The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and certainty) contained in paths along nodes and links in a network. Specifically, we derive from first principles a measure known as effective information and describe its behavior in common network models. Networks with higher effective information contain more information in the relationships between nodes. We show how subgraphs of nodes can be grouped into macronodes, reducing the size of a network while increasing its effective information (a phenomenon known as causal emergence). We find that informative higher scales are common in simulated and real networks across biological, social, informational, and technological domains. These results show that the emergence of higher scales in networks can be directly assessed and that these higher scales offer a way to create certainty out of uncertainty.

Is reduction always a good scientific strategy? The existence of the special sciences above physics suggests not. Previous research has shown that dimensionality reduction (macroscales) can increase the dependency between elements of a system (a phenomenon called ‘causal emergence’). Here, we provide an umbrella mathematical framework for emergence based on information conversion. We show evidence that coarse-graining can convert information from one ‘type’ to another. We demonstrate this using the well-understood mutual information measure applied to Boolean networks. Using partial information decomposition, the mutual information can be decomposed into redundant, unique and synergistic information atoms. Then by introducing a novel measure of the synergy bias of a given decomposition, we are able to show that the synergy component of a Boolean network’s mutual information can increase at macroscales. This can occur even when there is no difference in the total mutual information between a macroscale and its underlying microscale, proving information conversion. We relate this broad framework to previous work, compare it to other theories, and argue it complexifies any notion of universal reduction in the sciences, since such reduction would likely lead to a loss of synergistic information in scientific models. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.

Understanding of the evolved biological function of sleep has advanced considerably in the past decade. However, no equivalent understanding of dreams has emerged. Contemporary neuroscientific theories often view dreams as epiphenomena, and many of the proposals for their biological function are contradicted by the phenomenology of dreams themselves. Now, the recent advent of deep neural networks (DNNs) has finally provided the novel conceptual framework within which to understand the evolved function of dreams. Notably, all DNNs face the issue of overfitting as they learn, which is when performance on one dataset increases but the network's performance fails to generalize (often measured by the divergence of performance on training versus testing datasets). This ubiquitous problem in DNNs is often solved by modelers via “noise injections” in the form of noisy or corrupted inputs. The goal of this paper is to argue that the brain faces a similar challenge of overfitting and that nightly dreams evolved to combat the brain's overfitting during its daily learning. That is, dreams are a biological mechanism for increasing generalizability via the creation of corrupted sensory inputs from stochastic activity across the hierarchy of neural structures. Sleep loss, specifically dream loss, leads to an overfitted brain that can still memorize and learn but fails to generalize appropriately. Herein this ”overfitted brain hypothesis” is explicitly developed and then compared and contrasted with existing contemporary neuroscientific theories of dreams. Existing evidence for the hypothesis is surveyed within both neuroscience and deep learning, and a set of testable predictions is put forward that can be pursued both in vivo and in silico.

Actual causation is concerned with the question: “What caused what?” Consider a transition between two states within a system of interacting elements, such as an artificial neural network, or a biological brain circuit. Which combination of synapses caused the neuron to fire? Which image features caused the classifier to misinterpret the picture? Even detailed knowledge of the system’s causal network, its elements, their states, connectivity, and dynamics does not automatically provide a straightforward answer to the “what caused what?” question. Counterfactual accounts of actual causation, based on graphical models paired with system interventions, have demonstrated initial success in addressing specific problem cases, in line with intuitive causal judgments. Here, we start from a set of basic requirements for causation (realization, composition, information, integration, and exclusion) and develop a rigorous, quantitative account of actual causation, that is generally applicable to discrete dynamical systems. We present a formal framework to evaluate these causal requirements based on system interventions and partitions, which considers all counterfactuals of a state transition. This framework is used to provide a complete causal account of the transition by identifying and quantifying the strength of all actual causes and effects linking the two consecutive system states. Finally, we examine several exemplary cases and paradoxes of causation and show that they can be illuminated by the proposed framework for quantifying actual causation.

The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard experimental setup for testing these theories. Based on a theory’s application to some physical system, such as the brain, testing requires comparing a theory’s predicted experience (given some internal observables of the system like brain imaging data) with an inferred experience (using report or behavior). If there is a mismatch between inference and prediction, a theory is falsified. We show that if inference and prediction are independent, it follows that any minimally informative theory of consciousness is automatically falsified. This is deeply problematic since the field’s reliance on report or behavior to infer conscious experiences implies such independence, so this fragility affects many contemporary theories of consciousness. Furthermore, we show that if inference and prediction are strictly dependent, it follows that a theory is unfalsifiable. This affects theories which claim consciousness to be determined by report or behavior. Finally, we explore possible ways out of this dilemma.

The internal workings of biological systems are notoriously difficult to understand. Due to the prevalence of noise and degeneracy in evolved systems, in many cases the workings of everything from gene regulatory networks to protein–protein interactome networks remain black boxes. One consequence of this black-box nature is that it is unclear at which scale to analyze biological systems to best understand their function. We analyzed the protein interactomes of over 1800 species, containing in total 8 782 166 protein–protein interactions, at different scales. We show the emergence of higher order ‘macroscales’ in these interactomes and that these biological macroscales are associated with lower noise and degeneracy and therefore lower uncertainty. Moreover, the nodes in the interactomes that make up the macroscale are more resilient compared with nodes that do not participate in the macroscale. These effects are more pronounced in interactomes of eukaryota, as compared with prokaryota; these results hold even after sensitivity tests where we recalculate the emergent macroscales under network simulations where we add different edge weights to the interactomes. This points to plausible evolutionary adaptation for macroscales: biological networks evolve informative macroscales to gain benefits of both being uncertain at lower scales to boost their resilience, and also being ‘certain’ at higher scales to increase their effectiveness at information transmission. Our work explains some of the difficulty in understanding the workings of biological networks, since they are often most informative at a hidden higher scale, and demonstrates the tools to make these informative higher scales explicit.