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Authors

Rafał Karczewski, Markus Heinonen, and Vikas Garg

Abstract

We investigate what kind of images lie in the high-density regions of diffusion models. We introduce a theoretical mode-tracking process capable of pinpointing the exact mode of the denoising distribution, and we propose a practical high-density sampler that consistently generates images of higher likelihood than usual samplers. Our empirical findings reveal the existence of significantly higher likelihood samples that typical samplers do not produce, often manifesting as cartoon-like drawings or blurry images depending on the noise level. Curiously, these patterns emerge in datasets devoid of such examples. We also present a novel approach to track sample likelihoods in diffusion SDEs, which remarkably incurs no additional computational cost. Code is available at https://github.com/Aalto-QuML/high-density-diffusion

Authors

Aidan Scannell, Mohammadreza Nakhaeinezhadfard, Kalle Kujanpää, Yi Zhao, Kevin Sebastian Luck, Arno Solin, and Joni Pajarinen

Abstract

In reinforcement learning (RL), world models serve as internal simulators, enabling agents to predict environment dynamics and future outcomes in order to make informed decisions. While previous approaches leveraging discrete latent spaces, such as DreamerV3, have achieved strong performance in discrete action environments, they are typically outperformed in continuous control tasks by models with continuous latent spaces, like TD-MPC2. This paper explores the use of discrete latent spaces for continuous control with world models. Specifically, we demonstrate that quantized discrete codebook encodings are more effective representations for continuous control, compared to alternative encodings, such as one-hot and label-based encodings. Based on these insights, we introduce DCWM: Discrete Codebook World Model, a model-based RL method which surpasses recent state-of-the-art algorithms, including TD-MPC2 and DreamerV3, on continuous control benchmarks.

Authors

Alexandru Dumitrescu, Dani Korpela, Markus Heinonen, Yogesh Verma, Valerii Iakovlev, Vikas Garg, and Harri Lähdesmäki

Abstract

Obtaining the desired effect of drugs is highly dependent on their molecular geometries. Thus, the current prevailing paradigm focuses on 3D point-cloud atom representations, utilizing graph neural network (GNN) parametrizations, with rotational symmetries baked in via E(3) invariant layers. We prove that such models must necessarily disregard chirality, a geometric property of the molecules that cannot be superimposed on their mirror image by rotation and translation. Chirality plays a key role in determining drug safety and potency. To address this glaring issue, we introduce a novel field-based representation, proposing reference rotations that replace rotational symmetry constraints. The proposed model captures all molecular geometries including chirality, while still achieving highly competitive performance with E(3)-based methods across standard benchmarking metrics.

Authors

Najwa Laabid, Severi Rissanen, Markus Heinonen, Arno Solin, and Vikas Garg

Abstract

Graph diffusion models, dominant in graph generative modeling, remain underexplored for graph-to-graph translation tasks like chemical reaction prediction. We demonstrate that standard permutation equivariant denoisers face fundamental limitations in these tasks due to their inability to break symmetries in noisy inputs. To address this, we propose \emph{aligning} input and target graphs to break input symmetries while preserving permutation equivariance in non-matching graph portions. Using retrosynthesis (i.e., the task of predicting precursors for synthesis of a given target molecule) as our application domain, we show how alignment dramatically improves discrete diffusion model performance from 5\% to a SOTA-matching 54.7\% top-1 accuracy. Code is available at https://github.com/Aalto-QuML/DiffAlign.

Authors

Frida Marie Viset, Anton Kullberg, Frederiek Wesel, and Arno Solin

Abstract

The Hilbert-space Gaussian process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian process (GP) inference by projecting the GP onto M basis functions. These properties result in a favorable data-independent O(M³) computational complexity during hyperparameter optimization but require a dominating one-time precomputation of the precision matrix costing O(NM²) operations. In this paper, we lower this dominating computational complexity to O(NM) with no additional approximations. We can do this because we realize that the precision matrix can be split into a sum of Hankel-Toeplitz matrices, each having O(M) unique entries. Based on this realization we propose computing only these unique entries at O(NM) costs. Further, we develop two theorems that prescribe sufficient conditions for the complexity reduction to hold generally for a wide range of other approximate GP models, such as the Variational Fourier features approach. The two theorems do this with no assumptions on the data and no additional approximations of the GP models themselves. Thus, our contribution provides a pure speed-up of several existing, widely used, GP approximations, without further approximations.

Authors

Severi Rissanen, Markus Heinonen, and Arno Solin

Abstract

The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using (i) a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

Authors

Tiago Silva, Amauri Souza, Omar Rivasplata, Vikas Garg, Samuel Kaski, and Diego Mesquita

Abstract

Conventional wisdom attributes the success of Generative Flow Networks (GFlowNets) to their ability to exploit the compositional structure of the sample space for learning generalizable flow functions (Bengio et al., 2021). Despite the abundance of empirical evidence, formalizing this belief with verifiable non-vacuous statistical guarantees has remained elusive. We address this issue with the first data-dependent generalization bounds for GFlowNets. We also elucidate the negative impact of the state space size on the generalization performance of these models via Azuma-Hoeffding-type oracle PAC-Bayesian inequalities. We leverage our theoretical insights to design a novel distributed learning algorithm for GFlowNets, which we call Subgraph Asynchronous Learning (SAL). In a nutshell, SAL utilizes a divide-and-conquer strategy: multiple GFlowNets are trained in parallel on smaller subnetworks of the flow network, and then aggregated with an additional GFlowNet that allocates appropriate flow to each subnetwork. Our experiments with synthetic and real-world problems demonstrate the benefits of SAL over centralized training in terms of mode coverage and distribution matching.

Authors

Siddharth Ramchandran, Manuel Haussmann, and Harri Lähdesmäki

Abstract

Bayesian optimisation (BO) using a Gaussian process (GP)-based surrogate model is a powerful tool for solving black-box optimisation problems but does not scale well to high-dimensional data. Previous works have proposed to use variational autoencoders (VAEs) to project high-dimensional data onto a low-dimensional latent space and to implement BO in the inferred latent space. In this work, we propose a conditional generative model for efficient high-dimensional BO that uses a GP surrogate model together with GP prior VAEs. A GP prior VAE extends the standard VAE by conditioning the generative and inference model on auxiliary covariates, capturing complex correlations across samples with a GP. Our model incorporates the observed target quantity values as auxiliary covariates learning a structured latent space that is better suited for the GP-based BO surrogate model. It handles partially observed auxiliary covariates using a unifying probabilistic framework and can also incorporate additional auxiliary covariates that may be available in real-world applications. We demonstrate that our method improves upon existing latent space BO methods on simulated datasets as well as on commonly used benchmarks.

Authors

ÇaÄŸlar Hızlı, ÇaÄŸatay Yıldız, Matthias Bethge, S. T. John, and Pekka Marttinen 

Abstract

This work aims to recover the underlying states and their time evolution in a latent dynamical system from high-dimensional sensory measurements. Previous work on identifiable representation learning in dynamical systems focused on identifying latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear \ica, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. Our identifiability theory relies on two key assumptions: (i) sufficient variability in the latent noise, and (ii) the bijectivity of the augmented transition function. Drawing from this theory, we introduce a practical algorithm based on variational auto-encoders. We empirically demonstrate that it improves generalization and interpretability of target dynamical systems by (i) recovering latent state dynamics with high accuracy, (ii) correspondingly achieving high future prediction accuracy, and (iii) adapting fast to new environments. Additionally, for complex real-world dynamics, (iv) it produces state-of-the-art future prediction results for long horizons, highlighting its usefulness for practical scenarios.

Selected for Spotlight presentation - top 5 % of all submissions

Authors

Valerii Iakovlev, and Harri Lähdesmäki

Abstract

Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is collected randomly over time and space, as is often the case with sensor networks in real-world applications like crowdsourced earthquake detection or pollution monitoring. In response, we developed a new method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of observations. It outperforms existing methods on challenging spatiotemporal datasets by offering substantial improvements in predictive accuracy and computational efficiency, making it a useful tool for modeling and understanding complex dynamical systems observed under realistic, unconstrained conditions.

Selected for Spotlight presentation - top 5 % of all submissions

Authors

Xinyu Zhang, Daolang Huang, Samuel Kaski, and Julien Martinelli

Abstract

Preferential Bayesian Optimization (PBO) is a sample-efficient method to learn latent user utilities from preferential feedback over a pair of designs. It relies on a statistical surrogate model for the latent function, usually a Gaussian process, and an acquisition strategy to select the next candidate pair to get user feedback on. Due to the non-conjugacy of the associated likelihood, every PBO step requires a significant amount of computations with various approximate inference techniques. This computational overhead is incompatible with the way humans interact with computers, hindering the use of PBO in real-world cases. Building on the recent advances of amortized BO, we propose to circumvent this issue by fully amortizing PBO, meta-learning both the surrogate and the acquisition function. Our method comprises a novel transformer neural process architecture, trained using reinforcement learning and tailored auxiliary losses. On a benchmark composed of synthetic and real-world datasets, our method is several orders of magnitude faster than the usual Gaussian process-based strategies and often outperforms them in accuracy.

Authors

Yogesh Verma, Ayush Bharti, and Vikas Garg 

Abstract

Simulation-based inference (SBI) methods typically require fully observed data to infer parameters of models with intractable likelihood functions. However, datasets often contain missing values due to incomplete observations, data corruptions (common in astrophysics), or instrument limitations (e.g., in high-energy physics applications). In such scenarios, missing data must be imputed before applying any SBI method. We formalize the problem of missing data in SBI and demonstrate that naive imputation methods can introduce bias in the estimation of SBI posterior. We also introduce a novel amortized method that addresses this issue by jointly learning the imputation model and the inference network within a neural posterior estimation (NPE) framework. Extensive empirical results on SBI benchmarks show that our approach provides robust inference outcomes compared to standard baselines for varying levels of missing data. Moreover, we demonstrate the merits of our imputation model on two real-world bioactivity datasets (Adrenergic and Kinase assays). Code is available at https://github.com/Aalto-QuML/RISE.

Authors

Rui Li, Marcus Klasson, Arno Solin, and Martin Trapp

Abstract

The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo integration remaining the standard. In this work we examine streamlining prediction in BDL through a single forward pass without sampling. For this, we use local linearisation of activation functions and local Gaussian approximations at linear layers. Thus allowing us to analytically compute an approximation of the posterior predictive distribution. We showcase our approach for both MLP and transformers, such as ViT and GPT-2, and assess its performance on regression and classification tasks. Open-source library: https://github.com/AaltoML/SUQ.

Selected for Spotlight presentation - top 5 % of all submissions

Authors

Tiago Silva, Rodrigo Alves, Eliezer de Souza da Silva, Amauri Souza, Vikas Garg, Samuel Kaski, and Diego Mesquita

Abstract

Generative Flow Networks (GFlowNets) are an emerging class of sampling methods for distributions over discrete and compositional objects, e.g., graphs. In spite of their remarkable success in problems such as drug discovery and phylogenetic inference, the question of when and whether GFlowNets learn to sample from the target distribution remains underexplored. To tackle this issue, we first assess the extent to which a violation of the detailed balance of the underlying flow network might hamper the correctness of GFlowNet's sampling distribution. In particular, we demonstrate that the impact of an imbalanced edge on the model's accuracy is influenced by the total amount of flow passing through it and, as a consequence, is unevenly distributed across the network. We also argue that, depending on the parameterization, imbalance may be inevitable. In this regard, we consider the problem of sampling from distributions over graphs with GFlowNets parameterized by graph neural networks (GNNs) and show that the representation limits of GNNs delineate which distributions these GFlowNets can approximate. Lastly, we address these limitations by proposing a theoretically sound and computationally tractable metric for assessing GFlowNets, experimentally showing it is a better proxy for correctness than popular evaluation protocols.

Selected for Oral presentation - top 1% of all submissions

Authors

Yogesh Verma, Markus Heinonen, and Vikas Garg

Abstract

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Authors

Erik Schultheis, Wojciech Kotlowski, Marek Wydmuch, Rohit Babbar, Strom Borman, Krzysztof Dembczynski

Abstract

We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly labels predicted for each instance. These "macro-at-" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at- constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.

Authors

Aidan Scannell, Riccardo Mereu, Paul E. Chang, Ella Tamir, Joni Pajarinen, and Arno Solin 

Abstract

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL.

Authors

Trung Trinh, Markus Heinonen, Luigi Acerbi, and Samuel Kaski

Abstract

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

Selected for Spotlight presentation - top5% of all submissions

Authors

Lorenzo Loconte, Aleksanteri Sladek, Stefan Mengel, Martin Trapp, Arno Solin, Nicolas Gillis, and Antonio Vergari

Abstract

Mixture models are traditionally represented and learned by adding several distributions as components. Allowing mixtures to subtract probability mass or density can drastically reduce the number of components needed to model complex distributions. However, learning such subtractive mixtures while ensuring they still encode a non-negative function is challenging. We investigate how to learn and perform inference on deep subtractive mixtures by squaring them. We do this in the framework of probabilistic circuits, which enable us to represent tensorized mixtures and generalize several other subtractive models. We theoretically prove that the class of squared circuits allowing subtractions can be exponentially more expressive than traditional additive mixtures; and, we empirically show this increased expressiveness on a series of real-world distribution estimation tasks.