Adam Gaier

Taejong Joo, Shu Ishida, Ivan Sosnovik et al.

As a model-agnostic approach to long context modeling, multi-agent systems can process inputs longer than a large language model's context window without retraining or architectural modifications. However, their performance often heavily relies on hand-crafted multi-agent collaboration strategies and prompt engineering, which limit generalizability. In this work, we introduce a principled framework that formalizes the model-agnostic long context modeling problem as a compression problem, yielding an information-theoretic compression objective. Building on this framework, we propose Graph of Agents (GoA), which dynamically constructs an input-dependent collaboration structure that maximizes this objective. For Llama 3.1 8B and Qwen3 8B across six document question answering benchmarks, GoA improves the average $F_1$ score of retrieval-augmented generation by 5.7\% and a strong multi-agent baseline using a fixed collaboration structure by 16.35\%, respectively. Even with only a 2K context window, GoA surpasses the 128K context window Llama 3.1 8B on LongBench, showing a dramatic increase in effective context length. Our source code is available at https://github.com/tjoo512/graph-of-agents.

Yi Wang, Jieliang Luo, Adam Gaier et al.

World-building, the process of developing both the narrative and physical world of a game, plays a vital role in the game's experience. Critically-acclaimed independent and AAA video games are praised for strong world-building, with game maps that masterfully intertwine with and elevate the narrative, captivating players and leaving a lasting impression. However, designing game maps that support a desired narrative is challenging, as it requires satisfying complex constraints from various considerations. Most existing map generation methods focus on considerations about gameplay mechanics or map topography, while the need to support the story is typically neglected. As a result, extensive manual adjustment is still required to design a game world that facilitates particular stories. In this work, we approach this problem by introducing an extra layer of plot facility layout design that is independent of the underlying map generation method in a world-building pipeline. Concretely, we define (plot) facility layout tasks as the tasks of assigning concrete locations on a game map to abstract locations mentioned in a given story (plot facilities), following spatial constraints derived from the story. We present two methods for solving these tasks automatically: an evolutionary computation based approach through Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and a Reinforcement Learning (RL) based approach. We develop a method of generating datasets of facility layout tasks, create a gym-like environment for experimenting with and evaluating different methods, and further analyze the two methods with comprehensive experiments, aiming to provide insights for solving facility layout tasks. We will release the code and a dataset containing 10, 000 tasks of different scales.

Adam Gaier, James Stoddart, Lorenzo Villaggi et al.

Two fundamental challenges face generative models in engineering applications: the acquisition of high-performing, diverse datasets, and the adherence to precise constraints in generated designs. We propose a novel approach combining optimization, constraint satisfaction, and language models to tackle these challenges in architectural design. Our method uses Quality-Diversity (QD) to generate a diverse, high-performing dataset. We then fine-tune a language model with this dataset to generate high-level designs. These designs are then refined into detailed, constraint-compliant layouts using the Wave Function Collapse algorithm. Our system demonstrates reliable adherence to textual guidance, enabling the generation of layouts with targeted architectural and performance features. Crucially, our results indicate that data synthesized through the evolutionary search of QD not only improves overall model performance but is essential for the model's ability to closely adhere to textual guidance. This improvement underscores the pivotal role evolutionary computation can play in creating the datasets key to training generative models for design. Web article at https://tilegpt.github.io

Alexander Hagg, Adam Gaier, Dominik Wilde et al.

Novel techniques in evolutionary optimization, simulation and machine learning allow for a broad analysis of domains like fluid dynamics, in which computation is expensive and flow behavior is complex. Under the term of full domain analysis we understand the ability to efficiently determine the full space of solutions in a problem domain, and analyze the behavior of those solutions in an accessible and interactive manner. The goal of full domain analysis is to deepen our understanding of domains by generating many examples of flow, their diversification, optimization and analysis. We define a formal model for full domain analysis, its current state of the art, and requirements of subcomponents. Finally, an example is given to show what we can learn by using full domain analysis. Full domain analysis, rooted in optimization and machine learning, can be a helpful tool in understanding complex systems in computational physics and beyond.

Peter J Bentley, Soo Ling Lim, Adam Gaier et al.

Constrained optimization problems can be difficult because their search spaces have properties not conducive to search, e.g., multimodality, discontinuities, or deception. To address such difficulties, considerable research has been performed on creating novel evolutionary algorithms or specialized genetic operators. However, if the representation that defined the search space could be altered such that it only permitted valid solutions that satisfied the constraints, the task of finding the optimal would be made more feasible without any need for specialized optimization algorithms. We propose Constrained Optimization in Latent Space (COIL), which uses a VAE to generate a learned latent representation from a dataset comprising samples from the valid region of the search space according to a constraint, thus enabling the optimizer to find the objective in the new space defined by the learned representation. Preliminary experiments show promise: compared to an identical GA using a standard representation that cannot meet the constraints or find fit solutions, COIL with its learned latent representation can perfectly satisfy different types of constraints while finding high-fitness solutions.

Adam Gaier, Alexander Asteroth, Jean-Baptiste Mouret

The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Variational Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions -- but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinematics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.

Alexander Hagg, Martin Zaefferer, Jörg Stork et al.

Surrogate models are used to reduce the burden of expensive-to-evaluate objective functions in optimization. By creating models which map genomes to objective values, these models can estimate the performance of unknown inputs, and so be used in place of expensive objective functions. Evolutionary techniques such as genetic programming or neuroevolution commonly alter the structure of the genome itself. A lack of consistency in the genotype is a fatal blow to data-driven modeling techniques: interpolation between points is impossible without a common input space. However, while the dimensionality of genotypes may differ across individuals, in many domains, such as controllers or classifiers, the dimensionality of the input and output remains constant. In this work we leverage this insight to embed differing neural networks into the same input space. To judge the difference between the behavior of two neural networks, we give them both the same input sequence, and examine the difference in output. This difference, the phenotypic distance, can then be used to situate these networks into a common input space, allowing us to produce surrogate models which can predict the performance of neural networks regardless of topology. In a robotic navigation task, we show that models trained using this phenotypic embedding perform as well or better as those trained on the weight values of a fixed topology neural network. We establish such phenotypic surrogate models as a promising and flexible approach which enables surrogate modeling even for representations that undergo structural changes.

Adam Gaier, David Ha

Not all neural network architectures are created equal, some perform much better than others for certain tasks. But how important are the weight parameters of a neural network compared to its architecture? In this work, we question to what extent neural network architectures alone, without learning any weight parameters, can encode solutions for a given task. We propose a search method for neural network architectures that can already perform a task without any explicit weight training. To evaluate these networks, we populate the connections with a single shared weight parameter sampled from a uniform random distribution, and measure the expected performance. We demonstrate that our method can find minimal neural network architectures that can perform several reinforcement learning tasks without weight training. On a supervised learning domain, we find network architectures that achieve much higher than chance accuracy on MNIST using random weights. Interactive version of this paper at https://weightagnostic.github.io/

Adam Gaier, Alexander Asteroth, Jean-Baptiste Mouret

Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization algorithms because they produce diverse, high-quality solutions in a single run, instead of only a single near-optimal solution. Unfortunately, these algorithms currently require a large number of function evaluations, limiting their applicability. In this article we introduce a new illumination algorithm, Surrogate-Assisted Illumination (SAIL), that leverages surrogate modeling techniques to create a map of the design space according to user-defined features while minimizing the number of fitness evaluations. On a 2-dimensional airfoil optimization problem SAIL produces hundreds of diverse but high-performing designs with several orders of magnitude fewer evaluations than MAP-Elites or CMA-ES. We demonstrate that SAIL is also capable of producing maps of high-performing designs in realistic 3-dimensional aerodynamic tasks with an accurate flow simulation. Data-efficient design exploration with SAIL can help designers understand what is possible, beyond what is optimal, by considering more than pure objective-based optimization.

Adam Gaier, Alexander Asteroth, Jean-Baptiste Mouret

Surrogate-assistance approaches have long been used in computationally expensive domains to improve the data-efficiency of optimization algorithms. Neuroevolution, however, has so far resisted the application of these techniques because it requires the surrogate model to make fitness predictions based on variable topologies, instead of a vector of parameters. Our main insight is that we can sidestep this problem by using kernel-based surrogate models, which require only the definition of a distance measure between individuals. Our second insight is that the well-established Neuroevolution of Augmenting Topologies (NEAT) algorithm provides a computationally efficient distance measure between dissimilar networks in the form of "compatibility distance", initially designed to maintain topological diversity. Combining these two ideas, we introduce a surrogate-assisted neuroevolution algorithm that combines NEAT and a surrogate model built using a compatibility distance kernel. We demonstrate the data-efficiency of this new algorithm on the low dimensional cart-pole swing-up problem, as well as the higher dimensional half-cheetah running task. In both tasks the surrogate-assisted variant achieves the same or better results with several times fewer function evaluations as the original NEAT.

Adam Gaier, Alexander Asteroth, Jean-Baptiste Mouret

The MAP-Elites algorithm produces a set of high-performing solutions that vary according to features defined by the user. This technique has the potential to be a powerful tool for design space exploration, but is limited by the need for numerous evaluations. The Surrogate-Assisted Illumination algorithm (SAIL), introduced here, integrates approximative models and intelligent sampling of the objective function to minimize the number of evaluations required by MAP-Elites. The ability of SAIL to efficiently produce both accurate models and diverse high performing solutions is illustrated on a 2D airfoil design problem. The search space is divided into bins, each holding a design with a different combination of features. In each bin SAIL produces a better performing solution than MAP-Elites, and requires several orders of magnitude fewer evaluations. The CMA-ES algorithm was used to produce an optimal design in each bin: with the same number of evaluations required by CMA-ES to find a near-optimal solution in a single bin, SAIL finds solutions of similar quality in every bin.