Modular Neural Networks

Wireless sensing, traditionally relying on signal processing (SP) techniques, has recently shifted toward data-driven deep learning (DL) to achieve performance breakthroughs. However, existing deep wireless sensing models are typically end-to-end and task-specific, lacking reusability and interpretability. We propose RF-LEGO, a modular co-design framework that transforms interpretable SP algorithms into trainable, physics-grounded DL modules through deep unrolling. By replacing hand-tuned parameters with learnable ones while preserving core processing structures and mathematical operators, RF-LEGO ensures modularity, cascadability, and structure-aligned interpretability. Specifically, we introduce three deep-unrolled modules for critical RF sensing tasks: frequency transform, spatial angle estimation, and signal detection. Extensive experiments using real-world data for Wi-Fi, millimeter-wave, UWB, and 6G sensing demonstrate that RF-LEGO significantly outperforms existing SP and DL baselines, both standalone and when integrated into multiple downstream tasks. RF-LEGO pioneers a novel SP-DL co-design paradigm for wireless sensing via deep unrolling, shedding light on efficient and interpretable deep wireless sensing solutions. Our code is available at https://github.com/aiot-lab/RF-LEGO.

This paper introduces a neural network model that learns multiple attributes as images and performs associated, sequential recall of the learned memories. Briefly, the model presented here is an associative memory model that extends previous models [1] by increasing the number of attributes. In the real world, memory recall generates a chain of associations consisting of complex and diverse data with meaningful relations. However, because this experimental system is designed to implement and verify the processing operations behind such operations, we believe it is not a problem if the associative memory (i.e., the chain of data) is composed of attributes that do not necessarily have clear relation with each other. Accordingly, the attribute-processing systems prepared in this study consist of five types: the C.CB-RN system for processing color attributes, the S.CB-RN system for shape attributes, and the V.CB-RN system for size attributes, as adopted in our previous paper [1], as well as the SV.CB-RN system for processing the names of the world's most beautiful scenery (spectacular view names) and the CN.CB-RN system for processing constellation names. As before, the data presented to each CB-RN system are represented as image patterns using QR codes [2]. These five types of CB-RN systems will be combined and trained with QR code pattern images of the attribute elements of each system. After that, when a pattern image of an attribute element is presented to any of the CB-RN systems, a mechanism will be constructed in which a chain (associative) recall of pattern images of related attribute elements in the other trained systems will be generated.

We propose a neural network model for contextual regression in which the regression model depends on contextual features that determine the active submodel and an algorithm to fit the model. The proposed simple contextual neural network (SCtxtNN) separates context identification from context-specific regression, resulting in a structured and interpretable architecture with fewer parameters than a fully connected feed-forward network. We show mathematically that the proposed architecture is sufficient to represent contextual linear regression models using only standard neural network components. Numerical experiments are provided to support the theoretical result, showing that the proposed model achieves lower excess mean squared error and more stable performance than feed-forward neural networks with comparable numbers of parameters, while larger networks improve accuracy only at the cost of increased complexity. The results suggest that incorporating contextual structure can improve model efficiency while preserving interpretability.

This paper bridges neuroscience and artificial intelligence to propose a cortically inspired blueprint for modular perceptual AI. While current monolithic models such as GPT-4V achieve impressive performance, they often struggle to explicitly support interpretability, compositional generalization, and adaptive robustness - hallmarks of human cognition. Drawing on neuroscientific models of cortical modularity, predictive processing, and cross-modal integration, we advocate decomposing perception into specialized, interacting modules. This architecture supports structured, human-inspired reasoning by making internal inference processes explicit through hierarchical predictive feedback loops and shared latent spaces. Our proof-of-concept study provides empirical evidence that modular decomposition yields more stable and inspectable representations. By grounding AI design in biologically validated principles, we move toward systems that not only perform well, but also support more transparent and human-aligned inference.

This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read and write heads, a controller multi-layer perceptron (MLP), and a homogeneous set of functional MLP modules. Rather than learning an algorithm end to end from data, it realizes a given algorithm through analytically specified neural components with fixed interfaces and exact behavior. The control flow is represented inside the neural computation through one-hot module gates, where inactive modules are inhibited. Computation unfolds as a sequence of memory transformations generated by a fixed graph. The architecture is illustrated through three case studies: computing the minimum of an array, sorting an array in place, and executing A* search on a fixed problem instance. These examples show that algorithmic procedures can be compiled into modular neural components with external memory while preserving deterministic behavior and explicit intermediate state.

Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the success of neural networks. Despite its empirical success, a strong theoretical understanding of it is lacking. Here, we combine tools from Riemannian geometry, optimal control theory, and theoretical physics to advance this understanding. We make three key contributions: First, we revisit the derivation of backpropagation as a constrained optimization problem and combine it with the insight that Riemannian gradient descent trajectories can be understood as the minimum of an action. Second, we introduce a recursively defined layerwise Riemannian metric that exploits the modular structure of neural networks and can be efficiently computed using the Woodbury matrix identity, avoiding the $O(n^3)$ cost of full metric inversion. Third, we develop a framework of composable ``Riemannian modules'' whose convergence properties can be quantified using nonlinear contraction theory, providing algorithmic stability guarantees of order $O(κ^2 L/(ξμ\sqrt{n}))$ where $κ$ and $L$ are Lipschitz constants, $μ$ is the mass matrix scale, and $ξ$ bounds the condition number. Our layerwise metric approach provides a practical alternative to natural gradient descent. While we focus here on studying neural networks, our approach more generally applies to the study of systems made of modules that are optimized over time, as it occurs in biology during both evolution and development.

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addresses these limitations by decomposing PDEs using operator splitting methods, training separate neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions. This modular mixture-of-experts architecture enables generalisation to novel physical regimes by explicitly encoding the underlying operator structure. We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side, enabling continuous-in-time predictions through standard ODE solvers and implicitly enforcing PDE constraints. Demonstrated on incompressible and compressible Navier--Stokes equations, our approach achieves better convergence and superior performance when generalising to unseen physics. The method remains parameter-efficient, enabling temporal extrapolation beyond training horizons, and provides interpretable components whose behaviour can be verified against known physics.

Large language models deployed in the wild must adapt to evolving data, user behavior, and task mixtures without erasing previously acquired capabilities. In practice, this remains difficult: sequential updates induce catastrophic forgetting, while many stabilization methods rely on external procedures that are costly, brittle, or difficult to scale. We present TRC$^{2}$ (Thalamically Routed Cortical Columns), a decoder-only architecture that makes continual learning a property of the backbone itself. TRC$^{2}$ combines stacked cortical columns with a thalamic modulatory pathway for selective inter-column communication and a hippocampal pathway for event selective retrieval, delayed surprise-based writing, and replay-driven consolidation. This design localizes fast plasticity while preserving a slower stable computation pathway. We further introduce a causal memory-update scheme and an online replay controller that adjusts consolidation strength from measured forgetting. Across a task-sequential language-modeling stream over C4, WikiText-103, and GSM8K, TRC$^{2}$ consistently improves task-boundary modeling quality and substantially reduces cumulative forgetting relative to Transformer, Mamba, MoE, DeepSeek and continual learning baselines trained under the same pipeline. Ablations show that the thalamic and hippocampal components are central to the retention gains, while the full model remains competitive in throughput and training cost.

The remarkable performance of modern AI systems has been driven by unprecedented scales of data, computation, and energy -- far exceeding the resources required by human intelligence. This disparity highlights the need for new guiding principles and motivates drawing inspiration from the fundamental organizational principles of brain computation. Among these principles, modularity has been shown to be critical for supporting the efficient learning and strong generalization abilities consistently exhibited by humans. Furthermore, modularity aligns well with the No Free Lunch Theorem, which highlights the need for problem-specific inductive biases and motivates architectures composed of specialized components that solve subproblems. However, despite its fundamental role in natural intelligence and its demonstrated benefits across a range of seemingly disparate AI subfields, modularity remains relatively underappreciated in mainstream AI research. In this work, we review several research threads in artificial intelligence and neuroscience through a conceptual framework that highlights the central role of modularity in supporting both artificial and natural intelligence. In particular, we examine what computational advantages modularity provides, how it has emerged as a solution across several AI research areas, which modularity principles the brain exploits, and how modularity can help bridge the gap between natural and artificial intelligence.

Training large-scale generative models is resource-intensive and relies heavily on heuristic dataset weighting. We address two fundamental questions: Can we train Large Language Models (LLMs) modularly, combining small, domain-specific experts to match monolithic performance, and can we do so robustly for any data mixture, eliminating heuristic tuning? We present a theoretical framework for modular generative modeling where a set of pre-trained experts are combined via a gating mechanism. We define the space of normalized gating functions $\mathcal{G}_{1}$ and formulate the problem as a minimax game to find a single robust gate that minimizes divergence to the worst-case data mixture. We prove the existence of such a robust gate using Kakutani's fixed-point theorem and show that modularity acts as a strong regularizer, with generalization bounds scaling with the lightweight gate's complexity. Furthermore, we prove that this modular approach can theoretically outperform models retrained on aggregate data, with the gap characterized by the Jensen-Shannon Divergence. Finally, we introduce a scalable Stochastic Primal-Dual algorithm and a Structural Distillation method for efficient inference. Empirical results on synthetic and real-world datasets confirm that our modular architecture effectively mitigates gradient conflict and can robustly outperform monolithic baselines.

Large Language Models (LLMs) have reshaped our world with significant advancements in science, engineering, and society through applications ranging from scientific discoveries and medical diagnostics to Chatbots. Despite their ubiquity and utility, the underlying mechanisms of LLM remain concealed within billions of parameters and complex structures, making their inner architecture and cognitive processes challenging to comprehend. We address this gap by adopting approaches to understanding emerging cognition in biology and developing a network-based framework that links cognitive skills, LLM architectures, and datasets, ushering in a paradigm shift in foundation model analysis. The skill distribution in the module communities demonstrates that while LLMs do not strictly parallel the focalized specialization observed in specific biological systems, they exhibit unique communities of modules whose emergent skill patterns partially mirror the distributed yet interconnected cognitive organization seen in avian and small mammalian brains. Our numerical results highlight a key divergence from biological systems to LLMs, where skill acquisition benefits substantially from dynamic, cross-regional interactions and neural plasticity. By integrating cognitive science principles with machine learning, our framework provides new insights into LLM interpretability and suggests that effective fine-tuning strategies should leverage distributed learning dynamics rather than rigid modular interventions.

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph structure of neural networks and their predictive performance, they often limit themselves to a narrow range of model networks, particularly lacking mesoscale structures such as communities. Our work advances this area by conducting a more comprehensive investigation, incorporating realistic network structures characterized by heterogeneous degree distributions and community structures, which are typical characteristics of many real networks. These community structures offer a nuanced perspective on network architecture. Our analysis employs model networks such as random and scale-free networks, alongside a comparison with a biological neural network and its subsets for more detailed analysis. We examine the impact of these structural attributes on the performance of image classification tasks. Our findings reveal that structural properties do affect performance to some extent. Specifically, within moderate-depth architectures, networks featuring coherent, densely interconnected communities demonstrate enhanced learning capabilities. Crucially, we find that this advantage is strictly depth-dependent: extending the architecture to eight layers reverses the effect entirely. This comparison with the biological neural network emphasizes the relevance of our findings to real-world structures, suggesting an intriguing connection worth further exploration. This study contributes meaningfully to network science and machine learning, providing insights that could inspire the design of more biologically informed neural networks.

A universal controller for any robot morphology would greatly improve computational and data efficiency. Steps have been made towards such multi-robot control by utilizing contextual information about the properties of individual robots and exploiting their modular structure in the architecture of deep reinforcement learning agents. When the robots have highly dissimilar morphologies, however, this becomes a challenging problem, especially when the agent must generalize to new, unseen robots. In this paper, we posit that contextual features are often only partially available, but that they can be recovered through modular interactions. This can allow for better multi-robot control and generalization to contexts that are not seen during training. To this extent, we implement a transformer-based architecture with shared modular recurrence and evaluate its (generalization) performance on a large set of MuJoCo robots. The results show a substantial improvement in zero-shot generalization performance on robots with unseen dynamics, kinematics, and topologies, in four different environments.

The architecture of a neural network and the choice of its activation function are both fundamental to its performance. Equally important is ensuring that these two elements are well matched, as their alignment is key to effective representation and learning. In this paper, we introduce the Fourier Multi-Component and Multi-Layer Neural Network (FMMNN), a model that combines sine-type activations with the multi-component and multi-layer structure of MMNNs. In an FMMNN, each component is represented as a trainable linear combination of fixed random sine-type basis functions, while multi-layer composition generates more complex and adaptive high-frequency features. We establish that FMMNNs retain exponential expressive power for function approximation even under a low-rank architectural structure. We also analyze the optimization landscape of FMMNNs and find it to be substantially more favorable than that of standard fully connected neural networks, especially for high-frequency targets. In addition, we propose a scaled random initialization method for the first-layer weights in FMMNNs, which accelerates training and improves final performance when sufficient samples are available. Extensive numerical experiments support our theoretical insights, showing that FMMNNs achieve strong accuracy and favorable convergence behavior on oscillatory function-approximation benchmarks.