dataset our hybrid architecture achieves improvements in terms of detection performance (19.7% higher mAP for car class than next-best radar-only submission) and orientation estimates (11.5% relative orientation improvement) over networks from previous literature., Comment: (c) 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can only be captured to a limited extent. An alternative approach is to leverage machine learning techniques to learn a differentiable dynamics model of the system from data. In this work, we use trajectory optimization and model learning for performing highly dynamic and complex tasks with robotic systems in absence of accurate analytical models of the dynamics. We show that a neural network can model highly nonlinear behaviors accurately for large time horizons, from data collected in only 25 minutes of interactions on two distinct robots: (i) the Boston Dynamics Spot and an (ii) RC car. Furthermore, we use the gradients of the neural network to perform gradient-based trajectory optimization. In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car, and gives good performance in combination with trajectory optimization methods.

The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as output of neural networks. These neural network-based methods are often used in the form of an ensemble, e.g., based on multiple model runs from different random initializations or more sophisticated ensembling strategies such as dropout, resulting in a collection of forecast distributions that need to be aggregated into a final probabilistic prediction. With the aim of consolidating findings from the machine learning literature on ensemble methods and the statistical literature on forecast combination, we address the question of how to aggregate distribution forecasts based on such `deep ensembles'. Using theoretical arguments and a comprehensive analysis on twelve benchmark data sets, we systematically compare probability- and quantile-based aggregation methods for three neural network-based approaches with different forecast distribution types as output. Our results show that combining forecast distributions from deep ensembles can substantially improve the predictive performance. We propose a general quantile aggregation framework for deep ensembles that allows for corrections of systematic deficiencies and performs well in a variety of settings, often superior compared to a linear combination of the forecast densities. Finally, we investigate the effects of the ensemble size and derive recommendations of aggregating distribution forecasts from deep ensembles in practice.

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time- and length-scales inaccessible to all-atom simulations. Parameterizing CG force fields to match all-atom simulations has mainly relied on force-matching or relative entropy minimization, which require many samples from costly simulations with all-atom or CG resolutions, respectively. Here we present flow-matching, a new training method for CG force fields that combines the advantages of both methods by leveraging normalizing flows, a generative deep learning method. Flow-matching first trains a normalizing flow to represent the CG probability density, which is equivalent to minimizing the relative entropy without requiring iterative CG simulations. Subsequently, the flow generates samples and forces according to the learned distribution in order to train the desired CG free energy model via force matching. Even without requiring forces from the all-atom simulations, flow-matching outperforms classical force-matching by an order of magnitude in terms of data efficiency, and produces CG models that can capture the folding and unfolding transitions of small proteins.

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are hard for restricted classes of algorithms. Recent work has shown that, for certain covariance matrices, the broad class of Preconditioned Lasso programs provably cannot succeed on polylogarithmically sparse signals with a sublinear number of samples. However, this lower bound only shows that for every preconditioner, there exists at least one signal that it fails to recover successfully. This leaves open the possibility that, for example, trying multiple different preconditioners solves every sparse linear regression problem. In this work, we prove a stronger lower bound that overcomes this issue. For an appropriate covariance matrix, we construct a single signal distribution on which any invertibly-preconditioned Lasso program fails with high probability, unless it receives a linear number of samples. Surprisingly, at the heart of our lower bound is a new positive result in compressed sensing. We show that standard sparse random designs are with high probability robust to adversarial measurement erasures, in the sense that if $b$ measurements are erased, then all but $O(b)$ of the coordinates of the signal are still information-theoretically identifiable. To our knowledge, this is the first time that partial recoverability of arbitrary sparse signals under erasures has been studied in compressed sensing., Comment: 39 pages

We consider Ising models on the hypercube with a general interaction matrix $J$, and give a polynomial time sampling algorithm when all but $O(1)$ eigenvalues of $J$ lie in an interval of length one, a situation which occurs in many models of interest. This was previously known for the Glauber dynamics when *all* eigenvalues fit in an interval of length one; however, a single outlier can force the Glauber dynamics to mix torpidly. Our general result implies the first polynomial time sampling algorithms for low-rank Ising models such as Hopfield networks with a fixed number of patterns and Bayesian clustering models with low-dimensional contexts, and greatly improves the polynomial time sampling regime for the antiferromagnetic/ferromagnetic Ising model with inconsistent field on expander graphs. It also improves on previous approximation algorithm results based on the naive mean-field approximation in variational methods and statistical physics. Our approach is based on a new fusion of ideas from the MCMC and variational inference worlds. As part of our algorithm, we define a new nonconvex variational problem which allows us to sample from an exponential reweighting of a distribution by a negative definite quadratic form, and show how to make this procedure provably efficient using stochastic gradient descent. On top of this, we construct a new simulated tempering chain (on an extended state space arising from the Hubbard-Stratonovich transform) which overcomes the obstacle posed by large positive eigenvalues, and combine it with the SGD-based sampler to solve the full problem., Comment: 43 pages

Humans are able to learn to recognize new objects even from a few examples. In contrast, training deep-learning-based object detectors requires huge amounts of annotated data. To avoid the need to acquire and annotate these huge amounts of data, few-shot object detection aims to learn from few object instances of new categories in the target domain. In this survey, we provide an overview of the state of the art in few-shot object detection. We categorize approaches according to their training scheme and architectural layout. For each type of approaches, we describe the general realization as well as concepts to improve the performance on novel categories. Whenever appropriate, we give short takeaways regarding these concepts in order to highlight the best ideas. Eventually, we introduce commonly used datasets and their evaluation protocols and analyze reported benchmark results. As a result, we emphasize common challenges in evaluation and identify the most promising current trends in this emerging field of few-shot object detection., Comment: 27 pages, 13 figures, submitted to IEEE Transactions on Neural Networks and Learning Systems

Variational Autoencoders are one of the most commonly used generative models, particularly for image data. A prominent difficulty in training VAEs is data that is supported on a lower-dimensional manifold. Recent work by Dai and Wipf (2020) proposes a two-stage training algorithm for VAEs, based on a conjecture that in standard VAE training the generator will converge to a solution with 0 variance which is correctly supported on the ground truth manifold. They gave partial support for that conjecture by showing that some optima of the VAE loss do satisfy this property, but did not analyze the training dynamics. In this paper, we show that for linear encoders/decoders, the conjecture is true-that is the VAE training does recover a generator with support equal to the ground truth manifold-and does so due to an implicit bias of gradient descent rather than merely the VAE loss itself. In the nonlinear case, we show that VAE training frequently learns a higher-dimensional manifold which is a superset of the ground truth manifold., Comment: Accepted as a conference paper at ICLR 2022

We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in existing results, which are known to be crucial in high-dimensional settings, especially for understanding interpolation learning. As a special case, our analysis recovers the guarantee from Koehler et al. (2021), which tightly characterizes the population risk of low-norm interpolators under the benign overfitting conditions. Our optimistic rate bound, though, also analyzes predictors with arbitrary training error. This allows us to recover some classical statistical guarantees for ridge and LASSO regression under random designs, and helps us obtain a precise understanding of the excess risk of near-interpolators in the over-parameterized regime.

Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is Gaussian, but is widely known to break down when one deviates from this assumption, e.g. when the noise is heavy-tailed. Many ad hoc heuristics have been employed in practice for dealing with outliers. In a pioneering work, Schick and Mitter gave provable guarantees when the measurement noise is a known infinitesimal perturbation of a Gaussian and raised the important question of whether one can get similar guarantees for large and unknown perturbations. In this work we give a truly robust filter: we give the first strong provable guarantees for linear quadratic estimation when even a constant fraction of measurements have been adversarially corrupted. This framework can model heavy-tailed and even non-stationary noise processes. Our algorithm robustifies the Kalman filter in the sense that it competes with the optimal algorithm that knows the locations of the corruptions. Our work is in a challenging Bayesian setting where the number of measurements scales with the complexity of what we need to estimate. Moreover, in linear dynamical systems past information decays over time. We develop a suite of new techniques to robustly extract information across different time steps and over varying time scales., Comment: 57 pages, comments welcome

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations., Comment: Neural Information Proceessing Systems (NeurIPS) 2021

Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing communities. In particular, the Kamada-Kawai force-directed graph drawing method is equivalent to MDS and is one of the most popular ways in practice to embed graphs into low dimensions. Despite its ubiquity, our theoretical understanding of MDS remains limited as its objective function is highly non-convex. In this paper, we prove that minimizing the Kamada-Kawai objective is NP-hard and give a provable approximation algorithm for optimizing it, which in particular is a PTAS on low-diameter graphs. We supplement this result with experiments suggesting possible connections between our greedy approximation algorithm and gradient-based methods.