arXiv subjects

Armon Rasooli

Publications and source records attributed to Armon Rasooli.

4 recordsLinked to original sources

arXiv2026

CryptoL: Towards Scale Dominance and Physics Constraints Mitigation in Financial Multivariate Time Series Forecasting

Cryptocurrency forecasting presents a distinctive combination of extreme cross-asset scale heterogeneity, non-stationary dynamics, and structural dependencies among Open, High, Low, and Close (OHLC) variables. We present CryptoL, a unified framework designed to address these challenges within multivariate time-series forecasting. CryptoL evaluates forecasting error in context-normalized coordinates within the RevIN pipeline, preventing inverse normalization from introducing an additional squared-scale weighting into the MSE objective. We formally characterize this effect through the empirical risk and parameter-gradient geometry, establishing the conditions under which large-scale assets can disproportionately influence shared-model optimization. Beyond loss-space normalization, CryptoL examines channel-independent and channel-dependent normalization for OHLC data, showing that a shared channel-dependent affine transformation preserves candle-order relations that independent channel transformations need not preserve. The framework further incorporates scale-adaptive numerical stabilization to reduce distortions caused by a fixed normalization constant across assets spanning many orders of magnitude, together with a soft feasibility loss that penalizes violations of the defining OHLC inequalities. Experiments across heterogeneous cryptocurrency assets evaluate these components through controlled ablations and demonstrate improvements in forecasting accuracy, training stability, and the frequency of financially valid OHLC predictions relative to the considered baselines. CryptoL therefore provides an integrated approach to scale-balanced optimization, structure-preserving normalization, numerical stabilization, and constraint-aware cryptocurrency forecasting.

cs.AI↗

arXiv2026

Global minimax risk and acquisition laws for heterogeneous information fusion

We prove an all-allocation global target-risk theorem for independent Gaussian sources that share a scalar nuisance and an unknown contact coordinate. For a fixed immersed nuisance curve with finitely many multiple fibres and pairwise nonparallel branch tangents, squared target risk is comparable to a primary estimation floor plus a target-gap-weighted Gaussian discrimination profile. Independent localization, finite branch selection and target-class refitting give an estimator attaining this comparison across every nonnegative integer allocation. A full-box specialization has positive-definite primary Fisher information everywhere and globally identifies its target, yet models with identical derivatives of every order along a critical hypersurface have different polynomial risk exponents. We construct a finite certified estimator and quantify the numerical accuracy needed to preserve rare branch decisions and acquisition windows. A polynomial tangency family both demonstrates the geometric boundary and quantifies its repair: known auxiliary gain, source contact order and target vanishing order determine a risk law uniform through zero gain. For a shared spherical direction, a separately proved composite-testing result transfers through an unknown contact coordinate using only counted observations. These theorems distinguish the resources needed for local estimation, discrimination between parameter regions and nuisance alignment, and yield acquisition thresholds under explicit scalar-observation costs.

math.ST↗

arXiv2026

Sharp Minimax Limits and Compatibility Spectra for Critical Near-DFT Index-Only Frequency Estimation

An $M$-channel discrete Fourier transform (DFT) channelizer routes an on-grid sinusoid to a single output. When each frame reports only one energy-proportional channel index, signed sub-bin frequency estimation becomes nonregular: dark-channel probability is quadratic in the offset, whereas orientation enters cubically. We study $N$ independent labeled reports under a known uniform-replacement probability $\epsilon_N$ and a single deterministic unitary shared by all frequencies and frames, constrained to routing defect $\tau/N$. If $\sqrt{N}\epsilon_N \to \lambda < \infty$, we establish an attained global-in-frequency minimax limit at the critical scales $N^{-1/4}$ for frequency offset, $N^{-1/2}$ for unitary perturbation and replacement, and $N^{-1}$ for routing defect. The effective unitary tangent is a symmetric complete-graph edge field modulo one centering nuisance, and its first variation is a radius-dependent weighted divergence. For $\lambda>0$, evaluation at $k$ distinct normalized offset magnitudes yields an exact Fourier-Cauchy nullity spectrum: $\lfloor(M-1)/2\rfloor$ evaluations are necessary and sufficient, for every choice of distinct magnitudes, to certify neutrality at all magnitudes. The terminal nullspace has a greatest-common-divisor dimension formula and positive-definite aggregate curvature. Consequently, exact DFT routing is uniquely minimax within the complete critical tangent class for $M=3$, whereas every positive critical defect budget strictly improves the minimax constant for $M\geq4$. The analysis also yields a smallest-prime curvature-visibility law and, for $M\geq5$, discontinuous compatibility geometry but a continuous minimax value at the zero critical replacement floor $\lambda=0$.

eess.SP↗

arXiv2026

Compressed Single-Tone Frequency Estimation With Unknown Complex Gain: Singular Rates and Global Identifiability

Fixed linear compression can preserve local Fisher information for a sinusoid yet destroy global frequency identification, while a dark response can make local estimation nonregular. We study both failures for a single complex tone observed through a fixed complex-linear sketch with unknown nonzero complex gain and pre-sketch white Gaussian noise. Near an isolated analytic dark frequency, we separate radial signal vanishing from optimized projective contact between the two signed frequency branches. When the gain magnitude is constrained to a fixed nondegenerate interval, finite contact is equivalent to local quotient identifiability and minimax consistency. The sharp mean-square-error rate is determined by the sum of the radial and contact orders; infinite contact produces exact local aliases. Globally, we formulate a worst-frequency efficientinformation objective on whitened row spaces. We solve it exactly for every even output rank, prove uniqueness and quantitative rigidity of the symmetric-edge projector, and solve the evenaperture co-rank-one case. The rank-two optimum is aliased, and a winding obstruction gives a positive lower bound on the information price of global identification. From three outputs onward, sketches that are globally identifying with an immersive projective response are open and dense and have zero price at the level of suprema; for every even rank of at least four, the exact optimizer has this property. Thus local information preservation, singular recoverability, and global identifiability obey distinct compression laws within one estimation model.

eess.SP↗