arXiv subjects

Eyvind Niklasson

Publications and source records attributed to Eyvind Niklasson.

16 recordsLinked to original sources

arXiv2026

Tapes Together Strong: The Co-evolution of Computation and Cooperation

How does cooperation evolve in complex agentic systems? Prior work in evolutionary game theory studies why individuals are incentivized to cooperate by isolating social interactions from the physical costs of behavior, while artificial life models traditionally study emergent self-replication without formalizing the dilemma between acquiring resources and preserving the shared energy needed to reproduce. In contrast, we introduce Autopoietic Game Theory, a computational model where social interactions, replication mechanisms, and their associated computational costs are endogenous and simultaneously co-evolving. We study these dynamics using a computational substrate of randomly initialized programs in Z80 machine code, showing empirically, and motivating with a simplified theoretical model, that embedding a social dilemma directly into the physics of computation can favor the emergence of self-replicating, cooperative strategies. When resources are scarce, our analysis shows that defection can become self-limiting even in well-mixed populations: parasitic stealing destroys shared energy, slows execution, and can prevent reliable replication. Empirically, evolved programs suppress stealing across several Z80 environments, while spatial assortment further supports structural complexity and task performance. We further show that the framework can incorporate exogenous pressures, such as math tasks structured as sequential social dilemmas, when rewards are tied to computation budgets. These results suggest that coupling an agent's capacity for computation to its available energy transforms cooperation into a dominant scaffolding for building sustainable, self-organizing systems.

cs.MA↗

arXiv2026

Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning

Diffusion models and recursive reasoners are both iterative, but they carry information across iterations differently. We add a persistent hidden state to a diffusion denoiser and remove its timestep conditioning, leaving a single shared update that can be run to arbitrary depth. The result is an anytime solver: accuracy keeps improving with inference depth far beyond the rollout lengths and backpropagation window used in training, reaching 99.90% exact solve on Sudoku-Extreme. We also obtain 98.93% solve rate on Maze-Unique. Surprisingly, progressive denoising is unnecessary at inference: holding corruption at its maximum by replacing every non-clue variable with fresh Gaussian noise at each step retains near-perfect solving and converges to stable solutions. This simple noise-injection mechanism enables a single trajectory to efficiently explore the solution space and settle on the correct answer without parallel rollouts, candidate selection, or external verifiers required by prior reasoning models. Nonetheless, ordered annealed corruption remains critical during training, which suggests that diffusion's primary contribution to our anytime solver is not a sampling procedure at inference, but a denoising training curriculum.

cs.LG↗

arXiv2026

Coevolution of self-replication and function in a digital primordial soup

While traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital ``primordial soups''. This paper investigates the coevolution of such emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To couple computation with reproduction, we introduce a task-based validation step: correctly evaluating a polynomial raises a program's interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully coevolve from initial randomness. Second, the pressure to compute accelerates the emergence of compact, robust reproductive architectures that preserve memory for task execution. Third, applying metabolic constraints that penalize runtime promotes the emergence of sophisticated conditional execution patterns that reduce energy use. Finally, partitioning programs into interconnected task niches generates an emergent learning curriculum that utilizes simple solutions as stepping stones toward more complex tasks. Altogether, these results demonstrate an interactive feedback loop: environmental task demands actively shape the physical architecture of self-replication, while spontaneous replication alters the evolutionary trajectory of functional problem-solving.

cs.NE↗

arXiv2025

Differentiable Logic Cellular Automata: From Game of Life to Pattern Generation

This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are differentiable logic gates, combined into a circuit. During training, the model is fully end-to-end differentiable allowing gradient-based training, and at inference time it operates in a fully discrete state space. This enables learning local update rules for cellular automata while preserving their inherent discrete nature. We demonstrate the versatility of our approach through a series of milestones: (1) fully learning the rules of Conway's Game of Life, (2) generating checkerboard patterns that exhibit resilience to noise and damage, (3) growing a lizard shape, and (4) multi-color pattern generation. Our model successfully learns recurrent circuits capable of generating desired target patterns. For simpler patterns, we observe success with both synchronous and asynchronous updates, demonstrating significant generalization capabilities and robustness to perturbations. We make the case that this combination of DLGNs and NCA represents a step toward programmable matter and robust computing systems that combine binary logic, neural network adaptability, and localized processing. This work, to the best of our knowledge, is the first successful application of differentiable logic gate networks in recurrent architectures.

cs.AI↗

arXiv2024

Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction

The fields of Origin of Life and Artificial Life both question what life is and how it emerges from a distinct set of "pre-life" dynamics. One common feature of most substrates where life emerges is a marked shift in dynamics when self-replication appears. While there are some hypotheses regarding how self-replicators arose in nature, we know very little about the general dynamics, computational principles, and necessary conditions for self-replicators to emerge. This is especially true on "computational substrates" where interactions involve logical, mathematical, or programming rules. In this paper we take a step towards understanding how self-replicators arise by studying several computational substrates based on various simple programming languages and machine instruction sets. We show that when random, non self-replicating programs are placed in an environment lacking any explicit fitness landscape, self-replicators tend to arise. We demonstrate how this occurs due to random interactions and self-modification, and can happen with and without background random mutations. We also show how increasingly complex dynamics continue to emerge following the rise of self-replicators. Finally, we show a counterexample of a minimalistic programming language where self-replicators are possible, but so far have not been observed to arise.

cs.NE↗

arXiv2023

Mesh Neural Cellular Automata

Texture modeling and synthesis are essential for enhancing the realism of virtual environments. Methods that directly synthesize textures in 3D offer distinct advantages to the UV-mapping-based methods as they can create seamless textures and align more closely with the ways textures form in nature. We propose Mesh Neural Cellular Automata (MeshNCA), a method that directly synthesizes dynamic textures on 3D meshes without requiring any UV maps. MeshNCA is a generalized type of cellular automata that can operate on a set of cells arranged on non-grid structures such as the vertices of a 3D mesh. MeshNCA accommodates multi-modal supervision and can be trained using different targets such as images, text prompts, and motion vector fields. Only trained on an Icosphere mesh, MeshNCA shows remarkable test-time generalization and can synthesize textures on unseen meshes in real time. We conduct qualitative and quantitative comparisons to demonstrate that MeshNCA outperforms other 3D texture synthesis methods in terms of generalization and producing high-quality textures. Moreover, we introduce a way of grafting trained MeshNCA instances, enabling interpolation between textures. MeshNCA allows several user interactions including texture density/orientation controls, grafting/regenerate brushes, and motion speed/direction controls. Finally, we implement the forward pass of our MeshNCA model using the WebGL shading language and showcase our trained models in an online interactive demo, which is accessible on personal computers and smartphones and is available at https://meshnca.github.io.

cs.CV↗

arXiv2023

Uncovering mesa-optimization algorithms in Transformers

Some autoregressive models exhibit in-context learning capabilities: being able to learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. The origins of this phenomenon are still poorly understood. Here we analyze a series of Transformer models trained to perform synthetic sequence prediction tasks, and discover that standard next-token prediction error minimization gives rise to a subsidiary learning algorithm that adjusts the model as new inputs are revealed. We show that this process corresponds to gradient-based optimization of a principled objective function, which leads to strong generalization performance on unseen sequences. Our findings explain in-context learning as a product of autoregressive loss minimization and inform the design of new optimization-based Transformer layers.

cs.LG↗

arXiv2023

Differentiable Programming of Chemical Reaction Networks

We present a differentiable formulation of abstract chemical reaction networks (CRNs) that can be trained to solve a variety of computational tasks. Chemical reaction networks are one of the most fundamental computational substrates used by nature. We study well-mixed single-chamber systems, as well as systems with multiple chambers separated by membranes, under mass-action kinetics. We demonstrate that differentiable optimisation, combined with proper regularisation, can discover non-trivial sparse reaction networks that can implement various sorts of oscillators and other chemical computing devices.

q-bio.MN↗

arXiv2022

Transformers learn in-context by gradient descent

At present, the mechanisms of in-context learning in Transformers are not well understood and remain mostly an intuition. In this paper, we suggest that training Transformers on auto-regressive objectives is closely related to gradient-based meta-learning formulations. We start by providing a simple weight construction that shows the equivalence of data transformations induced by 1) a single linear self-attention layer and by 2) gradient-descent (GD) on a regression loss. Motivated by that construction, we show empirically that when training self-attention-only Transformers on simple regression tasks either the models learned by GD and Transformers show great similarity or, remarkably, the weights found by optimization match the construction. Thus we show how trained Transformers become mesa-optimizers i.e. learn models by gradient descent in their forward pass. This allows us, at least in the domain of regression problems, to mechanistically understand the inner workings of in-context learning in optimized Transformers. Building on this insight, we furthermore identify how Transformers surpass the performance of plain gradient descent by learning an iterative curvature correction and learn linear models on deep data representations to solve non-linear regression tasks. Finally, we discuss intriguing parallels to a mechanism identified to be crucial for in-context learning termed induction-head (Olsson et al., 2022) and show how it could be understood as a specific case of in-context learning by gradient descent learning within Transformers. Code to reproduce the experiments can be found at https://github.com/google-research/self-organising-systems/tree/master/transformers_learn_icl_by_gd .

cs.LG↗

arXiv2021

$\mu$NCA: Texture Generation with Ultra-Compact Neural Cellular Automata

We study the problem of example-based procedural texture synthesis using highly compact models. Given a sample image, we use differentiable programming to train a generative process, parameterised by a recurrent Neural Cellular Automata (NCA) rule. Contrary to the common belief that neural networks should be significantly over-parameterised, we demonstrate that our model architecture and training procedure allows for representing complex texture patterns using just a few hundred learned parameters, making their expressivity comparable to hand-engineered procedural texture generating programs. The smallest models from the proposed $\mu$NCA family scale down to 68 parameters. When using quantisation to one byte per parameter, proposed models can be shrunk to a size range between 588 and 68 bytes. Implementation of a texture generator that uses these parameters to produce images is possible with just a few lines of GLSL or C code.

cs.LG↗

arXiv2021

Differentiable Programming of Reaction-Diffusion Patterns

Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable optimization method for learning the RD system parameters to perform example-based texture synthesis on a 2D plane. We do this by representing the RD system as a variant of Neural Cellular Automata and using task-specific differentiable loss functions. RD systems generated by our method exhibit robust, non-trivial 'life-like' behavior.

cs.NE↗

arXiv2021

Texture Generation with Neural Cellular Automata

Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior they introduce lends itself to the generation of textures. Textures in the natural world are often generated by variants of locally interacting reaction-diffusion systems. Human-made textures are likewise often generated in a local manner (textile weaving, for instance) or using rules with local dependencies (regular grids or geometric patterns). We demonstrate learning a texture generator from a single template image, with the generation method being embarrassingly parallel, exhibiting quick convergence and high fidelity of output, and requiring only some minimal assumptions around the underlying state manifold. Furthermore, we investigate properties of the learned models that are both useful and interesting, such as non-stationary dynamics and an inherent robustness to damage. Finally, we make qualitative claims that the behaviour exhibited by the NCA model is a learned, distributed, local algorithm to generate a texture, setting our method apart from existing work on texture generation. We discuss the advantages of such a paradigm.

cs.AI↗

arXiv2020

MPLP: Learning a Message Passing Learning Protocol

We present a novel method for learning the weights of an artificial neural network - a Message Passing Learning Protocol (MPLP). In MPLP, we abstract every operations occurring in ANNs as independent agents. Each agent is responsible for ingesting incoming multidimensional messages from other agents, updating its internal state, and generating multidimensional messages to be passed on to neighbouring agents. We demonstrate the viability of MPLP as opposed to traditional gradient-based approaches on simple feed-forward neural networks, and present a framework capable of generalizing to non-traditional neural network architectures. MPLP is meta learned using end-to-end gradient-based meta-optimisation. We further discuss the observed properties of MPLP and hypothesize its applicability on various fields of deep learning.

cs.LG↗

arXiv2019

Learning to Map Natural Language Instructions to Physical Quadcopter Control using Simulated Flight

We propose a joint simulation and real-world learning framework for mapping navigation instructions and raw first-person observations to continuous control. Our model estimates the need for environment exploration, predicts the likelihood of visiting environment positions during execution, and controls the agent to both explore and visit high-likelihood positions. We introduce Supervised Reinforcement Asynchronous Learning (SuReAL). Learning uses both simulation and real environments without requiring autonomous flight in the physical environment during training, and combines supervised learning for predicting positions to visit and reinforcement learning for continuous control. We evaluate our approach on a natural language instruction-following task with a physical quadcopter, and demonstrate effective execution and exploration behavior.

cs.RO↗

arXiv2019

Mapping Instructions to Actions in 3D Environments with Visual Goal Prediction

We propose to decompose instruction execution to goal prediction and action generation. We design a model that maps raw visual observations to goals using LINGUNET, a language-conditioned image generation network, and then generates the actions required to complete them. Our model is trained from demonstration only without external resources. To evaluate our approach, we introduce two benchmarks for instruction following: LANI, a navigation task; and CHAI, where an agent executes household instructions. Our evaluation demonstrates the advantages of our model decomposition, and illustrates the challenges posed by our new benchmarks.

cs.CL↗

arXiv2014

Particle energization through time-periodic helical magnetic fields

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the PDF of kinetic energy is, at late times, close to a Gaussian but with steeper tails.

astro-ph.HE↗