Learning causal representations from observational and interventional data in the absence of known ground-truth graph structures necessitates implicit latent causal representation learning. Implicit learning of causal mechanisms typically involves two categories of interventional data: hard and soft interventions. In real-world scenarios, soft interventions are often more realistic than hard interventions, as the latter require fully controlled environments. Unlike hard interventions, which directly force changes in a causal variable, soft interventions exert influence indirectly by affecting the causal mechanism. However, the subtlety of soft interventions impose several challenges for learning causal models. One challenge is that soft intervention's effects are ambiguous, since parental relations remain intact. In this paper, we tackle the challenges of learning causal models using soft interventions while retaining implicit modelling. We propose ICLR-SM, which models the effects of soft interventions by employing a causal mechanism switch variable designed to toggle between different causal mechanisms. In our experiments, we consistently observe improved learning of identifiable, causal representations, compared to baseline approaches.
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Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a point-wise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multi-scale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. These scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.
Heterogeneous functional data are commonly seen in time series and longitudinal data analysis. To capture the statistical structures of such data, we propose the framework of Functional Singular Value Decomposition (FSVD), a unified framework with structure-adaptive interpretability for the analysis of heterogeneous functional data. We establish the mathematical foundation of FSVD by proving its existence and providing its fundamental properties using operator theory. We then develop an implementation approach for noisy and irregularly observed functional data based on a novel joint kernel ridge regression scheme and provide theoretical guarantees for its convergence and estimation accuracy. The framework of FSVD also introduces the concepts of intrinsic basis functions and intrinsic basis vectors, which represent two fundamental statistical structures for random functions and connect FSVD to various tasks including functional principal component analysis, factor models, functional clustering, and functional completion. We compare the performance of FSVD with existing methods in several tasks through extensive simulation studies. To demonstrate the value of FSVD in real-world datasets, we apply it to extract temporal patterns from a COVID-19 case count dataset and perform data completion on an electronic health record dataset.
Neural network generalizability is becoming a broad research field due to the increasing availability of datasets from different sources and for various tasks. This issue is even wider when processing medical data, where a lack of methodological standards causes large variations being provided by different imaging centers or acquired with various devices and cofactors. To overcome these limitations, we introduce a novel, generalizable, data- and task-agnostic framework able to extract salient features from medical images. The proposed quaternion wavelet network (QUAVE) can be easily integrated with any pre-existing medical image analysis or synthesis task, and it can be involved with real, quaternion, or hypercomplex-valued models, generalizing their adoption to single-channel data. QUAVE first extracts different sub-bands through the quaternion wavelet transform, resulting in both low-frequency/approximation bands and high-frequency/fine-grained features. Then, it weighs the most representative set of sub-bands to be involved as input to any other neural model for image processing, replacing standard data samples. We conduct an extensive experimental evaluation comprising different datasets, diverse image analysis, and synthesis tasks including reconstruction, segmentation, and modality translation. We also evaluate QUAVE in combination with both real and quaternion-valued models. Results demonstrate the effectiveness and the generalizability of the proposed framework that improves network performance while being flexible to be adopted in manifold scenarios and robust to domain shifts. The full code is available at: //github.com/ispamm/QWT.
While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.
Herein the topics of (natural) gradient descent, data decorrelation, and approximate methods for backpropagation are brought into a common discussion. Natural gradient descent illuminates how gradient vectors, pointing at directions of steepest descent, can be improved by considering the local curvature of loss landscapes. We extend this perspective and show that to fully solve the problem illuminated by natural gradients in neural networks, one must recognise that correlations in the data at any linear transformation, including node responses at every layer of a neural network, cause a non-orthonormal relationship between the model's parameters. To solve this requires a method for decorrelating inputs at each individual layer of a neural network. We describe a range of methods which have been proposed for decorrelation and whitening of node output, and expand on these to provide a novel method specifically useful for distributed computing and computational neuroscience. Implementing decorrelation within multi-layer neural networks, we can show that not only is training via backpropagation sped up significantly but also existing approximations of backpropagation, which have failed catastrophically in the past, benefit significantly in their accuracy and convergence speed. This has the potential to provide a route forward for approximate gradient descent methods which have previously been discarded, training approaches for analogue and neuromorphic hardware, and potentially insights as to the efficacy and utility of decorrelation processes in the brain.
Continuous glucose monitoring (CGM) data has revolutionized the management of type 1 diabetes, particularly when integrated with insulin pumps to mitigate clinical events such as hypoglycemia. Recently, there has been growing interest in utilizing CGM devices in clinical studies involving healthy and diabetes populations. However, efficiently exploiting the high temporal resolution of CGM profiles remains a significant challenge. Numerous indices -- such as time-in-range metrics and glucose variability measures -- have been proposed, but evidence suggests these metrics overlook critical aspects of glucose dynamic homeostasis. As an alternative method, this paper explores the clinical value of glucodensity metrics in capturing glucose dynamics -- specifically the speed and acceleration of CGM time series -- as new biomarkers for predicting long-term glucose outcomes. Our results demonstrate significant information gains, exceeding 20\% in terms of adjusted $R^2$, in forecasting glycosylated hemoglobin (HbA1c) and fasting plasma glucose (FPG) at five and eight years from baseline AEGIS data, compared to traditional non-CGM and CGM glucose biomarkers. These findings underscore the importance of incorporating more complex CGM functional metrics, such as the glucodensity approach, to fully capture continuous glucose fluctuations across different time-scale resolutions.
Mixed membership models are a flexible class of probabilistic data representations used for unsupervised and semi-supervised learning, allowing each observation to partially belong to multiple clusters or features. In this manuscript, we extend the framework of functional mixed membership models to allow for covariate-dependent adjustments. The proposed model utilizes a multivariate Karhunen-Lo\`eve decomposition, which allows for a scalable and flexible model. Within this framework, we establish a set of sufficient conditions ensuring the identifiability of the mean, covariance, and allocation structure up to a permutation of the labels. This manuscript is primarily motivated by studies on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). Specifically, we are interested in characterizing the heterogeneity of alpha oscillations for typically developing (TD) children and children with ASD. Since alpha oscillations are known to change as children develop, we aim to characterize the heterogeneity of alpha oscillations conditionally on the age of the child. Using the proposed framework, we were able to gain novel information on the developmental trajectories of alpha oscillations for children with ASD and how the developmental trajectories differ between TD children and children with ASD.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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