Investigating the computational principles of adaptive holographic systems — engineering substrates for Hebbian learning governed by the equations of Adaptive Holographic Theory.
Holographic Substrates · Hebbian Dynamics · Adaptive Systems
Investigating the computational principles of adaptive holographic systems — engineering substrates for Hebbian learning governed by the equations of Adaptive Holographic Theory.
Holographic Substrates · Hebbian Dynamics · Adaptive SystemsThe Adaptive Holographic Systems Lab (AHSL) investigates the fundamental principles underlying adaptive holographic systems—distributed architectures that store, recall, and refine information through interference-based encoding and Hebbian plasticity rules.
Our central hypothesis is that biological cognition operates as an adaptive holographic system: sensory inputs are encoded as distributed interference patterns across neural substrates, and learning emerges from activity-dependent synaptic modifications consistent with Hebbian dynamics.
We pursue this vision through both theoretical work—formalizing the equations of Adaptive Holographic Theory (AHT)—and experimental research aimed at identifying and engineering physical substrates capable of supporting holographic Hebbian learning in vitro and in silico.
To decode the holographic operating principles of adaptive biological systems and to translate those principles into engineered substrates that learn, generalize, and self-organize according to AHT dynamics.
Our work spans the theoretical foundations of adaptive holographic computation, the material science of learning-capable substrates, and the computational modeling of holographic memory systems.
Identification and characterization of physical and synthetic substrates capable of supporting distributed holographic storage with Hebbian plasticity. We investigate photorefractive crystals, phase-change materials, and neuromorphic thin-film architectures as candidate media for AHT-compliant learning.
Formal analysis of Hebbian learning rules within holographic reference frames. We study how local, activity-dependent weight updates give rise to global coherence in distributed memory systems, and derive stability and convergence guarantees within the AHT formalism.
Development of the mathematical framework unifying holographic information encoding with adaptive learning. AHT provides the field equations governing interference pattern formation, pattern recall, and experience-driven refinement in holographic memory substrates.
Large-scale simulations of holographic associative memories governed by AHT equations. We model pattern capacity, noise resilience, and generalization performance of adaptive holographic networks under varying substrate parameters and learning schedules.
Empirical testing of AHT predictions against neural recording data. We collaborate with neuroscience partners to assess whether cortical dynamics exhibit signatures of holographic encoding—distributed representations, interference-based recall, and Hebbian adaptation consistent with AHT field equations.
Design of hardware architectures that implement AHT-governed memory systems. We explore optical computing elements, memristive crossbar arrays, and hybrid opto-electronic platforms as potential substrates for scalable holographic associative memory.
Adaptive Holographic Theory provides a unified mathematical description of how holographic systems encode, store, and adaptively refine distributed representations through Hebbian learning dynamics.
The holographic field H(x) is formed by the interference of a reference wave R and object wave O over the substrate manifold. The phase kernel φ governs the spatial frequency spectrum of the resulting interference pattern.
Synaptic weights evolve according to the product of pre- and post-synaptic activities ξ, modulated by a learning rate η. The decay term λ ensures bounded weight growth and competitive dynamics.
The time evolution of the holographic field is governed by a diffusion term (α), a nonlinear Hebbian coupling functional F, and a dissipation rate γ that stabilizes the stored pattern manifold.
Reconstruction of a stored pattern is achieved by illuminating the holographic field with the conjugate reference wave R*. The kernel K(σ) parameterizes substrate-dependent noise and resolution characteristics.
We welcome inquiries from prospective collaborators, students, and researchers interested in adaptive holographic systems.
Adaptive Holographic Systems Lab
Millöckergasse 39
8010 Graz, Austria
Lab Director
bean@adaptive-holographics.com