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Non-negative matrix factorization (NMF) is a dimensionality reduction technique that has shown promise for analyzing noisy data, especially astronomical data. For these datasets, the observed data may contain negative values due to noise even when the true underlying physical signal is strictly positive. Prior NMF work has not treated negative data in a statistically consistent manner, which becomes problematic for low signal-to-noise data with many negative values. In this paper we present two algorithms, Shift-NMF and Nearly-NMF, that can handle both the noisiness of the input data and also any introduced negativity. Both of these algorithms use the negative data space without clipping, and correctly recover non-negative signals without any introduced positive offset that occurs when clipping negative data. We demonstrate this numerically on both simple and more realistic examples, and prove that both algorithms have monotonically decreasing update rules.

Symbolic regression (SR) is a powerful machine learning approach that searches for both the structure and parameters of algebraic models, offering interpretable and compact representations of complex data. Unlike traditional regression methods, SR explores progressively complex feature spaces, which can uncover simple models that generalize well, even from small datasets. Among SR algorithms, the Sure Independence Screening and Sparsifying Operator (SISSO) has proven particularly effective in the natural sciences, helping to rediscover fundamental physical laws as well as discover new interpretable equations for materials property modeling. However, its widespread adoption has been limited by performance inefficiencies and the challenges posed by its FORTRAN-based implementation, especially in modern computing environments. In this work, we introduce TorchSISSO, a native Python implementation built in the PyTorch framework. TorchSISSO leverages GPU acceleration, easy integration, and extensibility, offering a significant speed-up and improved accuracy over the original. We demonstrate that TorchSISSO matches or exceeds the performance of the original SISSO across a range of tasks, while dramatically reducing computational time and improving accessibility for broader scientific applications.

Intent detection is a critical component of task-oriented dialogue systems (TODS) which enables the identification of suitable actions to address user utterances at each dialog turn. Traditional approaches relied on computationally efficient supervised sentence transformer encoder models, which require substantial training data and struggle with out-of-scope (OOS) detection. The emergence of generative large language models (LLMs) with intrinsic world knowledge presents new opportunities to address these challenges. In this work, we adapt 7 SOTA LLMs using adaptive in-context learning and chain-of-thought prompting for intent detection, and compare their performance with contrastively fine-tuned sentence transformer (SetFit) models to highlight prediction quality and latency tradeoff. We propose a hybrid system using uncertainty based routing strategy to combine the two approaches that along with negative data augmentation results in achieving the best of both worlds ( i.e. within 2% of native LLM accuracy with 50% less latency). To better understand LLM OOS detection capabilities, we perform controlled experiments revealing that this capability is significantly influenced by the scope of intent labels and the size of the label space. We also introduce a two-step approach utilizing internal LLM representations, demonstrating empirical gains in OOS detection accuracy and F1-score by >5% for the Mistral-7B model.

To effectively study complex causal systems, it is often useful to construct representations that simplify parts of the system by discarding irrelevant details while preserving key features. The Information Bottleneck (IB) method is a widely used approach in representation learning that compresses random variables while retaining information about a target variable. Traditional methods like IB are purely statistical and ignore underlying causal structures, making them ill-suited for causal tasks. We propose the Causal Information Bottleneck (CIB), a causal extension of the IB, which compresses a set of chosen variables while maintaining causal control over a target variable. This method produces representations which are causally interpretable, and which can be used when reasoning about interventions. We present experimental results demonstrating that the learned representations accurately capture causality as intended.

Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the prediction error curve when plotted against the raw number of model parameters, or another simplistic notion of complexity. In this paper, we revisit model complexity from first principles, by first reinterpreting and then extending the classical statistical concept of (effective) degrees of freedom. Whereas the classical definition is connected to fixed-X prediction error (in which prediction error is defined by averaging over the same, nonrandom covariate points as those used during training), our extension of degrees of freedom is connected to random-X prediction error (in which prediction error is averaged over a new, random sample from the covariate distribution). The random-X setting more naturally embodies modern machine learning problems, where highly complex models, even those complex enough to interpolate the training data, can still lead to desirable generalization performance under appropriate conditions. We demonstrate the utility of our proposed complexity measures through a mix of conceptual arguments, theory, and experiments, and illustrate how they can be used to interpret and compare arbitrary prediction models.

The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for random vectors and matrices computation. By assuming the relative errors are independent random variables, we derive the approximate closed-form expressions for the expectation and variance of the rounding errors in various key computations for vectors and random matrices. Numerical experiments validate the accuracy of our derivations and demonstrate that our analytical expressions are generally at least two orders of magnitude tighter than alternative worst-case bounds, exemplified through the inner products.

Prior work has offered evidence for functional localization in the brain; different anatomical regions preferentially activate for certain types of visual input. For example, the fusiform face area preferentially activates for visual stimuli that include a face. However, the spectrum of visual semantics is extensive, and only a few semantically-tuned patches of cortex have so far been identified in the human brain. Using a multimodal (natural language and image) neural network architecture (CLIP) we train a highly accurate contrastive model that maps brain responses during naturalistic image viewing to CLIP embeddings. We then use a novel adaptation of the DBSCAN clustering algorithm to cluster the parameters of these participant-specific contrastive models. This reveals what we call Shared Decodable Concepts (SDCs): clusters in CLIP space that are decodable from common sets of voxels across multiple participants. Examining the images most and least associated with each SDC cluster gives us additional insight into the semantic properties of each SDC. We note SDCs for previously reported visual features (e.g. orientation tuning in early visual cortex) as well as visual semantic concepts such as faces, places and bodies. In cases where our method finds multiple clusters for a visuo-semantic concept, the least associated images allow us to dissociate between confounding factors. For example, we discovered two clusters of food images, one driven by color, the other by shape. We also uncover previously unreported areas such as regions of extrastriate body area (EBA) tuned for legs/hands and sensitivity to numerosity in right intraparietal sulcus, and more. Thus, our contrastive-learning methodology better characterizes new and existing visuo-semantic representations in the brain by leveraging multimodal neural network representations and a novel adaptation of clustering algorithms.

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their superior prediction abilities, especially in data-sparse scenarios, and their inherent ability to provide robust uncertainty estimates. Even so, their performance highly depends on intricate customizations of the core methodology, which often leads to dissatisfaction among practitioners when standard setups and off-the-shelf software tools are being deployed. Arguably the most important building block of a GP is the kernel function which assumes the role of a covariance operator. Stationary kernels of the Mat\'ern class are used in the vast majority of applied studies; poor prediction performance and unrealistic uncertainty quantification are often the consequences. Non-stationary kernels show improved performance but are rarely used due to their more complicated functional form and the associated effort and expertise needed to define and tune them optimally. In this perspective, we want to help ML practitioners make sense of some of the most common forms of non-stationarity for Gaussian processes. We show a variety of kernels in action using representative datasets, carefully study their properties, and compare their performances. Based on our findings, we propose a new kernel that combines some of the identified advantages of existing kernels.

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.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.