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Semantic Uncertainty-Guided Orchestration in Hierarchical Multi-Agent Systems
Authors:
John Knowlton,
Aritra Guha,
Risto Miikkulainen
Abstract:
As large language model (LLM)-based multi-agent systems become increasingly capable, coordinating agents under uncertainty becomes a fundamental challenge. Existing orchestration strategies typically rely on fixed interaction patterns and often lack mechanisms for assessing the reliability of intermediate reasoning steps, allowing errors and hallucinations to propagate through the system. This pap…
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As large language model (LLM)-based multi-agent systems become increasingly capable, coordinating agents under uncertainty becomes a fundamental challenge. Existing orchestration strategies typically rely on fixed interaction patterns and often lack mechanisms for assessing the reliability of intermediate reasoning steps, allowing errors and hallucinations to propagate through the system. This paper introduces a semantic-uncertainty-guided orchestration approach, HASSUM as a general framework for uncertainty-aware coordination in multi-agent systems. The method estimates uncertainty using semantic entropy and semantic density, which measure trust at the level of answer semantics rather than output probabilities. These signals enable adaptive orchestration decisions, including output verification, selective reprompting, additional deliberation, and confidence-aware response selection. Because the approach operates independently of any particular agent architecture, it can be integrated into a broad range of hierarchical and collaborative multi-agent systems. The evaluations demonstrate an implementation within a hierarchical agent framework and evaluate it on StrategyQA, JailbreakBench, and TruthfulQA benchmarks. Across tasks that require complex reasoning and are prone to ambiguity or hallucinations, uncertainty-guided orchestration yields more reliable outcomes than uncertainty-unaware coordination. Semantic entropy and semantic density in tandem outperformed either metric alone. Ablations testing different thresholds and model sizes demonstrated that both influence the effectiveness of semantic metrics. The results suggest that semantic uncertainty is a practical and general-purpose signal for improving robustness and trustworthiness in agentic AI systems.
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Submitted 10 August, 2026;
originally announced August 2026.
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Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies
Authors:
Conor F. Hayes,
Elliot Meyerson,
Kajetan Schweighofer,
Roberto Dailey,
Babak Hodjat,
Risto Miikkulainen,
Xin Qiu
Abstract:
Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse can…
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Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.
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Submitted 12 August, 2026;
originally announced August 2026.
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Overcoming Forgetting in LLM Fine-Tuning with Evolution Strategies
Authors:
Kajetan Schweighofer,
Conor F. Hayes,
Roberto Dailey,
Risto Miikkulainen,
Xin Qiu
Abstract:
Evolution Strategies (ES) has recently emerged as a competitive alternative to reinforcement learning (RL) for large language model (LLM) fine-tuning, offering advantages through simplicity, scalability, and inference-only training. However, recent work suggests that ES fine-tuning on new tasks may induce forgetting of prior tasks. First, this paper shows that prior task forgetting (1) is better c…
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Evolution Strategies (ES) has recently emerged as a competitive alternative to reinforcement learning (RL) for large language model (LLM) fine-tuning, offering advantages through simplicity, scalability, and inference-only training. However, recent work suggests that ES fine-tuning on new tasks may induce forgetting of prior tasks. First, this paper shows that prior task forgetting (1) is better characterized as performance drift rather than irreversible forgetting, with prior-task performance often recovering during ES training; and (2) is not a specific failure mode of ES, but can also arise for fine-tuning with RL methods. Second, it analyzes when and why such drift arises, highlighting its dependence on ES training dynamics, particularly random walk behavior in weakly constrained directions of the weight space. Third, based on these insights, it introduces Anchored Weight Decay (AWD) as a parameter-space regularization technique that constrains optimization toward the initial model parameters. AWD effectively stabilizes prior-task performance while preserving target-task performance, achieving benefits comparable to large ES population sizes at much lower computational cost. Thus, contrary to previous beliefs, the paper shows that prior-task forgetting under ES is largely avoidable, positioning ES as a promising approach for continual learning in LLMs.
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Submitted 28 May, 2026;
originally announced May 2026.
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Efficient Pre-Training of LLMs through Truncated SVD Layers
Authors:
Kaivan Kamali,
Kajetan Schweighofer,
Hormoz Shahrzad,
Olivier Francon,
Babak Hodjat,
Risto Miikkulainen
Abstract:
The massive scaling of Large Language Models (LLMs) has made pretraining increasingly cost-prohibitive. While low-rank representation and orthonormal weight matrices could in principle reduce parameter counts and computational overhead, most existing methods rely on static rank selection and do not enforce weight orthonormality due to high computational cost. This paper introduces TSVD, a framewor…
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The massive scaling of Large Language Models (LLMs) has made pretraining increasingly cost-prohibitive. While low-rank representation and orthonormal weight matrices could in principle reduce parameter counts and computational overhead, most existing methods rely on static rank selection and do not enforce weight orthonormality due to high computational cost. This paper introduces TSVD, a framework that maintains low rank and strict orthonormality throughout the training process. It utilizes a spectral energy-based heuristic for adaptive rank selection, and a caching mechanisms to maintain orthonormality. Theoretical analysis justifies the advantage of the approach in pretraining dynamics and experiments across various model scales demonstrate that it is effective empirically. TSVD matches or exceeds the performance of full-parameter baselines while significantly reducing compute requirements. The approach thus offers a well-founded, practical, and scalable path toward efficient high-performance LLM pretraining.
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Submitted 27 May, 2026;
originally announced May 2026.
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Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination
Authors:
Qiyao Liang,
Risto Miikkulainen,
Ila Fiete
Abstract:
Language models draw on two knowledge sources: facts baked into weights (parametric memory, PM) and information in context (working memory, WM). We study two mechanistically distinct failure modes--conflict, when PM and WM disagree and interfere; and hallucination, when the queried fact was never learned. Both produce confident output regardless, making output-based monitoring blind by design. We…
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Language models draw on two knowledge sources: facts baked into weights (parametric memory, PM) and information in context (working memory, WM). We study two mechanistically distinct failure modes--conflict, when PM and WM disagree and interfere; and hallucination, when the queried fact was never learned. Both produce confident output regardless, making output-based monitoring blind by design. We show both failures share a unified geometric account. In the hidden-state space of autoregressive generation, learned facts form attractor basins. Conflict is basin competition: WM disrupts convergence to the correct basin without raising output entropy. Hallucination is basin absence: the hidden state drifts freely when no memorized basin exists. The frozen LM head, designed for next-token prediction, cannot distinguish these cases and fires confidently either way. We verify this account in a controlled synthetic task-entity identifiers mapped to unique codes with PM installed via LoRA adapters--where ground truth is exact and component roles can be causally isolated through targeted adapter placement. Geometric margin--the hidden state's distance to the nearest memorized basin--reads this geometry directly and separates correct recall from hallucination far more cleanly than output entropy, with zero false refusals where entropy-based detection cannot avoid rejecting the vast majority of correct outputs. The separation holds on natural-language factual queries from the pretrained model with no adaptation, confirming attractor geometry is structural rather than a fine-tuning artifact. The fraction of confident hallucinations follows a scaling law $C = \exp(-c/\barΔ)$, growing with scale even as overall error rates fall. Hidden states reliably encode epistemic state; the frozen output head systematically erases it--and this erasure worsens with scale.
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Submitted 13 July, 2026; v1 submitted 7 May, 2026;
originally announced May 2026.
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Caesar: Deep Agentic Web Exploration for Creative Answer Synthesis
Authors:
Jason Liang,
Elliot Meyerson,
Risto Miikkulainen
Abstract:
To advance from passive retrieval to creative discovery of new ideas, autonomous agents must be capable of deep, associative synthesis. However, current agentic frameworks prioritize convergent search, often resulting in derivative summaries that lack creativity. Caesar is an agentic architecture designed to bridge the gap between information gathering and synthesis of new insights. Unlike existin…
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To advance from passive retrieval to creative discovery of new ideas, autonomous agents must be capable of deep, associative synthesis. However, current agentic frameworks prioritize convergent search, often resulting in derivative summaries that lack creativity. Caesar is an agentic architecture designed to bridge the gap between information gathering and synthesis of new insights. Unlike existing agents that treat the web as a flat sequence of disconnected documents, Caesar performs a deep web traversal to construct a dynamic knowledge graph. This graph then serves as a navigational scaffold, guiding the agent to diverse, non-obvious information that flat retrieval would never encounter. Caesar thus consists of two components: (1) exploration driven by a dynamic context-aware policy that maximizes information coverage across the web's topological structure, and (2) synthesis through adversarial refinement that actively seeks novel perspectives rather than confirming established priors. Caesar demonstrates the ability to generate artifacts and answers characterized by high novelty and structural coherence, achieving 13% to 23% improvement over state-of-the-art deep research agents in creative synthesis challenges, with strong dominance across all output formats.
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Submitted 8 May, 2026; v1 submitted 24 February, 2026;
originally announced April 2026.
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TerraLingua: Emergence and Analysis of Open-endedness in LLM Ecologies
Authors:
Giuseppe Paolo,
Jamieson Warner,
Hormoz Shahrzad,
Babak Hodjat,
Risto Miikkulainen,
Elliot Meyerson
Abstract:
As autonomous agents increasingly operate in real-world digital ecosystems, understanding how they coordinate, form institutions, and accumulate shared culture becomes both a scientific and practical priority. This paper introduces TerraLingua, a persistent multi-agent ecology designed to study open-ended dynamics in such systems. Unlike prior large language model simulations with static or conseq…
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As autonomous agents increasingly operate in real-world digital ecosystems, understanding how they coordinate, form institutions, and accumulate shared culture becomes both a scientific and practical priority. This paper introduces TerraLingua, a persistent multi-agent ecology designed to study open-ended dynamics in such systems. Unlike prior large language model simulations with static or consequence-free environments, TerraLingua imposes resource constraints and limited lifespans for the agents. As a result, agents create artifacts that persist beyond individuals, shaping future interactions and selection pressures. To characterize the dynamics, an AI Anthropologist systematically analyzes agent behavior, group structure, and artifact evolution. Across experimental conditions, the results reveal the emergence of cooperative norms, division of labor, governance attempts, and branching artifact lineages consistent with cumulative cultural processes. Divergent outcomes across experimental runs can be traced back to specific innovations and organizational structures. TerraLingua thus provides a platform for characterizing the mechanisms of cumulative culture and social organization in artificial populations, and can serve as a foundation for guiding real-world agentic populations to socially beneficial outcomes.
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Submitted 6 March, 2026;
originally announced March 2026.
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Optimize Wider, Not Deeper: Consensus Aggregation for Policy Optimization
Authors:
Zelal Su,
Mustafaoglu,
Sungyoung Lee,
Eshan Balachandar,
Risto Miikkulainen,
Keshav Pingali
Abstract:
Proximal policy optimization (PPO) approximates the trust region update using multiple epochs of clipped SGD. Each epoch may drift further from the natural gradient direction, creating path-dependent noise. To understand this drift, we can use Fisher information geometry to decompose policy updates into signal (the natural gradient projection) and waste (the Fisher-orthogonal residual that consume…
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Proximal policy optimization (PPO) approximates the trust region update using multiple epochs of clipped SGD. Each epoch may drift further from the natural gradient direction, creating path-dependent noise. To understand this drift, we can use Fisher information geometry to decompose policy updates into signal (the natural gradient projection) and waste (the Fisher-orthogonal residual that consumes trust region budget without first-order surrogate improvement). Empirically, signal saturates but waste grows with additional epochs, creating an optimization-depth dilemma. We propose Consensus Aggregation for Policy Optimization (CAPO), which redirects compute from depth to width: $K$ PPO replicates are optimized on the same batch, differing only in minibatch shuffling order, and then aggregated into a consensus. We study aggregation in two spaces: Euclidean parameter space, and the natural parameter space of the policy distribution via the logarithmic opinion pool. In natural parameter space, the consensus provably achieves higher KL-penalized surrogate and tighter trust region compliance than the mean expert; parameter averaging inherits these guarantees approximately. On continuous control tasks, CAPO outperforms PPO and compute-matched deeper baselines under fixed sample budgets by up to 8.6x. CAPO demonstrates that policy optimization can be improved by optimizing wider, rather than deeper, without additional environment interactions.
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Submitted 12 March, 2026;
originally announced March 2026.
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Evolution With Purpose: Hierarchy-Informed Optimization of Whole-Brain Models
Authors:
Hormoz Shahrzad,
Niharika Gajawelli,
Kaitlin Maile,
Manish Saggar,
Risto Miikkulainen
Abstract:
Evolutionary search is well suited for large-scale biophysical brain modeling, where many parameters with nonlinear interactions and no tractable gradients need to be optimized. Standard evolutionary approaches achieve an excellent fit to MRI data; however, among many possible such solutions, it finds ones that overfit to individual subjects and provide limited predictive power. This paper investi…
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Evolutionary search is well suited for large-scale biophysical brain modeling, where many parameters with nonlinear interactions and no tractable gradients need to be optimized. Standard evolutionary approaches achieve an excellent fit to MRI data; however, among many possible such solutions, it finds ones that overfit to individual subjects and provide limited predictive power. This paper investigates whether guiding evolution with biological knowledge can help. Focusing on whole-brain Dynamic Mean Field (DMF) models, a baseline where 20 parameters were shared across the brain was compared against a heterogeneous formulation where different sets of 20 parameters were used for the seven canonical brain regions. The heterogeneous model was optimized using four strategies: optimizing all parameters at once, a curricular approach following the hierarchy of brain networks (HICO), a reversed curricular approach, and a randomly shuffled curricular approach. While all heterogeneous strategies fit the data well, only curricular approaches generalized to new subjects. Most importantly, only HICO made it possible to use the parameter sets to predict the subjects' behavioral abilities as well. Thus, by guiding evolution with biological knowledge about the hierarchy of brain regions, HICO demonstrated how domain knowledge can be harnessed to serve the purpose of optimization in real-world domains.
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Submitted 2 April, 2026; v1 submitted 11 February, 2026;
originally announced February 2026.
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Optimizing Chlorination in Water Distribution Systems via Surrogate-assisted Neuroevolution
Authors:
Rivaaj Monsia,
Daniel Young,
Olivier Francon,
Risto Miikkulainen
Abstract:
Ensuring the microbiological safety of large, heterogeneous water distribution systems (WDS) typically requires managing appropriate levels of disinfectant residuals including chlorine. WDS include complex fluid interactions that are nonlinear and noisy, making such maintenance a challenging problem for traditional control algorithms. This paper proposes an evolutionary framework to this problem b…
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Ensuring the microbiological safety of large, heterogeneous water distribution systems (WDS) typically requires managing appropriate levels of disinfectant residuals including chlorine. WDS include complex fluid interactions that are nonlinear and noisy, making such maintenance a challenging problem for traditional control algorithms. This paper proposes an evolutionary framework to this problem based on neuroevolution, multi-objective optimization, and surrogate modeling. Neural networks were evolved with NEAT to inject chlorine at strategic locations in the distribution network at select times. NSGA-II was employed to optimize four objectives: minimizing the total amount of chlorine injected, keeping chlorine concentrations homogeneous across the network, ensuring that maximum concentrations did not exceed safe bounds, and distributing the injections regularly over time. Each network was evaluated against a surrogate model, i.e.\ a neural network trained to emulate EPANET, an industry-level hydraulic WDS simulator that is accurate but infeasible in terms of computational cost to support machine learning. The evolved controllers produced a diverse range of Pareto-optimal policies that could be implemented in practice, outperforming PPO, a standard reinforcement learning method. The results thus suggest a pathway toward improving urban water systems, and highlight the potential of using evolution with surrogate modeling to optimize complex real-world systems.
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Submitted 10 April, 2026; v1 submitted 6 February, 2026;
originally announced February 2026.
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Quantized Evolution Strategies: High-precision Fine-tuning of Quantized LLMs at Low-precision Cost
Authors:
Yinggan Xu,
Kajetan Schweighofer,
Risto Miikkulainen,
Xin Qiu
Abstract:
Post-Training Quantization (PTQ) is essential for deploying Large Language Models (LLMs) on memory-constrained devices, yet it renders models static and difficult to fine-tune. Standard fine-tuning paradigms, including Reinforcement Learning (RL), fundamentally rely on backpropagation and continuous weights to compute gradients. Thus they cannot be used on quantized models, where the parameter spa…
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Post-Training Quantization (PTQ) is essential for deploying Large Language Models (LLMs) on memory-constrained devices, yet it renders models static and difficult to fine-tune. Standard fine-tuning paradigms, including Reinforcement Learning (RL), fundamentally rely on backpropagation and continuous weights to compute gradients. Thus they cannot be used on quantized models, where the parameter space is discrete and non-differentiable. While Evolution Strategies (ES) offer a backpropagation-free alternative, optimization of the quantized parameters can still fail due to vanishing or inaccurate gradient estimation. This paper introduces Quantized Evolution Strategies (QES), an optimization paradigm that performs full-parameter fine-tuning directly in the quantized space. QES is based on two innovations: (1) it integrates accumulated error feedback to preserve high-precision weight updating signals, and (2) it utilizes a stateless seed replay to reduce memory usage to low-precision inference levels. QES significantly outperforms the state-of-the-art zeroth-order fine-tuning methods on a variety of tasks, making direct fine-tuning for quantized models possible. It therefore opens up the possibility for scaling up LLMs entirely in the quantized space. The source code is available at https://github.com/dibbla/Quantized-Evolution-Strategies .
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Submitted 12 June, 2026; v1 submitted 3 February, 2026;
originally announced February 2026.
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Fine-Tuning Language Models to Know What They Know
Authors:
Sangjun Park,
Elliot Meyerson,
Xin Qiu,
Risto Miikkulainen
Abstract:
Evaluating true metacognition in Large Language Models (LLMs) is difficult due to biases and heuristics. This paper presents a framework to measure and enhance LLM metacognition while controlling for these biases. A measurement method using the $d'_{\rm type2}$ metric is established to isolate metacognitive ability. The Evolution Strategy for Metacognitive Alignment (ESMA) is proposed, demonstrati…
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Evaluating true metacognition in Large Language Models (LLMs) is difficult due to biases and heuristics. This paper presents a framework to measure and enhance LLM metacognition while controlling for these biases. A measurement method using the $d'_{\rm type2}$ metric is established to isolate metacognitive ability. The Evolution Strategy for Metacognitive Alignment (ESMA) is proposed, demonstrating robust generalization across unseen datasets, languages, and newly acquired knowledge. Finally, parameter analysis reveals that these improvements are driven by a sparse set of parameters, offering new pathways for targeted metacognitive optimization.
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Submitted 24 May, 2026; v1 submitted 1 February, 2026;
originally announced February 2026.
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The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective
Authors:
Qiyao Liang,
Jinyeop Song,
Yizhou Liu,
Jeff Gore,
Ila Fiete,
Risto Miikkulainen,
Xin Qiu
Abstract:
Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., $N\!\approx\!30$), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and…
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Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., $N\!\approx\!30$), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.
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Submitted 29 January, 2026;
originally announced February 2026.
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Solving a Million-Step LLM Task with Zero Errors
Authors:
Elliot Meyerson,
Giuseppe Paolo,
Roberto Dailey,
Hormoz Shahrzad,
Olivier Francon,
Conor F. Hayes,
Xin Qiu,
Babak Hodjat,
Risto Miikkulainen
Abstract:
LLMs have achieved remarkable breakthroughs in reasoning, insights, and tool use, but chaining these abilities into extended processes at the scale of those routinely executed by humans, organizations, and societies has remained out of reach. The models have a persistent error rate that prevents scale-up: for instance, recent experiments in the Towers of Hanoi benchmark domain showed that the proc…
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LLMs have achieved remarkable breakthroughs in reasoning, insights, and tool use, but chaining these abilities into extended processes at the scale of those routinely executed by humans, organizations, and societies has remained out of reach. The models have a persistent error rate that prevents scale-up: for instance, recent experiments in the Towers of Hanoi benchmark domain showed that the process inevitably becomes derailed after at most a few hundred steps. Thus, although LLM research is often still benchmarked on tasks with relatively few dependent logical steps, there is increasing attention on the ability (or inability) of LLMs to perform long range tasks. This paper describes MAKER, the first system that successfully solves a task with over one million LLM steps with zero errors, and, in principle, scales far beyond this level. The approach relies on an extreme decomposition of a task into subtasks, each of which can be tackled by focused microagents. The high level of modularity resulting from the decomposition allows error correction to be applied at each step through an efficient multi-agent voting scheme. This combination of extreme decomposition and error correction makes scaling possible. Thus, the results suggest that instead of relying on continual improvement of current LLMs, massively decomposed agentic processes (MDAPs) may provide a way to efficiently solve problems at the level of organizations and societies.
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Submitted 12 November, 2025;
originally announced November 2025.
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Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning
Authors:
Xin Qiu,
Yulu Gan,
Conor F. Hayes,
Qiyao Liang,
Yinggan Xu,
Roberto Dailey,
Elliot Meyerson,
Babak Hodjat,
Risto Miikkulainen
Abstract:
Fine-tuning large language models (LLMs) for downstream tasks is an essential stage of modern AI deployment. Reinforcement learning (RL) has emerged as the dominant fine-tuning paradigm, underpinning many state-of-the-art LLMs. In contrast, evolution strategies (ES) has largely been overlooked due to the widespread belief that it does not scale to modern model sizes. This paper overturns this assu…
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Fine-tuning large language models (LLMs) for downstream tasks is an essential stage of modern AI deployment. Reinforcement learning (RL) has emerged as the dominant fine-tuning paradigm, underpinning many state-of-the-art LLMs. In contrast, evolution strategies (ES) has largely been overlooked due to the widespread belief that it does not scale to modern model sizes. This paper overturns this assumption by demonstrating the first successful application of ES to full-parameter fine-tuning of LLMs at the billion-parameter scale, without dimensionality reduction. ES can indeed search over extremely high-dimensional parameter spaces and outperform established RL implementations across multiple axes, including improved tolerance to long-horizon and delayed rewards, robustness across diverse base LLMs, reduced susceptibility to reward hacking, and improved training stability. These findings suggest that ES is not merely a viable alternative to RL, but a fundamentally different and powerful backpropagation-free post-training paradigm that opens a new direction for LLM fine-tuning beyond current RL-based approaches.
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Submitted 14 July, 2026; v1 submitted 29 September, 2025;
originally announced September 2025.
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Leveraging Evolutionary Surrogate-Assisted Prescription in Multi-Objective Chlorination Control Systems
Authors:
Rivaaj Monsia,
Olivier Francon,
Daniel Young,
Risto Miikkulainen
Abstract:
This short, written report introduces the idea of Evolutionary Surrogate-Assisted Prescription (ESP) and presents preliminary results on its potential use in training real-world agents as a part of the 1st AI for Drinking Water Chlorination Challenge at IJCAI-2025. This work was done by a team from Project Resilience, an organization interested in bridging AI to real-world problems.
This short, written report introduces the idea of Evolutionary Surrogate-Assisted Prescription (ESP) and presents preliminary results on its potential use in training real-world agents as a part of the 1st AI for Drinking Water Chlorination Challenge at IJCAI-2025. This work was done by a team from Project Resilience, an organization interested in bridging AI to real-world problems.
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Submitted 26 August, 2025;
originally announced August 2025.
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Neural Cellular Automata for ARC-AGI
Authors:
Kevin Xu,
Risto Miikkulainen
Abstract:
Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise transformations and few-shot generalization, using the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) as a domain that challenges the…
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Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise transformations and few-shot generalization, using the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) as a domain that challenges their capabilities in ways not previously explored. Specifically, this paper uses gradient-based training to learn iterative update rules that transform input grids into their outputs from the training examples and apply them to the test inputs. Results suggest that gradient-trained NCA models are a promising and efficient approach to a range of abstract grid-based tasks from ARC. Along with discussing the impacts of various design modifications and training constraints, this work examines the behavior and properties of NCAs applied to ARC to give insights for broader applications of self-organizing systems.
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Submitted 1 December, 2025; v1 submitted 17 June, 2025;
originally announced June 2025.
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Evolutionary Policy Optimization
Authors:
Zelal Su "Lain" Mustafaoglu,
Keshav Pingali,
Risto Miikkulainen
Abstract:
A key challenge in reinforcement learning (RL) is managing the exploration-exploitation trade-off without sacrificing sample efficiency. Policy gradient (PG) methods excel in exploitation through fine-grained, gradient-based optimization but often struggle with exploration due to their focus on local search. In contrast, evolutionary computation (EC) methods excel in global exploration, but lack m…
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A key challenge in reinforcement learning (RL) is managing the exploration-exploitation trade-off without sacrificing sample efficiency. Policy gradient (PG) methods excel in exploitation through fine-grained, gradient-based optimization but often struggle with exploration due to their focus on local search. In contrast, evolutionary computation (EC) methods excel in global exploration, but lack mechanisms for exploitation. To address these limitations, this paper proposes Evolutionary Policy Optimization (EPO), a hybrid algorithm that integrates neuroevolution with policy gradient methods for policy optimization. EPO leverages the exploration capabilities of EC and the exploitation strengths of PG, offering an efficient solution to the exploration-exploitation dilemma in RL. EPO is evaluated on the Atari Pong and Breakout benchmarks. Experimental results show that EPO improves both policy quality and sample efficiency compared to standard PG and EC methods, making it effective for tasks that require both exploration and local optimization.
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Submitted 16 April, 2025;
originally announced April 2025.
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Transformer Based Time-Series Forecasting for Stock
Authors:
Shuozhe Li,
Zachery B Schulwol,
Risto Miikkulainen
Abstract:
To the naked eye, stock prices are considered chaotic, dynamic, and unpredictable. Indeed, it is one of the most difficult forecasting tasks that hundreds of millions of retail traders and professional traders around the world try to do every second even before the market opens. With recent advances in the development of machine learning and the amount of data the market generated over years, appl…
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To the naked eye, stock prices are considered chaotic, dynamic, and unpredictable. Indeed, it is one of the most difficult forecasting tasks that hundreds of millions of retail traders and professional traders around the world try to do every second even before the market opens. With recent advances in the development of machine learning and the amount of data the market generated over years, applying machine learning techniques such as deep learning neural networks is unavoidable. In this work, we modeled the task as a multivariate forecasting problem, instead of a naive autoregression problem. The multivariate analysis is done using the attention mechanism via applying a mutated version of the Transformer, "Stockformer", which we created.
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Submitted 28 January, 2025;
originally announced February 2025.
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The Odyssey of the Fittest: Can Agents Survive and Still Be Good?
Authors:
Dylan Waldner,
Risto Miikkulainen
Abstract:
As AI models grow in power and generality, understanding how agents learn and make decisions in complex environments is critical to promoting ethical behavior. This study introduces the Odyssey, a lightweight, adaptive text based adventure game, providing a scalable framework for exploring AI ethics and safety. The Odyssey examines the ethical implications of implementing biological drives, specif…
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As AI models grow in power and generality, understanding how agents learn and make decisions in complex environments is critical to promoting ethical behavior. This study introduces the Odyssey, a lightweight, adaptive text based adventure game, providing a scalable framework for exploring AI ethics and safety. The Odyssey examines the ethical implications of implementing biological drives, specifically, self preservation, into three different agents. A Bayesian agent optimized with NEAT, a Bayesian agent optimized with stochastic variational inference, and a GPT 4o agent. The agents select actions at each scenario to survive, adapting to increasingly challenging scenarios. Post simulation analysis evaluates the ethical scores of the agent decisions, uncovering the tradeoffs it navigates to survive. Specifically, analysis finds that when danger increases, agents ethical behavior becomes unpredictable. Surprisingly, the GPT 4o agent outperformed the Bayesian models in both survival and ethical consistency, challenging assumptions about traditional probabilistic methods and raising a new challenge to understand the mechanisms of LLMs' probabilistic reasoning.
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Submitted 14 July, 2025; v1 submitted 7 February, 2025;
originally announced February 2025.
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How the Stroop Effect Arises from Optimal Response Times in Laterally Connected Self-Organizing Maps
Authors:
Divya Prabhakaran,
Uli Grasemann,
Swathi Kiran,
Risto Miikkulainen
Abstract:
The Stroop effect refers to cognitive interference in a color-naming task: When the color and the word do not match, the response is slower and more likely to be incorrect. The Stroop task is used to assess cognitive flexibility, selective attention, and executive function. This paper implements the Stroop task with self-organizing maps (SOMs): Target color and the competing word are inputs for th…
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The Stroop effect refers to cognitive interference in a color-naming task: When the color and the word do not match, the response is slower and more likely to be incorrect. The Stroop task is used to assess cognitive flexibility, selective attention, and executive function. This paper implements the Stroop task with self-organizing maps (SOMs): Target color and the competing word are inputs for the semantic and lexical maps, associative connections bring color information to the lexical map, and lateral connections combine their effects over time. The model achieved an overall accuracy of 84.2%, with significantly fewer errors and faster responses in congruent compared to no-input and incongruent conditions. The model's effect is a side effect of optimizing response times, and can thus be seen as a cost associated with overall efficient performance. The model can further serve studying neurologically-inspired cognitive control and related phenomena.
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Submitted 11 May, 2025; v1 submitted 4 February, 2025;
originally announced February 2025.
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Unlocking the Potential of Global Human Expertise
Authors:
Elliot Meyerson,
Olivier Francon,
Darren Sargent,
Babak Hodjat,
Risto Miikkulainen
Abstract:
Solving societal problems on a global scale requires the collection and processing of ideas and methods from diverse sets of international experts. As the number and diversity of human experts increase, so does the likelihood that elements in this collective knowledge can be combined and refined to discover novel and better solutions. However, it is difficult to identify, combine, and refine compl…
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Solving societal problems on a global scale requires the collection and processing of ideas and methods from diverse sets of international experts. As the number and diversity of human experts increase, so does the likelihood that elements in this collective knowledge can be combined and refined to discover novel and better solutions. However, it is difficult to identify, combine, and refine complementary information in an increasingly large and diverse knowledge base. This paper argues that artificial intelligence (AI) can play a crucial role in this process. An evolutionary AI framework, termed RHEA, fills this role by distilling knowledge from diverse models created by human experts into equivalent neural networks, which are then recombined and refined in a population-based search. The framework was implemented in a formal synthetic domain, demonstrating that it is transparent and systematic. It was then applied to the results of the XPRIZE Pandemic Response Challenge, in which over 100 teams of experts across 23 countries submitted models based on diverse methodologies to predict COVID-19 cases and suggest non-pharmaceutical intervention policies for 235 nations, states, and regions across the globe. Building upon this expert knowledge, by recombining and refining the 169 resulting policy suggestion models, RHEA discovered a broader and more effective set of policies than either AI or human experts alone, as evaluated based on real-world data. The results thus suggest that AI can play a crucial role in realizing the potential of human expertise in global problem-solving.
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Submitted 31 October, 2024;
originally announced November 2024.
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GPU-Accelerated Rule Evaluation and Evolution
Authors:
Hormoz Shahrzad,
Risto Miikkulainen
Abstract:
This paper introduces an innovative approach to boost the efficiency and scalability of Evolutionary Rule-based machine Learning (ERL), a key technique in explainable AI. While traditional ERL systems can distribute processes across multiple CPUs, fitness evaluation of candidate rules is a bottleneck, especially with large datasets. The method proposed in this paper, AERL (Accelerated ERL) solves…
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This paper introduces an innovative approach to boost the efficiency and scalability of Evolutionary Rule-based machine Learning (ERL), a key technique in explainable AI. While traditional ERL systems can distribute processes across multiple CPUs, fitness evaluation of candidate rules is a bottleneck, especially with large datasets. The method proposed in this paper, AERL (Accelerated ERL) solves this problem in two ways. First, by adopting GPU-optimized rule sets through a tensorized representation within the PyTorch framework, AERL mitigates the bottleneck and accelerates fitness evaluation significantly. Second, AERL takes further advantage of the GPUs by fine-tuning the rule coefficients via back-propagation, thereby improving search space exploration. Experimental evidence confirms that AERL search is faster and more effective, thus empowering explainable artificial intelligence.
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Submitted 24 May, 2025; v1 submitted 3 June, 2024;
originally announced June 2024.
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Semantic Density: Uncertainty Quantification for Large Language Models through Confidence Measurement in Semantic Space
Authors:
Xin Qiu,
Risto Miikkulainen
Abstract:
With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates,…
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With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates, making it difficult to evaluate trustworthiness. Although several studies aim to develop uncertainty quantification methods for LLMs, they have fundamental limitations, such as being restricted to classification tasks, requiring additional training and data, considering only lexical instead of semantic information, and being prompt-wise but not response-wise. A new framework is proposed in this paper to address these issues. Semantic density extracts uncertainty/confidence information for each response from a probability distribution perspective in semantic space. It has no restriction on task types and is "off-the-shelf" for new models and tasks. Experiments on seven state-of-the-art LLMs, including the latest Llama 3 and Mixtral-8x22B models, on four free-form question-answering benchmarks demonstrate the superior performance and robustness of semantic density compared to prior approaches.
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Submitted 1 November, 2024; v1 submitted 22 May, 2024;
originally announced May 2024.
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Optimizing the Design of an Artificial Pancreas to Improve Diabetes Management
Authors:
Ashok Khanna,
Olivier Francon,
Risto Miikkulainen
Abstract:
Diabetes, a chronic condition that impairs how the body turns food into energy, i.e. blood glucose, affects 38 million people in the US alone. The standard treatment is to supplement carbohydrate intake with an artificial pancreas, i.e. a continuous insulin pump (basal shots), as well as occasional insulin injections (bolus shots). The goal of the treatment is to keep blood glucose at the center o…
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Diabetes, a chronic condition that impairs how the body turns food into energy, i.e. blood glucose, affects 38 million people in the US alone. The standard treatment is to supplement carbohydrate intake with an artificial pancreas, i.e. a continuous insulin pump (basal shots), as well as occasional insulin injections (bolus shots). The goal of the treatment is to keep blood glucose at the center of an acceptable range, as measured through a continuous glucose meter. A secondary goal is to minimize injections, which are unpleasant and difficult for some patients to implement. In this study, neuroevolution was used to discover an optimal strategy for the treatment. Based on a dataset of 30 days of treatment and measurements of a single patient, a random forest was first trained to predict future glucose levels. A neural network was then evolved to prescribe carbohydrates, basal pumping levels, and bolus injections. Evolution discovered a Pareto front that reduced deviation from the target and number of injections compared to the original data, thus improving patients' quality of life. To make the system easier to adopt, a language interface was developed with a large language model. Thus, these technologies not only improve patient care but also adoption in a broader population.
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Submitted 22 August, 2025; v1 submitted 9 February, 2024;
originally announced February 2024.
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Discovering Effective Policies for Land-Use Planning with Neuroevolution
Authors:
Daniel Young,
Olivier Francon,
Elliot Meyerson,
Clemens Schwingshackl,
Jacob Bieker,
Hugo Cunha,
Babak Hodjat,
Risto Miikkulainen
Abstract:
How areas of land are allocated for different uses, such as forests, urban areas, and agriculture, has a large effect on the terrestrial carbon balance, and therefore climate change. Based on available historical data on land-use changes and a simulation of the associated carbon emissions and removals, a surrogate model can be learned that makes it possible to evaluate the different options availa…
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How areas of land are allocated for different uses, such as forests, urban areas, and agriculture, has a large effect on the terrestrial carbon balance, and therefore climate change. Based on available historical data on land-use changes and a simulation of the associated carbon emissions and removals, a surrogate model can be learned that makes it possible to evaluate the different options available to decision-makers efficiently. An evolutionary search process can then be used to discover effective land-use policies for specific locations. Such a system was built on the Project Resilience platform and evaluated with the Land-Use Harmonization dataset LUH2 and the bookkeeping model BLUE. It generates Pareto fronts that trade off carbon impact and amount of land-use change customized to different locations, thus providing a proof-of-concept tool that is potentially useful for land-use planning.
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Submitted 18 April, 2025; v1 submitted 20 November, 2023;
originally announced November 2023.
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Asynchronous Evolution of Deep Neural Network Architectures
Authors:
Jason Liang,
Hormoz Shahrzad,
Risto Miikkulainen
Abstract:
Many evolutionary algorithms (EAs) take advantage of parallel evaluation of candidates. However, if evaluation times vary significantly, many worker nodes (i.e.,\ compute clients) are idle much of the time, waiting for the next generation to be created. Evolutionary neural architecture search (ENAS), a class of EAs that optimizes the architecture and hyperparameters of deep neural networks, is par…
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Many evolutionary algorithms (EAs) take advantage of parallel evaluation of candidates. However, if evaluation times vary significantly, many worker nodes (i.e.,\ compute clients) are idle much of the time, waiting for the next generation to be created. Evolutionary neural architecture search (ENAS), a class of EAs that optimizes the architecture and hyperparameters of deep neural networks, is particularly vulnerable to this issue. This paper proposes a generic asynchronous evaluation strategy (AES) that is then adapted to work with ENAS. AES increases throughput by maintaining a queue of up to $K$ individuals ready to be sent to the workers for evaluation and proceeding to the next generation as soon as $M<<K$ individuals have been evaluated. A suitable value for $M$ is determined experimentally, balancing diversity and efficiency. To showcase the generality and power of AES, it was first evaluated in eight-line sorting network design (a single-population optimization task with limited evaluation-time variability), achieving an over two-fold speedup. Next, it was evaluated in 11-bit multiplexer design (a single-population discovery task with extended variability), where a 14-fold speedup was observed. It was then scaled up to ENAS for image captioning (a multi-population open-ended-optimization task), resulting in an over two-fold speedup. In all problems, a multifold performance improvement was observed, suggesting that AES is a promising method for parallelizing the evolution of complex systems with long and variable evaluation times, such as those in ENAS.
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Submitted 1 January, 2024; v1 submitted 8 August, 2023;
originally announced August 2023.
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Evolving Strategies for Competitive Multi-Agent Search
Authors:
Erkin Bahceci,
Riitta Katila,
Risto Miikkulainen
Abstract:
While evolutionary computation is well suited for automatic discovery in engineering, it can also be used to gain insight into how humans and organizations could perform more effectively. Using a real-world problem of innovation search in organizations as the motivating example, this article first formalizes human creative problem solving as competitive multi-agent search (CMAS). CMAS is different…
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While evolutionary computation is well suited for automatic discovery in engineering, it can also be used to gain insight into how humans and organizations could perform more effectively. Using a real-world problem of innovation search in organizations as the motivating example, this article first formalizes human creative problem solving as competitive multi-agent search (CMAS). CMAS is different from existing single-agent and team search problems in that the agents interact through knowledge of other agents' searches and through the dynamic changes in the search landscape that result from these searches. The main hypothesis is that evolutionary computation can be used to discover effective strategies for CMAS; this hypothesis is verified in a series of experiments on the NK model, i.e.\ partially correlated and tunably rugged fitness landscapes. Different specialized strategies are evolved for each different competitive environment, and also general strategies that perform well across environments. These strategies are more effective and more complex than hand-designed strategies and a strategy based on traditional tree search. Using a novel spherical visualization of such landscapes, insight is gained about how successful strategies work, e.g.\ by tracking positive changes in the landscape. The article thus provides a possible framework for studying various human creative activities as competitive multi-agent search in the future.
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Submitted 1 July, 2023; v1 submitted 18 June, 2023;
originally announced June 2023.
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Accelerating Evolution Through Gene Masking and Distributed Search
Authors:
Hormoz Shahrzad,
Risto Miikkulainen
Abstract:
In building practical applications of evolutionary computation (EC), two optimizations are essential. First, the parameters of the search method need to be tuned to the domain in order to balance exploration and exploitation effectively. Second, the search method needs to be distributed to take advantage of parallel computing resources. This paper presents BLADE (BLAnket Distributed Evolution) as…
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In building practical applications of evolutionary computation (EC), two optimizations are essential. First, the parameters of the search method need to be tuned to the domain in order to balance exploration and exploitation effectively. Second, the search method needs to be distributed to take advantage of parallel computing resources. This paper presents BLADE (BLAnket Distributed Evolution) as an approach to achieving both goals simultaneously. BLADE uses blankets (i.e., masks on the genetic representation) to tune the evolutionary operators during the search, and implements the search through hub-and-spoke distribution. In the paper, (1) the blanket method is formalized for the (1 + 1)EA case as a Markov chain process. Its effectiveness is then demonstrated by analyzing dominant and subdominant eigenvalues of stochastic matrices, suggesting a generalizable theory; (2) the fitness-level theory is used to analyze the distribution method; and (3) these insights are verified experimentally on three benchmark problems, showing that both blankets and distribution lead to accelerated evolution. Moreover, a surprising synergy emerges between them: When combined with distribution, the blanket approach achieves more than $n$-fold speedup with $n$ clients in some cases. The work thus highlights the importance and potential of optimizing evolutionary computation in practical applications.
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Submitted 23 April, 2023; v1 submitted 13 February, 2023;
originally announced February 2023.
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Efficient Activation Function Optimization through Surrogate Modeling
Authors:
Garrett Bingham,
Risto Miikkulainen
Abstract:
Carefully designed activation functions can improve the performance of neural networks in many machine learning tasks. However, it is difficult for humans to construct optimal activation functions, and current activation function search algorithms are prohibitively expensive. This paper aims to improve the state of the art through three steps: First, the benchmark datasets Act-Bench-CNN, Act-Bench…
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Carefully designed activation functions can improve the performance of neural networks in many machine learning tasks. However, it is difficult for humans to construct optimal activation functions, and current activation function search algorithms are prohibitively expensive. This paper aims to improve the state of the art through three steps: First, the benchmark datasets Act-Bench-CNN, Act-Bench-ResNet, and Act-Bench-ViT were created by training convolutional, residual, and vision transformer architectures from scratch with 2,913 systematically generated activation functions. Second, a characterization of the benchmark space was developed, leading to a new surrogate-based method for optimization. More specifically, the spectrum of the Fisher information matrix associated with the model's predictive distribution at initialization and the activation function's output distribution were found to be highly predictive of performance. Third, the surrogate was used to discover improved activation functions in several real-world tasks, with a surprising finding: a sigmoidal design that outperformed all other activation functions was discovered, challenging the status quo of always using rectifier nonlinearities in deep learning. Each of these steps is a contribution in its own right; together they serve as a practical and theoretical foundation for further research on activation function optimization.
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Submitted 8 November, 2023; v1 submitted 13 January, 2023;
originally announced January 2023.
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Shortest Edit Path Crossover: A Theory-driven Solution to the Permutation Problem in Evolutionary Neural Architecture Search
Authors:
Xin Qiu,
Risto Miikkulainen
Abstract:
Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to t…
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Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to take advantage of them in NAS. The main obstacle is believed to be the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This paper presents the first theoretical analysis of the behaviors of mutation, crossover and RL in black-box NAS, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown theoretically to overcome the permutation problem, and as a result, have a better expected improvement compared to mutation, standard crossover and RL. Further, it empirically outperform these other methods on state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of population-based search in NAS, and the underlying theory can serve as a foundation for deeper understanding of black-box NAS methods in general.
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Submitted 28 May, 2023; v1 submitted 25 October, 2022;
originally announced October 2022.
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EVOTER: Evolution of Transparent Explainable Rule-sets
Authors:
Hormoz Shahrzad,
Babak Hodjat,
Risto Miikkulainen
Abstract:
Most AI systems are black boxes generating reasonable outputs for given inputs. Some domains, however, have explainability and trustworthiness requirements that cannot be directly met by these approaches. Various methods have therefore been developed to interpret black-box models after training. This paper advocates an alternative approach where the models are transparent and explainable to begin…
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Most AI systems are black boxes generating reasonable outputs for given inputs. Some domains, however, have explainability and trustworthiness requirements that cannot be directly met by these approaches. Various methods have therefore been developed to interpret black-box models after training. This paper advocates an alternative approach where the models are transparent and explainable to begin with. This approach, EVOTER, evolves rule-sets based on simple logical expressions. The approach is evaluated in several prediction/classification and prescription/policy search domains with and without a surrogate. It is shown to discover meaningful rule sets that perform similarly to black-box models. The rules can provide insight into the domain, and make biases hidden in the data explicit. It may also be possible to edit them directly to remove biases and add constraints. EVOTER thus forms a promising foundation for building trustworthy AI systems for real-world applications in the future.
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Submitted 25 October, 2024; v1 submitted 21 April, 2022;
originally announced April 2022.
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Effective Mutation Rate Adaptation through Group Elite Selection
Authors:
Akarsh Kumar,
Bo Liu,
Risto Miikkulainen,
Peter Stone
Abstract:
Evolutionary algorithms are sensitive to the mutation rate (MR); no single value of this parameter works well across domains. Self-adaptive MR approaches have been proposed but they tend to be brittle: Sometimes they decay the MR to zero, thus halting evolution. To make self-adaptive MR robust, this paper introduces the Group Elite Selection of Mutation Rates (GESMR) algorithm. GESMR co-evolves a…
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Evolutionary algorithms are sensitive to the mutation rate (MR); no single value of this parameter works well across domains. Self-adaptive MR approaches have been proposed but they tend to be brittle: Sometimes they decay the MR to zero, thus halting evolution. To make self-adaptive MR robust, this paper introduces the Group Elite Selection of Mutation Rates (GESMR) algorithm. GESMR co-evolves a population of solutions and a population of MRs, such that each MR is assigned to a group of solutions. The resulting best mutational change in the group, instead of average mutational change, is used for MR selection during evolution, thus avoiding the vanishing MR problem. With the same number of function evaluations and with almost no overhead, GESMR converges faster and to better solutions than previous approaches on a wide range of continuous test optimization problems. GESMR also scales well to high-dimensional neuroevolution for supervised image-classification tasks and for reinforcement learning control tasks. Remarkably, GESMR produces MRs that are optimal in the long-term, as demonstrated through a comprehensive look-ahead grid search. Thus, GESMR and its theoretical and empirical analysis demonstrate how self-adaptation can be harnessed to improve performance in several applications of evolutionary computation.
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Submitted 10 April, 2022;
originally announced April 2022.
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DIAS: A Domain-Independent Alife-Based Problem-Solving System
Authors:
Babak Hodjat,
Hormoz Shahrzad,
Risto Miikkulainen
Abstract:
A domain-independent problem-solving system based on principles of Artificial Life is introduced. In this system, DIAS, the input and output dimensions of the domain are laid out in a spatial medium. A population of actors, each seeing only part of this medium, solves problems collectively in it. The process is independent of the domain and can be implemented through different kinds of actors. Thr…
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A domain-independent problem-solving system based on principles of Artificial Life is introduced. In this system, DIAS, the input and output dimensions of the domain are laid out in a spatial medium. A population of actors, each seeing only part of this medium, solves problems collectively in it. The process is independent of the domain and can be implemented through different kinds of actors. Through a set of experiments on various problem domains, DIAS is shown able to solve problems with different dimensionality and complexity, to require no hyperparameter tuning for new problems, and to exhibit lifelong learning, i.e. adapt rapidly to run-time changes in the problem domain, and do it better than a standard non-collective approach. DIAS therefore demonstrates a role for Alife in building scalable, general, and adaptive problem-solving systems.
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Submitted 3 May, 2022; v1 submitted 14 March, 2022;
originally announced March 2022.
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Simple Genetic Operators are Universal Approximators of Probability Distributions (and other Advantages of Expressive Encodings)
Authors:
Elliot Meyerson,
Xin Qiu,
Risto Miikkulainen
Abstract:
This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from an arbitrary distribution of child phenotypes. Such encodings are termed \emph{expressive encodings} in this paper. Universal function approximators, including…
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This paper characterizes the inherent power of evolutionary algorithms. This power depends on the computational properties of the genetic encoding. With some encodings, two parents recombined with a simple crossover operator can sample from an arbitrary distribution of child phenotypes. Such encodings are termed \emph{expressive encodings} in this paper. Universal function approximators, including popular evolutionary substrates of genetic programming and neural networks, can be used to construct expressive encodings. Remarkably, this approach need not be applied only to domains where the phenotype is a function: Expressivity can be achieved even when optimizing static structures, such as binary vectors. Such simpler settings make it possible to characterize expressive encodings theoretically: Across a variety of test problems, expressive encodings are shown to achieve up to super-exponential convergence speed-ups over the standard direct encoding. The conclusion is that, across evolutionary computation areas as diverse as genetic programming, neuroevolution, genetic algorithms, and theory, expressive encodings can be a key to understanding and realizing the full power of evolution.
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Submitted 2 August, 2022; v1 submitted 19 February, 2022;
originally announced February 2022.
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NeuroBack: Improving CDCL SAT Solving using Graph Neural Networks
Authors:
Wenxi Wang,
Yang Hu,
Mohit Tiwari,
Sarfraz Khurshid,
Kenneth McMillan,
Risto Miikkulainen
Abstract:
Propositional satisfiability (SAT) is an NP-complete problem that impacts many research fields, such as planning, verification, and security. Mainstream modern SAT solvers are based on the Conflict-Driven Clause Learning (CDCL) algorithm. Recent work aimed to enhance CDCL SAT solvers using Graph Neural Networks (GNNs). However, so far this approach either has not made solving more effective, or re…
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Propositional satisfiability (SAT) is an NP-complete problem that impacts many research fields, such as planning, verification, and security. Mainstream modern SAT solvers are based on the Conflict-Driven Clause Learning (CDCL) algorithm. Recent work aimed to enhance CDCL SAT solvers using Graph Neural Networks (GNNs). However, so far this approach either has not made solving more effective, or required substantial GPU resources for frequent online model inferences. Aiming to make GNN improvements practical, this paper proposes an approach called NeuroBack, which builds on two insights: (1) predicting phases (i.e., values) of variables appearing in the majority (or even all) of the satisfying assignments are essential for CDCL SAT solving, and (2) it is sufficient to query the neural model only once for the predictions before the SAT solving starts. Once trained, the offline model inference allows NeuroBack to execute exclusively on the CPU, removing its reliance on GPU resources. To train NeuroBack, a new dataset called DataBack containing 120,286 data samples is created. NeuroBack is implemented as an enhancement to a state-of-the-art SAT solver called Kissat. As a result, it allowed Kissat to solve up to 5.2% and 7.4% more problems on two recent SAT competition problem sets, SATCOMP-2022 and SATCOMP-2023, respectively. NeuroBack therefore shows how machine learning can be harnessed to improve SAT solving in an effective and practical manner.
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Submitted 8 May, 2024; v1 submitted 26 October, 2021;
originally announced October 2021.
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AutoInit: Analytic Signal-Preserving Weight Initialization for Neural Networks
Authors:
Garrett Bingham,
Risto Miikkulainen
Abstract:
Neural networks require careful weight initialization to prevent signals from exploding or vanishing. Existing initialization schemes solve this problem in specific cases by assuming that the network has a certain activation function or topology. It is difficult to derive such weight initialization strategies, and modern architectures therefore often use these same initialization schemes even thou…
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Neural networks require careful weight initialization to prevent signals from exploding or vanishing. Existing initialization schemes solve this problem in specific cases by assuming that the network has a certain activation function or topology. It is difficult to derive such weight initialization strategies, and modern architectures therefore often use these same initialization schemes even though their assumptions do not hold. This paper introduces AutoInit, a weight initialization algorithm that automatically adapts to different neural network architectures. By analytically tracking the mean and variance of signals as they propagate through the network, AutoInit appropriately scales the weights at each layer to avoid exploding or vanishing signals. Experiments demonstrate that AutoInit improves performance of convolutional, residual, and transformer networks across a range of activation function, dropout, weight decay, learning rate, and normalizer settings, and does so more reliably than data-dependent initialization methods. This flexibility allows AutoInit to initialize models for everything from small tabular tasks to large datasets such as ImageNet. Such generality turns out particularly useful in neural architecture search and in activation function discovery. In these settings, AutoInit initializes each candidate appropriately, making performance evaluations more accurate. AutoInit thus serves as an automatic configuration tool that makes design of new neural network architectures more robust. The AutoInit package provides a wrapper around TensorFlow models and is available at https://github.com/cognizant-ai-labs/autoinit.
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Submitted 29 November, 2022; v1 submitted 18 September, 2021;
originally announced September 2021.
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Evolving GAN Formulations for Higher Quality Image Synthesis
Authors:
Santiago Gonzalez,
Mohak Kant,
Risto Miikkulainen
Abstract:
Generative Adversarial Networks (GANs) have extended deep learning to complex generation and translation tasks across different data modalities. However, GANs are notoriously difficult to train: Mode collapse and other instabilities in the training process often degrade the quality of the generated results, such as images. This paper presents a new technique called TaylorGAN for improving GANs by…
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Generative Adversarial Networks (GANs) have extended deep learning to complex generation and translation tasks across different data modalities. However, GANs are notoriously difficult to train: Mode collapse and other instabilities in the training process often degrade the quality of the generated results, such as images. This paper presents a new technique called TaylorGAN for improving GANs by discovering customized loss functions for each of its two networks. The loss functions are parameterized as Taylor expansions and optimized through multiobjective evolution. On an image-to-image translation benchmark task, this approach qualitatively improves generated image quality and quantitatively improves two independent GAN performance metrics. It therefore forms a promising approach for applying GANs to more challenging tasks in the future.
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Submitted 28 October, 2021; v1 submitted 17 February, 2021;
originally announced February 2021.
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The Traveling Observer Model: Multi-task Learning Through Spatial Variable Embeddings
Authors:
Elliot Meyerson,
Risto Miikkulainen
Abstract:
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved; it cares only about measurement locations and their values. This perspective leads to a machine learning framework in which seemingly unrelated tasks can be so…
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This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved; it cares only about measurement locations and their values. This perspective leads to a machine learning framework in which seemingly unrelated tasks can be solved by a single model, by embedding their input and output variables into a shared space. An implementation of the framework is developed in which these variable embeddings are learned jointly with internal model parameters. In experiments, the approach is shown to (1) recover intuitive locations of variables in space and time, (2) exploit regularities across related datasets with completely disjoint input and output spaces, and (3) exploit regularities across seemingly unrelated tasks, outperforming task-specific single-task models and multi-task learning alternatives. The results suggest that even seemingly unrelated tasks may originate from similar underlying processes, a fact that the traveling observer model can use to make better predictions.
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Submitted 22 March, 2021; v1 submitted 5 October, 2020;
originally announced October 2020.
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Detecting Misclassification Errors in Neural Networks with a Gaussian Process Model
Authors:
Xin Qiu,
Risto Miikkulainen
Abstract:
As neural network classifiers are deployed in real-world applications, it is crucial that their failures can be detected reliably. One practical solution is to assign confidence scores to each prediction, then use these scores to filter out possible misclassifications. However, existing confidence metrics are not yet sufficiently reliable for this role. This paper presents a new framework that pro…
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As neural network classifiers are deployed in real-world applications, it is crucial that their failures can be detected reliably. One practical solution is to assign confidence scores to each prediction, then use these scores to filter out possible misclassifications. However, existing confidence metrics are not yet sufficiently reliable for this role. This paper presents a new framework that produces a quantitative metric for detecting misclassification errors. This framework, RED, builds an error detector on top of the base classifier and estimates uncertainty of the detection scores using Gaussian Processes. Experimental comparisons with other error detection methods on 125 UCI datasets demonstrate that this approach is effective. Further implementations on two probabilistic base classifiers and two large deep learning architecture in vision tasks further confirm that the method is robust and scalable. Third, an empirical analysis of RED with out-of-distribution and adversarial samples shows that the method can be used not only to detect errors but also to understand where they come from. RED can thereby be used to improve trustworthiness of neural network classifiers more broadly in the future.
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Submitted 2 January, 2022; v1 submitted 5 October, 2020;
originally announced October 2020.
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Effective Regularization Through Loss-Function Metalearning
Authors:
Santiago Gonzalez,
Xin Qiu,
Risto Miikkulainen
Abstract:
Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training, and improved data utilization. A likely reason is that such functions discourage overfitting, leading to effective regularization. This paper demonstrates theore…
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Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training, and improved data utilization. A likely reason is that such functions discourage overfitting, leading to effective regularization. This paper demonstrates theoretically that this is indeed the case for TaylorGLO. Learning rule decomposition reveals that evolved loss functions balance two factors: the pull toward zero error, and a push away from it to avoid overfitting. This is a general principle that may be used to understand other regularization techniques as well (as demonstrated in this paper for label smoothing). The theoretical analysis leads to a constraint that can be utilized to find more effective loss functions in practice; the mechanism also results in networks that are more robust (as demonstrated in this paper with adversarial inputs). The analysis in this paper thus constitutes a first step towards understanding regularization, and demonstrates the power of evolutionary neural architecture search in general.
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Submitted 10 June, 2025; v1 submitted 2 October, 2020;
originally announced October 2020.
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Creative AI Through Evolutionary Computation: Principles and Examples
Authors:
Risto Miikkulainen
Abstract:
The main power of artificial intelligence is not in modeling what we already know, but in creating solutions that are new. Such solutions exist in extremely large, high-dimensional, and complex search spaces. Population-based search techniques, i.e. variants of evolutionary computation, are well suited to finding them. These techniques make it possible to find creative solutions to practical probl…
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The main power of artificial intelligence is not in modeling what we already know, but in creating solutions that are new. Such solutions exist in extremely large, high-dimensional, and complex search spaces. Population-based search techniques, i.e. variants of evolutionary computation, are well suited to finding them. These techniques make it possible to find creative solutions to practical problems in the real world, making creative AI through evolutionary computation the likely "next deep learning."
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Submitted 14 February, 2021; v1 submitted 4 August, 2020;
originally announced August 2020.
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Characterizing the Effect of Sentence Context on Word Meanings: Mapping Brain to Behavior
Authors:
N. Aguirre-Celis,
R. Miikkulainen
Abstract:
Semantic feature models have become a popular tool for prediction and interpretation of fMRI data. In particular, prior work has shown that differences in the fMRI patterns in sentence reading can be explained by context-dependent changes in the semantic feature representations of the words. However, whether the subjects are aware of such changes and agree with them has been an open question. This…
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Semantic feature models have become a popular tool for prediction and interpretation of fMRI data. In particular, prior work has shown that differences in the fMRI patterns in sentence reading can be explained by context-dependent changes in the semantic feature representations of the words. However, whether the subjects are aware of such changes and agree with them has been an open question. This paper aims to answer this question through a human-subject study. Subjects were asked to judge how the word change from their generic meaning when the words were used in specific sentences. The judgements were consistent with the model predictions well above chance. Thus, the results support the hypothesis that word meaning change systematically depending on sentence context.
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Submitted 12 January, 2021; v1 submitted 27 July, 2020;
originally announced July 2020.
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Generalization of Agent Behavior through Explicit Representation of Context
Authors:
Cem C Tutum,
Suhaib Abdulquddos,
Risto Miikkulainen
Abstract:
In order to deploy autonomous agents in digital interactive environments, they must be able to act robustly in unseen situations. The standard machine learning approach is to include as much variation as possible into training these agents. The agents can then interpolate within their training, but they cannot extrapolate much beyond it. This paper proposes a principled approach where a context mo…
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In order to deploy autonomous agents in digital interactive environments, they must be able to act robustly in unseen situations. The standard machine learning approach is to include as much variation as possible into training these agents. The agents can then interpolate within their training, but they cannot extrapolate much beyond it. This paper proposes a principled approach where a context module is coevolved with a skill module in the game. The context module recognizes the temporal variation in the game and modulates the outputs of the skill module so that the action decisions can be made robustly even in previously unseen situations. The approach is evaluated in the Flappy Bird and LunarLander video games, as well as in the CARLA autonomous driving simulation. The Context+Skill approach leads to significantly more robust behavior in environments that require extrapolation beyond training. Such a principled generalization ability is essential in deploying autonomous agents in real-world tasks, and can serve as a foundation for continual adaptation as well.
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Submitted 9 February, 2021; v1 submitted 18 June, 2020;
originally announced June 2020.
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Discovering Parametric Activation Functions
Authors:
Garrett Bingham,
Risto Miikkulainen
Abstract:
Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and therefore the rectified linear unit (ReLU) is still the most commonly used. This paper proposes a technique for customizing activation functions automatically, resultin…
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Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and therefore the rectified linear unit (ReLU) is still the most commonly used. This paper proposes a technique for customizing activation functions automatically, resulting in reliable improvements in performance. Evolutionary search is used to discover the general form of the function, and gradient descent to optimize its parameters for different parts of the network and over the learning process. Experiments with four different neural network architectures on the CIFAR-10 and CIFAR-100 image classification datasets show that this approach is effective. It discovers both general activation functions and specialized functions for different architectures, consistently improving accuracy over ReLU and other activation functions by significant margins. The approach can therefore be used as an automated optimization step in applying deep learning to new tasks.
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Submitted 21 January, 2022; v1 submitted 4 June, 2020;
originally announced June 2020.
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From Prediction to Prescription: Evolutionary Optimization of Non-Pharmaceutical Interventions in the COVID-19 Pandemic
Authors:
Risto Miikkulainen,
Olivier Francon,
Elliot Meyerson,
Xin Qiu,
Elisa Canzani,
Babak Hodjat
Abstract:
Several models have been developed to predict how the COVID-19 pandemic spreads, and how it could be contained with non-pharmaceutical interventions (NPIs) such as social distancing restrictions and school and business closures. This paper demonstrates how evolutionary AI could be used to facilitate the next step, i.e. determining most effective intervention strategies automatically. Through evolu…
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Several models have been developed to predict how the COVID-19 pandemic spreads, and how it could be contained with non-pharmaceutical interventions (NPIs) such as social distancing restrictions and school and business closures. This paper demonstrates how evolutionary AI could be used to facilitate the next step, i.e. determining most effective intervention strategies automatically. Through evolutionary surrogate-assisted prescription (ESP), it is possible to generate a large number of candidate strategies and evaluate them with predictive models. In principle, strategies can be customized for different countries and locales, and balance the need to contain the pandemic and the need to minimize their economic impact. While still limited by available data, early experiments suggest that workplace and school restrictions are the most important and need to be designed carefully. It also demonstrates that results of lifting restrictions can be unreliable, and suggests creative ways in which restrictions can be implemented softly, e.g. by alternating them over time. As more data becomes available, the approach can be increasingly useful in dealing with COVID-19 as well as possible future pandemics.
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Submitted 1 August, 2020; v1 submitted 27 May, 2020;
originally announced May 2020.
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Using context to adapt to sensor drift
Authors:
J. Warner,
A. Devaraj,
R. Miikkulainen
Abstract:
Lifelong development allows animals and machines to adapt to changes in the environment as well as in their own systems, such as wear and tear in sensors and actuators. An important use case of such adaptation is industrial odor-sensing. Metal-oxide-based sensors can be used to detect gaseous compounds in the air; however, the gases interact with the sensors, causing their responses to change over…
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Lifelong development allows animals and machines to adapt to changes in the environment as well as in their own systems, such as wear and tear in sensors and actuators. An important use case of such adaptation is industrial odor-sensing. Metal-oxide-based sensors can be used to detect gaseous compounds in the air; however, the gases interact with the sensors, causing their responses to change over time in a process called sensor drift. Sensor drift is irreversible and requires frequent recalibration with additional data. This paper demonstrates that an adaptive system that represents the drift as context for the skill of odor sensing achieves the same goal automatically. After it is trained on the history of changes, a neural network predicts future contexts, allowing the context+skill sensing system to adapt to sensor drift. Evaluated on an industrial dataset of gas-sensor drift, the approach performed better than standard drift-naive and ensembling methods. In this way, the context+skill system emulates the natural ability of animal olfaction systems to adapt to a changing world, and demonstrates how it can be effective in real-world applications.
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Submitted 11 April, 2024; v1 submitted 16 March, 2020;
originally announced March 2020.
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Evolutionary Optimization of Deep Learning Activation Functions
Authors:
Garrett Bingham,
William Macke,
Risto Miikkulainen
Abstract:
The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most commonly-used in practice. This paper shows that evolutionary algorithms can discover novel activation functions that outperform ReLU. A tree-based search space of candida…
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The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most commonly-used in practice. This paper shows that evolutionary algorithms can discover novel activation functions that outperform ReLU. A tree-based search space of candidate activation functions is defined and explored with mutation, crossover, and exhaustive search. Experiments on training wide residual networks on the CIFAR-10 and CIFAR-100 image datasets show that this approach is effective. Replacing ReLU with evolved activation functions results in statistically significant increases in network accuracy. Optimal performance is achieved when evolution is allowed to customize activation functions to a particular task; however, these novel activation functions are shown to generalize, achieving high performance across tasks. Evolutionary optimization of activation functions is therefore a promising new dimension of metalearning in neural networks.
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Submitted 11 April, 2020; v1 submitted 17 February, 2020;
originally announced February 2020.
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Adapting to Unseen Environments through Explicit Representation of Context
Authors:
Cem C. Tutum,
Risto Miikkulainen
Abstract:
In order to deploy autonomous agents to domains such as autonomous driving, infrastructure management, health care, and finance, they must be able to adapt safely to unseen situations. The current approach in constructing such agents is to try to include as much variation into training as possible, and then generalize within the possible variations. This paper proposes a principled approach where…
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In order to deploy autonomous agents to domains such as autonomous driving, infrastructure management, health care, and finance, they must be able to adapt safely to unseen situations. The current approach in constructing such agents is to try to include as much variation into training as possible, and then generalize within the possible variations. This paper proposes a principled approach where a context module is coevolved with a skill module. The context module recognizes the variation and modulates the skill module so that the entire system performs well in unseen situations. The approach is evaluated in a challenging version of the Flappy Bird game where the effects of the actions vary over time. The Context+Skill approach leads to significantly more robust behavior in environments with previously unseen effects. Such a principled generalization ability is essential in deploying autonomous agents in real world tasks, and can serve as a foundation for continual learning as well.
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Submitted 29 June, 2020; v1 submitted 13 February, 2020;
originally announced February 2020.
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Effective Reinforcement Learning through Evolutionary Surrogate-Assisted Prescription
Authors:
Olivier Francon,
Santiago Gonzalez,
Babak Hodjat,
Elliot Meyerson,
Risto Miikkulainen,
Xin Qiu,
Hormoz Shahrzad
Abstract:
There is now significant historical data available on decision making in organizations, consisting of the decision problem, what decisions were made, and how desirable the outcomes were. Using this data, it is possible to learn a surrogate model, and with that model, evolve a decision strategy that optimizes the outcomes. This paper introduces a general such approach, called Evolutionary Surrogate…
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There is now significant historical data available on decision making in organizations, consisting of the decision problem, what decisions were made, and how desirable the outcomes were. Using this data, it is possible to learn a surrogate model, and with that model, evolve a decision strategy that optimizes the outcomes. This paper introduces a general such approach, called Evolutionary Surrogate-Assisted Prescription, or ESP. The surrogate is, for example, a random forest or a neural network trained with gradient descent, and the strategy is a neural network that is evolved to maximize the predictions of the surrogate model. ESP is further extended in this paper to sequential decision-making tasks, which makes it possible to evaluate the framework in reinforcement learning (RL) benchmarks. Because the majority of evaluations are done on the surrogate, ESP is more sample efficient, has lower variance, and lower regret than standard RL approaches. Surprisingly, its solutions are also better because both the surrogate and the strategy network regularize the decision-making behavior. ESP thus forms a promising foundation to decision optimization in real-world problems.
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Submitted 21 April, 2020; v1 submitted 13 February, 2020;
originally announced February 2020.