What should a neuron aim for? Designing local objective functions based on information theory

In modern deep neural networks, the learning dynamics of the individual neurons is often obscure, as the networks are trained via global optimization. Conversely, biological systems build on self-organized, local learning, achieving robustness and efficiency with limited global information. We here show how self-organization between individual artificial neurons can be achieved by designing abstract bio-inspired local learning goals. These goals are parameterized using a recent extension of information theory, Partial Information Decomposition (PID), which decomposes the information that a set of information sources holds about an outcome into unique, redundant and synergistic contributions. Our framework enables neurons to locally shape the integration of information from various input classes, i.e. feedforward, feedback, and lateral, by selecting which of the three inputs should contribute uniquely, redundantly or synergistically to the output. This selection is expressed as a weighted sum of PID terms, which, for a given problem, can be directly derived from intuitive reasoning or via numerical optimization, offering a window into understanding task-relevant local information processing. Achieving neuron-level interpretability while enabling strong performance using local learning, our work advances a principled information-theoretic foundation for local learning strategies.

Infomorphic networks: Locally learning neural networks derived from partial information decomposition

Understanding the intricate cooperation among individual neurons in performing complex tasks remains a challenge to this date. In this paper, we propose a novel type of model neuron that emulates the functional characteristics of biological neurons by optimizing an abstract local information processing goal. We have previously formulated such a goal function based on principles from partial information decomposition (PID). Here, we present a corresponding parametric local learning rule which serves as the foundation of "infomorphic networks" as a novel concrete model of neural networks. We demonstrate the versatility of these networks to perform tasks from supervised, unsupervised and memory learning. By leveraging the explanatory power and interpretable nature of the PID framework, these infomorphic networks represent a valuable tool to advance our understanding of cortical function.

Evaluating vaccine allocation strategies using simulation-assisted causal modelling

Early on during a pandemic, vaccine availability is limited, requiring prioritisation of different population groups. Evaluating vaccine allocation is therefore a crucial element of pandemics response. In the present work, we develop a model to retrospectively evaluate age-dependent counterfactual vaccine allocation strategies against the COVID-19 pandemic. To estimate the effect of allocation on the expected severe-case incidence, we employ a simulation-assisted causal modelling approach which combines a compartmental infection-dynamics simulation, a coarse-grained, data-driven causal model and literature estimates for immunity waning. We compare Israel's implemented vaccine allocation strategy in 2021 to counterfactual strategies such as no prioritisation, prioritisation of younger age groups or a strict risk-ranked approach; we find that Israel's implemented strategy was indeed highly effective. We also study the marginal impact of increasing vaccine uptake for a given age group and find that increasing vaccinations in the elderly is most effective at preventing severe cases, whereas additional vaccinations for middle-aged groups reduce infections most effectively. Due to its modular structure, our model can easily be adapted to study future pandemics. We demonstrate this flexibility by investigating vaccine allocation strategies for a pandemic with characteristics of the Spanish Flu. Our approach thus helps evaluate vaccination strategies under the complex interplay of core epidemic factors, including age-dependent risk profiles, immunity waning, vaccine availability and spreading rates.

Partial Information Decomposition Reveals the Structure of Neural Representations

In neural networks, task-relevant information is represented jointly by groups of neurons. However, the specific way in which the information is distributed among the individual neurons is not well understood: While parts of it may only be obtainable from specific single neurons, other parts are carried redundantly or synergistically by multiple neurons. We show how Partial Information Decomposition (PID), a recent extension of information theory, can disentangle these contributions. From this, we introduce the measure of "Representational Complexity", which quantifies the difficulty of accessing information spread across multiple neurons. We show how this complexity is directly computable for smaller layers. For larger layers, we propose subsampling and coarse-graining procedures and prove corresponding bounds on the latter. Empirically, for quantized deep neural networks solving the MNIST task, we observe that representational complexity decreases both through successive hidden layers and over training. Overall, we propose representational complexity as a principled and interpretable summary statistic for analyzing the structure of neural representations.