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arXiv2026

Genetic Algorithms for Tractable Bayesian Network Fusion via Pre-Fusion Edge Pruning

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

cs.NE↗

arXiv2026

Inference-Time Optimization of Prompt Embeddings in Diffusion Models: A Comparison of sep-CMA-ES and Adam

Deep diffusion models have revolutionized image generation by producing high-quality outputs. However, achieving specific objectives with these models often requires costly adaptations such as fine-tuning, which can be resource-intensive and time-consuming. An alternative approach is inference-time control, which involves optimizing the prompt embeddings to guide the generation process without altering the model weights. We explore prompt-embedding search optimization for the Stable Diffusion XL Turbo model, comparing a gradient-free evolutionary approach, the Separable Covariance Matrix Adaptation Evolution Strategy (sep-CMA-ES), against the widely used gradient-based optimizer Adaptive Moment Estimation (Adam). Candidate images are evaluated by a weighted objective that combines LAION Aesthetic Predictor V2 and CLIPScore, enabling explicit trade-offs between aesthetic quality and prompt-image alignment. On 36 prompts sampled from Parti Prompts (P2) under three weight settings (aesthetics-only, balanced, alignment-only), sep-CMA-ES consistently achieves higher objective values than Adam. We additionally analyze divergence from the unoptimized baseline using cosine similarity and SSIM and report the compute and memory footprints. These results suggest that sep-CMA-ES is an effective inference-time optimizer for prompt-embedding search, improving aesthetics-alignment trade-offs and resource usage without model fine-tuning.

cs.NE↗

arXiv2026

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

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

cs.NE↗

arXiv2026

Rethinking Learnability in Offline Data-driven Optimization

Black-Box Optimization (BBO) has broad applications, while traditional algorithms such as evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization has been the most popular paradigm to improve the efficiency of BBO, by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. Our experiments show that UGTL achieves the best average rank, 3.1/25, among 25 methods on Design-Bench tasks, and confirm that our trajectory construction plays a significant role in the improvement.

cs.LG↗

arXiv2026

Neural Logic, Invariance, and the Retina---McCulloch and Pitts

This chapter reconstructs the McCulloch-Pitts program as a physics of neural computation rather than the familiar cartoon of a binary neuron. The 1943 logical calculus is developed in both directions: given a net, characterize the propositions realized by its activity; given an admissible logical expression, construct a net that realizes it. We recover the original distinction between thresholded excitatory summation and absolute inhibitory veto-one the weighted-threshold form cannot preserve for arbitrarily large excitatory inputs-and read unit-time delay as the physical realization of logical depth. Recurrence is treated exactly: an autonomous, deterministic network of finitely many binary units has a finite state space, so every trajectory eventually enters a periodic orbit-a fact about finite-state dynamics, not unbounded Turing computation. A single threshold element realizes only linearly separable Boolean functions, whereas finite feedforward networks of them synthesize any Boolean function on a finite domain. We then follows McCulloch and Pitts beyond threshold logic. The 1945 heterarchy paper turns cyclic preference into an obstruction to representation by a scalar utility. The 1947 work on universals asks how a physical network can identify inputs related by nuisance transformations, developed here via group averaging and feedback canonicalization. The 1959 frog-retina study makes the adequate-stimulus question experimental, revealing parallel invariant operations before the brain proper. Spike-triggered analysis shows how a nonlinearly driven neuron can have a vanishing first-order average while second-order statistics recover its hidden selectivity: methodological failure can masquerade as physiological absence. Modern mathematical tools are used without projecting their notation onto the historical papers, and limitations of the idealization are stated explicitly.

q-bio.NC↗

arXiv2026

Memory as an Energy Landscape---Hopfield

This chapter reconstructs the Hopfield network as a physical theory of memory rather than merely an early neural-network algorithm. It begins with the problem as it stood before 1982-threshold logic, Hebbian association, correlation memories, and recurrent binary networks-and isolates what Hopfield's synthesis added: a dynamical definition of content-addressable memory, a symmetric recurrent architecture with a Lyapunov function, a Hebbian embedding of patterns in its couplings, and a physical account of basins, robustness, and graceful degradation. The binary and graded-response energy functions are derived in full, together with the signal-crosstalk decomposition governing pattern stability, the mean-field theory of retrieval at extensive load, and the zero-temperature retrieval spinodal at (alpha 0.138) established by Amit, Gutfreund, and Sompolinsky. The energy-based program is then followed through analog optimization networks, polynomial dense associative memories, exponential interactions, and modern continuous Hopfield updates, including the precise conditions under which the update becomes scaled dot-product attention. Throughout, capacity claims are tied to their disorder ensemble, scaling limit, and success criterion, showing why numerically different storage limits need not conflict. A closing assessment distinguishes established results from surviving principles, assumption-bound limitations, and open problems, treating the Hopfield network as an effective theory whose symmetry, locality, and point-neuron assumptions delimit its biological reach. Fixed-seed numerical experiments expose the mechanisms discussed but do not substitute for analytical results.

cs.NE↗

arXiv2026

LLM-Driven Joint Evolution of Coupled Heuristics Components for Routing Optimization

Heuristic design for combinatorial optimization remains heavily reliant on expert knowledge, while existing large language model (LLM)-enhanced evolutionary methods typically evolve isolated algorithmic components, even when one determines the search state on which another operates. This paper proposes LLM-driven Heuristic Components Joint Generation (LLM-HCJG), a population-based framework that jointly generates and co-evolves interdependent heuristic components under a shared design blueprint. Applied to guided local search (GLS), LLM-HCJG couples solution initialization with penalty construction and embeds the generated pair into an enhanced online search mechanism. The resulting form is further transferred from the traveling salesman problem (TSP) to the capacitated vehicle routing problem (CVRP). Theoretical analysis establishes the non-separable state-transition effects between the two components and the advantage in generation consistency. Across synthetic instances and 41 public TSPLIB/CVRPLIB benchmarks, LLM-HCJG attains consistently low optimality gaps, including best or tied-best results on 28 of 29 TSPLIB instances and all 12 CVRPLIB instances. Ablation and structural analyses further indicate that these gains are associated with cross-component compatibility and alignment rather than isolated-component recombination. These results support effective cross-instance transfer within the evaluated routing settings under limited-sample, modest-cost training.

cs.NE↗

arXiv2026

Semantics-Guided Automatic Tensorization for Multiobjective Evolutionary Algorithms: A Multi-Agent Framework

Multiobjective evolutionary algorithms (MOEAs) naturally expose population-level parallelism, but many mature implementations encode their computation in sequential program structures designed for central processing units. Exploiting modern tensor computing platforms therefore requires more than direct code translation: the implementation must be restructured without changing the defining optimization mechanism of the underlying MOEA. We formulate automatic tensorization for MOEAs as semantics-guided computational restructuring and develop Evolutionary Code Conversion (EvoCoCo), a multi-agent framework that realizes this formulation. EvoCoCo reconstructs algorithm-specific states, dependencies, operators, and update logic into a structured semantic representation and organizes them through a shared tensorization blueprint. Specialized transformation branches then explore alternative tensor realizations, while execution feedback guides validation, repair, and candidate selection. Experiments on a benchmark of 48 MOEAs evaluate migration reliability, optimization fidelity, and computational scalability. Under matched large language model backends, EvoCoCo attains higher migration reliability than direct one-shot translation. Across the benchmark suites, 88.2% of valid comparisons satisfy the predefined optimization-fidelity criterion. The tensorized implementations also exhibit increasing acceleration on graphics processing units as population size or decision dimension grows, with median measured speedups ranging from $22.6\times$ under population scaling to $80.2\times$ under decision-dimension scaling. External-source and ablation studies further assess transfer beyond the main benchmark and the roles of the major framework components.

cs.NE↗

arXiv2026

Model-Free Surrogate-Assisted Neural Architecture Search for Evolving Variable-Length Dense Blocks

Neural Architecture Search (NAS) has emerged as a powerful paradigm for automatically designing deep neural networks; however, its practical adoption is often limited by substantial computational cost. To alleviate expensive full-training evaluations, surrogate-based methods have been introduced to estimate network performance efficiently. Nevertheless, existing approaches-particularly model-based surrogates-require training many candidate architectures and involve additional optimization overhead. In this work, we propose a Model-Free Surrogate PSO Network (MFSPNet) for evolving convolutional neural network architectures. The proposed method integrates a lightweight model-free surrogate predictor within a particle swarm optimization (PSO) framework, eliminating the need for pre-trained surrogate models. Specifically, MFSPNet introduces two key contributions: (1) a validation-loss-driven exponential moving average estimator (VLE-EMA) that captures early generalization behavior for reliable architecture ranking; and (2) a block-based dense connection strategy that enables effective stacking of evolved blocks while mitigating vanishing-gradient issues. This design also facilitates transferability of learned blocks across datasets. Extensive experiments demonstrate that MFSPNet achieves competitive performance with reduced computational cost. Under a consistent training protocol with ten independent runs, the proposed method attains error rates of 3.91%, 17.68%, and 1.91% on CIFAR-10, CIFAR-100, and SVHN, respectively, along with top-1/top-5 error rates of 28.29%/12.82% on ImageNet, while requiring less than three GPU days for architecture search. Due to computational constraints, the ImageNet result is based on a single run and should be interpreted as indicative of scalability. Overall, MFSPNet provides an efficient and reliable framework for cost-aware neural architecture search.

cs.NE↗

arXiv2026

H3DNAS: Hardware-Aware ONNX-Native 3D Point Cloud Model Compression

Deploying 3D point cloud models on edge hardware such as the NVIDIA Jetson Orin Nano is severely constrained by compute and memory budgets. Existing compression methods require access to the model's original source code, rendering them inapplicable to the Open Neural Network Exchange (ONNX) binaries commonly distributed by vendors and model repositories. We present \textbf{H3DNAS}, a hardware-aware model compression framework that operates directly on ONNX computational graphs without requiring original source code, architecture class definition, or gradient access during search. H3DNAS makes three contributions: (1) a \textbf{Channel Dependency Graph (CDG)} that classifies ONNX operators into four constraint classes and formally establishes that the free parameter fraction $ρ_f$ is topological invariant, a provable compression ceiling computable in $\mathcal{O}(|V|+|E|)$; (2) a \textbf{Two-Stage Hierarchical Search} that prunes candidate architectures by $L_1$-importance channel selection, ranks them by output fidelity as a zero-shot label-free proxy, and applies GhostConv structural mutation to Pareto-optimal candidates; and (3) the \textbf{first source-code-free compression pipeline for 3D point cloud models}, operating entirely via ONNX graph surgery with no original architecture definition required. On ModelNet40, H3DNAS reduces the number of parameters in PointNet, PointNet++, and PointMLP by $65.5\%$, $43.2\%$, and $49.1\%$, respectively, while achieving $1.99\times$, $1.29\times$, and $1.67\times$ inference speedups with negligible loss in accuracy. The source code is publicly available\footnote{https://github.com/ClarityLab-Org/h3dnas}.

cs.LG↗

arXiv2026

Explainable Information Processing in Particle Swarm Optimization through Landscape and Search Behavior Analysis

Swarm-based optimization algorithms have demonstrated remarkable success in solving complex problems, yet their widespread adoption remains limited due to poor transparency in how algorithmic components influence performance. This work presents a multi-faceted explainability framework for Particle Swarm Optimization (PSO) through two complementary perspectives: landscape-based and algorithmic explainability. From the landscape-based perspective, we develop a comprehensive characterization framework using Exploratory Landscape Analysis (ELA) to quantify problem difficulty, multimodality, and ruggedness, extracting ELA meta-features, dispersion measures, and information content statistics, while a machine learning approach employing Decision Tree and Random Forest classifiers enables prediction of optimal topology-specific hyperparameter configurations for unseen problems. From the algorithmic explainability perspective, we integrate IOHxplainer for temporal convergence profiling and Search Trajectory Networks (STN) for spatial navigation mapping, proposing three novel STN metrics-Connectivity Density, Fragmentation Score, and Search Efficiency-that enhance visual explainability by quantifying topology-specific search organization and transition effectiveness. Through systematic experimentation across 24 benchmark functions in multiple dimensions with Star, Ring, and Von Neumann topologies, we establish practical guidelines for topology selection and parameter configuration. Our findings uncover the black-box nature of PSO, providing greater transparency and interpretability to swarm intelligence systems. The source code is available at https://github.com/GitNitin02/ioh_pso.

cs.NE↗

arXiv2026

Online Regime-aware Calibration for Black-box Social Simulators via Posterior-assisted Evolutionary Dynamic Optimization

Evolutionary dynamic optimization (EDO) commonly assumes that environmental changes can be detected from fitness variations and handled through random re-initialization, historical solutions, or learned transition patterns. Online calibration of black-box simulators introduces a different setting, where the dynamic objective is induced by sequential observations and a changing calibration window, rather than being controlled by explicit variables. Fitness variations therefore cannot be directly attributed to regime changes, while the unknown relationship between successive regimes limits conventional adaptation. We formulate this setting as an observation-driven dynamic optimization problem and propose PosEDO, which augments fitness-based EDO with an observation-conditioned parameter-space signal. PosEDO learns this signal online as a posterior distribution over simulator parameters from parameter-trajectory pairs generated during evolutionary evaluation, using posterior shifts for change detection and posterior samples for population adaptation. The new evaluation records are further utilized for online posterior updating without additional simulator calls. Experiments on nonstationary economic and financial simulators show that PosEDO improves calibration accuracy, optimization performance, and change-detection quality over representative EDO baselines.

cs.NE↗

arXiv2026

Evolutionary design of thermodynamic logic gates and their heat emission

Landauer's principle bounds the heat generated by logical operations, but in practice the thermodynamic cost of computation is dominated by the control systems that implement logic. CMOS gates dissipate energy far above the Landauer bound, while laboratory demonstrations of near-Landauer erasure rely on external measurement or feedback systems whose energy costs exceed that of the logic operation by many orders of magnitude. Here we use simulations to show that a genetic algorithm can program a thermodynamic computer to implement logic operations in which the total heat emitted by the control system is of a similar order of magnitude to that of the information-bearing degrees of freedom. Moreover, the computer can be programmed so that heat is drawn away from the information-bearing degrees of freedom and dissipated within the control unit, suggesting the possibility of computing architectures in which heat management is an integral part of the program design.

cond-mat.stat-mech↗

arXiv2026

Heaviside Continuity of Rolling Coefficients for Eliminating Epistemic Entropy in Large Language Models

Large language models (LLMs) generate fluent outputs that can be wrong. Unlike humans, who often exhibit cues when providing false information, LLMs produce errors that are difficult to detect because autoregressive decoding provides no mechanism for verifying intermediate reasoning before state progression. We introduce Heaviside Continuity of Rolling Coefficients (HCRC), a verification-first execution framework that reformulates inference as predicate-gated state transitions governed by a Heaviside Gate. HCRC combines model confidence with independent verification signals from a parallel worker architecture, allowing execution to advance only when predefined correctness predicates are satisfied. This prevents invalid intermediate states from propagating, reducing epistemic entropy without modifying the underlying model. We evaluate HCRC on software-engineering and reasoning tasks across thirteen proposers from four providers. On capable proposers, the gate reduces the false-completion rate (FCR) from 4--7% to 0% while remaining latency-competitive and, in some settings, faster than the unwrapped model. On weaker proposers, it converts false completions into honest halts instead of corrupting downstream state. Beyond benchmarking, HCRC has operated for months as the production control plane of an agentic coding environment, authorizing file mutations, verification-driven progress reporting, and memory compaction. These results establish HCRC as a general framework for verification-driven LLM execution, showing that reliable reasoning can be achieved through principled execution control rather than model scale alone.

cs.AI↗

arXiv2026

Shallower ReLU Network Representations via Exact Linear Algebra

We study the depth required by ReLU networks to exactly represent piecewise linear functions, focusing specifically on the maximum function. This problem has recently received significant attention in both the ML and TCS literature. We prove that $\max_n(x)=\max\{x_1,\ldots,x_n\}$ is exactly representable with two hidden layers for every $n\leq 12$. Previously, this was only known up to $n\leq5$ [Bakaev, Brunck, Hertrich, Stade, Yehudayoff, STOC'26]. We obtain our constructions through an exact computer-assisted search within a space of candidate solutions: After a symmetry reduction, we obtain a finite system of linear equations over $\mathbb{Q}$ such that any solution yields a valid representation of the maximum function. The resulting constructions have a structured first hidden layer, which enables recursive substitution into deeper networks. This yields an exact ReLU representation of $\max_n$ with at most $\lceil \log_6(n/2) \rceil+1$ hidden layers. Consequently, every continuous piecewise-linear function on $\mathbb{R}^d$ admits an exact representation with at most $\lceil\log_6((d+1)/2)\rceil+1$ hidden layers; in particular, two hidden layers suffice for $d\leq 11$. Again, these results improve upon [Bakaev, Brunck, Hertrich, Stade, Yehudayoff, STOC'26], who proved analogous logarithmic bounds with base three.

cs.LG↗

arXiv2026

GeoPAR: Large-Scale Multi-Agent Combinatorial Optimization with Geometry-Guided Parallel Autoregressive Learning

Multi-agent combinatorial optimization problems are notoriously challenging due to their NP-hard nature. Recent parallel autoregressive neural solvers improve inference efficiency by allowing agents to make decisions simultaneously, but their performance often degrades on large-scale instances. This is largely attributable to weak modeling of local geometric structures and the fact that conflicting task selections are handled only after action generation. To address these limitations, we propose GeoPAR, a geometry-guided parallel autoregressive reinforcement learning framework for scalable multi-agent combinatorial optimization. GeoPAR integrates three key components: (1) a projection-window sparse geometry mechanism that builds lightweight local candidate neighborhoods through multi-directional projections, (2) sparse edge-biased attention that injects these geometric relations into node representations, and (3) cache-guided conflict-aware assignment that reuses the geometric cache during decoding to suppress duplicate selections of exclusive tasks. Experiments on heterogeneous vehicle routing and open multi-depot pickup-and-delivery problems show that GeoPAR improves large-scale zero-shot generalization while substantially reducing rollout steps and maintaining efficient inference.

cs.LG↗

arXiv2026

Self-Reports Are Not Verification: Environment-Grounded Auditing of LLM Operators in Evolutionary Search

Language model agents increasingly propose actions, observe external feedback, and explain their own behavior. Their confidence and rationales are convenient monitoring signals, but convenience is not verification. We introduce an environment-grounded audit in which every intermediate proposal receives an exact outcome. A language model operates an evolutionary Contexto search whose feedback function assigns every valid guess an exact rank without human annotation. Across 200 runs spanning five configurations and three model families, four reporting configurations produce 12,249 self-reports. We test three assumptions: stated confidence is calibrated, inherited rationales affect later proposals, and fitness-based selection improves report quality. All three fail. Operators overstate top-100 success by factors of 4.8 to 9.3, while calibration and discrimination dissociate across model families. Controlled interventions on 754 inherited rationales bound any measured benefit of the genuine rationale to roughly 250 ranks. Neither fitness-based nor random selection produces a detectable selection differential or parent-to-offspring transmission in report accuracy, despite sharply different search behavior. Agent self-reports should therefore be treated as claims to verify against the environment, not as evidence of their own reliability.

cs.AI↗

arXiv2026

Denoising Diffusion Generative Models Secretly Calculate Attentions

Denoising diffusion models are the dominant architecture for image generation, whereas most natural language generation and modeling are primarily handled by well-known transformer architectures employing attention mechanism. Here, we show that diffusion models also inherently use an attention mechanism very similar to that of transformers. Therefore, attention emerges as a universal machine learning principle, based on a general training objective. We also show similarities in basic functional principle of auto-encoders and attention-based models. These equivalences allows us to interchange these designs based on practical requirements. As an example, we can reformulate the diffusion framework to reduce the lengthy training process and computation-intensive image generation. Using this approach, a simplified algorithm is proposed for image generation which is based on attention mechanism. Results show that the attention-based implementation achieves comparable performance with significantly less effort and computational resources.

cs.AI↗