Maximum Entropy Encoding of Energy-Weighted Spherical Moments

• URL: http://arxiv.org/abs/2608.20429v1
• Date: Thu, 20 Aug 2026 00:58:59 GMT
• Title: Maximum Entropy Encoding of Energy-Weighted Spherical Moments
• Abstract summary: We study how angular energy signals composed of non-negative Monte Carlo path samples can be compressed and reconstructed for irradiance using finite moments.<n>Experiments cover 981 Poly Haven HDRI 2K scenes and three Debevec probes.
• Score: 2.1503190497152453
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study how angular energy signals composed of non-negative Monte Carlo path samples can be compressed and reconstructed for irradiance using finite moments. Writing each sample as an energy-weighted directional feature $x = r u$, we adopt total energy, the first directional moment, and the traceless second moment as $1+3+5$ linearly additive, rotationally covariant statistics. Under a fixed Lebesgue reference measure, the maximum-entropy closure yields $p(r,u) \propto \exp(-βr g(u))$, where $g(u) = 1 - b \cdot u + u^T Q u$, whose directional probability and angular energy density are proportional to $g^{-3}$ and $g^{-4}$, respectively. When $g_{\min} > 0$ the closure is normalizable and the reconstruction is strictly positive. We further provide analytic moment matching, variance, inverse sampling, and closed-form diffuse response for the pure-dipole four-parameter subfamily, as well as the realizability domain, partition function, azimuthal algebraic integral, and LUT-oriented reconstruction form for the dipole-second-moment coaxial five-parameter subfamily. Experiments cover 981 Poly Haven HDRI 2K scenes and three Debevec probes. Five-parameter MaxEnt achieves a 78.7% per-scene win rate against stored QZH, with mean luminance RMSE reduced by 15.8%; the advantage is more pronounced in scenes with strong directionality. Both MaxEnt variants maintain zero negative irradiance across all scenes. Full second-order SH-2 yields the lowest overall error, while five-parameter MaxEnt ranks second and outperforms SH-2 in the high-directionality bucket; the coaxial subfamily shows systematic closure error on non-coaxial multi-source scenes.

Related papers

• $\ ext{GSF-}χ$: Global Stereochemical Fields for Chiral Graph Transformers [49.85093436361195]
  We introduce GSF-$$, a graph transformer in which stereogenic units modulate all pairwise interactions.<n>A $C$ projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs.<n>GSF-$$ leads every central-ECD output and improves axial Rotation and Symbol by $12.6%$ and $7.9%$ over the strongest baseline.
  arXiv  Detail & Related papers  (2026-09-11T07:41:20Z)
• Model-level synthetic-flux control of hyperchaos order and matched-resource sensing in dissipative optomechanics [0.11545092788508222]
  We present a synthetic-flux phase $_rm syn$ control coordinate that selects the emphorder of a drive- and coupling-gated hyperchaos transition.<n>A phase-consistent Floquet--Lyapunov protocol (cross-checked by monodromy multipliers, dissipative volume balance $sum_i=nameTr(J)=-1.04$ and a 180-run three-seed audit) localizes the onset to a Neimark--Sacker bifurcation at $E*=num1.060
  arXiv  Detail & Related papers  (2026-09-02T17:13:43Z)
• How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis [53.063298916923976]
  We study the feedback in a Gaussian single-index model with $r*(x) = *(langle *, xrangle)$ and $x sim N(0, I_d)$.<n>We analyze a two-stage neural reward model that first learns the hidden direction $*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression.
  arXiv  Detail & Related papers  (2026-05-23T22:00:38Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Towards the "puzzle" of Chromium dimer Cr$_2$: predicting the Born-Oppenheimer rovibrational spectrum [44.99833362998488]
  This paper calculates the potential energy curve for the state $X1Sigma+$ of the Cr$$$ dimer. It is found for the first time for the whole range of internuclear distances $R$.
  arXiv  Detail & Related papers  (2024-01-06T17:00:12Z)
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain [0.771303749110121]
  We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions. We find that the universal ratio of the SR limit does not hold for $alpha_mathrmLR 2$, implying a deviation in the criticality.
  arXiv  Detail & Related papers  (2023-08-18T17:58:36Z)
• Globally optimal interferometry with lossy twin Fock probes [0.0]
  We show that a method of moments readout of two quadratic spin observables $J_z2$ and $J_+2+J_-2$ is globally optimal for Dicke state probes. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states.
  arXiv  Detail & Related papers  (2023-08-10T22:56:12Z)
• Dynamics of Open Quantum Systems II, Markovian Approximation [0.0]
  We show that for fixed, small values of the coupling constant $lambda$, the true reduced dynamics of the system is approximated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is $O(lambda|1/4)$ for all times.
  arXiv  Detail & Related papers  (2021-04-30T18:09:35Z)
• Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergence [8.873449722727026]
  We show that the rate estimate $widetildemathcalO(depsilon-1)$ improves the previously known rates in both of these metrics. In particular, for convex and firstorder smooth potentials, we show that LMC algorithm achieves the rate estimate $widetildemathcalO(depsilon-1)$ which improves the previously known rates in both of these metrics.
  arXiv  Detail & Related papers  (2020-07-22T18:18:28Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.