This paper explores image caption generation using conditional variational auto-encoders (CVAEs). Standard CVAEs with a fixed Gaussian prior yield descriptions with too little variability. Instead, we propose two models that explicitly structure the latent space around K components corresponding to different types of image content, and combine components to create priors for images that contain multiple types of content simultaneously (e.g., several kinds of objects). Our first model uses a Gaussian Mixture model (GMM) prior, while the second one defines a novel Additive Gaussian (AG) prior that linearly combines component means. We show that both models produce captions that are more diverse and more accurate than a strong LSTM baseline or a "vanilla" CVAE with a fixed Gaussian prior, with AG-CVAE showing particular promise.

For example, while prior work has suggested that theglobally optimal VAEsolution canlearn thecorrect manifold dimension, anecessary (butnotsufficient)condition forproducing samplesfrom the true data distribution, this has never been rigorously proven. Moreover, it remains unclear how such considerations would change when various types of conditioning variablesare introduced, or when the data support is extended to a union of manifolds (e.g., as is likely the case for MNIST digits and related). In this work, we address these points by first proving that VAE global minima are indeed capable of recovering the correct manifold dimension.

To do so, we describe the encoder termI(Z;X), which is calculated as the Kullback-Leibler divergence(DKL)betweenpφ(z|x)andp(z). However upon this point, we have only learned the parameters ofthe Gaussian distribution. Thenaiveapproach requires estimating the joint distribution of the variables. Anumberofmethodsestimating lower bounds of mutual information exist [1, 11]. Such bounds, however, suffer from inherent statistical limitations [8].

Although the variational autoencoder (VAE) and its conditional extension (CVAE) are capable of state-of-the-art results across multiple domains, their precise behavior is still not fully understood, particularly in the context of data (like images) that lie on or near a low-dimensional manifold. For example, while prior work has suggested that the globally optimal VAE solution can learn the correct manifold dimension, a necessary (but not sufficient) condition for producing samples from the true data distribution, this has never been rigorously proven. Moreover, it remains unclear how such considerations would change when various types of conditioning variables are introduced, or when the data support is extended to a union of manifolds (e.g., as is likely the case for MNIST digits and related). In this work, we address these points by first proving that VAE global minima are indeed capable of recovering the correct manifold dimension. We then extend this result to more general CVAEs, demonstrating practical scenarios whereby the conditioning variables allow the model to adaptively learn manifolds of varying dimension across samples. Our analyses, which have practical implications for various CVAE design choices, are also supported by numerical results on both synthetic and real-world datasets.

This paper explores image caption generation using conditional variational auto-encoders (CVAEs). Standard CVAEs with a fixed Gaussian prior yield descriptions with too little variability. Instead, we propose two models that explicitly structure the latent space around K components corresponding to different types of image content, and combine components to create priors for images that contain multiple types of content simultaneously (e.g., several kinds of objects). Our first model uses a Gaussian Mixture model (GMM) prior, while the second one defines a novel Additive Gaussian (AG) prior that linearly combines component means. We show that both models produce captions that are more diverse and more accurate than a strong LSTM baseline or a "vanilla" CVAE with a fixed Gaussian prior, with AG-CVAE showing particular promise.

The chemical space of drug-like molecules is vast, motivating the development of generative models that must learn broad chemical distributions, enable conditional generation by capturing structure-property representations, and provide fast molecular generation. Meeting the objectives depends on modeling choices, including the probabilistic modeling approach, the conditional generative formulation, the architecture, and the molecular input representation. To address the challenges, we present STAR-VAE (Selfies-encoded, Transformer-based, AutoRegressive Variational Auto Encoder), a scalable latent-variable framework with a Transformer encoder and an autoregressive Transformer decoder. It is trained on 79 million drug-like molecules from PubChem, using SELFIES to guarantee syntactic validity. The latent-variable formulation enables conditional generation: a property predictor supplies a conditioning signal that is applied consistently to the latent prior, the inference network, and the decoder. Our contributions are: (i) a Transformer-based latent-variable encoder-decoder model trained on SELFIES representations; (ii) a principled conditional latent-variable formulation for property-guided generation; and (iii) efficient finetuning with low-rank adapters (LoRA) in both encoder and decoder, enabling fast adaptation with limited property and activity data. On the GuacaMol and MOSES benchmarks, our approach matches or exceeds baselines, and latent-space analyses reveal smooth, semantically structured representations that support both unconditional exploration and property-aware generation. On the Tartarus benchmarks, the conditional model shifts docking-score distributions toward stronger predicted binding. These results suggest that a modernized, scale-appropriate VAE remains competitive for molecular generation when paired with principled conditioning and parameter-efficient finetuning.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute con-founder from local treatment vectors using a conditional variational autoencoder (CV AE) with a spatial prior, then estimates causal effects via a flexible outcome model. We show that this approach enables nonparametric identification of both direct and spillover effects under weak assumptions--without requiring multiple treatment types or a known model of the latent field. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world datasets in environmental health and social science. By turning interference into a multi-cause signal, our framework bridges spatial and deconfounding literatures to advance robust causal inference in structured data. Causal inference in spatial settings is critical for science and policy, from estimating the health effects of pollution to evaluating land use, climate interventions, and the spread of infectious disease. Most data in these domains are observational, since large-scale interventions are typically infeasible or unethical, so robust methodology is needed to draw valid conclusions. Y et observational studies in these settings face two fundamental challenges that standard methods rarely address together: (1) spillover (interference), where the treatment at one site affects outcomes at nearby sites, violating the Stable Unit Treatment V alue Assumption (SUTV A), and (2) spatially structured unobserved confounding, where latent fields such as weather or socioeconomic context jointly drive exposures and outcomes.

Pan-cancer classification using transcriptomic (RNA-Seq) data can inform tumor subtyping and therapy selection, but is challenging due to extremely high dimensionality and limited sample sizes. In this study, we propose a novel deep learning framework that uses a class-conditional variational autoencoder (cVAE) to augment training data for pan-cancer gene expression classification. Using 801 tumor RNA-Seq samples spanning 5 cancer types from The Cancer Genome Atlas (TCGA), we first perform feature selection to reduce 20,531 gene expression features to the 500 most variably expressed genes. A cVAE is then trained on this data to learn a latent representation of gene expression conditioned on cancer type, enabling the generation of synthetic gene expression samples for each tumor class. We augment the training set with these cVAE-generated samples (doubling the dataset size) to mitigate overfitting and class imbalance. A two-layer multilayer perceptron (MLP) classifier is subsequently trained on the augmented dataset to predict tumor type. The augmented framework achieves high classification accuracy (~98%) on a held-out test set, substantially outperforming a classifier trained on the original data alone. We present detailed experimental results, including VAE training curves, classifier performance metrics (ROC curves and confusion matrix), and architecture diagrams to illustrate the approach. The results demonstrate that cVAE-based synthetic augmentation can significantly improve pan-cancer prediction performance, especially for underrepresented cancer classes.