Papers

High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit exceptional storage capabilities and robustness. Previous empirical studies identified a hyperparameter regime, the "Ridge of Optimization," where attractor stability is maximized. However, the geometric nature of this regime and the optimization dynamics required to reach it have remained unclear. In this paper, we investigate the static geometry of the parameter space and the learning trajectory of Gradient Descent (GD) in KLR-trained Hopfield networks. Using the eigenvalue spectrum of the Hessian, we reveal that the Ridge corresponds to a phase boundary located adjacent to a rank-1 spectral collapse, acting as a geometric singularity where the principal curvature is massively amplified. Furthermore, we demonstrate that the learning dynamics exhibit a transient self-stabilizing behavior driven by the Edge of Stability (EoS) phenomenon. Rather than seeking flat regions, the network parameters are driven toward a state where the local curvature dynamically equilibrates near the stability limit dictated by the learning rate, allowing the optimization to survive the initial instability. We provide analytical derivations for both the rank-1 asymptotic collapse and the dynamic feedback loop governing this equilibration. These findings suggest that optimal, high-capacity memory representations are not formed in flat minima, but are dynamically sculpted at the highly curved boundaries of geometric singularities.

High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit a "Ridge of Optimization" characterized by extreme stability and a highly skewed weight spectrum. However, the dynamical process by which learning converges to this critical regime has remained unclear. This paper provides a geometric analysis of the learning trajectories on the statistical manifold of a KLR-trained Hopfield network. By comparing the paths of Gradient Descent (GD) and Natural Gradient Descent (NGD), we elucidate the mechanisms governing the optimization process. Our analysis reveals that learning on the Ridge proceeds in two distinct phases. We show that the extreme curvature of the Ridge causes standard GD to follow a highly oscillatory, non-geodesic path. In stark contrast, NGD explicitly corrects for this geometry, following the ideal geodesic path and completely overcoming the instabilities faced by GD. We demonstrate experimentally that NGD not only converges significantly faster but also achieves a solution with superior generalization performance. These results establish that the highly structured geometry of the Ridge is optimally suited for information-geometric optimization, providing a new perspective on the interplay between learning dynamics and emergent representation geometry.

UAVs have emerged as highly flexible platforms for data sensing in Wireless Sensor Networks (WSNs). Path planning for UAVs in such tasks plays a key role to assure remote sensing effectiveness and friendly energy consumption. However, existing approaches show two key limitations: i) they are primarily hand-crafted with certain design biases that harm adaptation on unseen tasks. ii) they predominantly assume idealized spatial complexities of actual environments through simplified simulation, causing them to underperform during real-world deployment. In this paper, we propose a novel learning-assisted planning framework, termed Landscape-Aware Meta Differential Evolution (LAMDE), to tackle the mentioned limitations. The major contributions come from the following aspects. We first re-formulate such UAV path planning problem to embrace challenging constraints. To efficiently navigate this highly constrained space, we propose a bi-level learning to optimize approach, where the meta-level is a trainable algorithm configuration policy that meta-learns an adaptable planning strategy for low-level planning algorithm. To address the potential training data scarcity and distribution shift in real-world environments, we introduce a landscape-aware automatic augmentation scheme that enriches training data. At the low-level, a Differential Evolution algorithm is deployed for solving the path planning tasks. To enhance the solving flexibility, we further design a variable-length encoding strategy that dynamically prunes redundant hover points and optimizes continuous flight parameters concurrently within a unified search space. Based on all proposed designs, we meta-train LAMDE and compare it with representative baselines. Comprehensive experiments demonstrate that LAMDE achieves state-of-the-art performance on the tested complex UAV path planning tasks in WSN data collection scenarios.

Developmental encodings are often motivated by the expectation that a structured genotype-to-phenotype process can improve evolvability, robustness, and adaptation. Yet an encoding that expands phenotypic variation may simultaneously make useful parental structure harder to preserve under mutation and recombination. We test this trade-off in a controlled evolutionary-robotics benchmark comparing three matched representations: direct encoding, a static generative encoding, and a temporal zygotic developmental encoding. All three conditions use 34 genome parameters, 34 adult-controller parameters, identical initial genome matrices, the same optimizer, the same mutation and crossover operators, the same environments, and the same number of fitness evaluations. Across 30 paired evolutionary runs per representation, developmental encoding does not reliably exceed direct encoding in final training or out-of-distribution fitness. It does, however, substantially increase final population phenotypic diversity and mutant-reachable phenotype diversity. The same representation exhibits lower mutation viability, lower genotype–phenotype locality, sharply reduced crossover offspring fitness and viability, and increased recombination novelty. Continued developmental dynamics also attenuate damage applied early in development relative to otherwise identical late damage. These results identify a representation-level trade-off: development can enlarge the neighborhood of reachable phenotypes and provide within-development damage attenuation while degrading the local inheritance of already-adapted structure. We argue that developmental encodings should therefore be evaluated not by performance alone, but by a joint geometry of generativity, locality, robustness, and inheritance compatibility.

The hippocampus, a key brain region for learning and memory, exhibits rich structural diversity, sparse communication, and robust dynamics with incredible energy efficiency. It offers promising insights for novel computing capabilities, particularly when co-designed with emerging hardware technologies. In this work, we draw inspiration from the rodent CA3 hippocampal subregion to develop the first spiking neural network with neuronal diversity and biologically-realistic resting state dynamics demonstrated on memristor hardware. We propose a network downscaling methodology utilizing a 4-prong objective function and demonstrate a small-scale CA3-inspired network with 179 Izhikevich-modeled neurons, 3 neuronal types and 17,996 synapses with similar resting-state dynamics as the orders-of-magnitude larger full-scale network. The small-scale network is mapped to an FPGA/memristor platform using a greedy algorithm and 18,316 memristors. Benefiting from memristor noise, the hardware implementation shows continuous periodic behavior, outperforming simulated hardware. This work showcases the potential of biologically-realistic algorithms on emerging hardware for neuromorphic computing.

Astrocytes are non-neuronal glial cells that are receiving widespread attention due to their emerging role in neural computation. In this paper, we propose and study dynamical mechanisms by which astrocytes may augment the ability of neural networks to infer context in reinforcement learning (RL) settings. We construct a biologically inspired, two-level dynamical neural-astrocyte network with distinct spatial and temporal organization. We train this model on a hierarchical multi-context task that requires the agent to infer changes in latent task rules based on derived rewards. We find that in this setting, astrocytes enable evidence accumulation of changes in context and subsequent context-specific modulation of neural dynamics. We show that these functions are implemented via two dynamical mechanisms: (i) reward-induced bifurcations that relocate an asymptotically stable attractor into different, context-specific regions of state space, and (ii) the relative shallowness of these attractors, mediated by the entropy of the environment, giving rise to behavioral stickiness. Together, these mechanisms amount to a hybrid automaton, in which uncertainty accumulates until, eventually, the neural dynamics are switched to a new context. This model provides a neuro-dynamic schema, compatible with neural-astrocyte biology and prior empirical observations, for how astrocytes may integrate information from the periphery and drive contextual changes in neural circuits.

We study a practical question: can a small correction module fix errors in a frozen language model's outputs without degrading its base capabilities? We propose CRN v2, a lightweight logit-level correction module (~34M trainable parameters, 0.73% of the 4.65B text module) that sits atop a fully frozen Gemma 4 E2B model. The base model is never updated; only the correction module learns, via supervised fine-tuning followed by reference-free DPO on 83,400 error-correction pairs. On a 60-question domain exam (CEHRI: Certified Human-Robot Intelligence, covering facts, arithmetic, and implicit-goal reasoning), CRN v2 corrects 53.3% of base-model errors (reworded variant: 43.3%) while showing no degradation on tested capability benchmarks (MMLU/BoolQ N=200; car-wash N=8). A LoRA baseline at the matched CRN v1 budget (6.6M params, rank 19) achieves 83.3% correction but suffers 30-75% capability loss on the same benchmarks – the correction-capability tradeoff. An ablation shows that the KL preservation term (lambda=0.1) is critical: lowering it to 0.01 degrades correction to 35.0%. A hidden-state injection variant at earlier layers (1.6M params, SFT-only) reaches 50.0%/55.8% but does not exceed logit correction; shallower injection (layer 4) drops to 30.0%/28.3%; multi-depth logit correction (~35M) reaches only 40%; and longer training (5,000 SFT + 2,000 DPO) stays at 53.3% – none of the alternative configurations we tested exceeded the rank-128 logit result, consistent with a best-achieved result of ~53% rather than a floor. This is a study of a design principle (frozen base + logit correction + KL anchoring), not a claim of architectural novelty. All code, main-result weights, and evaluation scripts are released (deep variant as code only – no trained deep checkpoints).

Scientific agents contribute to hypothesis discovery by synthesizing evidence, assessing proposals, and developing new explanations. Recent systems combine scientific agents with evolutionary search through critique, comparison, and revision. However, how different forms of agent collaboration affect hypothesis quality remains an open question. Answering this question requires separating the effects of agents' scientific capabilities from those of their collaboration. A framework must therefore preserve agents' scientific roles and support rules for combining, revising, and retaining hypotheses. Building on this view, we introduce HypoEvolve, which makes collaboration explicit through successive updates to a hypothesis population. Specifically, we propose a generational genetic algorithm to coordinate specialized large language model (LLM) agents that integrate mechanistic arguments, reconsider assumptions, and assess evidence and testability. Each generation specifies how scientific judgments and new proposals reshape the population, making collaboration effects on hypothesis quality directly testable. Moreover, we design our evaluation around scientifically meaningful hypotheses that explain how a proposed intervention could work. Drug repurposing links these explanations to target-level biological claims assessed against external evidence. Specifically, we adapt DepMap and Open Targets into complementary external measures grounded in experimental, genetic, and clinical evidence. Across 34 cancer types, HypoEvolve achieves the highest scores against six baselines on both measures. DepMap selectivity reaches 0.171, versus 0.115 for the strongest baseline. Gains over single-pass generation also generalize to held-out cancer types. HypoEvolve advances a vision of autonomous science in which AI research teams achieve a capacity for discovery beyond that of individual models.

Spiking neural networks (SNNs) have shown promise for sparse, event-driven computation through stateful processing that is naturally compatible with low-power edge hardware. These properties align with cyber monitoring, where data arrives asynchronously, and malicious behavior often emerges through temporal patterns across event sequences. However, cyber streams are not composed solely of continuous numeric signals: their informative structure is also carried by categorical identifiers, irregular timing, and local behavioral context. Traditional rate- and population-based spike encodings are not naturally suited to these heterogeneous semantics, while conventional intrusion detection system (IDS) pipelines typically resolve the mismatch by converting raw events into flows, fixed aggregation windows, or dense tensors. Although useful for conventional classifiers, these transformations introduce buffering latency, obscure native temporal structure, and weaken the computational advantages of event-driven neuromorphic processing. We introduce an event-native symbolic-temporal spike encoding framework that maps heterogeneous cyber events directly into sparse, spike-compatible inputs. By assigning encoding roles to semantic identity, local frequency context, and inter-event timing, the framework preserves categorical semantics and temporal dynamics. We validate the approach on packet-level Network IDS and extend it to message-level CAN IDS, using both domains to evaluate whether the encoding exposes usable structure for recurrent SNNs operating directly on native event streams. Under edge-oriented, $\mu$Caspian-aligned hardware constraints, compact recurrent SNNs achieve strong anomaly detection performance, with an operational hybrid metric ($J_{hybrid}$) of 0.987 on Network IDS and 0.980 on CAN IDS.

Complete suffix prediction is challenging in sequential decision settings, where the same prefix can remain compatible with several plausible suffixes. We propose a graphbased metric-learning framework that reformulates complete suffix prediction as latent retrieval over process graphs. Prefixes and suffixes are represented as directed attributed graphs and encoded by edge-conditioned graph neural networks, allowing event-level activities and transition-level durations to be modelled jointly. Prefix representations are projected into the latent suffix space through a predictor trained with a joint reconstruction and contrastive objective strengthened using process-aware hard negatives. To stabilise the learned retrieval geometry, spectral normalisation, and retrieval robustness, spectral normalisation is applied to enforce a Lipschitz constraint on both encoders and predictor. Experiments on two real-life process datasets demonstrate that the proposed framework achieves the best overall results across nearly all evaluated criteria. It improves semantic suffix accuracy measured by normalized Damerau-Levenshtein distance, yields strong retrieval quality through Recall@1, Recall@5, and MRR@5, and maintains temporal plausibility according to Mean Absolute Error. These results show that graph-based latent retrieval is an effective alternative to sequential suffix prediction for recommendation-oriented process monitoring under structural and KPI-related constraints.

Large brains are metabolically costly, and associations with changing environments do not imply they evolved there, as the Cognitive Buffer Hypothesis (CBH) would suggest. They may instead evolve in stable conditions and later facilitate colonization of changing environments. Using neuro-evolution in an artificial seasonal foraging task, we compared agents evolving exclusively in changing environments to agents first evolved in static environments before transitioning. Results show that larger neural networks in dynamic environments arise mainly from prior static evolution, achieving superior performance under unpredictable changes. Our results challenge strict CBH predictions, provide agent-based (computational) support for a colonization-based account and highlight the role of evolutionary history in brain size evolution.

This work presents a fully analog memristive synaptic circuit for online spike-timing-dependent plasticity (STDP) learning in spiking neural networks (SNNs). The proposed synapse integrates a local STDP circuit generating gradual timing-dependent conductance updates directly from pre- and post-synaptic spikes. Learning occurs during normal network operation without requiring external digital control or explicit STDP waveform synthesis. Post-layout simulations of the memristive synapse implemented in a 130 nm CMOS technology show spike-timing-dependent conductance adaptation during SNN operation. A 2x2 SNN simulation further illustrates online neuron specialization through unsupervised learning.

Molecular design is typically approached as a problem of finding molecules which can adopt a single bioactive conformation. In reality, molecules occupy a distribution over conformations, and many of the properties which determine whether a candidate is viable depend on that distribution rather than on any single conformer. We reframe molecular design as an optimisation of both the modes and properties of molecules' conformational ensembles, where modes can be represented as shapes, pharmacophore profiles or protein pockets, and properties are aggregate scalars computed over the whole distribution. To realise this we introduce ensemble-conditioned guidance, a framework which conditions 3D molecular generative models on both axes simultaneously. Mode conditions are composed adaptively at inference by combining the vector fields produced under each condition. Conditions may be targeted or avoided, mixed across modalities and combined in arbitrary numbers, allowing a wide range of design tasks to be expressed with a single trained model. We introduce adaptive symmetry learning to allow conditions from different reference frames to be composed, and extend our generative framework to enable flexible-size generation. We evaluate on new benchmarks for multi-mode conditioning and ensemble property optimisation, and apply the framework to two practical drug discovery tasks, dual-target binder design and active-state-selective agonist design, where in both cases conditioning on the additional state improves the desired outcome over single-state conditioning.

Autonomous agents operating on multisensory data cannot assume that all sensory modalities remain consistently informative. In real environments, sensory streams are frequently corrupted by noise, missing data, or inter-modal incongruence, requiring adaptive arbitration between competing sensory hypotheses. While active inference provides a principled framework for uncertainty-guided inference, the role of dynamically inferred sensory precision in generative multimodal arbitration under sensory conflict remains comparatively underexplored. We propose a multimodal perceptual inference model in which latent beliefs and modality-specific sensory precisions are jointly updated through iterative free-energy minimization. In our proposed model, sensory precision dynamics not only reflect sensory uncertainty but actively shape the evolution of latent beliefs during multimodal conflict. In addition, we introduce a learned prior over sensory precisions that induces structured, class-dependent precision patterns and influences cross-modal inference dynamics. We evaluate the model using a synthetic multimodal MNIST dataset combining visual, auditory, and tactile representations of digit classes under controlled sensory noise and inter-modal incongruence. Results show that dynamic precision inference improves reconstruction robustness under corrupted sensory evidence, supports coherent latent inference from reduced sensory evidence, and enables stable arbitration between conflicting modalities. Furthermore, learned precision priors generate interpretable precision structures that shape inference dynamics and cross-modal latent structure. These findings support sensory precision inference as a mechanistic control process for adaptive multimodal belief formation under uncertainty, highlighting precision dynamics as a computational mechanism for robust and interpretable multisensory integration.

Large language models (LLMs) are increasingly being employed as variation operators in metaheuristics, generating or modifying candidate solutions, heuristics, or programs inside iterative search loops. This shift reframes variation as a model call conditioned on different types of information. We introduce an operator-level framework with two descriptors: (1) the type of prompt-conditioning information at variation time (Numeric, Symbolic, Linguistic), and (2) artifact persistence, identifying what survives the model call (Transient, Amortized, Transfer). The tutorial shows how to classify, build, and select these operators through a worked build template, a method survey, an evidence table, and a cost-aware decision guide.

Variational quantum algorithms recast state preparation as classical nonconvex optimization, but it is often unclear when multistart local search suffices and when population-based global search justifies its evaluation cost. Using a landscape-first design, controlled QAOA experiments identify two mechanisms making local search unreliable: parameter reuse across circuit layers and competition between 2-local and 3-local cost terms. Increasing QAOA depth alone does not replicate this effect. We test these mechanisms across eight unseen spin glasses, fresh $N=10$ and $N=12$ instances, and standard MaxCut, transverse-field Ising, and Heisenberg models. On all eight unseen spin glasses, adaptive differential evolution (DE) achieves lower median error than both multistart BFGS and multistart Powell on the two difficult constructions, whereas the independent-depth control does not. The parameter-reuse effect transfers to MaxCut at both sizes, while standard VQE models remain favorable to local search. A pre-benchmark landscape score combining random-start local outcomes and 1D parameter slices is fixed from confirmation data before evaluating new optimizers. It predicts whether adaptive DE outperforms multistart BFGS by over one spectral-range percentage point on 50 new quantum objectives with 80–86% condition-level accuracy. The clearest indicator of global-search utility is that local search frequently traps in inferior basins, rather than circuit depth or curvature anisotropy. The findings motivate whether quantum circuit complexity can be traded for harder classical optimization when robust global search is available.

Dynamic multi-mode resource-constrained project scheduling requires decisions to be made under precedence constraints, limited resources, multiple execution modes, and uncertain activity durations. Genetic programming (GP) can automatically evolve heuristic rules for such problems, but its simulation-based fitness evaluation is computationally expensive. This study investigates phenotypic characterisation (PC) in surrogate-assisted GP to evolve higher-quality scheduling heuristics under a fixed budget of full simulation-based fitness evaluations. A key question is how GP individuals should be encoded into phenotypic characterisations to support effective fitness estimation. To answer this question, three PC encoding schemes with different levels of information richness are designed: priority-value encoding, which preserves raw rule outputs; rank encoding, which captures candidate ordering; and binary encoding, which represents final scheduling decisions. These encodings are combined with different distance metrics to measure behavioural similarity between GP individuals. The experimental results show that binary encoding with Euclidean distance provides the most effective and robust surrogate guidance. Further analyses show that surrogate estimation accuracy alone does not fully explain the performance differences. The PC representation also determines how effectively phenotypically redundant offspring are removed and how much behavioural diversity is retained after preselection. Ablation experiments further demonstrate that duplicate removal and surrogate preselection provide complementary benefits, with their combination producing the largest improvement. These findings highlight that effective surrogate-assisted GP depends not only on identifying promising offspring, but also on controlling redundancy and preserving useful diversity during evolutionary search.

Evolutionary Ensemble Search (EES) constructs machine-learning procedures through expert-guided program evolution. A role-specialized council turns task evidence and experimental results into structured search directions. An orchestrator allocates these directions to execution specialists and an evolutionary engine. The engine selects measured parents, diagnoses their errors, and produces descendants through code mutation, structured pipeline edits, and crossover. Each child must execute and acquire its own validation evidence. Population archives retain useful alternatives, while compatible predictions compete in a validation-gated ensemble stage. Search adapts through parent-relative operator credit, session memory, and problem-indexed lessons retrieved across runs. We specify these mechanisms, distinguish their execution profiles, and define the contracts required to compare candidates as their computations change. A public MLE-bench Lite development ledger records medal-threshold artifacts on 19 of 22 tasks (86.36%), with best outcomes of 11 gold, five silver, and three bronze. The procedures span text, images, tables, audio, scientific geometry, and deterministic transformations. The campaign includes grade feedback between runs, external-source routes, and mixed confirmation procedures; its aggregate is an achieved development result, not a blind autonomous-agent success rate. The report contributes a concrete architecture for cumulative executable search and a versioned account of its cross-modal development outcomes.

Most hyperparameter configurations for Evolvable-Substrate HyperNEAT (ES-HyperNEAT) produce networks that stagnate at random-guessing performance, wasting computational resources. We frame early stopping as binary classification on early fitness trajectories: for each trial, we compute the cumulative median of best-per-generation fitness and test it against a threshold derived by maximizing the F1 score on an initial 90-trial dataset. The resulting rule (generation G* = 3, threshold T* = 0.140) achieves F1 = 0.872 on 180 independent validation trials, retaining over 90% of successful trials while cutting computational cost by 41.6%. Compared to Hyperband, our domain-specific rule is 64% more efficient with higher mean fitness, though Hyperband occasionally discovers higher peak solutions. On a converged search population the rule becomes too aggressive (recall 31.1%), motivating adaptive thresholds. The specific thresholds are ES-HyperNEAT-specific, but the methodology, deriving stopping criteria from fitness dynamics classification, is applicable to other evolutionary algorithms with stagnation-prone hyperparameter spaces.

State-of-charge (SoC) estimation for electric vertical take-off and landing (eVTOL) aircraft must run on the vehicle under hard energy and certification budgets, on a duty cycle unlike anything in the automotive literature. In this study an event-driven spiking network, the state-estimation core of the nBMS neuromorphic battery management architecture, is designed for per-timestep SoC estimation and evaluated on a public 22-cell eVTOL dataset with an automotive cross-check. A delta and population encoder, a second-order sigma-delta spiking layer, and a rate-accumulator readout hold 34{,}433 int16 parameters with zero dense multiply-accumulate (MAC) operations. The estimator reaches 2.45% root-mean-square error (RMSE) against 1.74% for a tuned long short-term memory (LSTM) baseline, a gap characterized as a temporal-mixing limit in cruise; in exchange it degrades 1.6 times slower than an adaptive leaky integrate-and-fire control under sensor noise and needs roughly 3{,}500 additions per step where the LSTM needs 67{,}700 multiply-accumulates. The full core is deployed on a low-cost automotive-qualified Artix-7 field-programmable gate array at 87% block-RAM utilization, meets timing at 50~MHz, and reproduces the frozen fixed-point reference bit-exactly over a real 491-step flight segment on silicon. Fully annotated post-implementation analysis gives 1.30~$\mu$J per inference, an average of 0.65~$\mu$W at the 0.5~Hz mission cadence.

We present three robotic art installations which explore the aesthetics of adaptive behavior. Through embodied machine leaning and digital evolution, these works draw viewers into an artificial ecosystem in which open-ended novelty, trial-and-error learning, competition, and cooperation emerge in real time. Research-creation practices are examined in relation to these works, focusing on how they redefine the role of artists within a human-machine collective while examining points of convergence and divergence between artistic and engineering approaches to adaptive robotics. The systems in question use learning and evolutionary processes not as a means to optimize a specific solution, but as an aesthetic experience on its own, suggesting new modes of interdisciplinary art-science research. Finally, we discuss strategies and practices to elevate the aesthetic experience for audiences, including contexts of presentation as well as temporal and material considerations for artworks based on embodied adaptive systems.

This paper proposes a novel membrane algorithm based on artificial protozoa optimizer (MAAPO) for global optimization problems. The artificial protozoa optimizer (APO) is adopted as the base meta-heuristic algorithm due to its novelty and competitive performance. MAAPO integrates two key innovations:(1) a membrane computing (MC) framework that introduces a parallel distributed paradigm to improve population diversity and search dynamics, and (2) an enhanced autotrophic model within APO that uses a roulette-based fitness-distance balance (RFDB) mechanism for adaptive reference point selection. These strategies collectively enhance the algorithm's exploration-exploitation balance and global search capabilities. To validate its performance, MAAPO is tested against 12 advanced algorithms on the CEC2017 test suite, and further applied to the multilevel thresholding image segmentation problem using Otsu and Kapur entropy as objective functions. The quality of segmented images is assessed using peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and feature similarity index (FSIM) metrics. Experimental results demonstrate that MAAPO outperforms its counterparts, delivering superior segmentation quality. This research on MAAPO contributes an effective enhancement strategy to meta-heuristic algorithms and introduces a novel, highly applicable approach for complex image segmentation tasks.

For the (1+1) evolutionary algorithm with standard bit mutation, we study the sensitivity of the expected hitting time $H_p=\mathbb{E}_x T$ to the mutation rate. We first point out an easily overlooked formalization pitfall: the improvement event is not monotone in the mutation mask, so the unsigned (total-influence) form of the Margulis-Russo formula does not apply; the correct object is the signed endpoint difference. Second, we give an exact three-dimensional separation: two fitness functions share the entire one-step success-rate curve, yet their expected hitting times are two different exact rational numbers; hence one-step success-rate quantities do not determine the expected hitting time. Building on the runtime derivative $H'_p=(I-Q_p)^{-1}Q'_p H_p$, we construct computable double-residual sign certificates, prove a per-initial-state sign theorem on OneMax (for every non-optimal initial state, $\partial_c H<0$ on $0<c<1$, where $p=c/n$; at $c=1$ only the distance-one state is stationary), and extend the framework to non-lumpable positive linear families: an explicit non-lumpability witness, a block-interval double-residual certificate that covers all states without enumerating them, a uniform sign bound $\partial_c\mathbb{E}T\le -9n/16$ over the whole interval $c\in[1/4,1/2]$ for an explicit family at all even scales $n\ge 8$, and a heterogeneous instance certificate $H'_x\le -1/6$ on 57 of 63 states across $c=1$. All finite verifications use exact rational arithmetic. A bounded systematic literature search did not uncover this exact combination, although the underlying tools are well established; we therefore make no novelty claim beyond the stated combination.

Biological neurons achieve computational diversity through specialized types: tonic, bursting, adapting, and fast-spiking cells coexist within the same circuit. Artificial neural networks, by contrast, apply a single activation function uniformly to all nodes, which limits what they can represent. We show that this uniformity creates hard limits for evolutionary search: across sparse evolved substrates, monotonic functions fail to solve parity beyond its smallest instance, XOR, while a single oscillatory unit suffices at all tested scales. The gap is one of search and sparsity, not representation: monotonic networks can represent parity with a modest number of hidden units, and gradient descent recovers that solution. We evolve, to our knowledge for the first time in indirect encoding, per-node activation function assignments from an 18-function palette across more than 4,500 experimental runs spanning Boolean logic, regression, and spatial classification. Testing each of the 18 functions individually on Parity-4 reveals a three-tier solvability structure: oscillatory functions achieve 100%, intermediate functions 6.7-80%, and all 9 monotonic functions 0%. This divide is not universal. Recurrence collapses it, and gradient descent inverts it entirely, showing that the barrier is specific to evolutionary search in sparse substrates. What activation functions a network can use, beyond its topology and weights, determines what evolutionary search can solve. Indirect encoding discovers heterogeneous per-node activation assignments unlikely to be chosen by hand.

Open-ended artificial life systems must acquire diverse competencies from a single evolving genotype. Biological brains combine neuromodulation, which reconfigures circuits without changing connections, with diverse neuron types matched to specific computational roles. Can artificial evolution achieve something analogous in indirectly encoded substrates? Using indirectly encoded substrates evolved via CPPNs, we show through more than 10,000 experiments that neuromodulation alone is insufficient: under evolutionary search, monotonic activation functions impose a 75% ceiling on parity tasks that persists regardless of capacity, topology, or population size. This is an evolutionary search barrier, not a representational limit, since Adam gradient descent achieves 100% on the identical architecture. We combine neuromodulation with per-task activation function selection, matching oscillatory primitives to parity tasks and monotonic to threshold tasks, producing multi-behavioral evolved substrates. The result: 100% simultaneous 5-task success across all 30 seeds (median 14 generations). This generalizes across the oscillatory activation class: all four functions reach 100% (30 seeds each). Neither mechanism suffices alone. The barrier extends to higher-arity and asymmetric tasks, while multi-layer depth provides an alternative path. For open-ended evolution, the computational primitive should itself be an evolvable trait. At inference, one evolved genotype expresses many behaviors.

We investigate whether a Chern-Simons (CS) context reservoir is a viable computational substrate and whether evolving its gauge connection provides a benefit beyond simpler mechanisms. The reservoir state is a density fluctuation on a two-dimensional context manifold, whose drift is generated by a density-sourced connection. To separate generic reservoir behavior from gauge-specific effects, we compare four matched models: reciprocal transport, instantaneous transverse reconstruction, local nonlinear feedback, and fully coupled conserved-current CS dynamics. Across ten random seeds, the fully coupled CS dynamics propagates Gauss law to numerical precision, converges under spatial and temporal refinement, remains stable under constraint-compatible noise, and satisfies the spatial CS equation more accurately than the instantaneous controls. All four models exhibit fading scalar memory and distinguish matched pulse-order histories in density, with no resolved general advantage for coupled CS. The distinction appears in the flow geometry: coupled evolution supports circulating and longitudinal history channels simultaneously, retains them briefly after input removal, and yields a combined-feature pulse-order accuracy of \(0.879\pm0.035\), compared with \(0.679\pm0.065\) for the instantaneous-transverse control. The evolved connection also cannot be reconstructed from an instantaneous density snapshot or replaced by a fitted local multiplier. We therefore find a task-specific advantage for geometry- and order-sensitive processing, rather than generic reservoir superiority. Here “topological” refers to the gauge organization of the state; the reported memory and cyclic-lag measures are not topological invariants.

Introducing large language models (LLMs) into evolutionary computation enables semantic generation of candidates, but the classical problem of maintaining population diversity remains. Inspired by the thermodynamical genetic algorithm (TDGA), we propose T-GADE (Thermodynamical Generative-AI-Driven Evolution of LLM Artifacts), an evolutionary computation framework extended through LLMs. T-GADE keeps the notions of a population and genetic operators, takes structured artifacts generated by an LLM as individuals, and implements crossover and mutation as LLM operators. It further introduces the HoxLM, an LLM that attempts self-repair of an individual after evaluation and before survival selection; two update schemes, generational and steady-state; and Fermi-type and Bose-type occupancy rules that define solution identity and whether duplicates are permitted. Survival selection is unified as minimization of the free energy $F_T=\langle E\rangle-TH$, and the selection temperature $T$ explicitly controls the balance between quality and diversity. We tested an implementation example aligned with Evolution of Heuristics (EoH) on the online bin-packing task, where the excess is the bin count in excess of the volume lower bound, relative to that bound. The HoxLM-equipped configuration reached lower excess with fewer total LLM calls than EoH. In the preregistered comparison at 400 total calls it won 9 of 10 seed-paired runs, with a median sealed excess of 0.836% against 3.912%, and it was also better in the mean and in the worst case. Temperature controls the spread of the retained population under both update schemes, and a small positive temperature improves training quality over the collapsed $T=0$ point in the generational Bose-type scheme. The evolved heuristics are shown as readable scoring rules.

Membership inference attacks (MIAs) are widely used to audit the privacy disclosure risk of machine learning models, however current state-of-the-art attacks require training computationally expensive shadow models, making large-scale privacy evaluation impractical. In this work, we investigate whether inexpensive spectral metrics derived from the heavy-tailed self-regularisation framework can serve as proxies for MIA vulnerability. We evaluate several WeightWatcher spectral metrics on image and tabular classification tasks and compare their relationship with MIA privacy leakage against conventional measures of generalisation. Across datasets, stable rank exhibits a strong positive correlation with overall MIA success, while Log alpha-Norm shows a consistent negative correlation with MIA vulnerability at the low false-positive regime. These associations are observed to be stronger than those obtained using the generalisation gap. The results indicate that neural network spectra may contain information about privacy leakage that is not fully captured by conventional measures of overfitting, motivating spectral analysis as a promising direction for scalable privacy auditing.

Evolvable-Substrate HyperNEAT (ES-HyperNEAT), a bio-inspired indirect encoding that determines neuron placement and connection weights from spatial coordinates, exhibits a failure mode on MNIST as a diagnostic benchmark. Because input pixels map to a coordinate space centered at the origin, evolved networks converge on a small central cluster of input pixels, a spatial-concentration bias; prior work observed only 21% mean accuracy in this regime. Is this bias an optimization artifact or an architectural ceiling? Inspired by Mixture-of-Experts (MoE) principles, we partition the input into non-overlapping spatial segments, each assigned to a separately evolved specialist network. With 13 such experts, this design reaches 43% mean accuracy, a 106% relative improvement over the baseline. The architectural gain does not depend on data-driven aggregation: equal-weighted averaging, which uses no validation data, already yields a 70% improvement; the gain comes from partitioning, not the weighting. Receptive-field analysis shows the mechanism: partitioning forces evolution to discover features across the entire image, expanding active pixel coverage from 4% to 79%. Absolute accuracy stays below gradient-trained baselines, but the relative gain points to central bias, not the evolutionary search. Two tools are designed to generalize beyond MNIST: a receptive-field diagnostic for silent input-coverage collapse, and a spatial-partitioning remedy that restores coverage.

Reconfigurable robots can change their contact geometry when a fixed body cannot negotiate an obstacle. A variable-geometry truss (VGT) distributes this shape change through a load-bearing structure, but coupling it to a mobile base creates a high-dimensional coordination problem. GeoTrussRover combines an electrically actuated VGT, a wheeled base, and contact-semantic morphology planning and control. We solve one source traversal and extract four contact-semantic primitives that describe coordination among 21 members. Physics-constrained projection adapts them to unseen step heights with the same contact topology. When every phase remains feasible, adaptation does not recompute the complete motion. If one phase violates the new physical constraints, only that phase is recomputed. A full-space QP then tracks the adapted motion and corrects member and wheel errors. For transfer from 0.10m to 0.075m, the method reduces objective-function evaluations by 63.7% relative to full recomputation. Contact-phase feasibility analysis covers step heights from 0.10 to 0.46m, or 1.08 to 4.97 wheel radii, with the upper value near the theoretical feasible boundary. The electric prototype traverses 2.11 wheel radii. The resulting low-dimensional representation stores task coordination in a hyper-redundant, load-bearing morphology and reuses it during locomotion.