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We demonstrate the existence of a non-terminating game of Beggar-My-Neighbor, discovered by lead author Brayden Casella. We detail the method for constructing this game and identify a cyclical structure of 62 tricks that is reached by 30 distinct starting hands. We further present a short history of the search for this solution since the problem was posed, and a record of previously found longest terminating games. The existence of this non-terminating game provides a solution to a long-standing question which John H. Conway called an `anti-Hilbert problem.'

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and 'social forces' such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modelling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically-observed collective phenomena, including cohesion, milling and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference -- without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal non-trivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly., Comment: 29 pages (main text), 29 pages (supplemental appendices), 4 figures, 1 supplemental figure, 5 movies

Theoretical results underpinning the Wisdom of Crowds, such as the Condorcet Jury Theorem, point to substantial accuracy gains through aggregation of decisions or opinions, but the foundations of this theorem are routinely undermined in circumstances where individuals are able to adapt their own choices based after observing what other agents have chosen. In sequential decision-making, rational agents use the choices of others as a source of information about the correct decision, creating powerful correlations between different agents' choices that violate the assumptions of independence on which the Condorcet Jury Theorem depends. In this paper I show how such correlations emerge when agents are rewarded solely based on their individual accuracy, and the impact of this on collective accuracy. I then demonstrate how a simple competitive reward scheme, where agents' rewards are greater if they correctly choose options that few have already chosen, can induce rational agents to make independent choices, returning the group to optimal levels of collective accuracy. I further show that this reward scheme is robust, offering improvements to collective accuracy across of wide range of competition strengths, suggesting that such schemes could be effectively implemented in real-world contexts to improve collective wisdom., Comment: 10 pages, 2 figures

Humans and other animals often follow the decisions made by others because these are indicative of the quality of possible choices, resulting in `social response rules': observed relationships between the probability that an agent will make a specific choice and the decisions other individuals have made. The form of social responses can be understood by considering the behaviour of rational agents that seek to maximise their expected utility using both social and private information. Previous derivations of social responses assume that agents observe all others within a group, but real interaction networks are often characterised by sparse connectivity. Here I analyse the observable behaviour of rational agents that attend to the decisions made by a subset of others in the group. This reveals an adaptive strategy in sparsely-connected networks based on highly-simplified social information: the difference in the observed number of agents choosing each option. Where agents employ this strategy, collective outcomes and decision-making efficacy are controlled by the social connectivity at the time of the decision, rather than that to which the agents are accustomed, providing an important caveat for sociality observed in the laboratory and suggesting a basis for the social dynamics of highly-connected online communities.

Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios. Yet, previous modeling work on agent learning and decision-making either lacks a systematic way to describe this source of uncertainty or puts the focus on obtaining optimal policies using complex models of the world that would impose an unrealistically high cognitive demand on real agents. In this work we aim to efficiently describe the emergent behavior of biologically plausible and parsimonious learning agents faced with partially observable worlds. Therefore we derive and present deterministic reinforcement learning dynamics where the agents observe the true state of the environment only partially. We showcase the broad applicability of our dynamics across different classes of partially observable agent-environment systems. We find that partial observability creates unintuitive benefits in a number of specific contexts, pointing the way to further research on a general understanding of such effects. For instance, partially observant agents can learn better outcomes faster, in a more stable way and even overcome social dilemmas. Furthermore, our method allows the application of dynamical systems theory to partially observable multiagent leaning. In this regard we find the emergence of catastrophic limit cycles, a critical slowing down of the learning processes between reward regimes and the separation of the learning dynamics into fast and slow directions, all caused by partial observability. Therefore, the presented dynamics have the potential to become a formal, yet practical, lightweight and robust tool for researchers in biology, social science and machine learning to systematically investigate the effects of interacting partially observant agents., Comment: 15 pages, 8 figures

The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better representations than the standard transform. With this in mind, we extend our previous method for learning filters for the 1D and 2D wavelet transforms into the dual-tree domain. We show that with few modifications to our original model, we can learn directional filters that leverage the properties of the dual-tree wavelet transform., Comment: 19 pages, 20 figures

We have successfully produced infrasound, as a duplicate of that produced by Industrial Wind Turbines. We have been able to produce this Infrasound inside a research chamber, capable of accommodating a human test subject. It is our vision that this project will permit others, with appropriate medical training and ethical oversight, to research human thresholds and the effects of this infrasound on humans. Our role has focused on producing the tools, systems, and hardware required, to permit this research to go forward. This paper describes the evolution of our project from the original vision, through the construction of proof of concept prototypes, a series of improved models and their associated accessories /operating systems, to the final test chamber as it stands now ready to deploy. Also included are the mathematical and computational data supporting our claim that infrasound conditions inside the chamber can be made to duplicate those from actual Industrial wind turbines at approved setback distances., Comment: Keywords: Infra sound, wind turbines, acoustics, sound measurement, sound generation

In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network that is trained using gradient descent. We show that the model is capable of learning structured wavelet filters from synthetic and real data. The learned wavelets are shown to be similar to traditional wavelets that are derived using Fourier methods. Our method is simple to implement and easily incorporated into neural network architectures. A major advantage to our model is that we can learn from raw audio data., Comment: 7 pages, 5 figures

In this paper we present a mathematical model of the Empirical Mode Decomposition (EMD). Although EMD is a powerful tool for signal processing, the algorithm itself lacks an appropriate theoretical basis. The interpolation and iteration processes involved in the EMD method have been obstacles for mathematical modelling. Here, we propose a novel forward heat equation approach to represent the mean envelope and sifting process. This new model can provide a better mathematical analysis of classical EMD as well as identifying its limitations. Our approach achieves a better performance for a "mode-mixing" signal as compared to the classical EMD approach and is more robust to noise. Furthermore, we discuss the ability of EMD to separate signals and possible improvements by adjusting parameters.

Collective intelligence is the ability of a group to perform more effectively than any individual alone. Diversity among group members is a key condition for the emergence of collective intelligence, but maintaining diversity is challenging in the face of social pressure to imitate one's peers. We investigate the role incentives play in maintaining useful diversity through an evolutionary game-theoretic model of collective prediction. We show that market-based incentive systems produce herding effects, reduce information available to the group and suppress collective intelligence. In response, we propose a new incentive scheme that rewards accurate minority predictions, and show that this produces optimal diversity and collective predictive accuracy. We conclude that real-world systems should reward those who have demonstrated accuracy when majority opinion has been in error.

This paper will detail the basis of our previously developed predictive model for pigeon flight paths based on observations of the specific individual being predicted. We will then describe how this model can be adapted to predict the flight of a new, unobserved bird, based on observations of other individuals from the same release site. We will test the accuracy of these predictions relative to naive models with no previous flight information and those trained on the focal bird's own previous flights, and discuss the implications of these results for the nature of navigational cue use in the familiar area. Finally we will discuss how visual cues may be explicitly encoded in the model in future work., Comment: 8 pages, 2 figures, Royal Institute of Navigation Conference on Animal Navigation 2016

The escape trajectories animals take following a predatory attack appear to show high degrees of apparent 'randomness' - a property that has been described as 'protean behaviour'. Here we present a method of quantifying the escape trajectories of individual animals using a path complexity approach. When fish (Pseudomugil signifer) were attacked either on their own or in groups, we find that an individual's path rapidly increases in entropy (our measure of complexity) following the attack. For individuals on their own, this entropy remains elevated (indicating a more random path) for a sustained period (10 seconds) after the attack, whilst it falls more quickly for individuals in groups. The entropy of the path is context dependent. When attacks towards single fish come from greater distances, a fish's path shows less complexity compared to attacks that come from short range. This context dependency effect did not exist, however, when individuals were in groups. Nor did the path complexity of individuals in groups depend on a fish's local density of neighbours. We separate out the components of speed and direction changes to determine which of these components contributes to the overall increase in path complexity following an attack. We found that both speed and direction measures contribute similarly to an individual's path's complexity in absolute terms. Our work highlights the adaptive behavioural tactics that animals use to avoid predators and also provides a novel method for quantifying the escape trajectories of animals., Comment: 9 pages

In this paper, we identify a radically new viewpoint on the collective behaviour of groups of intelligent agents. We first develop a highly general abstract model for the possible future lives that these agents may encounter as a result of their decisions. In the context of these possible futures, we show that the causal entropic principle, whereby agents follow behavioural rules that maximise their entropy over all paths through the future, predicts many of the observed features of social interactions between individuals in both human and animal groups. Our results indicate that agents are often able to maximise their future path entropy by remaining cohesive as a group, and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of future paths that are possible. We derive social interaction rules that are consistent with maximum-entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber's law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus-response mechanism, and providing a novel basis for the common assumption of linearly additive 'social forces' in simulation studies of collective behaviour., Comment: 7 pages, 6 figures

Background: Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we address specifically the problem of what interaction responses support different nearest neighbour configurations in terms of mutual position and distance. Results: We find that the different interaction rules observed in different animal species may be a simple consequence of the relative positions that individuals assume when they move together, and of the noise inherent with the movement of animals, or associated with tracking inaccuracy. Conclusions: The anisotropic positioning of individuals with respect to their neighbours, in combination with noise, can explain several aspects of the movement responses observed in real animal groups, and should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, we provide a frame to discriminate movement interactions that signal directional conflict from those underlying consensual group motion.

We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optimal policies. We provide three contributions. In addition to introducing the active surveying problem, we extend previous work on active search in two ways. First, we prove a novel theoretical result, that less-myopic approximations to the optimal policy can outperform more-myopic approximations by any arbitrary degree. We then derive bounds that for certain models allow us to reduce (in practice dramatically) the exponential search space required by a naive implementation of the optimal policy, enabling further lookahead while still ensuring that optimal decisions are always made., Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)