{"title":"Discovering Partial Differential Equations With Neural Cellular Automata.","authors":"Ehsan Pajouheshgar, Yitao Xu, Sabine Süsstrunk","doi":"10.1162/ARTL.a.454","DOIUrl":"https://doi.org/10.1162/ARTL.a.454","url":null,"abstract":"<p><p>Neural cellular automata (NCA) are a class of cellular automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this article, we focus on NCA models used for texture synthesis, where the update rule is inspired by partial differential equations (PDEs) describing reaction-diffusion systems. To train the NCA model, the spatiotemporal domain is discretized, and Euler integration is used to numerically simulate the dynamics. Crucially, it is unclear whether a ground-truth PDE even exists for the task, and NCA training only supervises the final steady state without any trajectory supervision, leaving it an open question whether a trained NCA truly learns continuous dynamics or merely overfits the discretization used during training. We study NCA models at the limit where space-time discretization approaches continuity. We find that existing NCA models tend to overfit the training discretization, especially in the proximity of the initial condition, also called a \"seed.\" To address this, we propose a solution that utilizes uniform noise as the initial condition. We demonstrate the effectiveness of our approach in preserving the consistency of NCA dynamics across a wide range of spatiotemporal granularities. We further show that the resulting model is robust to a stochastic updating scheme and modest additive Gaussian noise. Our improved NCA model enables two new test-time interactions by allowing continuous control over the speed of pattern formation and the scale of the synthesized patterns. We demonstrate this new NCA feature in our interactive online demo. Our work reveals that NCA models can learn continuous dynamics and opens new avenues to studying NCA as a class of PDEs and from a dynamical system's perspective.</p>","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":" ","pages":"1-19"},"PeriodicalIF":1.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147629391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"If Turing Played Piano With an Artificial Partner.","authors":"Dobromir Dotov, Dante Camarena, Zack Harris, Joanna Spyra, Pietro Gagliano, Laurel Trainor","doi":"10.1162/ARTL.a.455","DOIUrl":"https://doi.org/10.1162/ARTL.a.455","url":null,"abstract":"<p><p>Music is an inherently social activity that allows people to share experiences and feel connected with one another. There has been progress in neural network architectures that implement large-language-like generative models producing realistic musical scores, but less progress has been made to enable social experiences for a human playing interactively along with an artificial partner. Playing music socially sometimes works better without a score: Each participant must complement the ideas of other musicians. We investigated whether a generative model trained for passive production of musical scores, not for interaction, could enable social interaction with high quantitative measures of experience. The model, a variational autoencoder pretrained on a very large corpus of digitized and quantized piano scores, was adapted for a timed call-and-response task with a human partner. Human participants played piano with another human and separately with artificial partners parameterized for different time spans, tendencies for variation, and imitation of the human. Improvisation was not required from the humans, but it was encouraged. After each trial, participants rated the performance quality and their experience of self-other integration. Overall, the artificial partners failed at enabling convincing improvisation but were seen as adequate for basic practice. Performance differences among configurations of the artificial partner suggested paths for the future evolution of such partners. The ones with the simplest architecture and highest similarity were rated highest and were not statistically different from the human partners on realism, ease to interact with, and self-other integration. We discuss what principles may be needed, including open-ended evolution in Artificial Life, to arrive at artificial partners that enable genuinely interactive experience.</p>","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":" ","pages":"1-20"},"PeriodicalIF":1.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147629326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"To Engineer an Angel, First Validate the Devil: Analyzing the “Could Be” in Artificial Life’s “Life as-It-Could-Be”","authors":"Alan Dorin;Susan Stepney","doi":"10.1162/ARTL.e.452","DOIUrl":"10.1162/ARTL.e.452","url":null,"abstract":"","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 4","pages":"397-400"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145776723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Untapped Potential in Self-Optimization of Hopfield Networks: The Creativity of Unsupervised Learning","authors":"Natalya Weber;Christian Guckelsberger;Tom Froese","doi":"10.1162/ARTL.a.10","DOIUrl":"10.1162/ARTL.a.10","url":null,"abstract":"The self-optimization (SO) model can be considered as the third operational mode of the classical Hopfield network, leveraging the power of associative memory to enhance optimization performance. Moreover, it has been argued to express characteristics of minimal agency, which renders it useful for the study of Artificial Life. In this article, we draw attention to another facet of the SO model: its capacity for creativity. Drawing on creativity studies, we argue that the model satisfies the necessary and sufficient conditions of a creative process. Moreover, we show that learning is needed to find creative outcomes above chance probability. Furthermore, we demonstrate that modifying the learning parameters in the SO model gives rise to four different regimes that can account for both creative products and inconclusive outcomes, thus providing a framework for studying and understanding the emergence of creative behaviors in artificial systems that learn.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 4","pages":"435-464"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145338317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"System 0/1/2/3: Quad-Process Theory for Multitimescale Embodied Collective Cognitive Systems","authors":"Tadahiro Taniguchi;Yasushi Hirai;Masahiro Suzuki;Shingo Murata;Takato Horii;Kazutoshi Tanaka","doi":"10.1162/ARTL.a.12","DOIUrl":"10.1162/ARTL.a.12","url":null,"abstract":"This article introduces the System 0/1/2/3 framework as an extension of dual-process theory, employing a quad-process model of cognition. Expanding upon System 1 (fast, intuitive thinking) and System 2 (slow, deliberative thinking), we incorporate System 0, which represents precognitive embodied processes, and System 3, which encompasses collective intelligence and symbol emergence. We contextualize this model within Bergson’s philosophy by adopting multiscale time theory to unify the diverse temporal dynamics of cognition. System 0 emphasizes morphological computation and passive dynamics, illustrating how physical embodiment enables adaptive behavior without explicit neural processing. Systems 1 and 2 are explained from a constructive perspective, incorporating neurodynamical and artificial intelligence (AI) viewpoints. In System 3, we introduce collective predictive coding to explain how societal-level adaptation and symbol emergence operate over extended timescales. This comprehensive framework ranges from rapid embodied reactions to slow-evolving collective intelligence, offering a unified perspective on cognition across multiple timescales, levels of abstraction, and forms of human intelligence. The System 0/1/2/3 model provides a novel theoretical foundation for understanding the interplay between adaptive and cognitive processes, thereby opening new avenues for research in cognitive science, AI, robotics, and collective intelligence.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 4","pages":"465-496"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145776714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vants and Turmites","authors":"Greg Turk","doi":"10.1162/ARTL.a.9","DOIUrl":"10.1162/ARTL.a.9","url":null,"abstract":"The two-dimensional Turing machine is a promising but under used simulation tool for Artificial Life. Single-state 2-D Turing machines exhibit a variety of interesting behaviors, some of which have already been explored. Multistate 2-D Turing machines, despite their potential for simulating even more diverse behaviors, have received little attention to date. We demonstrate the potential of such automata for studying biological phenomena by showing how they can be used to simulate self-similar growth, the spread of disease, and self-reproduction. Some of the results presented here are from investigations that were performed around the time of Dewdney (1989), but they have not been published until now.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 4","pages":"401-434"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145338283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Artificial LifePub Date : 2025-09-04DOI: 10.1162/artl_c_00461
Larry Bull
{"title":"Neurons as Autoencoders","authors":"Larry Bull","doi":"10.1162/artl_c_00461","DOIUrl":"10.1162/artl_c_00461","url":null,"abstract":"This letter presents the idea that neural backpropagation is exploiting dendritic processing to enable individual neurons to perform autoencoding. Using a very simple connection weight search heuristic and artificial neural network model, the effects of interleaving autoencoding for each neuron in a hidden layer of a feedforward network are explored. This is contrasted with the equivalent standard layered approach to autoencoding. It is shown that such individualized processing is not detrimental and can improve network learning.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 3","pages":"250-255"},"PeriodicalIF":1.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142633468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Artificial LifePub Date : 2025-09-04DOI: 10.1162/artl_a_00460
Alessandro Fontana;Borys Wróbel
{"title":"Evolvability in Artificial Development of Large, Complex Structures and the Principle of Terminal Addition","authors":"Alessandro Fontana;Borys Wróbel","doi":"10.1162/artl_a_00460","DOIUrl":"10.1162/artl_a_00460","url":null,"abstract":"Epigenetic tracking (ET) is a model of development that is capable of generating diverse, arbitrary, complex three-dimensional cellular structures starting from a single cell. The generated structures have a level of complexity (in terms of the number of cells) comparable to multicellular biological organisms. In this article, we investigate the evolvability of the development of a complex structure inspired by the “French flag” problem: an “Italian Anubis” (a three-dimensional, doglike figure patterned in three colors). Genes during development are triggered in ET at specific developmental stages, and the fitness of individuals during simulated evolution is calculated after a certain stage. When this evaluation stage was allowed to evolve, genes that were triggered at later stages of development tended to be incorporated into the genome later during evolutionary runs. This suggests the emergence of the property of terminal addition in this system. When the principle of terminal addition was explicitly incorporated into ET, and was the sole mechanism for introducing morphological innovation, evolvability improved markedly, leading to the development of structures much more closely approximating the target at a much lower computational cost.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 3","pages":"276-288"},"PeriodicalIF":1.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142559566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Artificial LifePub Date : 2025-09-04DOI: 10.1162/artl_a_00475
Thomas M. Gaul;Eduardo J. Izquierdo
{"title":"Cognitive Distinctions as a Language for Cognitive Science: Comparing Methods of Description in a Model of Referential Communication","authors":"Thomas M. Gaul;Eduardo J. Izquierdo","doi":"10.1162/artl_a_00475","DOIUrl":"10.1162/artl_a_00475","url":null,"abstract":"An analysis of the language we use in scientific practice is critical to developing more rigorous and sound methodologies. This article argues that how certain methods of description are commonly employed in cognitive science risks obscuring important features of an agent’s cognition. We propose to make explicit a method of description whereby the concept of cognitive distinctions is the core principle. A model of referential communication is developed and analyzed as a platform to compare methods of description. We demonstrate that cognitive distinctions, realized in a graph theoretic formalism, better describe the behavior and perspective of a simple model agent than other, less systematic or natural language–dependent methods. We then consider how different descriptions relate to one another in the broader methodological framework of minimally cognitive behavior. Finally, we explore the consequences of, and challenges for, cognitive distinctions as a useful concept and method in the tool kit of cognitive scientists.","PeriodicalId":55574,"journal":{"name":"Artificial Life","volume":"31 3","pages":"345-367"},"PeriodicalIF":1.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144683586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}