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The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are…
We investigate the geometry of predictive information across the layers of large language models (LLMs). We repurpose representation lenses-learned affine maps trained to predict the next token from intermediate residual streams-as…
Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…
This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…
Large language models (LLMs) often struggle with strict memory, latency, and power demands. To meet these demands, various forms of dynamic sparsity have been proposed that reduce compute on an input-by-input basis. These methods improve…
Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…
We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…
Geometric analyses of large language model (LLM) representations reveal structured variation across depth but remain fundamentally correlational with respect to token prediction formation. Meanwhile, causal interventions expose…
The ResNet architecture has been widely adopted in deep learning due to its significant boost to performance through the use of simple skip connections, yet the underlying mechanisms leading to its success remain largely unknown. In this…
The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, we show that there are certain mesoscale subgraphs…
Streets networks provide an invaluable source of information about the different temporal and spatial patterns emerging in our cities. These streets are often represented as graphs where intersections are modelled as nodes and streets as…
Vision-language models (VLMs) achieve strong multimodal performance, yet how computation is organized across populations of neurons remains poorly understood. In this work, we study VLMs through the lens of neural topology, representing…
The recent theoretical analysis of deep neural networks in their infinite-width limits has deepened our understanding of initialisation, feature learning, and training of those networks, and brought new practical techniques for finding…
Large Language Models (LLMs) frequently prioritize conflicting in-context information over pre-existing parametric memory, a phenomenon often termed sycophancy or compliance. However, the mechanistic realization of this behavior remains…
Transformers deliver outstanding performance across a wide range of tasks and are now a dominant backbone architecture for large language models (LLMs). Their task-solving performance is improved by increasing parameter size, as shown in…
Decades of cognitive science establish that humans navigate environments by forming cognitive maps, defined as allocentric and topology-preserving representations of 3D space. While modern Vision-Language Models (VLMs) demonstrate emergent…
In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving…