DTD-VAE: Disentangled Temporal Dependencies VAE for Credit Risk Prediction

Evaluating customer creditworthiness is crucial for retail banking operations, as it impacts marketing strategies, customer relationship management, and credit risk control. Traditional methods often struggle to capture complex temporal dependencies and extract pertinent information from customer data, crucial for accurate risk assessment. Specifically, they fail to differentiate between temporal patterns indicative of credit risk and those reflecting general customer behavior or preferences, leading to suboptimal risk predictions. In this study, we introduce the Disentangled Temporal Dependencies Variational Autoencoder (DTD-VAE), an advancement over conventional VAE, designed to disentangle temporal dependencies and distinguish credit risk-related features from past customer preferences. The feature inference module of the DTD-VAE incorporates an autoregressive temporal dependency learning mechanism that adeptly captures the temporal dependencies among latent variables, enriching the model's comprehension of the inherent data structure. Furthermore, the feature generative module utilizes an element-wise gating mechanism that assigns independent weights to each dimension of the expert models, enabling a finer-grained disentanglement of latent variables, particularly those relevant to credit risk prediction. Extensive experiments on six real-world datasets demonstrate that the proposed framework consistently outperforms existing methods, achieving performance gains of 3.2%-4.86% in ROC-AUC and 6.41%-9.71% in Accuracy Ratio.

The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning

Disentangled representation learning seeks latent representations whose indicidual dimensions each align with a distinct covariate. Unsupervised approaches typically target latent dimension independence, yet this gives no guarantee that the resulting dimensions align with semantically meaningful covariates. Supervised approaches structure the latent space using observed covariates, but under correlated covariates they cannot simultaneously control one-to-one latent-covariate alignment and latent independence. We introduce a unified, supervised framework that couples latent dimension-covariate dependence with constraints on the latent structure. Within this framework, we show an inherent trade-off, where enforcing latent independence or exclusive one-to-one latent-covariate dependence comes at a provable cost in latent-covariate alignment. We prove that the resulting disentanglement regimes are ordered by the strength of that alignment. Each regime admits a closed-form transformation of the latent space. We apply these transformations post-hoc to realign the representations of pretrained models such as CLIP, DINOv2, and ViT, and we fold them into the inference of informed factor analysis (iFA), a probabilistic model with covariate-informed factors. On simulated and real multi-omics data, we show that both post-hoc alignment and iFA enable controllability of structured latent representations.

FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data

Determining the complexity, or Intrinsic Dimension (ID), of data is fundamental to efficient and interpretable representation learning. This is particularly challenging in multi-modal settings when trying to learn disentangled representations for shared and private information. Existing techniques leave a critical gap: they are often static, uni-modal, or in the case of contrastive methods, adapt only to the shared ID implicitly. We introduce Fidelity-Guided Rank Optimization (FiGuRO), a framework for approximating the ID of uni- and multi-modal data under constraints of model capacity and hyperparameters. FiGuRO learns the dimensions of low-rank projections using truncated singular value decomposition and an algorithm that determines when to reduce or increase dimension and in which latent space. Disentanglement of shared and private information arises as an emergent property of this optimization, eliminating the need for complex auxiliary loss functions. We demonstrate that FiGuRO outperforms existing ID estimation techniques and is more robust to hyperparameter changes. Across simulations and real-world data, FiGuRO captures distinct ID scales and varying subspace ratios, and decomposes shared and private information successfully. Furthermore, we show that FiGuRO can be applied to modern uni-modal pretrained models, enabling efficient, post-hoc disentanglement of multi-modal representations.

Soft-Constrained Optimization of Latent Space in Variational Autoencoders

The usefulness of a variational autoencoder (VAE) depends on two properties of its latent space that are hard to obtain together: high encoding capacity in the individual latent variables, and a low-dimensional, disentangled organization of those variables. Weakening the Kullback-Leibler regularization raises capacity but degrades disentanglement, while strengthening it prunes latent variables away entirely. We formulate VAE training as a soft-constrained optimization problem that addresses both. First, we impose an entropy-based constraint (EC) on individual latent variables, showing that the entropy of a latent code upper-bounds the mutual information it carries about the generative factors of the data. Second, we propose a weight-filter method that exploits the slack of the soft constraint to prune low-entropy dimensions during downstream training. On dSprites, the EC raises the aggregate latent-variable activation score by 43-62% over a vanilla VAE, attains the highest FactorVAE score among the \b{eta} \b{eta}-VAE variants (0.891 vs 0.847), and lowers reconstruction error by up to 38%. On MNIST, the weight filter reduces the latent dimensionality supplied to a downstream classifier from ten to two while holding accuracy above 90%, converging in 37% fewer epochs than the same procedure without the EC. We also find that low-entropy discrete factors tend to merge into a single latent variable, whereas high-entropy continuous factors are distributed across several.

Disentanglement with Holographic Reduced Representations

Disentanglement, the separation of factors of variation in data using neural networks, remains a long-standing challenge in machine learning. Prior work has addressed this problem with variational autoencoders and generative adversarial networks that incorporate ideas from variational inference and information-theoretic constraints. In contrast to methods that rely on continuous representations, we propose a design that treats disentangled representations as symbolic structures, motivated by the compositional relationships among the concepts that make up samples from a distribution. However, learning discrete symbolic structures with neural networks while maintaining differentiability is difficult and often requires complex architectures. To address this, we introduce an unsupervised learning algorithm that uses holographic reduced representations (HRR) for neural disentanglement. We show that the HRR unbinding operation provides an inductive bias for separating factors and yields competitive results against baselines, as measured by latent traversals and disentanglement metrics. We complement these empirical findings with an information-theoretic analysis of the HRR unbinding channel. We prove that unbinding induces approximately independent symbol-value pairs and derive a per-slot capacity bound that quantifies how many distinct symbolic concepts can be reliably encoded, giving a quantitative account of the inductive bias toward disentanglement. The resulting representations differ from standard autoencoder-based models, in that their latent units are vectors that are summed together, rather than scalar dimensions of a low-dimensional latent vector. We show that this HRR representation is more robust to noise than other disentangled representations and maintains reconstruction quality across a range of SNRs.

Disentanglement Beyond Generative Models with Riemannian ICA

There is a gap between the theoretical foundations of disentanglement and the practice of modern representation learning. Existing theoretical frameworks, particularly Independent Component Analysis (ICA) and its nonlinear variants, assume a generative model with statistically independent latent variables underlying the data so that disentanglement amounts to identifying the latents that could have generated the data. This generative framework is interpretable and theoretically justified, but its strong assumptions make it difficult to apply to modern representation learning. Modern pretrained encoders often learn features that exhibit disentangled properties without making generative assumptions, yet there is no general theory for interpreting these features as independent factors of variation. We take a step toward such a theory by introducing Riemannian ICA (RICA), which replaces ICA's global generative model with local geometric structure. RICA is founded on the observation that in ICA, the factors of variation underlying a data point can be understood through radial curves emanating from the point that map to axis-aligned lines in the latent space. We formalize this perspective using Riemannian geometry and introduce our theory in a way that is consistent with the existing generative approach. Our main contribution is the disentanglement tensor, which encodes a second-order notion of disentanglement that we call pointwise disentanglement. This tensor depends on the Hessian of the data log likelihood as well as the Ricci curvature induced by the model. In a controlled source recovery setting with known ground-truth sources, RICA recovers sources across several manifolds, while the success of ICA baselines depends on the coordinates used to represent the observations. Our work provides a theoretical basis for studying local disentanglement without assuming a global generative model.

Winner-Take-All bottlenecks enforce disentangled symbolic representations in multi-task learning

Winner-take-all (WTA) networks constitute a central circuit motif in cortical networks of the brain. In addition, WTA-like activations are abundant in modern deep learning models in the form of the softmax activation for example in attention layers of transformers. While their role in the extraction of latent factors has been studied for relatively simple generative models, their role in the context of highly non-linearly entangled latent factors has remained elusive. In this article, we show that a WTA bottleneck within a deep neural network can enforce under certain well-defined conditions the extraction of categorical latent factors of the data in a multi-task learning setup. In particular, we prove that the representation that emerges in the WTA bottleneck is highly symbolic, where a single neuron or a population of neurons encodes the presence of a single abstract feature such as a specific object, color, or position. We furthermore show empirically on two datasets, that this also holds for architectures and setups that do not fully comply with the assumptions of our theorem and demonstrate the advantages of the acquired symbolic representation for generalization. Our proposed model provides insights into the generalization capabilities of deep neural networks with WTA-like components and may serve as an interface between symbolic and subsymbolic AI systems.