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Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response. Such simulations, however, are prohibitively expensive and time consuming for high-dimensional nonlinear systems. Here we propose to decrease this numerical burden significantly by reducing the full system to very low-dimensional, attracting, random invariant manifolds in its phase space and performing the Monte Carlo simulations on that reduced dynamical system. The random spectral submanifolds (SSMs) we construct for this purpose generalize the concept of SSMs from deterministic systems under uniformly bounded random forcing. We illustrate the accuracy and speed of random SSM reduction by computing the SSM-reduced power spectral density of the randomly forced mechanical systems that range from simple oscillator chains to finite-element models of beams and plates.

Proton resonance frequency (PRF) based MR thermometry is essential for focused ultrasound (FUS) thermal ablation therapies. This work aims to enhance temporal resolution in dynamic MR temperature map reconstruction using an improved deep learning method. The training-optimized methods and five classical neural networks were applied on the 2-fold and 4-fold under-sampling k-space data to reconstruct the temperature maps. The enhanced training modules included offline/online data augmentations, knowledge distillation, and the amplitude-phase decoupling loss function. The heating experiments were performed by a FUS transducer on phantom and ex vivo tissues, respectively. These data were manually under-sampled to imitate acceleration procedures and trained in our method to get the reconstruction model. The additional dozen or so testing datasets were separately obtained for evaluating the real-time performance and temperature accuracy. Acceleration factors of 1.9 and 3.7 were found for 2 times and 4 times k-space under-sampling strategies and the ResUNet-based deep learning reconstruction performed exceptionally well. In 2-fold acceleration scenario, the RMSE of temperature map patches provided the values of 0.888 degree centigrade and 1.145 degree centigrade on phantom and ex vivo testing datasets. The DICE value of temperature areas enclosed by 43 degree centigrade isotherm was 0.809, and the Bland-Altman analysis showed a bias of -0.253 degree centigrade with the apart of plus or minus 2.16 degree centigrade. In 4 times under-sampling case, these evaluating values decreased by approximately 10%. This study demonstrates that deep learning-based reconstruction can significantly enhance the accuracy and efficiency of MR thermometry for clinical FUS thermal therapies.

User intentions are typically formalized as evaluation rewards to be maximized when fine-tuning language models (LMs). Existing alignment methods, such as Direct Preference Optimization (DPO), are mainly tailored for pairwise preference data where rewards are implicitly defined rather than explicitly given. In this paper, we introduce a general framework for LM alignment, leveraging Noise Contrastive Estimation (NCE) to bridge the gap in handling reward datasets explicitly annotated with scalar evaluations. Our framework comprises two parallel algorithms, NCA and InfoNCA, both enabling the direct extraction of an LM policy from reward data as well as preference data. Notably, we show that the DPO loss is a special case of our proposed InfoNCA objective under pairwise preference settings, thereby integrating and extending current alignment theories. By comparing NCA and InfoNCA, we demonstrate that the well-observed decreasing-likelihood trend of DPO/InfoNCA is caused by their focus on adjusting relative likelihood across different responses. In contrast, NCA optimizes the absolute likelihood for each response, thereby effectively preventing the chosen likelihood from decreasing. We evaluate our methods in both reward and preference settings with Mistral-8*7B and 7B models. Experiments suggest that InfoNCA/NCA surpasses various preference baselines when reward datasets are available. We also find NCA significantly outperforms DPO in complex reasoning tasks like math and coding.

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d.\ Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix $\Sigma$. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.

Generative modeling seeks to approximate the statistical properties of real data, enabling synthesis of new data that closely resembles the original distribution. Generative Adversarial Networks (GANs) and Denoising Diffusion Probabilistic Models (DDPMs) represent significant advancements in generative modeling, drawing inspiration from game theory and thermodynamics, respectively. Nevertheless, the exploration of generative modeling through the lens of biological evolution remains largely untapped. In this paper, we introduce a novel family of models termed Generative Cellular Automata (GeCA), inspired by the evolution of an organism from a single cell. GeCAs are evaluated as an effective augmentation tool for retinal disease classification across two imaging modalities: Fundus and Optical Coherence Tomography (OCT). In the context of OCT imaging, where data is scarce and the distribution of classes is inherently skewed, GeCA significantly boosts the performance of 11 different ophthalmological conditions, achieving a 12% increase in the average F1 score compared to conventional baselines. GeCAs outperform both diffusion methods that incorporate UNet or state-of-the art variants with transformer-based denoising models, under similar parameter constraints. Code is available at: //github.com/xmed-lab/GeCA.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.

Generalization to out-of-distribution (OOD) data is a capability natural to humans yet challenging for machines to reproduce. This is because most learning algorithms strongly rely on the i.i.d.~assumption on source/target data, which is often violated in practice due to domain shift. Domain generalization (DG) aims to achieve OOD generalization by using only source data for model learning. Since first introduced in 2011, research in DG has made great progresses. In particular, intensive research in this topic has led to a broad spectrum of methodologies, e.g., those based on domain alignment, meta-learning, data augmentation, or ensemble learning, just to name a few; and has covered various vision applications such as object recognition, segmentation, action recognition, and person re-identification. In this paper, for the first time a comprehensive literature review is provided to summarize the developments in DG for computer vision over the past decade. Specifically, we first cover the background by formally defining DG and relating it to other research fields like domain adaptation and transfer learning. Second, we conduct a thorough review into existing methods and present a categorization based on their methodologies and motivations. Finally, we conclude this survey with insights and discussions on future research directions.

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.