Who Does What in Deep Learning? Multidimensional Game-Theoretic Attribution of Function of Neural Units

Neural networks now generate text, images, and speech with billions of parameters, producing a need to know how each neural unit contributes to these high-dimensional outputs. Existing explainable-AI methods, such as SHAP, attribute importance to inputs, but cannot quantify the contributions of neural units across thousands of output pixels, tokens, or logits. Here we close that gap with Multiperturbation Shapley-value Analysis (MSA), a model-agnostic game-theoretic framework. By systematically lesioning combinations of units, MSA yields Shapley Modes, unit-wise contribution maps that share the exact dimensionality of the model's output. We apply MSA across scales, from multi-layer perceptrons to the 56-billion-parameter Mixtral-8x7B and Generative Adversarial Networks (GAN). The approach demonstrates how regularisation concentrates computation in a few hubs, exposes language-specific experts inside the LLM, and reveals an inverted pixel-generation hierarchy in GANs. Together, these results showcase MSA as a powerful approach for interpreting, editing, and compressing deep neural networks.

Causal Influences Decouple From Their Underlying Network Structure In Echo State Networks

Echo State Networks (ESN) are versatile recurrent neural network models in which the hidden layer remains unaltered during training. Interactions among nodes of this static backbone produce diverse representations of the given stimuli that are harnessed by a read-out mechanism to perform computations needed for solving a given task. ESNs are accessible models of neuronal circuits, since they are relatively inexpensive to train. Therefore, ESNs have become attractive for neuroscientists studying the relationship between neural structure, function, and behavior. For instance, it is not yet clear how distinctive connectivity patterns of brain networks support effective interactions among their nodes and how these patterns of interactions give rise to computation. To address this question, we employed an ESN with a biologically inspired structure and used a systematic multi-site lesioning framework to quantify the causal contribution of each node to the network's output, thus providing a causal link between network structure and behavior. We then focused on the structure-function relationship and decomposed the causal influence of each node on all other nodes, using the same lesioning framework. We found that nodes in a properly engineered ESN interact largely irrespective of the network's underlying structure. However, in a network with the same topology and a non-optimal parameter set, the underlying connectivity patterns determine the node interactions. Our results suggest that causal structure-function relations in ESNs can be decomposed into two components, direct and indirect interactions. The former are based on influences relying on structural connections. The latter describe the effective communication between any two nodes through other intermediate nodes. These widely distributed indirect interactions may crucially contribute to the efficient performance of ESNs.