The Inference Report

Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.

We present NeuronSoup, a neural computation architecture that replaces synchronous layer-by-layer processing with asynchronous, delay-mediated signal propagation through a pool of shared neurons. Each path in the network routes a continuous-valued signal from one input neuron to one output neuron through a variable number of intermediate hidden neurons. Hidden neurons are physically shared across paths: when two paths pass through the same neuron, the second arrival encounters the accumulated state left by the first, producing constructive or destructive interference that depends on signal polarity and arrival timing. The entire architecture -- topology, weights, delays, and connectivity -- is co-evolved by a genetic algorithm operating on a flat real-valued genome of 14,602 genes. On 10-class MNIST digit classification using frozen ResNet18 features as input, the system evolves a network of 204 active paths through 266 hidden neurons (156 shared across multiple paths, with one neuron participating in 11 distinct paths) and achieves 85.9\% test accuracy after 10,000 generations. The trained model occupies 115 KB. We argue that this architecture addresses fundamental limitations of current deep learning: it requires no differentiable computation graph, adapts its computation depth per-sample, and discovers lateral interactions between processing pathways that current architectures must engineer explicitly. We discuss why genetic algorithms are the correct optimization tool for this problem class, why CMA-ES fails at this scale, and how the architecture generalizes to arbitrary domains by substituting the encoder and output structure.

Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs. We present a global operator theory of the \emph{F-adjoint} framework, which reformulates the layerwise backward recursion of an $L$-depth feedforward network into a single linear system $(I-\cB)\Xs=\bG$, where $\bG$ is a source vector. We prove that the global backward operator $\cB$ is strictly block upper-triangular and nilpotent of index at most $L$. This nilpotency guarantees the exact termination of the Neumann series solution after at most $L$ terms, revealing classical backpropagation to be mathematically equivalent to block back-substitution on an upper bidiagonal system. We formalise \emph{F-symmetry} -- the condition in which the backward pass perfectly mirrors the forward pass -- identifying orthogonal weight matrices as canonical examples. Through worked numerical examples, we demonstrate how this operator perspective exposes the single-path collapse of strictly feedforward networks and its breakdown in residual architectures. Finally, we leverage this compositional structure to rigorously derive the mechanics of residual networks (gradient highways) and transfer learning (gradient truncation). This framework elevates backpropagation from an algorithmic recipe to a global nilpotent-operator formulation.

This article is about the development of a fuzzy cognitive map using a local large language model. In the light of recent advances it is evident that large language models, and even local large language models are capable of extracting quantities from textual data. In other words, a local LLM like Qwen2.5-32B, or probably larger, can accept entities as prompt input and determine relevant quantitative data as the model output. In turn, this output can be utilized for the construction of a data driven fuzzy cognitive map. Hence, this implementation is achieved and then the model is thoroughly tested; Qwen2.5-32B is used and the data is extracted from hotel reviews from TripAdvisor. Furthermore, the extracted documents pass through the model unfiltered and then a fuzzy cognitive map is trained and evaluated. A case is made about Greek reviews where a star topology FCM is formed that indicates the preferences of the reviewers. Finally, external validation is performed to establish whether the fuzzy cognitive map can correlate the star rating of the review -an outcome outside the model's inference scope -with its predicted satisfaction.

This paper studies whether the Metabolic Multi-Agent Optimizer (MMAO) can act as a credible outer-loop optimizer for classification model selection. We propose MMAO-Cls, a mixed-space realization in which each agent jointly encodes a binary feature mask and classifier hyperparameters, while private energy, communal budget, role drift, and lifecycle turnover are mapped to the accuracy-complexity tradeoff of wrapper learning. The implementation is strengthened by deriving feature-budget adaptation from feature-information priors and by regularizing validation reward with both subset compactness and train-validation overfitting gap. We evaluate MMAO-Cls on seven standard tabular benchmarks with three seeds each and compare it against RandomSearch, GA-lite, PSO-lite, and an endogenous no-sharing ablation. On the aggregate validation objective, MMAO-Cls ranks second ($0.9433$) behind GA-lite ($0.9446$). On held-out test performance, it reaches mean score $0.8882$, improving over RandomSearch ($0.8808$) and GA-lite ($0.8857$), remaining close to PSO-lite ($0.8874$) and the no-sharing ablation ($0.8900$), while using the most compact mean held-out feature subset among all compared methods (feature ratio $0.4881$). Pairwise tests show that these margins are not yet statistically significant. The resulting claim is therefore conservative: MMAO-Cls supports classification applicability and compact mixed-space search more clearly than it isolates communal sharing as a decisive standalone advantage.

Wave Function Collapse (WFC) is a widely used procedural content generation method that learns local adjacency constraints from example inputs to generate larger outputs. In this paper, we explore combining WFC with evolutionary search by evolving the small input examples used by WFC rather than directly evolving complete levels. In this approach, WFC acts as a genotype-to-phenotype mapping. The generated levels are then evaluated through domain-specific fitness functions. We evaluate the method in two domains with different relationships between local and global structure: Maze connectivity maps and Zelda-style dungeon layouts. Our results show that evolutionary optimization over WFC inputs improves generation quality in domains where properties emerge from local relationships, while domains requiring global constraints remain challenging. These findings suggest that evolutionary search can effectively guide WFC generation when target objectives align with local structure.