This paper proposes a novel stable learning theory for recurrent neural networks (RNNs), so-called variational adaptive noise and dropout (VAND). As stabilizing factors for RNNs, noise and dropout on the internal state of RNNs have been separately confirmed in previous studies. We reinterpret the optimization problem of RNNs as variational inference, showing that noise and dropout can be derived simultaneously by transforming the explicit regularization term arising in the optimization problem into implicit regularization. Their scale and ratio can also be adjusted appropriately to optimize the main objective of RNNs, respectively. In an imitation learning scenario with a mobile manipulator, only VAND is able to imitate sequential and periodic behaviors as instructed. https://youtu.be/UOho3Xr6A2w
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable this, we present two novel frameworks for applying principles of constrained optimization to the new variational inference algorithm Stein variational gradient descent. Our general framework supports multiple types of constrained optimizers and can handle arbitrary constraints. We demonstrate on a variety of problems that we are able to learn to approximate distributions without violating constraints. Specifically, we show that we can build distributions of: robot motion plans that exactly avoid collisions, robot arm joint angles on the SE(3) manifold with exact table placement constraints, and object poses from point clouds with table placement constraints.
Deep learning approaches process data in a layer-by-layer way with intermediate (or latent) features. We aim at designing a general solution to optimize the latent manifolds to improve the performance on classification, segmentation, completion and/or reconstruction through probabilistic models. This paper proposes a variational inference model which leads to a clustered embedding. We introduce additional variables in the latent space, called \textbf{nebula anchors}, that guide the latent variables to form clusters during training. To prevent the anchors from clustering among themselves, we employ the variational constraint that enforces the latent features within an anchor to form a Gaussian distribution, resulting in a generative model we refer as Nebula Variational Coding (NVC). Since each latent feature can be labeled with the closest anchor, we also propose to apply metric learning in a self-supervised way to make the separation between clusters more explicit. As a consequence, the latent variables of our variational coder form clusters which adapt to the generated semantic of the training data, \textit{e.g.} the categorical labels of each sample. We demonstrate experimentally that it can be used within different architectures designed to solve different problems including text sequence, images, 3D point clouds and volumetric data, validating the advantage of our proposed method.
Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric families or neural networks with expensive variational inference procedures. In this work, we propose a novel approach that leverages alternative representations for permutations, including Lehmer codes, Fisher-Yates draws, and Insertion-Vectors. These representations form a bijection with the symmetric group, allowing for unconstrained learning using conventional deep learning techniques, and can represent any probability distribution over permutations. Our approach enables a trade-off between expressivity of the model family and computational requirements. In the least expressive and most computationally efficient case, our method subsumes previous families of well established probabilistic models over permutations, including Mallow's and the Repeated Insertion Model. Experiments indicate our method significantly outperforms current approaches on the jigsaw puzzle benchmark, a common task for permutation learning. However, we argue this benchmark is limited in its ability to assess learning probability distributions, as the target is a delta distribution (i.e., a single correct solution exists). We therefore propose two additional benchmarks: learning cyclic permutations and re-ranking movies based on user preference. We show that our method learns non-trivial distributions even in the least expressive mode, while traditional models fail to even generate valid permutations in this setting.
Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this challenge, but their formal relationship is unexplored. Here, we prove that the combination of VIP and a full-rank Gaussian can be represented exactly as a forward autoregressive flow augmented with a translation term and input from the model's prior. Guided by this theoretical insight, we introduce the Model-Informed Flow (MIF) architecture, which adds the necessary translation mechanism, prior information, and hierarchical ordering. Empirically, MIF delivers tighter posterior approximations and matches or exceeds state-of-the-art performance across a suite of hierarchical and non-hierarchical benchmarks.
We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it is computationally challenging due to the iterative nature of maximizing the ELBO. In this work, we propose to decompose the control term into linear and residual non-linear components and derive an optimal control term for linear SDEs, using stochastic optimal control. Modeling the non-linear component by a neural network, we show how to efficiently train neural SDEs without sacrificing their expressive power. Since the linear part of the control term is optimal and does not need to be learned, the training is initialized at a lower cost and we observe faster convergence.
We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at an almost dimension-independent rate. Specifically, for strongly log-concave and log-smooth targets, the number of iterations for BBVI with a sub-Gaussian family to achieve an objective $\epsilon$-close to the global optimum is $\mathrm{O}(\log d)$, which improves over the $\mathrm{O}(d)$ dependence of full-rank location-scale families. For heavy-tailed families, we provide a weaker $\mathrm{O}(d^{2/k})$ dimension dependence, where $k$ is the number of finite moments. Additionally, if the Hessian of the target log-density is constant, the complexity is free of any explicit dimension dependence. We also prove that our bound on the gradient variance, which is key to our result, cannot be improved using only spectral bounds on the Hessian of the target log-density.
Recent contributions of semantic information theory reveal the set-element relationship between semantic and syntactic information, represented as synonymous relationships. In this paper, we propose a synonymous variational inference (SVI) method based on this synonymity viewpoint to re-analyze the perceptual image compression problem. It takes perceptual similarity as a typical synonymous criterion to build an ideal synonymous set (Synset), and approximate the posterior of its latent synonymous representation with a parametric density by minimizing a partial semantic KL divergence. This analysis theoretically proves that the optimization direction of perception image compression follows a triple tradeoff that can cover the existing rate-distortion-perception schemes. Additionally, we introduce synonymous image compression (SIC), a new image compression scheme that corresponds to the analytical process of SVI, and implement a progressive SIC codec to fully leverage the model's capabilities. Experimental results demonstrate comparable rate-distortion-perception performance using a single progressive SIC codec, thus verifying the effectiveness of our proposed analysis method.
Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of architecture, hyperparameters and optimization procedure. However, deploying deep learning models out-of-distribution, in sequential decision-making tasks, or in safety-critical domains, necessitates reliable uncertainty quantification, not just a point estimate. The machinery of modern approximate inference -- Bayesian deep learning -- should answer the need for uncertainty quantification, but its effectiveness has been challenged by our inability to define useful explicit inductive biases through priors, as well as the associated computational burden. Instead, in this work we demonstrate, both theoretically and empirically, how to regularize a variational deep network implicitly via the optimization procedure, just as for standard deep learning. We fully characterize the inductive bias of (stochastic) gradient descent in the case of an overparametrized linear model as generalized variational inference and demonstrate the importance of the choice of parametrization. Finally, we show empirically that our approach achieves strong in- and out-of-distribution performance without tuning of additional hyperparameters and with minimal time and memory overhead over standard deep learning.
Kernels are key to encoding prior beliefs and data structures in Gaussian process (GP) models. The design of expressive and scalable kernels has garnered significant research attention. Deep kernel learning enhances kernel flexibility by feeding inputs through a neural network before applying a standard parametric form. However, this approach remains limited by the choice of base kernels, inherits high inference costs, and often demands sparse approximations. Drawing on Mercer's theorem, we introduce a fully data-driven, scalable deep kernel representation where a neural network directly represents a low-rank kernel through a small set of basis functions. This construction enables highly efficient exact GP inference in linear time and memory without invoking inducing points. It also supports scalable mini-batch training based on a principled variational inference framework. We further propose a simple variance correction procedure to guard against overconfidence in uncertainty estimates. Experiments on synthetic and real-world data demonstrate the advantages of our deep kernel GP in terms of predictive accuracy, uncertainty quantification, and computational efficiency.
Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference and control, introducing Diffusion Trajectory Matching (DTM) that enables guiding pretrained diffusion trajectories to satisfy a terminal cost. DTM unifies a broad class of guidance methods and enables novel instantiations. We introduce a new method within this framework that achieves state-of-the-art results on several linear, non-linear, and blind inverse problems without requiring additional model training or specificity to pixel or latent space diffusion models. Our code will be available at https://github.com/czi-ai/oc-guidance
Meta-reinforcement learning trains a single reinforcement learning agent on a distribution of tasks to quickly generalize to new tasks outside of the training set at test time. From a Bayesian perspective, one can interpret this as performing amortized variational inference on the posterior distribution over training tasks. Among the various meta-reinforcement learning approaches, a common method is to represent this distribution with a point-estimate using a recurrent neural network. We show how one can augment this point estimate to give full distributions through the Laplace approximation, either at the start of, during, or after learning, without modifying the base model architecture. With our approximation, we are able to estimate distribution statistics (e.g., the entropy) of non-Bayesian agents and observe that point-estimate based methods produce overconfident estimators while not satisfying consistency. Furthermore, when comparing our approach to full-distribution based learning of the task posterior, our method performs on par with variational baselines while having much fewer parameters.
Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is allowing uncertainty quantification. The parameters of BPCA are typically learned using mean-field variational inference, and in particular, the coordinate ascent variational inference (CAVI) algorithm. So far, the convergence speed of CAVI for BPCA has not been characterized. In our paper, we fill this gap in the literature. Firstly, we prove a precise exponential convergence result in the case where the model uses a single principal component (PC). Interestingly, this result is established through a connection with the classical $\textit{power iteration algorithm}$ and it indicates that traditional PCA is retrieved as points estimates of the BPCA parameters. Secondly, we leverage recent tools to prove exponential convergence of CAVI for the model with any number of PCs, thus leading to a more general result, but one that is of a slightly different flavor. To prove the latter result, we additionally needed to introduce a novel lower bound for the symmetric Kullback--Leibler divergence between two multivariate normal distributions, which, we believe, is of independent interest in information theory.
Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given multitask learning problem. Ideally, the "right" latent task structure should be learned in a data-driven manner. We present a flexible, nonparametric Bayesian model that posits a mixture of factor analyzers structure on the tasks. The nonparametric aspect makes the model expressive enough to subsume many existing models of latent task structures (e.g, mean-regularized tasks, clustered tasks, low-rank or linear/non-linear subspace assumption on tasks, etc.). Moreover, it can also learn more general task structures, addressing the shortcomings of such models. We present a variational inference algorithm for our model. Experimental results on synthetic and real-world datasets, on both regression and classification problems, demonstrate the effectiveness of the proposed method.
Personalized Bayesian federated learning (PBFL) handles non-i.i.d. client data and quantifies uncertainty by combining personalization with Bayesian inference. However, existing PBFL methods face two limitations: restrictive parametric assumptions in client posterior inference and naive parameter averaging for server aggregation. To overcome these issues, we propose FedWBA, a novel PBFL method that enhances both local inference and global aggregation. At the client level, we use particle-based variational inference for nonparametric posterior representation. At the server level, we introduce particle-based Wasserstein barycenter aggregation, offering a more geometrically meaningful approach. Theoretically, we provide local and global convergence guarantees for FedWBA. Locally, we prove a KL divergence decrease lower bound per iteration for variational inference convergence. Globally, we show that the Wasserstein barycenter converges to the true parameter as the client data size increases. Empirically, experiments show that FedWBA outperforms baselines in prediction accuracy, uncertainty calibration, and convergence rate, with ablation studies confirming its robustness.
IntrinsicTimescales.jl is a Julia package to perform estimation of intrinsic neural timescales (INTs). INTs are defined as the time window in which prior information from an ongoing stimulus can affect the processing of newly arriving information. INTs are estimated either from the autocorrelation function (ACF) or the power spectral density (PSD) of time-series data. In addition to the model-free estimates of INTs, IntrinsicTimescales.jl offers implementations of novel techniques of timescale estimation via performing parameter estimation of an Ornstein-Uhlenbeck process with adaptive approximate Bayesian computation (aABC) and automatic differentiation variational inference (ADVI).
We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain a gradient flow that does so. By approximating the latter with a system of interacting particles, we obtain the algorithm, which we underpin it theoretically by providing error guarantees. The novel algorithm compares favorably in experiments with previous particle-based methods and variational inference analogues.
Recent advances in self-supervised learning (SSL) have revolutionized computer vision through innovative architectures and learning objectives, yet they have not fully leveraged insights from biological visual processing systems. Recently, a brain-inspired SSL model named PhiNet was proposed; it is based on a ResNet backbone and operates on static image inputs with strong augmentation. In this paper, we introduce PhiNet v2, a novel Transformer-based architecture that processes temporal visual input (that is, sequences of images) without relying on strong augmentation. Our model leverages variational inference to learn robust visual representations from continuous input streams, similar to human visual processing. Through extensive experimentation, we demonstrate that PhiNet v2 achieves competitive performance compared to state-of-the-art vision foundation models, while maintaining the ability to learn from sequential input without strong data augmentation. This work represents a significant step toward more biologically plausible computer vision systems that process visual information in a manner more closely aligned with human cognitive processes.
Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from distinct modalities or be structured according to an underlying graph. We introduce Neural Adaptive Shrinkage (Nash), a unified framework that integrates covariate-specific side information into sparse regression via neural networks. Nash adaptively modulates penalties on a per-covariate basis, learning to tailor regularization without cross-validation. We develop a variational inference algorithm for efficient training and establish connections to empirical Bayes regression. Experiments on real data demonstrate that Nash can improve accuracy and adaptability over existing methods.
Multi-modal and high-dimensional posteriors present significant challenges for variational inference, causing mode-seeking behavior and collapse despite the theoretical expressiveness of normalizing flows. Traditional annealing methods require temperature schedules and hyperparameter tuning, falling short of the goal of truly black-box variational inference. We introduce FlowVAT, a conditional tempering approach for normalizing flow variational inference that addresses these limitations. Our method tempers both the base and target distributions simultaneously, maintaining affine-invariance under tempering. By conditioning the normalizing flow on temperature, we leverage overparameterized neural networks' generalization capabilities to train a single flow representing the posterior across a range of temperatures. This preserves modes identified at higher temperatures when sampling from the variational posterior at $T = 1$, mitigating standard variational methods' mode-seeking behavior. In experiments with 2, 10, and 20 dimensional multi-modal distributions, FlowVAT outperforms traditional and adaptive annealing methods, finding more modes and achieving better ELBO values, particularly in higher dimensions where existing approaches fail. Our method requires minimal hyperparameter tuning and does not require an annealing schedule, advancing toward fully-automatic black-box variational inference for complicated posteriors.