Neural Module Networks (NMNs) aim at Visual Question Answering (VQA) via composition of modules that tackle a sub-task. NMNs are a promising strategy to achieve systematic generalization, i.e., overcoming biasing factors in the training distribution. However, the aspects of NMNs that facilitate systematic generalization are not fully understood. In this paper, we demonstrate that the degree of modularity of the NMN have large influence on systematic generalization. In a series of experiments on three VQA datasets (VQA-MNIST, SQOOP, and CLEVR-CoGenT), our results reveal that tuning the degree of modularity, especially at the image encoder stage, reaches substantially higher systematic generalization. These findings lead to new NMN architectures that outperform previous ones in terms of systematic generalization.

In the context of learning to map an input $I$ to a function $h_I:\mathcal{X}\to \mathbb{R}$, two alternative methods are compared: (i) an embedding-based method, which learns a fixed function in which $I$ is encoded as a conditioning signal $e(I)$ and the learned function takes the form $h_I(x) = q(x,e(I))$, and (ii) hypernetworks, in which the weights $\theta_I$ of the function $h_I(x) = g(x;\theta_I)$ are given by a hypernetwork $f$ as $\theta_I=f(I)$. In this paper, we define the property of modularity as the ability to effectively learn a different function for each input instance $I$. For this purpose, we adopt an expressivity perspective of this property and extend the theory of~\cite{devore} and provide a lower bound on the complexity (number of trainable parameters) of neural networks as function approximators, by eliminating the requirements for the approximation method to be robust. Our results are then used to compare the complexities of $q$ and $g$, showing that under certain conditions and when letting the functions $e$ and $f$ be as large as we wish, $g$ can be smaller than $q$ by orders of magnitude.

Circuits in the brain commonly exhibit modular architectures that factorise complex tasks, resulting in the ability to compositionally generalise and reduce catastrophic forgetting. In contrast, artificial neural networks (ANNs) appear to mix all processing, because modular solutions are difficult to find as they are vanishing subspaces in the space of possible solutions. Here, we draw inspiration from fault-tolerant computation and the Poisson-like firing of real neurons to show that activity-dependent neural noise, combined with nonlinear neural responses, drives the emergence of solutions that reflect an accurate understanding of modular tasks, corresponding to acquisition of a correct world model. We find that noise-driven modularisation can be recapitulated by a deterministic regulariser that multiplicatively combines weights and activations, revealing rich phenomenology not captured in linear networks or by standard regularisation methods. Though the emergence of modular structure requires sufficiently many training samples (exponential in the number of modular task dimensions), we show that pre-modularised ANNs exhibit superior noise-robustness and the ability to generalise and extrapolate well beyond training data, compared to ANNs without such inductive biases. Together, our work demonstrates a regulariser and architectures that could encourage modularity emergence to yield functional benefits.

In community detection, many methods require the user to specify the number of clusters in advance since an exhaustive search over all possible values is computationally infeasible. While some classical algorithms can infer this number directly from the data, this is typically not the case for graph neural networks (GNNs): even when a desired number of clusters is specified, standard GNN-based methods often fail to return the exact number due to the way they are designed. In this work, we address this limitation by introducing a flexible and principled way to control the number of communities discovered by GNNs. Rather than assuming the true number of clusters is known, we propose a framework that allows the user to specify a plausible range and enforce these bounds during training. However, if the user wants an exact number of clusters, it may also be specified and reliably returned.

This paper presents the software architecture and deployment strategy behind the MoonBot platform: a modular space robotic system composed of heterogeneous components distributed across multiple computers, networks and ultimately celestial bodies. We introduce a principled approach to distributed, heterogeneous modularity, extending modular robotics beyond physical reconfiguration to software, communication and orchestration. We detail the architecture of our system that integrates component-based design, a data-oriented communication model using ROS2 and Zenoh, and a deployment orchestrator capable of managing complex multi-module assemblies. These abstractions enable dynamic reconfiguration, decentralized control, and seamless collaboration between numerous operators and modules. At the heart of this system lies our open-source Motion Stack software, validated by months of field deployment with self-assembling robots, inter-robot cooperation, and remote operation. Our architecture tackles the significant hurdles of modular robotics by significantly reducing integration and maintenance overhead, while remaining scalable and robust. Although tested with space in mind, we propose generalizable patterns for designing robotic systems that must scale across time, hardware, teams and operational environments.

Real-world applications of reinforcement learning often involve environments where agents operate on complex, high-dimensional observations, but the underlying ("latent") dynamics are comparatively simple.

We would like to thank each of the reviewers for reading our manuscript and providing very useful feedback. Below, we address the key points in detail. To calculate Eq. 6, it takes ELBO bound on each edge. Moreover, vGraph is efficient and scalable compared to classical community detection methods. We have updated the manuscript to make this more clear.

This paper focuses on the privacy risks of disclosing the community structure in an online social network.

In Appendix A.1, we describe the attributes and the comparisons in the VQA-MNIST datasets. A.1 Attributes and Comparisons Visual attributes. This corresponds to a total of 21 attribute instances. The sub-tasks for comparison of spatial relations are in Table App.2. Sub-tasks for attribute comparison between pairs of separated objects.