arXiv subjects

Amirhossein Samandar

Publications and source records attributed to Amirhossein Samandar.

11 recordsLinked to original sources

arXiv2026

Cosmic topology. Part Va. Information content of the observable Universe

If the Universe possesses a compact spatial topology with characteristic scale not much larger than the diameter of the observable Universe, then the associated symmetry transformations imprint specific statistical correlations on density perturbations. We derive the covariance between perturbation modes in the full topology volume and compute the induced covariance between modes in the observable subvolume. We then use this covariance to estimate the available information about topology contained in the full set of observable linear perturbations. For two sample Euclidean examples - the cubic three-torus ($E_1$) and a three-torus with a quarter turn ($E_3$) - the three-dimensional density field carries enough information to detect topology on scales up to 25 percent larger than those accessible from the two-dimensional cosmic microwave background anisotropies alone. Future probes of the cosmic density field using deep galaxy surveys or neutral-hydrogen 21-cm intensity mapping, combined with computationally intensive searches over the large parameter space of admissible topologies, thus offer a plausible avenue to extending the range of detectable cosmic topologies.

astro-ph.CO↗

arXiv2026

Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility

Large language models can solve harder reasoning problems with more inference-time compute. The term "test-time scaling," however, covers several inference algorithms: extending deliberation along one trajectory, sampling completed candidates and aggregating them by voting or verification, and searching over partial states. These algorithms differ in statistical structure, compute requirements, and failure modes. Treating them as interchangeable under a scalar "budget," or reporting accuracy without specifying the inference protocol, makes results difficult to compare across studies. We study test-time scaling along three axes. First, we formalize it as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the full inference system as the evaluated object and separate end-to-end performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and require compute accounting and uncertainty estimates that match the protocol. Third, we distinguish exact replay from distributional reproducibility and state the requirements for each. We also organize open-weight reasoning models by model-side and interface mechanisms. Our empirical study covers broad knowledge, symbolic reasoning, and competition mathematics, and we publicly release 1,403,520 sampled model attempts. The project website is available at https://mohsenhariri.github.io/scorio/tts. The released datasets are Trace (https://huggingface.co/datasets/harimo/scorio-trace), Lite (https://huggingface.co/datasets/harimo/scorio-lite), Math (https://huggingface.co/buckets/harimo/scorio-math), and SuperGPQA (https://huggingface.co/buckets/harimo/scorio-gpqa).

cs.LG↗

arXiv2026

The Topology of the Universe

Is the Universe infinite in all directions? The only way to know is to look. A non-trivial cosmic topology would imprint subtle signatures on the cosmic microwave background (CMB) and on the three-dimensional distribution of matter, breaking statistical isotropy and, potentially, homogeneity at the largest scales. If the topology scale is small enough, these signatures would be observable. Over the past three decades, successive space missions, most notably WMAP and $\textit{Planck}$, have enabled sophisticated searches for these signatures, using methods ranging from looking for matched circle pairs to full Bayesian likelihood analysis based on topology-dependent covariance matrices. Although these searches have yielded no definitive evidence for non-trivial topology, current constraints exclude only some topologies, parameter ranges, and observer positions. Recent advances show that detectable signals may persist even when the topology scale exceeds the size of the visible Universe. Planned CMB experiments, including LiteBIRD and $\textit{Taurus}$, and high-precision galaxy and line intensity-mapping surveys, could expand the detectable parameter space by exploiting polarisation data, and by exploring topology-induced correlations at all accessible redshifts. Whether cosmic topology is observable remains uncertain, but current and future data offer an unprecedented opportunity to probe the global structure of the Universe.

astro-ph.CO↗

arXiv2026

Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation

Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained. We present a principled Bayesian evaluation framework that replaces Pass$@k$ and average accuracy over $N$ trials (avg$@N$) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences. Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate. Theoretically, under a uniform prior, the Bayesian posterior mean is order-equivalent to average accuracy (Pass$@1$), explaining its empirical robustness while adding principled uncertainty. Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT'25, and BrUMO'25, the posterior-based procedure achieves faster convergence and greater rank stability than Pass$@k$ and recent variants, enabling reliable comparisons at far smaller sample counts. The framework clarifies when observed gaps are statistically meaningful (non-overlapping credible intervals) versus noise, and it naturally extends to graded, rubric-based evaluations. Together, these results recommend replacing Pass$@k$ for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit. Source code is available at https://github.com/mohsenhariri/scorio

cs.AI↗

arXiv2026

Quantum Signatures of Cosmic Topology: How Casimir Backreaction Transmits Isotropy Violation

A finite, scheme-independent Casimir contribution to the stress-energy tensor arises naturally for quantum fields in universes with non-trivial spatial topology. We compute this Casimir stress-energy tensor contribution for a conformally coupled scalar field and for a minimally coupled scalar field. We show that, for the conformally coupled case, the backreaction of this contribution to the Einstein equations during an expanding de Sitter phase drives anisotropic expansion even when the Universe begins in a locally homogeneous and isotropic state. We conclude that quantum imprints of the underlying non-trivial topology inevitably give rise to local departures from homogeneity and isotropy.

hep-th↗

arXiv2026

Cosmic topology. Part IIc. Detectability with non-standard primordial power spectrum

Non-trivial spatial topology of the Universe can imprint potentially observable signatures on the cosmic microwave background (CMB). In this study, we investigate how deviations from the standard nearly-scale-free primordial power spectrum impact observables for the fully compact, orientable Euclidean topologies ($E_1$--$E_6$). We examine how such deviations modify the detectability of the underlying topology, depending on whether they are an intrinsic consequence of non-trivial topology or independent of it. We compute CMB temperature correlation matrices across a range of topologies, fundamental domain sizes, and observer locations for both standard and modified primordial power spectra. The impact of these modifications on the detectability of topology is quantified using the Kullback-Leibler divergence, providing an estimate of the distinguishability of non-trivial and simply-connected topologies based solely on CMB temperature observations. In addition, we employ the CatBoost machine learning algorithm to classify harmonic-space realizations of CMB temperature maps and thereby assess the observational prospects for topology detection. Signatures of non-trivial topology are encoded in the off-diagonal structure of the CMB temperature correlation matrices and are most prominent on the largest angular scales. Deviations from the simple power-law primordial spectrum at these scales can substantially alter the detectability of topology, either enhancing its characteristic CMB imprints or suppressing them below observational sensitivity. Our results demonstrate that uncertainties in the primordial power spectrum must be carefully accounted for in robust searches for cosmic topology using the CMB.

astro-ph.CO↗

arXiv2025

Cosmic topology. Part IIb. Eigenmodes, correlation matrices, and detectability of non-orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. In this paper we consider the non-orientable Euclidean topologies \E{7}--\E{10}, \E{13}--\E{15}, and \E{17}, encompassing the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the CMB sky. We find that in manifolds where the distance to our nearest clone is less than about $1.2$ times the diameter of the last scattering surface of the CMB, we expect a correlation signal that is larger than cosmic variance noise in the CMB. Our limited selection of manifold parameters are exemplary of interesting behaviors, but not necessarily representative. Future searches for topology will require a thorough exploration of the parameter space to determine what values of the parameters predict statistical correlations that are convincingly attributable to topology.[Abridged]

astro-ph.CO↗

arXiv2025

Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds

We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing $\ell$ and $m$ and across every possible pair of temperature and $E$- and $B$-modes of polarization. This includes normally forbidden $TB$ and $EB$ correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest $\ell$ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.

astro-ph.CO↗

arXiv2025

Cosmic topology. Part Ic. Limits on lens spaces from circle searches

Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $Λ$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative curvature, i.e., $\vertΩ_K\vert\ll1$. However, whether the geometry is flat ($E^3$), positively curved ($S^3$) or negatively curved ($H^3$), there are many possible topologies. Among the topologies of $S^3$ geometry, the lens spaces $L(p,q)$, where $p$ and $q$ ($p>1$ and $0<q<p$) are positive integers, are quotients of the covering space of $S^3$ (the three-sphere) by ${\mathbb{Z}}_p$, the cyclic group of order $p$. We use the absence of any pair of circles on the CMB sky with matching patterns of temperature fluctuations to establish constraints on $p$ and $q$ as a function of the curvature scale that are considerably stronger than those previously asserted for most values of $p$ and $q$. The smaller the value of $\vertΩ_K\vert$, i.e., the larger the curvature radius, the larger the maximum allowed value of $p$. For example, if $\vertΩ_K\vert\simeq 0.05$ then $p\leq 9 $, while if $\vertΩ_K\vert\simeq 0.02$, $p$ can be as high as 24. Future work will extend these constraints to a wider set of $S^{3}$ topologies.

astro-ph.CO↗

arXiv2024

Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics

The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these predictions, large-angle CMB temperature anomalies generically involve correlations between even-$\ell$ and odd-$\ell$ angular power spectrum $C_\ell$, while recent analyses of CMB polarization have revealed non-zero equal-$\ell$ $EB$ correlations. These findings challenge the conventional understanding, suggesting deviations from statistical isotropy, violations of parity, or both. Cosmic topology, which involves changing only the boundary conditions of space relative to standard cosmology, offers a compelling framework to potentially account for such parity-violating observations. Topology inherently breaks statistical isotropy, and can also break homogeneity and parity, providing a natural paradigm for explaining observations of parity-breaking observables without the need to add parity violation to the underlying microphysics. Our investigation delves into the harmonic space implications of topology for CMB correlations, using as an illustrative example $EB$ correlations generated by tensor perturbations under both parity-preserving and parity-violating scenarios. Consequently, these findings not only challenge the foundational assumptions of the standard cosmological model but also open new avenues for exploring the topological structure of the Universe through CMB observations.

astro-ph.CO↗

arXiv2024

Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean $E_1$ topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic $E_1$ topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

astro-ph.CO↗