Hasi Hays

Hasi Hays, William J. Richardson

Network topology excels at structural predictions but fails to capture functional semantics encoded in biomedical literature. We present RAG-GNN, an end-to-end trainable retrieval-augmented graph neural network framework that integrates GNN representations with dynamically retrieved literature-derived knowledge through a jointly optimized retrieval projection, gated fusion mechanism, and contrastive alignment. In a cancer signaling case study (379 proteins, 3,498 interactions, 14 functional categories), RAG-GNN improves functional clustering from silhouette $= -0.237 \pm 0.065$ (GNN-only) to $-0.144 \pm 0.066$, a consistent improvement of $+0.093 \pm 0.022$ across 10 random seeds, while the learned retrieval achieves mean precision@10 $= 0.242$, a 152\% improvement over the random baseline ($0.096$). Heuristic information decomposition with bootstrap confidence intervals reveals that topology and retrieval encode overwhelmingly shared information (95.6\%), with retrieval improving both intra-cluster cohesion (silhouette) and cluster agreement (ARI $+0.021 \pm 0.015$). Counterfactual experiments confirm that adversarial, absent, and random retrieval all degrade performance, validating that the gated fusion mechanism depends on document content. Benchmarking against eight established embedding methods demonstrates task-specific complementarity: topology-focused methods achieve strong link prediction, while retrieval augmentation consistently improves functional clustering within the controlled GNN-only ablation. DDR1 subnetwork analysis provides confirmatory validation consistent with established synthetic lethality relationships. These results establish that topology-only and retrieval-augmented approaches serve complementary purposes for precision medicine applications.

Hasi Hays, William J. Richardson

Extracellular matrix (ECM) remodeling is central to a wide variety of healthy and diseased tissue processes. Unfortunately, predicting ECM remodeling under various chemical and mechanical conditions has proven to be excessively challenging, due in part to its complex regulation by intracellular and extracellular molecular reaction networks that are spatially and temporally dynamic. We introduce ECMSim, which is a highly interactive, real-time, and web application designed to simulate heterogeneous matrix remodeling. The current model simulates cardiac scar tissue with configurable input conditions using a large-scale model of the cardiac fibroblast signaling network. Cardiac fibrosis is a major component of many forms of heart failure. ECMSim solves 1.37 million coupled ordinary differential equations (ODEs) and executes approximately 4.84 million operations per time step in real time, encompassing 137 molecular species and 259 regulatory interactions per cell across a 100x100 spatial array (10,000 cells), which accounts for inputs, receptors, intracellular signaling cascades, ECM production, feedback loops, and molecular diffusion. The algorithm is represented by a set of ODEs that are coupled with ECM molecular diffusion. The equations are solved on demand using compiled C++ and the WebAssembly standard. The software enables the investigation of pathological or experimental conditions, hypothetical scenarios, matrix remodeling, or the testing of the effects of an experimental drug(s) with a target receptor.

Hasi Hays, Yue Yu, William Richardson

Cellular signaling networks represent complex information processing systems that have been modeled via traditional mathematical or statistical approaches. However, these methods often struggle to capture context-dependent signaling, pathway cross-talk, and temporal dynamics across multiple biological scales. Here, we introduce hierarchical molecular language models (HMLMs), a novel architecture that proposes a molecular network-specific large language model (LLM) to use in intracellular communication as a specialized molecular language, which includes molecules as tokens, protein interactions, post-translational modifications, and regulatory events modeled as semantic relationships within an adapted transformer architecture. HMLMs employ graph-structured attention mechanisms to accommodate signaling network topology while integrating information across the molecular, pathway, and cellular scales through hierarchical attention patterns. We demonstrate HMLM superiority using a cardiac fibroblast signaling network comprising over 100 molecular species across functional modules connected by regulatory edges. HMLM achieved a mean squared error (MSE) of 0.058 for temporal signaling predictions, representing 30% improvement over graph neural networks (GNNs: 0.083) and 52% improvement over ordinary differential equation models (ODEs: 0.121), with particular advantages under sparse temporal sampling conditions where HMLM maintained MSE = 0.041 with only 4 time-points. The HMLMs offer a foundation for AI-driven biology and medicine with predictable scaling characteristics suitable for interactive applications. By bridging molecular mechanisms with cellular phenotypes through AI-driven molecular language representation, HMLMs provide a powerful paradigm for systems biology that advances precision medicine applications and therapeutic discovery in the era of AI.

Hasi Hays

We introduce Resonant Sparse Geometry Networks (RSGN), a brain-inspired architecture with self-organizing sparse hierarchical input-dependent connectivity. Unlike Transformer architectures that employ dense attention mechanisms with O(n^2) computational complexity, RSGN embeds computational nodes in learned hyperbolic space where connection strength decays with geodesic distance, achieving dynamic sparsity that adapts to each input. The architecture operates on two distinct timescales: fast differentiable activation propagation optimized through gradient descent, and slow Hebbian-inspired structural learning for connectivity adaptation through local correlation rules. We provide rigorous mathematical analysis demonstrating that RSGN achieves O(n*k) computational complexity, where k << n represents the average active neighborhood size. Experimental evaluation on hierarchical classification and long-range dependency tasks demonstrates that RSGN achieves 96.5% accuracy on long-range dependency tasks while using approximately 15x fewer parameters than standard Transformers. On challenging hierarchical classification with 20 classes, RSGN achieves 23.8% accuracy (compared to 5% random baseline) with only 41,672 parameters, nearly 10x fewer than the Transformer baselines which require 403,348 parameters to achieve 30.1% accuracy. Our ablation studies confirm the contribution of each architectural component, with Hebbian learning providing consistent improvements. These results suggest that brain-inspired principles of sparse, geometrically-organized computation offer a promising direction toward more efficient and biologically plausible neural architectures.

Hasi Hays

The Transformer architecture has become the foundation of modern deep learning, yet its core self-attention mechanism suffers from quadratic computational complexity and lacks grounding in biological neural computation. We propose Selective Synchronization Attention (SSA), a novel attention mechanism that replaces the standard dot-product self-attention with a closed-form operator derived from the steady-state solution of the Kuramoto model of coupled oscillators. In SSA, each token is represented as an oscillator characterized by a learnable natural frequency and phase; the synchronization strength between token pairs, determined by a frequency-dependent coupling and phase-locking condition, serves as the attention weight. This formulation provides three key advantages: (i) natural sparsity arising from the phase-locking threshold, whereby tokens with incompatible frequencies automatically receive zero attention weight without explicit masking; (ii) unified positional-semantic encoding through the natural frequency spectrum, eliminating the need for separate positional encodings; and (iii) a single-pass, closed-form computation that avoids iterative ODE integration, with all components (coupling, order parameter, synchronization) derived from the oscillatory framework. We instantiate SSA within the Oscillatory Synchronization Network (OSN), a drop-in replacement for the Transformer block. Analysis of the synchronization matrices reveals non-uniform, head-diverse coupling patterns even at initialization, demonstrating a stronger architectural inductive bias than the approximately uniform attention produced by randomly initialized Transformers.