arXiv subjects

Dibakar Sigdel

Publications and source records attributed to Dibakar Sigdel.

7 recordsLinked to original sources

arXiv2026

Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity

We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework rests on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix $\mathbf{J}$ corresponds to unitary gate evolution, and the positive-semidefinite dissipation matrix $\mathbf{R}$ to Measurement-Induced NonLinearity (MINL), realised by mid-circuit measurement with classical feedforward. Conservation and passivity are then enforced by construction rather than by penalty terms, and dissipation becomes an intrinsically quantum effect: energy leaves through the act of measurement. We instantiate the IHM in three architectures: a Quantum HNN that extracts Hamilton's equations via the Parameter-Shift Rule; a Q-pHNN that dissipates through MINL; and a topology-entangled Quantum Graph Neural Network lifting both channels to $N$-node coupled-phasor networks. In simulation, where every model here was trained, we obtain $1.35\%$ relative energy drift under a symplectic integrator, $100\%$ energy monotonicity for the single-oscillator MINL circuit, and $92$--$98\%$ phase-space energy decay across ring, star and chain networks at $N\in\{3,6,9\}$. On an IBM Heron processor the trained energy surface and its parameter-shift gradients reproduce their simulated values, with an error budget dominated by readout rather than gate infidelity; the dissipative channel executes natively, but its decay is not separable from measurement back-action at these depths.

cs.LG↗

arXiv2026

A Physics-Inspired Classical Digital Twin of Cortical Dynamics: A Band-Stratified Metriplectic Port-Hamiltonian Neural Network Learned from Brain-Computer-Interface EEG

We present a physics-inspired classical digital twin of brain-computer- interface (BCI) data: a graph neural network constrained to a band-stratified, metriplectic port-Hamiltonian form, with parameters learned from scalp EEG recorded during rest and motor imagery. The port-Hamiltonian structure is a modelling choice - it buys passivity, a certified steady-state power balance, and a clean separation of storage, routing and dissipation - not a claim about what the brain is. The state pairs each channel's instantaneous phase with its angular frequency, and stored energy decomposes over the five canonical frequency bands. A phase-locking prior measured from the same recordings gates the learned connectome, and a metriplectic formulation places the twin at a non- equilibrium steady state sustained by a metabolic port. Fitted to $1{,}109{,}250$ phasor samples from the PhysioNet EEG Motor Movement/Imagery database under a leakage-free split, the twin reaches a held-out reconstruction error of $1.30\times10^{-4}$. Scored free-running against invariants it did not author, the verdict is mixed: it reproduces near-critical avalanche branching ($σ\approx1$) but not the aperiodic $1/f$ slope or the long-range temporal correlations of the recordings. Skew-symmetry and non-negative dissipation hold by construction rather than by penalty, making the twin a structure-preserving substrate on which closed-loop neuromodulation can be designed and tested.

q-bio.NC↗

arXiv2026

PhasorFlow: A Python Library for Unit Circle Based Computing

We present PhasorFlow, an open-source Python library for computing on the $S^1$ unit circle. Inputs are encoded as complex phasors $z=e^{iϕ}$ on the $N$-torus ($\mathbb{T}^N$); as computation proceeds through unitary wave-interference gates, global norm is preserved while components drift into $\mathbb{C}^N$, letting algorithms leverage continuous geometric gradients. PhasorFlow makes three contributions. First, we formalize the Phasor Circuit model ($N$ threads, $M$ gates) with a 22-gate library spanning standard-unitary, non-linear, neuromorphic, and encoding operations under full matrix-algebra simulation. Second, we introduce the Variational Phasor Circuit (VPC), a trainable phase-native classifier analogous to variational quantum circuits. Third, we introduce the Phasor Transformer block and Large Phasor Model (LPM), replacing $QK^TV$ attention with a parameter-free DFT token-mixing layer. We validate the framework on financial volatility detection, neuromorphic associative memory, neural binding, period finding, and algorithmic logic applications that are unique to the library. This positions unit-circle computing as a deterministic, lightweight paradigm on classical hardware. Available at https://github.com/mindverse-computing/phasorflow.

cs.LG↗

arXiv2026

The RG-Flow Transformer: Encoding Scale-Free Dynamics in Scarce EEG

Brain field potentials are scale-free: their power spectra follow a $1/f^β$ law whose aperiodic exponent $β$ tracks cortical state, and sleep depth in particular is a shift in $β$. We ask whether a transformer endowed with an explicit renormalization-group (RG) inductive bias the RG-Flow Transformer, which couples ordinary self-attention to a scale-aware stream with a learnable anomalous dimension $γ$, block-spin coarse-graining, and an entropy-gated synchronization bridge has an advantage over a parameter-matched vanilla transformer on \emph{real, scarce} EEG. Using the PhysioNet Sleep-EDF corpus with a strict leakage-free by-subject hold-out, we (i) benchmark RG-Flow against a param-matched vanilla transformer and a hierarchy-only ablation on 5-class AASM sleep staging, (ii) sweep the per-subject data budget to look for the inductive-bias crossover predicted when data are scarce, and (iii) test whether RG-Flow's learned $γ$ tracks the measured spectral exponent $β$ out-of-sample a quantity the vanilla model does not possess. Across $5$ subjects and $5$ seeds under leave-one-subject-out cross-validation, RG-Flow and the vanilla transformer are statistically indistinguishable on 5-class staging (77.3\% vs 77.0\% accuracy; paired $p=0.294$), and the predicted scarce-data crossover does not appear: vanilla is numerically ahead at every data-limited budget. What does separate the models is interpretability RG-Flow recovers the continuous spectral exponent out-of-sample ($β$-recovery $R^2 = 0.416$), a capability the vanilla architecture has no analogue for.

cs.LG↗

arXiv2026

The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the Phasor Transformer block, a phase-native alternative representing sequence states on the unit-circle manifold $S^1$. Each block combines lightweight trainable phase-shifts with parameter-free Discrete Fourier Transform (DFT) token coupling, achieving global $\mathcal{O}(N\log N)$ mixing without explicit attention maps. Stacking these blocks defines the Large Phasor Model (LPM). We validate LPM on autoregressive time-series prediction over synthetic multi-frequency benchmarks against honest baselines: it beats a zero-parameter persistence baseline and, with the corrected gradient path, improves monotonically with depth before saturating, while remaining competitive-but-not-superior to self-attention at a fraction of the parameter count. Our results establish an explicit efficiency--accuracy frontier, showing that scalable temporal modeling in oscillatory domains can emerge from geometry-constrained phase computation with deterministic global coupling.

cs.LG↗

arXiv2026

Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification

We present the Variational Phasor Circuit (VPC), a deterministic classical learning architecture on the continuous $S^1$ unit-circle manifold. Inspired by variational quantum circuits, VPC replaces dense weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space, giving a unified method for binary and multi-class classification of spatially distributed signals. We evaluate VPC on real motor-imagery electroencephalography (EEG) from the PhysioNet Motor Movement/Imagery database (10 subjects, Common Spatial Pattern features, subject-wise cross-validation), where it attains a mean decoding accuracy of $0.60$ -- the highest among standard brain--computer-interface baselines (linear discriminant analysis, logistic regression, RBF-SVM, and a multilayer perceptron) -- using an order of magnitude fewer parameters and the lowest cross-subject variance. We also characterize capacity honestly: with phase-only shifts and unitary mixing, VPC realizes a linear decision function in a fixed cosine/sine feature lifting, well matched to the largely separable band-power structure of EEG but unable to represent parity-type functions, a ceiling that depth does not raise. These results position unit-circle phase interference as a parameter-efficient alternative to dense neural computation for signal classification, and motivate VPC both as a standalone classifier and a front-end for hybrid phasor-quantum systems.

cs.LG↗

arXiv2014

Correlation between Polyakov loops oriented in two different directions in SU(N) gauge theory on a two dimensional torus

We consider SU(N) gauge theories on a two dimensional torus with finite area, $A$. Let $T_μ(A)$ denote the Polyakov loop operator in the $μ$ direction. Starting from the lattice gauge theory on the torus, we derive a formula for the continuum limit of $\langle g_1(T_1(A)) g_2(T_2(A)) \rangle$ as a function of the area of the torus where $g_1$ and $g_2$ are class functions. We show that there exists a class function $ξ_0$ for SU(2) such that $\langle ξ_0(T_1(A)) ξ_0(T_2(A))\rangle > 1$ for all finite area of the torus with the limit being unity as the area of the torus goes to infinity. Only the trivial representation contributes to $ξ_0$ as $A\to\infty$ whereas all representations become equally important as $A\to 0$.

hep-th↗