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.

This paper presents the Nemosine Framework, a modular cognitive architecture designed to support assisted reasoning, structured thinking, and systematic analysis. The model operates through functional cognitive modules ("personas") that organize tasks such as planning, evaluation, cross-checking, and narrative synthesis. The framework combines principles from metacognition, distributed cognition, and modular cognitive systems to offer an operational structure for assisted problem-solving and decision support. The architecture is documented through formal specification, internal consistency criteria, and reproducible structural components. The goal is to provide a clear conceptual basis for future computational implementations and to contribute to the study of symbolic-modular architectures for reasoning.

From neuroscience and genomics to systems biology and ecology, researchers rely on clustering similarity data to uncover modular structure. Yet widely used clustering methods, such as hierarchical clustering, k-means, and WGCNA, lack principled model selection, leaving them susceptible to noise. A common workaround sparsifies a correlation matrix representation to remove noise before clustering, but this extra step introduces arbitrary thresholds that can distort the structure and lead to unreliable results. To detect reliable clusters, we capitalize on recent advances in network science to unite sparsification and clustering with principled model selection. We test two Bayesian community detection methods, the Degree-Corrected Stochastic Block Model and the Regularized Map Equation, both grounded in the Minimum Description Length principle for model selection. In synthetic data, they outperform traditional approaches, detecting planted clusters under high-noise conditions and with fewer samples. Compared to WGCNA on gene co-expression data, the Regularized Map Equation identifies more robust and functionally coherent gene modules. Our results establish Bayesian community detection as a principled and noise-resistant framework for uncovering modular structure in high-dimensional data across fields.

We also use our approach for estimating covariance structure for a number of real-world datasets and show that it consistently outperforms state-of-the-art estimators at a fraction of the computational cost.

Pretraining on large, semantically rich datasets is key for developing language models. Surprisingly, recent studies have shown that even synthetic data, generated procedurally through simple semantic-free algorithms, can yield some of the same benefits as natural language pretraining. It is unclear what specific capabilities such simple synthetic data instils in a model, where these capabilities reside in the architecture, and how they manifest within its weights. In this short paper, we identify several beneficial forms of procedural data, together with specific algorithmic reasoning skills that improve in small transformers. Our core finding is that different procedural rules instil distinct but complementary inductive structures in the model. With extensive ablations and partial-transfer experiments, we discover that these structures reside in different parts of the model. Attention layers often carry the most transferable information, but some pretraining rules impart useful structure to MLP blocks instead. Most interestingly, the structures induced by multiple rules can be composed to jointly reinforce multiple capabilities. These results suggest an exciting possibility of disentangling the acquisition of knowledge from reasoning in language models, with the goal of improving their robustness and data efficiency.

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

This work examines the presence of modularity in pre-trained Transformers, a feature commonly found in human brains and thought to be vital for general intelligence. In analogy to human brains, we consider two main characteristics of modularity: (1) functional specialization of neurons: we evaluate whether each neuron is mainly specialized in a certain function, and find that the answer is yes. (2) function-based neuron grouping: we explore finding a structure that groups neurons into modules by function, and each module works for its corresponding function. Given the enormous amount of possible structures, we focus on Mixture-of-Experts as a promising candidate, which partitions neurons into experts and usually activates different experts for different inputs. Experimental results show that there are functional experts, where clustered are the neurons specialized in a certain function. Moreover, perturbing the activations of functional experts significantly affects the corresponding function. Finally, we study how modularity emerges during pre-training, and find that the modular structure is stabilized at the early stage, which is faster than neuron stabilization. It suggests that Transformers first construct the modular structure and then learn fine-grained neuron functions. Our code and data are available at https://github.com/THUNLP/modularity-analysis.

Instruction tuning has recently been recognized as an effective way of aligning Large Language Models (LLMs) to enhance their generalization ability across various tasks. However, when tuning publicly accessible, centralized LLMs with private instruction data, privacy concerns are inevitable. While direct transfer of parameterized modules between models is a plausible approach to address this, its implications and effectiveness need further exploration. This paper focuses on Offsite-Tuning (OFT), a representative technique that transfers transformer blocks between centralized LLMs and downstream emulators. Given the limited understanding of the underlying mechanism of OFT, we perform an empirical analysis on LLMs from the perspectives of representation and functional similarity. Interestingly, our findings reveal a unique modular structure within the layers of LLMs that appears to emerge as the model size expands. Simultaneously, we note subtle but potentially significant changes in representation and intermediate predictions across the layers. Inspired by these observations, we propose CRaSh, involving Clustering, Removing, and Sharing, a training-free strategy to derive improved emulators from LLMs. CRaSh significantly boosts performance of OFT with billions of parameters. Furthermore, we investigate the optimal solutions yielded by fine-tuning with and without full model through the lens of loss landscape. Our findings demonstrate a linear connectivity among these optima falling over the same basin, thereby highlighting the effectiveness of CRaSh and OFT. The source code is publicly available at https://github.com/TsinghuaC3I/CRaSh.

Incorporating modular designs into neural networks demonstrates superior out-of-generalization, learning efficiency, etc. Existing modular neural networks are generally $\textit{explicit}$ because their modular architectures are pre-defined, and individual modules are expected to implement distinct functions. Conversely, recent works reveal that there exist $\textit{implicit}$ modular structures in standard pre-trained transformers, namely $\textit{Emergent Modularity}$. They indicate that such modular structures exhibit during the early pre-training phase and are totally spontaneous. However, most transformers are still treated as monolithic models with their modular natures underutilized. Therefore, given the excellent properties of explicit modular architecture, we explore $\textit{whether and how dense pre-trained transformers can benefit from emergent modular structures.}$ To study this question, we construct \textbf{E}mergent $\textbf{M}$ixture-$\textbf{o}$f-$\textbf{E}$xperts (EMoE). Without introducing additional parameters, EMoE can be seen as the modular counterpart of the original model and can be effortlessly incorporated into downstream tuning. Extensive experiments (we tune 1785 models) on various downstream tasks (vision and language) and models (22M to1.5B) demonstrate that EMoE effectively boosts in-domain and out-of-domain generalization abilities. Further analysis and ablation study suggest that EMoE mitigates negative knowledge transfer and is robust to various configurations. Code is available at \url{https://github.com/qiuzh20/EMoE}

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using Gaussian graphical models, requiring regularization to sparsify the models. Acknowledging that the modular structure of the inferred network is often studied, we suggest module-based regularization to balance under- and overfitting. Compared with the graphical lasso, a standard approach using the Gaussian log-likelihood for estimating the regularization strength, this approach better recovers and infers modular structure in noisy synthetic and real data. The module-based regularization technique improves the usefulness of Gaussian graphical models in the many applications where they are employed.