arXiv subjects

Vikas Garg

Publications and source records attributed to Vikas Garg.

At least 37 records · Page 2Linked to original sources

arXiv2025

Positional Encoding meets Persistent Homology on Graphs

The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two promising approaches to mitigate this issue. PE schemes endow GNNs with location-aware features, while PH methods enhance GNNs with multiresolution topological features. However, a rigorous theoretical characterization of the relative merits and shortcomings of PE and PH has remained elusive. We bridge this gap by establishing that neither paradigm is more expressive than the other, providing novel constructions where one approach fails but the other succeeds. Our insights inform the design of a novel learnable method, PiPE (Persistence-informed Positional Encoding), which is provably more expressive than both PH and PE. PiPE demonstrates strong performance across a variety of tasks (e.g., molecule property prediction, graph classification, and out-of-distribution generalization), thereby advancing the frontiers of graph representation learning. Code is available at https://github.com/Aalto-QuML/PIPE.

cs.LG↗

arXiv2025

Diffusion Models as Cartoonists: The Curious Case of High Density Regions

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.

cs.CV↗

arXiv2025

Devil is in the Details: Density Guidance for Detail-Aware Generation with Flow Models

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality. Code is available at https://github.com/Aalto-QuML/density-guidance.

cs.LG↗

arXiv2025

Employing Federated Learning for Training Autonomous HVAC Systems

Buildings account for 40% of global energy consumption. A considerable portion of building energy consumption stems from heating, ventilation, and air conditioning (HVAC), and thus implementing smart, energy-efficient HVAC systems has the potential to significantly impact the course of climate change. In recent years, model-free reinforcement learning algorithms have been increasingly assessed for this purpose due to their ability to learn and adapt purely from experience. They have been shown to outperform classical controllers in terms of energy cost and consumption, as well as thermal comfort. However, their weakness lies in their relatively poor data efficiency, requiring long periods of training to reach acceptable policies, making them inapplicable to real-world controllers directly. In this paper, we demonstrate that using federated learning to train the reinforcement learning controller of HVAC systems can improve the learning speed, as well as improve their ability to generalize, which in turn facilitates transfer learning to unseen building environments. In our setting, a global control policy is learned by aggregating local policies trained on multiple data centers located in different climate zones. The goal of the policy is to minimize energy consumption and maximize thermal comfort. We perform experiments evaluating three different optimizers for local policy training, as well as three different federated learning algorithms against two alternative baselines. Our experiments show that these effects lead to a faster learning speed, as well as greater generalization capabilities in the federated policy compared to any individually trained policy. Furthermore, the learning stability is significantly improved, with the learning process and performance of the federated policy being less sensitive to the choice of parameters and the inherent randomness of reinforcement learning.

math.OC↗

arXiv2025

Heterophily-informed Message Passing

Graph neural networks (GNNs) are known to be vulnerable to oversmoothing due to their implicit homophily assumption. We mitigate this problem with a novel scheme that regulates the aggregation of messages, modulating the type and extent of message passing locally thereby preserving both the low and high-frequency components of information. Our approach relies solely on learnt embeddings, obviating the need for auxiliary labels, thus extending the benefits of heterophily-aware embeddings to broader applications, e.g., generative modelling. Our experiments, conducted across various data sets and GNN architectures, demonstrate performance enhancements and reveal heterophily patterns across standard classification benchmarks. Furthermore, application to molecular generation showcases notable performance improvements on chemoinformatics benchmarks.

cs.LG↗

arXiv2025

E(3)-equivariant models cannot learn chirality: Field-based molecular generation

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.

cs.LG↗

arXiv2025

What Ails Generative Structure-based Drug Design: Expressivity is Too Little or Too Much?

Several generative models with elaborate training and sampling procedures have been proposed to accelerate structure-based drug design (SBDD); however, their empirical performance turns out to be suboptimal. We seek to better understand this phenomenon from both theoretical and empirical perspectives. Since most of these models apply graph neural networks (GNNs), one may suspect that they inherit the representational limitations of GNNs. We analyze this aspect, establishing the first such results for protein-ligand complexes. A plausible counterview may attribute the underperformance of these models to their excessive parameterizations, inducing expressivity at the expense of generalization. We investigate this possibility with a simple metric-aware approach that learns an economical surrogate for affinity to infer an unlabelled molecular graph and optimizes for labels conditioned on this graph and molecular properties. The resulting model achieves state-of-the-art results using 100x fewer trainable parameters and affords up to 1000x speedup. Collectively, our findings underscore the need to reassess and redirect the existing paradigm and efforts for SBDD. Code is available at https://github.com/rafalkarczewski/SimpleSBDD.

cs.LG↗

arXiv2025

Robust Simulation-Based Inference under Missing Data via Neural Processes

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.

cs.LG↗

arXiv2024

Algebraic Positional Encodings

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an interpretation as orthogonal operators. This design preserves the algebraic characteristics of the source domain, ensuring that the model upholds its desired structural properties. Our scheme can accommodate various structures, ncluding sequences, grids and trees, as well as their compositions. We conduct a series of experiments to demonstrate the practical applicability of our approach. Results suggest performance on par with or surpassing the current state-of-the-art, without hyper-parameter optimizations or "task search" of any kind. Code is available at https://github.com/konstantinosKokos/ape.

cs.LG↗

arXiv2024

Diffusion Twigs with Loop Guidance for Conditional Graph Generation

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.

cs.LG↗

arXiv2024

Topological Neural Networks go Persistent, Equivariant, and Continuous

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

cs.LG↗

arXiv2024

Graph4GUI: Graph Neural Networks for Representing Graphical User Interfaces

Present-day graphical user interfaces (GUIs) exhibit diverse arrangements of text, graphics, and interactive elements such as buttons and menus, but representations of GUIs have not kept up. They do not encapsulate both semantic and visuo-spatial relationships among elements. To seize machine learning's potential for GUIs more efficiently, Graph4GUI exploits graph neural networks to capture individual elements' properties and their semantic-visuo-spatial constraints in a layout. The learned representation demonstrated its effectiveness in multiple tasks, especially generating designs in a challenging GUI autocompletion task, which involved predicting the positions of remaining unplaced elements in a partially completed GUI. The new model's suggestions showed alignment and visual appeal superior to the baseline method and received higher subjective ratings for preference. Furthermore, we demonstrate the practical benefits and efficiency advantages designers perceive when utilizing our model as an autocompletion plug-in.

cs.HC↗

arXiv2024

ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs

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.

cs.AI↗

arXiv2023

Going beyond persistent homology using persistent homology

Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood. Augmenting these graph models with topological features via persistent homology (PH) has gained prominence, but identifying the class of attributed graphs that PH can recognize remains open. We introduce a novel concept of color-separating sets to provide a complete resolution to this important problem. Specifically, we establish the necessary and sufficient conditions for distinguishing graphs based on the persistence of their connected components, obtained from filter functions on vertex and edge colors. Our constructions expose the limits of vertex- and edge-level PH, proving that neither category subsumes the other. Leveraging these theoretical insights, we propose RePHINE for learning topological features on graphs. RePHINE efficiently combines vertex- and edge-level PH, achieving a scheme that is provably more powerful than both. Integrating RePHINE into MP-GNNs boosts their expressive power, resulting in gains over standard PH on several benchmarks for graph classification.

cs.LG↗

arXiv2023

Compositional Sculpting of Iterative Generative Processes

High training costs of generative models and the need to fine-tune them for specific tasks have created a strong interest in model reuse and composition. A key challenge in composing iterative generative processes, such as GFlowNets and diffusion models, is that to realize the desired target distribution, all steps of the generative process need to be coordinated, and satisfy delicate balance conditions. In this work, we propose Compositional Sculpting: a general approach for defining compositions of iterative generative processes. We then introduce a method for sampling from these compositions built on classifier guidance. We showcase ways to accomplish compositional sculpting in both GFlowNets and diffusion models. We highlight two binary operations $\unicode{x2014}$ the harmonic mean ($p_1 \otimes p_2$) and the contrast ($p_1 \unicode{x25D1}\,p_2$) between pairs, and the generalization of these operations to multiple component distributions. We offer empirical results on image and molecular generation tasks.

cs.LG↗

arXiv2023

AbODE: Ab Initio Antibody Design using Conjoined ODEs

Antibodies are Y-shaped proteins that neutralize pathogens and constitute the core of our adaptive immune system. De novo generation of new antibodies that target specific antigens holds the key to accelerating vaccine discovery. However, this co-design of the amino acid sequence and the 3D structure subsumes and accentuates some central challenges from multiple tasks, including protein folding (sequence to structure), inverse folding (structure to sequence), and docking (binding). We strive to surmount these challenges with a new generative model AbODE that extends graph PDEs to accommodate both contextual information and external interactions. Unlike existing approaches, AbODE uses a single round of full-shot decoding and elicits continuous differential attention that encapsulates and evolves with latent interactions within the antibody as well as those involving the antigen. We unravel fundamental connections between AbODE and temporal networks as well as graph-matching networks. The proposed model significantly outperforms existing methods on standard metrics across benchmarks.

cs.LG↗

arXiv2023

Graph Neural Network Autoencoders for Efficient Quantum Circuit Optimisation

Reinforcement learning (RL) is a promising method for quantum circuit optimisation. However, the state space that has to be explored by an RL agent is extremely large when considering all the possibilities in which a quantum circuit can be transformed through local rewrite operations. This state space explosion slows down the learning of RL-based optimisation strategies. We present for the first time how to use graph neural network (GNN) autoencoders for the optimisation of quantum circuits. We construct directed acyclic graphs from the quantum circuits, encode the graphs and use the encodings to represent RL states. We illustrate our proof of concept implementation on Bernstein-Vazirani circuits and, from preliminary results, we conclude that our autoencoder approach: a) maintains the optimality of the original RL method; b) reduces by 20 \% the size of the table that encodes the learned optimisation strategy. Our method is the first realistic first step towards very large scale RL quantum circuit optimisation.

quant-ph↗

arXiv2022

Modular Flows: Differential Molecular Generation

Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis. Flows can generate molecules effectively by inverting the encoding process, however, existing flow models either require artifactual dequantization or specific node/edge orderings, lack desiderata such as permutation invariance, or induce discrepancy between the encoding and the decoding steps that necessitates post hoc validity correction. We circumvent these issues with novel continuous normalizing E(3)-equivariant flows, based on a system of node ODEs coupled as a graph PDE, that repeatedly reconcile locally toward globally aligned densities. Our models can be cast as message-passing temporal networks, and result in superlative performance on the tasks of density estimation and molecular generation. In particular, our generated samples achieve state-of-the-art on both the standard QM9 and ZINC250K benchmarks.

cs.LG↗