The capacity to transfer knowledge across scientific domains relies on shared organizational principles. However, existing transfer-learning methodologies often fail to bridge radically heterogeneous systems, particularly under severe data scarcity or stochastic noise. This study formalizes Explainable Cross-Domain Transfer Learning (X-CDTL), a framework unifying network science and explainable artificial intelligence to identify structural invariants that generalize across biological, linguistic, molecular, and social networks. By introducing the Importance Inversion Transfer (IIT) mechanism, the framework prioritizes domain-invariant structural anchors over idiosyncratic, highly discriminative features. In anomaly detection tasks, models guided by these principles achieve significant performance gains - exhibiting a 56% relative improvement in decision stability under extreme noise - over traditional baselines. These results provide evidence for a shared organizational signature across heterogeneous domains, establishing a principled paradigm for cross-disciplinary knowledge propagation. By shifting from opaque latent representations to explicit structural laws, this work advances machine learning as a robust engine for scientific discovery.
Scientific progress increasingly necessitates the synthesis of knowledge across domains that differ radically in scale, modality, and underlying mechanisms. Meaningful crossdisciplinary propagation-ranging from leveraging biological analogies to predict engineering failures to inferring linguistic organization from social networks-presupposes shared organizational principles [1,2]. Identifying these principles is not merely a descriptive exercise but a fundamental prerequisite for principled generalization and robust knowledge transfer.
Transfer learning (TL) facilitates the adaptation of predictive functions across disparate datasets by leveraging commonalities in feature representations or underlying generative processes [3,4]. This paradigm shift from isolated learning to knowledge propagation addresses the inherent limitations of standard machine learning when facing novel domains with distinct probability distributions. However, domain adaptation theory posits that the error bound on a target task remains strictly contingent upon the divergence between source and target distributions [5][6][7]. In real-world scientific applications, stochastic corruption and feature noise exacerbate this divergence, frequently causing standard alignment methods to collapse and necessitating more robust approaches to isolate domain-invariant representations.
Furthermore, existing transfer methodologies primarily target closely related settings where datasets share similar generative dynamics [3,8]. When applied across fundamentally heterogeneous systems, conventional latent alignment techniques often yield uninterpretable, domain-specific embeddings that obscure the mechanistic pathways of knowledge propagation. This lack of transparency hinders the identification of the structural properties that consistently connect disparate domains [9,10].
Network science represents a powerful abstraction for cross-disciplinary synthesis, as entities and interactions in systems ranging from molecular graphs to social structures can be mapped onto complex networks [11,12]. By representing interactions as nodes and edges, this approach demonstrates extensive utility across fields as diverse as materials science, cosmology, and systems biology, enabling the analysis of fundamental phenomena such as phase transitions, information diffusion, and technological innovation [13][14][15][16][17][18][19][20][21][22].
However, the current reliance on handcrafted descriptors often fails to distinguish functionally meaningful invariants from artifacts of sampling or idiosyncratic domain constraints, particularly when faced with noisy or scarce datasets [23,24]. To resolve this impasse, the present study formalizes Explainable Cross-Domain Transfer Learning (X-CDTL), a paradigm unifying network science with explainable artificial intelligence (XAI). Building upon the theoretical foundations established in [25], this framework facilitates the identification of shared structural principles that remain invariant across disparate disciplines. Through this lens, complex systems with small-world architectures of social ego-networks to the sparse, valency-constrained layouts of molecular graphs. These structural fingerprints provide the morphological basis for evaluating the framework generalization capacity across fundamentally different generative dynamics. Representative graph samples illustrate distinct density, modularity, and branching patterns. Connectivity definitions vary across scientific scales: in social networks, nodes represent users connected by friendships; in molecular graphs, nodes denote atoms joined by chemical bonds; in protein networks, nodes represent amino acids linked by physical interactions; and in linguistic networks, nodes denote words connected by contextual co-occurrence. These architectures underpin the X-CDTL framework by providing a heterogeneous set of structural priors for the manifold alignment pipeline.
A set of twelve topological descriptors, spanning connectivity, clustering, spectral, and modular dimensions, quantifies this diversity (ensemble statistics in Supplementary Table 8). The selected domains occupy non-overlapping topological regimes, as demonstrated by the high separability in the structural feature space (Supplementary Fig. 5). Social networks exhibit quasi-clique architectures characterized by high local redundancy, with a mean clustering coefficient of 0.84±0.06 and a density (0.65±0.17) significantly exceeding all other domains. Conversely, molecular graphs constitute a sparse, nearly acyclic space where connectivity is governed by chemical valence constraints, resulting in near-zero average clustering (0.01 ± 0.03). Protein and linguistic networks occupy intermediate regimes; notably, protein networks are uniquely distinguished by high modularity (0.52 ± 0.11), reflecting the hierarchical community organization essential for biological function.
Spectral fingerprints further emphasize these d
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