Variational autoencoders generate samples from probabilistic latent representations but do not distinguish uncertainty about the latent location from variability around it. We formulate ELVAE, an evidential learning-based VAE in which each latent coordinate is governed by an input-dependent normal-inverse-gamma posterior. This hierarchy yields an explicit latent-location uncertainty that can be used during generation, not merely reported after inference: low-uncertainty anchors support more reliable synthetic samples, while high-uncertainty anchors can be deliberately exploited for stress testing. The objective is an exact evidence lower bound, and we show that direct regularization of the full hierarchy is required, since the marginalized latent law alone cannot identify the uncertainty decomposition. In an MNIST generation pilot with a frozen external classifier, this uncertainty clearly stratified the semantic reliability of generated digits. A zero-displacement control revealed that most of the effect reflects how reliably an anchor can be re-generated, while a smaller but distinct component is attributable to uncertainty-scaled perturbation itself. The effect holds only under within-class uncertainty ranking, and its magnitude varies across seeds. These findings support the learned latent-location uncertainty as a practical control variable for uncertainty-aware generation, separating anchor reliability from perturbation-induced failure.
Generating mixed-type tabular data requires jointly modeling diverse feature distributions and their complex cross-column dependencies. Variational flow matching handles distinct endpoints via factorized distributions, yet leaves feature-specific processing and cross-column interactions implicit within a shared backbone. We introduce Feature-wise Unified Specialization with cross-column Exchange (FUSE) to explicitly separate these roles. FUSE applies separate adaptive mixture modules to numerical and categorical features, allowing each feature to combine shared specialized subnetworks, while joint attention preserves information exchange across all columns. We also characterize the excess population risk from restricted conditioning contexts and bound the continuous Wasserstein generation error by endpoint-prediction risk. Comprehensive experiments on eight tabular datasets demonstrate that FUSE achieves strong and consistent performance across distributional fidelity and downstream utility metrics.
Statistical regularities are routinely offered as evidence that undeciphered sign systems encode language; the Indus script debate is the canonical example. Any such inference rests on specificity: the reported outcome must be unusual among plausible structured non-languages. We test that premise constructively with SIGIL, a purpose-built generative emblem system whose 3,000-text core corpus carries explicit compositional meanings although no sign has a phonological value. A literature registry compiled in advance of evaluation records 54 methods and admits a method to exact scoring when both the published Indus outcome and a source-defined decision rule can be reproduced. SIGIL receives the same category as the Indus corpus on every criterion scored this way, across repetition, directional-asymmetry, and lexical-distribution tests. Declared reconstructions of entropy, frequency, positional, predictive, classifier, and network measures reproduce the familiar Indus-like signatures as well. A sequential decipherment stress test then reaches high dictionary coverage for English, Sanskrit, and Tamil on the same corpus, while grouped held-out declines and unstable keys reveal how little that coverage identifies. The construction does not decide what the Indus signs encode: it shows that the evaluated measures detect organization without being specific to language, and therefore cannot, on their own, establish encoded speech.
Santu Mondal, Chayan Maitra, Rajat K. Decs.LG cs.AI
In real-world machine learning applications, incomplete observations create a fundamental challenge. Researchers have come up with several ideas to address this crucial problem. However, current models still face challenges in balancing scalability and structural consistency. This study proposes a feature imputation method, called FILLER, that deliberately searches the two-dimensional latent space produced by a generative model and fills the missing values with appropriate entries. The generative model is trained on fully observed data to generate samples from the latent space, and FILLER uses this trained model to impute the values missing in the corrupted test samples. In this study, G-NeuroDAVIS serves the purpose of the generative model. This work also presents a mathematical proof on the convergence of the iterative search. Finally, FILLER has been evaluated on several image datasets under random and structured missingness patterns with varying levels of imputation complexities. In order to justify the efficacy of FILLER, it has been compared against existing state-of-the-art solution strategies in terms of RMSE, PSNR, and SSIM. In addition, Wilcoxon signed-rank test has been carried out to validate statistical significance. Moreover, downstream analyses (classification and clustering) have also established the quality of imputation in terms of standard metrics.
Generative models trained on a source domain often produce samples that are poorly aligned with shifted target domains, limiting their effectiveness for target-domain data augmentation. Although target-specific adaptation can reduce this mismatch, it typically requires additional optimization and domain-specific parameters. We propose a Similarity-based Generative Network (SGN), a reusable framework that is trained once on labeled source data and applied to new target domains without parameter updates. SGN learns a latent space structured by label-induced pairwise similarities while preserving reconstructive information through an encoder-decoder architecture. At generation time, a small labeled representative set from the target domain is encoded and combined in the learned latent space, allowing the generated samples to inherit target-specific characteristics while maintaining class consistency. We further analyze the realizability and dimensionality requirements of the proposed similarity structure. Experiments on image and tabular datasets demonstrate the effectiveness of SGN for target-guided data augmentation under source-to-target distribution shifts.
The Forward-Forward (FF) algorithm trains each layer locally, so that a scalar goodness - the sum of squared activations - is high on real inputs and low on contrastive ones, with activations normalized between layers. Both choices are usually treated as heuristics. Under an explicit generative model they are not: the squared goodness is the sufficient statistic of a likelihood-ratio test between two zero-mean populations differing in scale, and the FF threshold is its boundary. It generalizes: anisotropic populations yield a Mahalanobis goodness, the plain square being its isotropic case; heavy-tailed populations yield a saturating statistic whose slope is a posterior precision - divisive normalization - with bounded evidence and an advantage only under aggregation. The same lens characterizes the inter-layer normalization: it must remove the length while preserving per-coordinate energy, explaining a depth collapse we observe under unit-norm normalization; and the pairwise objective admits a scale-inflation shortcut that a whitened goodness removes.
Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets. This mismatch can limit reconstruction accuracy, reduce sample quality, and constrain the expressive power of the learned latent space. We propose the eXact-Prior Variational Autoencoder (X-VAE), a framework that replaces the conventional standard normal prior with a Gaussian prior derived from the latent representations of a pretrained autoencoder (AE). Specifically, the empirical mean and standard deviation of the AE latent codes are used to parameterize a data-adaptive prior that more closely reflects the underlying structure of the training data. During generation, X-VAE introduces a latent scaling factor that enables explicit control over the variance of the sampled latent vectors, providing a simple mechanism for balancing sample diversity and fidelity. This flexibility makes the proposed approach particularly well suited for applications such as industrial and engineering design, where generated solutions must satisfy strict structural or functional constraints while still permitting meaningful design exploration. We present the mathematical formulation of well-suited X-VAE, derive the corresponding KL divergence objective for the proposed prior, and evaluate the method on standard benchmark datasets. Experimental results demonstrate that X-VAE preserves reconstruction quality while producing latent representations that better align with the empirical data distribution, leading to improved controllability and more realistic generated samples.
Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.