Learning latent representations that are simultaneously expressive, geometrically well-structured, and reliably calibrated remains a central challenge for Variational Autoencoders (VAEs). Standard VAEs typically assume a diagonal Gaussian posterior, which simplifies optimization but rules out correlated uncertainty and often yields entangled or redundant latent dimensions. We introduce the Multivariate Variational Autoencoder (MVAE), a tractable full-covariance extension of the VAE that augments the encoder with sample-specific diagonal scales and a global coupling matrix. This induces a multivariate Gaussian posterior of the form $N(μ_ϕ(x), C \operatorname{diag}(σ_ϕ^2(x)) C^\top)$, enabling correlated latent factors while preserving a closed-form KL divergence and a simple reparameterization path. Beyond likelihood, we propose a multi-criterion evaluation protocol that jointly assesses reconstruction quality (MSE, ELBO), downstream discrimination (linear probes), probabilistic calibration (NLL, Brier, ECE), and unsupervised structure (NMI, ARI). Across Larochelle-style MNIST variants, Fashion-MNIST, and CIFAR-10/100, MVAE consistently matches or outperforms diagonal-covariance VAEs of comparable capacity, with particularly notable gains in calibration and clustering metrics at both low and high latent dimensions. Qualitative analyses further show smoother, more semantically coherent latent traversals and sharper reconstructions. All code, dataset splits, and evaluation utilities are released to facilitate reproducible comparison and future extensions of multivariate posterior models.

Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variational Autoencoder Graph Convolutional Neural Network framework for generating synthetic Abdominal Aorta Aneurysms (AAA). Using a small real-world dataset, our approach extracts key anatomical features and captures complex statistical relationships within a compact disentangled latent space. To address data limitations, low-impact data augmentation based on Procrustes analysis was employed, preserving anatomical integrity. The generation strategies, both deterministic and stochastic, manage to enhance data diversity while ensuring realism. Compared to PCA-based approaches, our model performs more robustly on unseen data by capturing complex, nonlinear anatomical variations. This enables more comprehensive clinical and statistical analyses than the original dataset alone. The resulting synthetic AAA dataset preserves patient privacy while providing a scalable foundation for medical research, device testing, and computational modeling.

We propose a novel family of language models, Latent-Thought Language Models (LTMs), which incorporate explicit latent thought vectors that follow an explicit prior model in latent space. These latent thought vectors guide the autoregressive generation of ground tokens through a Transformer decoder. Training employs a dual-rate optimization process within the classical variational Bayes framework: fast learning of local variational parameters for the posterior distribution of latent vectors, and slow learning of global decoder parameters. Empirical studies reveal that LTMs possess additional scaling dimensions beyond traditional LLMs, yielding a structured design space. Higher sample efficiency can be achieved by increasing training compute per token, with further gains possible by trading model size for more inference steps. Designed based on these scaling properties, LTMs demonstrate superior sample and parameter efficiency compared to conventional autoregressive models and discrete diffusion models. They significantly outperform these counterparts in validation perplexity and zero-shot language modeling. Additionally, LTMs exhibit emergent few-shot in-context reasoning capabilities that scale with model and latent size, and achieve competitive performance in conditional and unconditional text generation.

Learning a continuous and reliable representation of physical fields from sparse sampling is challenging and it affects diverse scientific disciplines. In a recent work, we present a novel model called MMGN (Multiplicative and Modulated Gabor Network) with implicit neural networks. In this work, we design additional studies leveraging explainability methods to complement the previous experiments and further enhance the understanding of latent representations generated by the model. The adopted methods are general enough to be leveraged for any latent space inspection. Preliminary results demonstrate the contextual information incorporated in the latent representations and their impact on the model performance. As a work in progress, we will continue to verify our findings and develop novel explainability approaches.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a stateof-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields. Achieving accurate and comprehensive representation of complex physical fields is pivotal for tasks spanning system monitoring and control, analysis, and design. However, in a multitude of applications, encompassing geophysics (Reichstein et al., 2019), astronomy (Gabbard et al., 2022), biochemistry (Zhong et al., 2021), fluid mechanics (Deng et al., 2023), and others, using a sparse sensor network proves to be the most practical and effective solution. In meteorology and oceanography, variables such as atmospheric pressure, temperature, salinity/humidity, and wind/current velocity must be reconstructed from sparsely sampled observations. Currently, two distinct approaches are used to reconstruct full fields from sparse observations. Traditional physics model-based approaches are based on partial differential equations (PDEs). These approaches draw upon theoretical techniques to derive PDEs rooted in conservation laws and fundamental physical principles (Hughes, 2012). Yet, in complex systems such as weather (Brunton et al., 2016) and epidemiology (Massucci et al., 2016), deriving comprehensive models that are both sufficiently accurate and computationally efficient remains elusive.

Current methods for estimating the required neural-network size for a given problem class have focused on methods that can be computationally intensive, such as neural-architecture search and pruning. In contrast, methods that add capacity to neural networks as needed may provide similar results to architecture search and pruning, but do not require as much computation to find an appropriate network size. Here, we present a network-growth method that searches for explainable error in the network's residuals and grows the network if sufficient error is detected. We demonstrate this method using examples from classification, imitation learning, and reinforcement learning. Within these tasks, the growing network can often achieve better performance than small networks that do not grow, and similar performance to networks that begin much larger.

In artificial neural networks, weights are a static representation of synapses. However, synapses are not static, they have their own interacting dynamics over time. To instill weights with interacting dynamics, we use a model describing synchronization that is capable of capturing core mechanisms of a range of neural and general biological phenomena over time. An ideal fit for these Temporal Weights (TW) are Neural ODEs, with continuous dynamics and a dependency on time. The resulting recurrent neural networks efficiently model temporal dynamics by computing on the ordering of sequences, and the length and scale of time. By adding temporal weights to a model, we demonstrate better performance, smaller models, and data efficiency on sparse, irregularly sampled time series datasets.

The idea is to generate the same image through the model for a given sample image. The application is to use the model architecture and complete the occluded(half-filled) image. A basic encoder-decoder and deep CNN encoder-decoder models are implemented from scratch, trained, and analysed on three datasets. The Analysis is also on finding a good size hidden representation of the image for every dataset, which can be used for applications. Some well-known approaches for image generation are Autoencoders, Generative Adversarial Networks(GANs), Auto-Regressive models(PixelRNN, PixelCNN), DRAW.