arXiv subjects

Byung Gyu Chae

Publications and source records attributed to Byung Gyu Chae.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Episodic AI: Cognitive Field Networks for Biologically Inspired Persistent Cognition

Cognitive Field Theory (CFT) proposes that cognition arises from memory-dressed collective dynamics that generate a persistent macroscopic cognitive field. Here we develop a Cognitive Field Network (CFN), a recurrent Transformer in which the organized hidden field re-enters subsequent inference through \[ Φ_{n+1}=F_θ(X_{n+1},Φ_n). \] Rather than prescribing an explicit memory operation, the CFN allows new information to act on an already history-dependent collective state. We find that learning organizes persistent, content-dependent recurrent dynamics whose timescale increases systematically with the trained recurrent horizon. Semantic continuation propagates the recurrent state far beyond this horizon without replay of the target answer. Without content-specific support, the field exhibits finite passive relaxation, whereas periodic re-exposure to relevant input repeatedly renews the surviving state and drives it toward an approximately stationary nonzero regime. Unrelated-input and recurrence-off controls do not reproduce this behavior, while near-paraphrased re-exposure produces weaker renewal, demonstrating representation-sensitive persistence. These results distinguish three dynamical processes: collective memory dressing forms and sustains a history-dependent cognitive field, structured input reorganizes this field, and cross-cycle re-entry makes the resulting state causally available to subsequent inference. The CFN therefore provides a controlled computational platform for studying persistent, history-dependent cognitive dynamics without a separately prescribed memory system.

cs.AI↗

arXiv2026

Infrared Universality of Collective Dynamics across Transformer and State-Space Architectures

Whether distinct neural architectures develop common collective dynamics remains an open question. Recent analysis of Transformer language models revealed a nearly flat, weakly infrared-enhanced time-scale density of states (TDOS) associated with near-marginal long-memory dynamics. Here we test whether a closely related organization emerges in Mamba, whose selective state-space dynamics provides a fundamentally different microscopic mechanism. Mamba allows relaxation dynamics to be resolved at three levels: the intrinsic spectrum of the learned state-space generator, its input-conditioned selective rescaling, and the collective TDOS of the complete block measured from its Jacobian. These spectra are not identical: selective dynamics and the remaining block transformations substantially reorganize the microscopic relaxation hierarchy. Nevertheless, the full block develops a reproducible slow-mode continuum whose infrared sector becomes progressively better resolved with increasing sequence length. Cumulative analysis yields $ρ(λ)\simλ^β$, with the long-sequence Mamba exponent stabilizing near $β_{\rm M}\simeq-0.17$. The corresponding memory dynamics follows $K(t)\sim t^{-(1+β)}$, close to the marginal $1/t$ regime. Despite fundamentally different microscopic dynamics, Transformer full-block spectra exhibit closely related infrared organization, with representative exponents of order $β_{\rm Tr}\sim-0.1$. These results separate explicit state-space memory from collective infrared organization and show that distinct sequence architectures can develop closely related near-marginal slow-mode dynamics. They extend infrared collective organization beyond Transformers and provide an independent test of the dynamical structure described by Cognitive Field Theory.

cs.LG↗

arXiv2026

Infrared Organization and Critical Cognitive Field Formation in Transformer Dynamics

Large language models exhibit remarkable emergent behaviors, yet the physical mechanism governing their collective dynamics remains poorly understood. Cognitive Field Theory predicts that learning reorganizes the collective relaxation spectrum, thereby modifying memory self-energy, long-memory dynamics, and collective susceptibility through the infrared organization of slow relaxation modes. Here we test this framework directly in Transformer dynamics. Using publicly available Pythia language models, we extract relaxation spectra from layer Jacobians throughout training, prompt ensembles, network depth, and model scale, allowing the collective observables of Cognitive Field Theory to be measured quantitatively. The measurements reveal pronounced infrared reorganization of the relaxation spectrum. Learning substantially redistributes spectral weight while preserving a nearly flat but weakly infrared-enhanced time-scale density of states, $ ρ(λ)\simλ^β, \qquad β\simeq-0.1, $ with a corresponding memory kernel exhibiting robust long-memory scaling close to $ K(t)\sim\frac{1}{t}. $ The collective observables further reveal a critical formation process: the memory self-energy reaches a transient maximum during early training before relaxing toward a metastable near-critical regime. Prompt-resolved and token-subspace measurements show that distinct local Jacobians recover a common macroscopic TDOS with shared infrared scaling, consistent with infrared fixed-point organization under coarse graining. The reproducibility of this infrared organization across training, prompt ensembles, network depth, and Transformer model scales supports infrared slow-mode organization as a robust collective principle of Transformer dynamics, providing a quantitative experimental realization of the collective observables predicted by Cognitive Field Theory.

cs.LG↗

arXiv2026

Cognitive Field Theory: Memory-Dressed Collective Dynamics of Intelligence

Learning, inference, memory, and emergence in biological and artificial systems are often described using disparate theoretical frameworks. Here we develop a cognitive field theory in which cognition is described as a collective nonequilibrium phenomenon governed by the geometry and collective spectrum of a learned cognitive manifold. Starting from a stochastic cognitive-field equation on an adaptive Riemannian manifold, we derive an effective cognitive field theory incorporating nonlocal memory kernels and retarded self-energy feedback. The learned cognitive geometry generates a complex collective spectrum characterized by the time-scale density of states $ρ(λ,ω)$, whose relaxation and circulation sectors govern memory persistence and temporal coherence. Integrating out latent slow collective modes produces non-Markovian memory feedback that renormalizes the cognitive forgetting gap $r_{\rm cog}$, enhances collective cognitive susceptibility, and drives the system toward a protected near-critical regime characterized by long-time contextual persistence and scale-free temporal organization. The observable cognitive field emerges as a macroscopic order parameter, $ϕ=Ae^{iψ}$, whose amplitude encodes collective cognitive organization and whose phase encodes temporal coherence across distributed collective modes. Within this framework, learning organizes cognitive geometry, cognitive geometry generates a collective spectrum, and the resulting memory feedback stabilizes a memory-dressed cognitive field. The theory provides a unified dynamical description of learning, memory, inference, selfhood, and emergent intelligence in terms of the infrared organization of collective cognitive dynamics.

q-bio.NC↗

arXiv2026

Memory-Dominated Quantum Criticality as a Universal Route to High-Temperature Superconductivity

Understanding the dynamical origin of high-temperature superconductivity remains a central challenge in strongly correlated quantum matter. Near quantum criticality, diverging correlation times reorganize the infrared dynamics into a scale-free continuum of collective relaxation processes. We show that the infrared behavior of interacting electrons is generically controlled by the relaxation-rate spectrum of the underlying many-body dynamics. Starting from a microscopic fermionic theory, we derive that the Cooper-channel kernel admits a universal spectral representation in terms of the time-scale density of states (TDOS) of collective decay modes, without invoking a specific bosonic mediator. The superconducting instability follows directly from the vanishing of the quadratic kernel via a standard ladder resummation and Thouless criterion, with the pairing interaction determined entirely by the infrared structure of the relaxation spectrum. A finite TDOS at vanishing relaxation rate produces a memory-dominated regime characterized by long-time kernels $K(t)\sim 1/t$ and logarithmic enhancement of the retarded pairing interaction, leading to a BCS-like exponential transition scale set by infrared spectral weight. More generally, infrared-singular spectra generate power-law response and algebraic enhancement of the transition scale. The same relaxation spectrum controls normal-state dynamics, giving rise to long-time correlations, non-Markovian response, and strange-metal behavior. These results identify the spectral organization of relaxation modes as a universal organizing principle of quantum critical matter and establish memory-dominated criticality as a natural mechanism for enhanced pairing.

cond-mat.str-el↗

arXiv2026

Emergence of Superintelligence from Collective Near-Critical Dynamics in Reentrant Neural Fields

Superintelligence is commonly envisioned as a quantitative extrapolation of human cognitive abilities driven by scale and computational power. Here we show that qualitative transitions in intelligence instead arise as dynamical phase transitions governed by collective critical dynamics. Building on a unified dynamical field-theoretic framework for cognition, we demonstrate that progressive collective coupling generated by reentrant mixing drives the system toward an infrared critical regime in which an extensive band of slow collective modes emerges. This spectral condensation reorganizes cognitive dynamics from localized relaxation to coherent motion along emergent low-dimensional manifolds. Through numerical analysis of the time-scale density of states, we identify robust power-law scaling of collective relaxation rates with well-defined critical exponents, placing the system within the universality class of self-organized critical many-body dynamics. Criticality alone would generically lead to instability. We further show that homeostatic regulation introduces a gapped stabilizing direction that protects the collective critical sector, yielding a dynamically maintained meta-stable infrared phase in which long-lived inference trajectories persist without collapse. The coexistence of scale-free collective dynamics and global stabilization defines a protected sector-critical regime in which coherence and internal flexibility coexist. Superintelligence therefore corresponds to a distinct dynamical stability class--a self-organized critical phase embedded within a stabilized cognitive manifold--rather than a smooth quantitative continuation of existing cognitive systems.

physics.bio-ph↗

arXiv2026

Self-Organized Criticality from Protected Mean-Field Dynamics: Loop Stability and Internal Renormalization in Reflective Neural Systems

The reflective homeostatic dynamics provides a minimal mechanism for self-organized criticality in neural systems. Starting from a reduced stochastic description, we demonstrate within the MSRJD field-theoretic framework that fluctuation effects do not destabilize the critical manifold. Instead, loop corrections are dynamically regularized by homeostatic curvature, yielding a protected mean-field critical surface that remains marginally stable under coarse-graining. Beyond robustness, we show that response-driven structural adaptation generates intrinsic parameter flows that attract the system toward this surface without external fine tuning. Together, these results unify loop renormalization and adaptive response in a single framework and establish a concrete route to autonomous criticality in reentrant neural dynamics.

nlin.AO↗

arXiv2025

Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks

Reentrant computation-recursive self-coupling in which a network continuously reinjects and reinterprets its own internal state-plays a central role in biological cognition but remains poorly characterized in neural network architectures. We introduce a minimal continuous-time formulation of a homeostatically regulated reentrant network (FHRN) and show that its population dynamics admit an exact reduction to a one-dimensional radial flow. This reduction reveals a dynamically fixed threshold for sustained reflective activity and enables a complete renormalization-group (RG) analysis of the reentry-homeostasis interaction. We derive a closed RG system for the parameters governing structural gain, homeostatic stiffness, and reentrant amplification, and show that all trajectories are attracted to a critical surface defined by $γρ=1$, where intrinsic leak and reentrant drive exactly balance. The resulting phase structure comprises quenched, reactive, and reflective regimes and exhibits a mean-field critical onset with universal scaling. Our results provide an RG-theoretic characterization of reflective computation and demonstrate how homeostatic fields stabilize deep reentrant transformations through scale-dependent self-regulation.

physics.comp-ph↗

arXiv2025

Continuous-Time Homeostatic Dynamics for Reentrant Inference Models

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule $x_t = x_t^{(\mathrm{ex})} + γ\, W_r\, g(\|y_{t-1}\|)\, y_{t-1}$, we derive the coupled system $\dot{y}=-y+f(W_ry;\,x,\,A)+g_{\mathrm{h}}(y)$ showing that the network couples fast associative memory with global radial homeostasis. The dynamics admit bounded attractors governed by an energy functional, yielding a ring-like manifold. A Jacobian spectral analysis identifies a \emph{reflective regime} in which reentry induces stable oscillatory trajectories rather than divergence or collapse. Unlike continuous-time recurrent neural networks or liquid neural networks, FHRN achieves stability through population-level gain modulation rather than fixed recurrence or neuron-local time adaptation. These results establish the reentry network as a distinct class of self-referential neural dynamics supporting recursive yet bounded computation.

math.DS↗

arXiv2025

Solution for the finite space-bandwidth limitation in digital holography

A lensless digital holography enables wide-field microscopic imaging without the limitations imposed by optical lens performance. However, conventional holographic imaging often relies on magnifying optical systems to compensate for the low resolution of holograms captured by image sensors. The spatial resolution of the reconstructed image is fundamentally constrained by the space-bandwidth of the hologram due to aliasing errors at insufficient sampling rates. This study analyzes the spatial distribution of the angular spectrum in undersampled holograms using angle modulation techniques. Aliased replica functions are identified as phase-modulated functions by multiples of the sampling frequency, with the spatial frequency components continuously extending into the replica regions. Optical imaging simulations demonstrate that image reconstruction beyond the space-bandwidth limitation of digital holograms is feasible. In particular, high-order diffraction fields, characterized by orthogonality, can be effectively eliminated through an upsampling process. By sequentially removing high-order terms and applying a learning-based denoising algorithm, wide-field high-resolution optical imaging is achieved. This approach demonstrates that only a captured low-resolution hologram can reconstruct a high-resolution image, thereby overcoming the limitations imposed by the finite space-bandwidth of digital holography.

physics.optics↗

arXiv2024

High-precision and low-noise dielectric tensor tomography using a micro-electromechanical system mirror

Dielectric tensor tomography is an imaging technique for mapping three-dimensional distributions of dielectric properties in transparent materials. This work introduces an enhanced illumination strategy employing a micro-electromechanical system mirror to achieve high precision and reduced noise in imaging. This illumination approach allows for precise manipulation of light, significantly improving the accuracy of angle control and minimizing diffraction noise compared to traditional beam steering approaches. Our experiments have successfully reconstructed the dielectric properties of liquid crystal droplets, which are known for their anisotropic structures, while demonstrating a notable reduction in background noise of the imag-es. Additionally, the technique has been applied to more complex samples, revealing its capability to achieve a high signal-to-noise ratio. This development represents a significant step forward in the field of birefringence imaging, offering a powerful tool for detailed study of materials with anisotropic properties.

physics.optics↗

arXiv2024

Spatial resolution enhancement in holographic imaging via angular spectrum expansion

Digital holography numerically restores three-dimensional image information using optically captured diffractive waves. The required bandwidth is larger than that of hologram pixel at a closer distance in the Fresnel diffraction regime, which results in the formation of aliased replica patterns in digital hologram. From the analysis of sampling phenomenon, the replica functions are revealed to be the components of higher angular spectra of hologram. Undersampled hologram consists of the moire patterns formed by the modulation of original function by complex exponential function. There is a one-to-one correspondence between the replicas in both real and Fourier spaces. The possibility to acquire high-resolution images over a wide field view is explored in terms of the expansion process of angular spectrum by using replicas. Only a low-NA hologram captured over a wide field restores a high-resolution image when using an optimization algorithm. Numerical simulations and optical experiments are performed to investigate the proposed scheme.

physics.optics↗

arXiv2023

Viewing-angle expansion of holographic image using enhanced-NA Fresnel hologram

The expansion of viewing angle is a crucial factor in holographic displays implemented with a spatial light modulator having a finite space-bandwidth. The enhanced-NA Fresnel hologram reconstructs a holographic image at an angle larger than the diffraction angle by a hologram pixel, where it has a difficulty in achieving this without an interference of high-order noises. This study presents the theoretical foundation for optimizing the enhanced-NA Fresnel hologram to recover the low space-bandwidth. The higher spectrum components of the digital hologram beyond the bandwidth exists in the form of their replications. The expansion of angular spectrum by its repetition during optimization procedure increases the image resolution, resulting in a viewing angle that is dependent on the hologram numerical aperture. We numerically and experimentally verify our strategy to expand a viewing angle of holographic image.

physics.optics↗

arXiv2022

Expansion of image space in enhanced-NA Fresnel holographic display

The enhanced-NA Fresnel hologram reconstructs a holographic image at a viewing angle larger than the diffraction angle of a hologram pixel. The image space is limited by the bandwidth of a digital hologram. In this study, we investigate the property of image formation in the extended image space beyond a diffraction zone. A numerical simulation using the phase Fresnel hologram is carried out to observe an extension of image space and the effect of this on the changes in the angular field of view. The phase Fresnel hologram, synthesized by restricting the angular view range to a diffraction angle, can reconstruct a uniform image without high-order noises within the primary viewing zone, which is well confirmed by optical experiments. On the other hand, the overlapping of high-order images is inevitable when the viewing angle depends on the hologram numerical aperture. The high-order images are distributed in the direction cosine space, which could be effectively removed through an angular low-pass filter. We discuss the development of method for expanding the image space while maintaining the viewing angle of a holographic image.

physics.optics↗

arXiv2021

Wide viewing-angle holographic display based on enhanced-NA Fresnel hologram

The viewing-angle enlargement of a holographic image is a crucial factor for realizing the holographic display. The numerical aperture (NA) of digital hologram other than a pixel specification has been known to determine the angular field extent of image. Here, we provide a valid foundation for the dependence of viewing angle on the hologram numerical aperture by investigating mathematically the internal structure of the sampled point spread function showing a self-similarity of its modulating curves. The enhanced-NA Fresnel hologram reconstructs the images at a viewing angle larger than a diffraction angle by a hologram pixel pitch where its angle value is expressed in terms of the NA of whole hologram aperture, which is systematically observed by optical hologram imaging. Finally, we found that the aliased replica noises generated in the enhanced-NA Fresnel diffraction regime are effectively suppressed within the diffraction scope by a digitized pixel. This characteristic enables us to overcome the image reduction and to remove the interference of high-order images, which leads to the wide viewing-angle holographic display. Optical experiments are shown to be consistent with the results of numerical simulation.

physics.optics↗

arXiv2021

Viewing angle analysis of reconstructed image from digital Fresnel hologram with enhanced numerical aperture

The viewing-angle enlargement of a holographic image is a crucial factor for realizing the holographic display. The numerical aperture (NA) of digital hologram other than a pixel specification has been known to determine the angular field extent of image. Here, we provide a valid foundation for the dependence of viewing angle on the hologram numerical aperture by investigating mathematically the internal structure of the sampled point spread function showing a self-similarity of its modulating curves and especially, analyzing this scheme on the basis of quantum mechanical framework. The enhanced-NA Fresnel hologram generates the multiple images with a high resolution, which can lead to the higher viewing angle represented as the NA of whole aperture of hologram. Optical experiment shows the consistent result with quantum mechanical description of viewing angle of holographic images. Finally, we discuss the method for enlarging viewing angle of holographic image without sacrificing image size by using this scheme.

physics.optics↗

arXiv2020

Analysis on image recovery for digital Fresnel hologram with aliased fringe generated from self-similarity of point spread function

We analyze the aliasing phenomenon for digital Fresnel hologram with an enhanced numerical aperture (NA). The enhanced-NA digital hologram acquired computationally or optically at a closer distance from the object has an aliased fringe generated by undersampling process of the Fresnel prefactor. The point spread function known as Fresnel factor reveals a self-similar envelope when being sampled, which becomes a crucial mechanism in making this type of aliasing fringe of hologram. We describe that as the enhanced-NA hologram involves already the complementary aliased fringe that might come up in the reconstruction process, the robust recovery of object image can be realized. These behaviors are confirmed through numerical simulation. Based on the analysis of aliased hologram fringe, we provide a method for reconstructing the object image from the enhanced-NA digital Fresnel hologram without the shrinkage of image size.

physics.optics↗

arXiv2020

Methods for extending viewing-angle of holographic image by using digital hologram with high numerical aperture

We investigate the angular field of view (AFOV) of a holographic image reconstructed from the digital Fresnel hologram in holographic display. The theoretical analysis reveals that the AFOV of a holographic image is fundamentally determined by the hologram numerical aperture (HNA) other than a diffraction angle of pixel pitch of a pixelated modulator. This property is proved for various types of the digital holograms by using a numerical simulation and optical experiments. The high-HNA hologram reconstructs the image with a high viewing-angle, although the image contraction is inevitable due to the Nyquist sampling criterion. We propose the method for extending the viewing-angle of a holographic image in the manner of increasing the object size during the high-HNA hologram synthesis and removing the high-order aliasing images.

physics.optics↗