The Inference Report

Symbolic knowledge (motif counts, ring counts, label constraints) is routinely added to graph neural networks (GNNs) and justified by their limited expressivity. We replace this yardstick with an exact one. The largest log-loss reduction a rule $S$ can give a model family is $I(Y;S\midσ)$ given what the family computes; every realised gain splits exactly into this term plus repaid neural debt; and for a trained network with representation $T$ the value is $I(Y;S\mid T)$, the label information training failed to extract. Rule design thus becomes rule discovery: we score candidates on the network's out-of-fold residual against calibrated permutation nulls with family-wise error control. On ZINC, discovery recovers the hidden ring term $\max(0,\ell_{\max}-6)$ of the target in three independent runs ($p_{\mathrm{adj}}=0.001$) and beats expert cycle counts; frozen and applied to five unseen datasets it is never significantly worse than the plain network or the expert rule, and on BBBP it significantly beats both.

Transforming the spike trains produced by spiking neural networks (SNNs) into continuous signals through biologically inspired mechanisms remains an open challenge in generative and regression tasks. In biological systems, a similar transformation occurs when muscles integrate neural spikes to produce smooth, coordinated movements. Inspired by this mechanism, we introduce a muscle-response model, a biologically motivated dynamical layer that converts spike trains into continuous representations. Our approach uses second-order dynamics to model the temporal integration of spiking activity. We investigate how the number of spiking neurons and temporal resolution affect the quality of the generated signals in a text-to-speech task, showing that increasing representational capacity has a greater impact than increasing temporal resolution under the evaluated configurations. Furthermore, an analysis of the learned dynamics reveals that, without explicit constraints on the response type, most neurons converge toward non-oscillatory behavior. These results demonstrate the potential of biologically inspired dynamical decoders for bridging spiking neural computation and continuous signal generation.

Hopfield neural networks and noncooperative games provide seemingly different approaches to understanding how collective outcomes emerge from local interactions. In a neural network, individual units adjust their states according to local signals; in a game, players choose actions to maximise individual payoffs. I establish an exact equivalence between symmetric binary Hopfield networks and binary-action games that admit a quadratic potential. The equivalence identifies stable network configurations with pure-strategy Nash equilibria, and asynchronous neural updating with best-response dynamics. More broadly, the storage and retrieval of memories in neural networks correspond, respectively, to the design and selection of equilibria in games.

Automated failure discovery can be framed as a diversity problem: the objective is to expose distinct ways a system fails rather than a single critical adversarial case. Yet uniform parent sampling provides no way to allocate search effort toward individuals likely to produce durable archive contributions. We study this credit assignment problem in an unstructured Quality-Diversity (QD) archive, testing whether signals available before an individual has reproduced distinguish offspring that merely enter the archive from those still retained generations later. Across a planar-arm benchmark and two robotic-locomotion tasks, the same signals are often associated with entry and persistence in opposite directions. In particular, lineage depth is the clearest such signal, and its persistence discrimination grows with population capacity, which is associated with lower turnover. Biasing parent selection toward the signals with the strongest measured association to survival nevertheless does not improve search: moderate bias matches uniform sampling, and strong bias reduces QD-score.

Continuous relaxations are commonly used as an encoding scheme for evolutionary multitasking optimization (EMTO), allowing heterogeneous tasks to be optimized within a unified search space. However, these continuous representations fundamentally reshape the induced fitness landscape, and their impact on optimization behavior and knowledge transfer remains underexplored. In this work, we bridge the gap by analyzing the interaction between the representation-induced fitness landscape and optimizer behavior through fitness landscape analysis. Using piano fingering estimation as a representative case of the subset selection problem, we introduce several encoding variants and investigate how their induced landscapes influence search dynamics and solution quality under EMTO. Our analysis indicates that transfer efficacy is strongly associated with changes in representation-induced landscape characteristics, rather than algorithmic factors alone, highlighting the representation design as the key factor of effective knowledge transfer in multitasking optimization.

Automatic operator design (AOD) has increasingly adopted large language models (LLMs) to generate problem-specific search and variation operators for multi-objective combinatorial optimization (MOCO). Yet most methods evolve the operators while leaving the process that discovers them fixed. This limits adaptation as new Pareto trade-offs and operator interactions change where and how the search should proceed. We introduce HEMO, which makes the AOD harness itself a self-evolving optimization target. HEMO maintains a persistent harness state and updates one module at a time, revising the logic that determines which experience to retrieve, which operators to improve, which parents to select, and how to formulate the orchestration of search steps. Downstream solution quality and runtime guide these updates, while a discounted UCB scheduler directs adaptation toward promising modules as their utility changes. A persistent memory filesystem preserves candidate outcomes and diagnostic feedback across harness states, enabling successive states to build on accumulated optimization experience. Experiments across eight MOCO tasks and two structurally distinct evolutionary backbones demonstrate strong performance against conventional evolutionary, neural, and LLM-based AOD baselines, together with effective transfer to related tasks. HEMO extends automatic operator design beyond evolving individual operators to improving the search process that discovers them.