Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies

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.

Semantic Uncertainty-Guided Orchestration in Hierarchical Multi-Agent Systems

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.

Overcoming Forgetting in LLM Fine-Tuning with Evolution Strategies

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.

Efficient Pre-Training of LLMs through Truncated SVD Layers

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.

Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination

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.

Optimize Wider, Not Deeper: Consensus Aggregation for Policy Optimization

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.

Evolution With Purpose: Hierarchy-Informed Optimization of Whole-Brain Models

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.

Optimizing Chlorination in Water Distribution Systems via Surrogate-assisted Neuroevolution

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 standard reinforcement learning methods such as PPO. 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.

Quantized Evolution Strategies: High-precision Fine-tuning of Quantized LLMs at Low-precision Cost

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 high-precision 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. 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 gradient 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 method on arithmetic reasoning 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 .

Fine-Tuning Language Models to Know What They Know

Metacognition is a critical component of intelligence, specifically regarding the awareness of one's own knowledge. While humans rely on shared internal memory for both answering questions and reporting their knowledge state, this dependency in LLMs remains underexplored. This study proposes a framework to measure metacognitive ability $d_{\rm{type2}}'$ using a dual-prompt method, followed by the introduction of Evolution Strategy for Metacognitive Alignment (ESMA) to bind a model's internal knowledge to its explicit behaviors. ESMA demonstrates robust generalization across diverse untrained settings, indicating a enhancement in the model's ability to reference its own knowledge. Furthermore, parameter analysis attributes these improvements to a sparse set of significant modifications.