The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively.

Geological Reservoir: " Kimberlina Family " is built under DOE's National Risk Assessment Program

Training a single model for multilingual, multi-task speech processing (MSP) is severely hampered by conflicting objectives between tasks like speech recognition and translation. While multi-objective optimization (MOO) aims to align gradient updates, its effectiveness diminishes as the number of tasks grows, making it difficult to find a common descent direction. This raises a fundamental question: should highly conflicting objectives be optimized jointly or separated into a hierarchical structure? To address this question, this paper investigates three multi-objective MSP formulations, which we refer to as \textbf{objective soup recipes}. These formulations apply multi-objective optimization at different optimization levels to mitigate potential conflicts among all objectives. To ensure efficiency, we introduce a lightweight layer-selection mechanism that computes the conflict-avoiding gradient using only the most problematic layers, minimizing computational and memory overhead. Extensive experiments on CoVoST v2, LibriSpeech, and AISHELL-1 reveal that a bi-level recipe separating recognition and translation tasks consistently outperforms standard flat optimization. Our work demonstrates that hierarchical MOO is a more effective and scalable approach for building state-of-the-art MSP models. Our code has been released at https://github.com/afmsaif/Objective_Soups.

We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula interprets this sensitivity as partial derivatives of the inverse mapping associated with the vector of 1-D conditional distributions. The second formula, intended for optimization methods that tolerate inexact gradients, introduces a diagonal approximation that reduces computational cost at the cost of some accuracy. We additionally provide four second-order numerical algorithms to approximate both formulae when closed forms are unavailable. We performed verification and validation studies to demonstrate the correctness of these numerical algorithms and the effectiveness of the proposed formulae. A nuclear physics application showcases how our work enables uncertainty quantification and parameter inference for quantum correlation functions. Our approach differs from existing methods by avoiding the need for model fitting, knowledge of sampling algorithms, and evaluation of high-dimensional integrals. It is therefore particularly useful for sample-based inverse problems when the sampler operates as a black box or requires expensive physics simulations. Moreover, our method renders arbitrary sampling subroutines differentiable, facilitating their integration into programming frameworks for deep learning and automatic differentiation. Algorithmic details and code implementations are provided in this paper and in our open-source software DistroSA to enable reproducibility and further development.

The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning techniques to fit the dual signal. Machine learning minimizes the loss function which compromises between fitting the original time series and penalizing irregularities of the dual signal. The latter includes terms based on the first and second order derivatives along time. To preserve special patterns, weighting of the regularization components of the loss function has been introduced based on Statistical Process Control methodology. The proposed decomposition can be applied as a smoothing algorithm against the mean and dispersion of the time series. By isolating noise, the proposed decomposition can be seen as a denoising algorithm. Two approaches of the learning process have been considered: sequential and jointly. The former approach learns the mean signal first and then dispersion. The latter approach fits the dual signal jointly. Jointly learning can uncover complex relationships for the time series with heteroskedasticity. Learning has been set by solving the direct non-linear unconstrained optimization problem or by applying neural networks that have sequential or twin output architectures. Tuning of the loss function hyperparameters focuses on the isolated noise to be a stationary stochastic process without autocorrelation properties. Depending on the applications, the hyperparameters of the learning can be tuned towards either the discrete states by stepped signal or smoothed series. The decomposed dual signal can be represented on the 2D space and used to learn inherent structures, to forecast both mean and dispersion, or to analyze cross effects in case of multiple time series.

The use of diverse modalities, such as omics, medical images, and clinical data can not only improve the performance of prognostic models but also deepen an understanding of disease mechanisms and facilitate the development of novel treatment approaches. However, medical data are complex, often incomplete, and contains missing modalities, making effective handling its crucial for training multimodal models. We introduce impuTMAE, a novel transformer-based end-to-end approach with an efficient multimodal pre-training strategy. It learns inter- and intra-modal interactions while simultaneously imputing missing modalities by reconstructing masked patches. Our model is pre-trained on heterogeneous, incomplete data and fine-tuned for glioma survival prediction using TCGA-GBM/LGG and BraTS datasets, integrating five modalities: genetic (DNAm, RNA-seq), imaging (MRI, WSI), and clinical data. By addressing missing data during pre-training and enabling efficient resource utilization, impuTMAE surpasses prior multimodal approaches, achieving state-of-the-art performance in glioma patient survival prediction. Our code is available at https://github.com/maryjis/mtcp

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise