Arend Hintze

Clifford Bohm, Vincent R. Ragusa, Arend Hintze et al.

A central challenge in analyzing multivariate interactions within complex systems is to decompose how multiple inputs jointly determine an output. Existing approaches generally operate on observed probability distributions and can conflate a system's intrinsic functional logic with statistical artifacts of limited data. As a result, distinct systems can yield identical observations, rendering information decomposition fundamentally underdetermined and obscuring true higher-order interactions. We introduce Functional Information Decomposition (FID), both a computational and theoretical framework, which defines informational components with respect to a system's complete input-output mapping, thereby addressing a core cross-scale inference problem: determining how information carried by individual components combines to shape system-level behavior. When the mapping is fully specified, FID provides a unique decomposition into independent and synergistic contributions. Crucially, given only partial observations, FID characterizes the entire space of consistent decompositions by sampling compatible functions, making inferential limits explicit. A complementary geometric perspective clarifies the structural origin of informational components. We demonstrate FID's interdisciplinary utility on canonical logical functions, Conway's Game of Life, and gene-expression-based prediction of cancer drug response, and provide an open-source implementation. By separating functional architecture from observational distribution, FID offers a principled foundation for analyzing multivariate dependence in both fully and partially observed complex systems.

Arend Hintze, Christoph Adami

Deep learning of artificial neural networks (ANNs) is creating highly functional processes that are, unfortunately, nearly as hard to interpret as their biological counterparts. Identification of functional modules in natural brains plays an important role in cognitive and neuroscience alike, and can be carried out using a wide range of technologies such as fMRI, EEG/ERP, MEG, or calcium imaging. However, we do not have such robust methods at our disposal when it comes to understanding functional modules in artificial neural networks. Ideally, understanding which parts of an artificial neural network perform what function might help us to address a number of vexing problems in ANN research, such as catastrophic forgetting and overfitting. Furthermore, revealing a network's modularity could improve our trust in them by making these black boxes more transparent. Here, we introduce a new information-theoretic concept that proves useful in understanding and analyzing a network's functional modularity: the relay information $I_R$. The relay information measures how much information groups of neurons that participate in a particular function (modules) relay from inputs to outputs. Combined with a greedy search algorithm, relay information can be used to identify computational modules in neural networks. We also show that the functionality of modules correlates with the amount of relay information they carry.

Jory Schossau, Bamshad Shirmohammadi, Arend Hintze

Autonomous agents that act with each other on behalf of humans are becoming more common in many social domains, such as customer service, transportation, and health care. In such social situations greedy strategies can reduce the positive outcome for all agents, such as leading to stop-and-go traffic on highways, or causing a denial of service on a communications channel. Instead, we desire autonomous decision-making for efficient performance while also considering equitability of the group to avoid these pitfalls. Unfortunately, in complex situations it is far easier to design machine learning objectives for selfish strategies than for equitable behaviors. Here we present a simple way to reward groups of agents in both evolution and reinforcement learning domains by the performance of their weakest member. We show how this yields ``fairer'' more equitable behavior, while also maximizing individual outcomes, and we show the relationship to biological selection mechanisms of group-level selection and inclusive fitness theory.

Arend Hintze, Christoph Adami

The tragedy of the commons illustrates a fundamental social dilemma where individual rational actions lead to collectively undesired outcomes, threatening the sustainability of shared resources. Strategies to escape this dilemma, however, are in short supply. In this study, we explore how artificial intelligence (AI) agents can be leveraged to enhance cooperation in public goods games, moving beyond traditional regulatory approaches to using AI as facilitators of cooperation. We investigate three scenarios: (1) Mandatory Cooperation Policy for AI Agents, where AI agents are institutionally mandated always to cooperate; (2) Player-Controlled Agent Cooperation Policy, where players evolve control over AI agents' likelihood to cooperate; and (3) Agents Mimic Players, where AI agents copy the behavior of players. Using a computational evolutionary model with a population of agents playing public goods games, we find that only when AI agents mimic player behavior does the critical synergy threshold for cooperation decrease, effectively resolving the dilemma. This suggests that we can leverage AI to promote collective well-being in societal dilemmas by designing AI agents to mimic human players.

Arend Hintze, Asadullah Najam, Jory Schossau

Understanding the internal dynamics of Recurrent Neural Networks (RNNs) is crucial for advancing their interpretability and improving their design. This study introduces an innovative information-theoretic method to identify and analyze information-transfer nodes within RNNs, which we refer to as \textit{information relays}. By quantifying the mutual information between input and output vectors across nodes, our approach pinpoints critical pathways through which information flows during network operations. We apply this methodology to both synthetic and real-world time series classification tasks, employing various RNN architectures, including Long Short-Term Memory (LSTM) networks and Gated Recurrent Units (GRUs). Our results reveal distinct patterns of information relay across different architectures, offering insights into how information is processed and maintained over time. Additionally, we conduct node knockout experiments to assess the functional importance of identified nodes, significantly contributing to explainable artificial intelligence by elucidating how specific nodes influence overall network behavior. This study not only enhances our understanding of the complex mechanisms driving RNNs but also provides a valuable tool for designing more robust and interpretable neural networks.

Arend Hintze

While prompt engineering has emerged as a crucial technique for optimizing large language model performance, the underlying optimization landscape remains poorly understood. Current approaches treat prompt optimization as a black-box problem, applying sophisticated search algorithms without characterizing the landscape topology they navigate. We present a systematic analysis of fitness landscape structures in prompt engineering using autocorrelation analysis across semantic embedding spaces. Through experiments on error detection tasks with two distinct prompt generation strategies -- systematic enumeration (1,024 prompts) and novelty-driven diversification (1,000 prompts) -- we reveal fundamentally different landscape topologies. Systematic prompt generation yields smoothly decaying autocorrelation, while diversified generation exhibits non-monotonic patterns with peak correlation at intermediate semantic distances, indicating rugged, hierarchically structured landscapes. Task-specific analysis across 10 error detection categories reveals varying degrees of ruggedness across different error types. Our findings provide an empirical foundation for understanding the complexity of optimization in prompt engineering landscapes.

Arend Hintze, Clifford Bohm

Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can emerge unassisted -- and that it can do so in a distributed, multi-component form. Building on prior work identifying complex dynamics in the Outlier rule, we introduce a data-driven framework that reconstructs the full causal ancestry of patterns in a deterministic cellular automaton. This allows us to rigorously identify self-replicating structures via explicit causal lineages. Our results show definitively that self-replicators in the Outlier CA are not only spontaneous and robust, but are also often composed of multiple disjoint clusters working in coordination, raising questions about some conventional notions of individuality and replication in artificial life systems.

Arend Hintze, Douglas Kirkpatrick, Christoph Adami

Artificial neural networks (ANNs), while exceptionally useful for classification, are vulnerable to misdirection. Small amounts of noise can significantly affect their ability to correctly complete a task. Instead of generalizing concepts, ANNs seem to focus on surface statistical regularities in a given task. Here we compare how recurrent artificial neural networks, long short-term memory units, and Markov Brains sense and remember their environments. We show that information in Markov Brains is localized and sparsely distributed, while the other neural network substrates "smear" information about the environment across all nodes, which makes them vulnerable to noise.

Jory Schossau, Larissa Albantakis, Arend Hintze

Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked systems, both digital and biological, each component receives inputs, performs a simple computation, and creates an output. When these components have multiple outputs, we intuitively assume that the outputs are causally dependent on the inputs but are themselves independent of each other given the state of their shared input. However, this intuition can be violated for components with probabilistic logic, as these typically cannot be decomposed into separate logic gates with one output each. This violation of conditional independence on the past system state is equivalent to instantaneous interaction --- the idea is that some information between the outputs is not coming from the inputs and thus must have been created instantaneously. Here we compare evolved artificial neural systems with and without instantaneous interaction across several task environments. We show that systems without instantaneous interactions evolve faster, to higher final levels of performance, and require fewer logic components to create a densely connected cognitive machinery.

Arend Hintze, Jeffrey A. Edlund, Randal S. Olson et al.

Markov Brains are a class of evolvable artificial neural networks (ANN). They differ from conventional ANNs in many aspects, but the key difference is that instead of a layered architecture, with each node performing the same function, Markov Brains are networks built from individual computational components. These computational components interact with each other, receive inputs from sensors, and control motor outputs. The function of the computational components, their connections to each other, as well as connections to sensors and motors are all subject to evolutionary optimization. Here we describe in detail how a Markov Brain works, what techniques can be used to study them, and how they can be evolved.

Leigh Sheneman, Arend Hintze

There are two common approaches for optimizing the performance of a machine: genetic algorithms and machine learning. A genetic algorithm is applied over many generations whereas machine learning works by applying feedback until the system meets a performance threshold. Though these are methods that typically operate separately, we combine evolutionary adaptation and machine learning into one approach. Our focus is on machines that can learn during their lifetime, but instead of equipping them with a machine learning algorithm we aim to let them evolve their ability to learn by themselves. We use evolvable networks of probabilistic and deterministic logic gates, known as Markov Brains, as our computational model organism. The ability of Markov Brains to learn is augmented by a novel adaptive component that can change its computational behavior based on feedback. We show that Markov Brains can indeed evolve to incorporate these feedback gates to improve their adaptability to variable environments. By combining these two methods, we now also implemented a computational model that can be used to study the evolution of learning.

Randal S. Olson, Arend Hintze, Fred C. Dyer et al.

A common idiom in biology education states, "Eyes in the front, the animal hunts. Eyes on the side, the animal hides." In this paper, we explore one possible explanation for why predators tend to have forward-facing, high-acuity visual systems. We do so using an agent-based computational model of evolution, where predators and prey interact and adapt their behavior and morphology to one another over successive generations of evolution. In this model, we observe a coevolutionary cycle between prey swarming behavior and the predator's visual system, where the predator and prey continually adapt their visual system and behavior, respectively, over evolutionary time in reaction to one another due to the well-known "predator confusion effect." Furthermore, we provide evidence that the predator visual system is what drives this coevolutionary cycle, and suggest that the cycle could be closed if the predator evolves a hybrid visual system capable of narrow, high-acuity vision for tracking prey as well as broad, coarse vision for prey discovery. Thus, the conflicting demands imposed on a predator's visual system by the predator confusion effect could have led to the evolution of complex eyes in many predators.

Peter Kvam, Joseph Cesario, Jory Schossau et al.

Most research on adaptive decision-making takes a strategy-first approach, proposing a method of solving a problem and then examining whether it can be implemented in the brain and in what environments it succeeds. We present a method for studying strategy development based on computational evolution that takes the opposite approach, allowing strategies to develop in response to the decision-making environment via Darwinian evolution. We apply this approach to a dynamic decision-making problem where artificial agents make decisions about the source of incoming information. In doing so, we show that the complexity of the brains and strategies of evolved agents are a function of the environment in which they develop. More difficult environments lead to larger brains and more information use, resulting in strategies resembling a sequential sampling approach. Less difficult environments drive evolution toward smaller brains and less information use, resulting in simpler heuristic-like strategies.

Arend Hintze, Randal S. Olson, Christoph Adami et al.

Risk aversion is a common behavior universal to humans and animals alike. Economists have traditionally defined risk preferences by the curvature of the utility function. Psychologists and behavioral economists also make use of concepts such as loss aversion and probability weighting to model risk aversion. Neurophysiological evidence suggests that loss aversion has its origins in relatively ancient neural circuitries (e.g., ventral striatum). Could there thus be an evolutionary origin to risk avoidance? We study this question by evolving strategies that adapt to play the equivalent mean payoff gamble. We hypothesize that risk aversion in the equivalent mean payoff gamble is beneficial as an adaptation to living in small groups, and find that a preference for risk averse strategies only evolves in small populations of less than 1,000 individuals, while agents exhibit no such strategy preference in larger populations. Further, we discover that risk aversion can also evolve in larger populations, but only when the population is segmented into small groups of around 150 individuals. Finally, we observe that risk aversion only evolves when the gamble is a rare event that has a large impact on the individual's fitness. These findings align with earlier reports that humans lived in small groups for a large portion of their evolutionary history. As such, we suggest that rare, high-risk, high-payoff events such as mating and mate competition could have driven the evolution of risk averse behavior in humans living in small groups.

Randal S. Olson, Arend Hintze, Fred C. Dyer et al.

Swarming behaviors in animals have been extensively studied due to their implications for the evolution of cooperation, social cognition, and predator-prey dynamics. An important goal of these studies is discerning which evolutionary pressures favor the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator-prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behavior in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator's visual field, favoring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator's consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint--predator confusion--could have pervasive evolutionary effects on prey behavior, predator sensory mechanisms, and the ecological interactions between predators and prey.

Lars Marstaller, Arend Hintze, Christoph Adami

Representations are internal models of the environment that can provide guidance to a behaving agent, even in the absence of sensory information. It is not clear how representations are developed and whether or not they are necessary or even essential for intelligent behavior. We argue here that the ability to represent relevant features of the environment is the expected consequence of an adaptive process, give a formal definition of representation based on information theory, and quantify it with a measure R. To measure how R changes over time, we evolve two types of networks---an artificial neural network and a network of hidden Markov gates---to solve a categorization task using a genetic algorithm. We find that the capacity to represent increases during evolutionary adaptation, and that agents form representations of their environment during their lifetime. This ability allows the agents to act on sensorial inputs in the context of their acquired representations and enables complex and context-dependent behavior. We examine which concepts (features of the environment) our networks are representing, how the representations are logically encoded in the networks, and how they form as an agent behaves to solve a task. We conclude that R should be able to quantify the representations within any cognitive system, and should be predictive of an agent's long-term adaptive success.