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Amir Mohammadi

Publications and source records attributed to Amir Mohammadi.

At least 19 recordsLinked to original sources
arXiv2026

Polynomially effective equidistribution for unipotent orbits in products of $\mathrm{SL}_2$ factors

We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\mathbf K$-forms of $\mathrm{SL}_2^{\mathsf n}$ where $\mathbf K$ is a number field. This gives an effective version of equidistribution results of Ratner and Shah with a polynomial rate. The key new phenomenon is the existence of many intermediate groups between the $\mathrm{SL}_2$ containing our unipotent and the ambient group, which introduces potential local and global obstruction to equidistribution. Our approach relies on a Bourgain-type projection theorem in the presence of obstructions, together with a careful analysis of these obstructions.

math.DS↗
arXiv2025

Effective equidistribution for some one parameter unipotent flows

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

math.NT↗
arXiv2025

Detecting Text Manipulation in Images using Vision Language Models

Recent works have shown the effectiveness of Large Vision Language Models (VLMs or LVLMs) in image manipulation detection. However, text manipulation detection is largely missing in these studies. We bridge this knowledge gap by analyzing closed- and open-source VLMs on different text manipulation datasets. Our results suggest that open-source models are getting closer, but still behind closed-source ones like GPT- 4o. Additionally, we benchmark image manipulation detection-specific VLMs for text manipulation detection and show that they suffer from the generalization problem. We benchmark VLMs for manipulations done on in-the-wild scene texts and on fantasy ID cards, where the latter mimic a challenging real-world misuse.

cs.CV↗
arXiv2025

Investigation of Accuracy and Bias in Face Recognition Trained with Synthetic Data

Synthetic data has emerged as a promising alternative for training face recognition (FR) models, offering advantages in scalability, privacy compliance, and potential for bias mitigation. However, critical questions remain on whether both high accuracy and fairness can be achieved with synthetic data. In this work, we evaluate the impact of synthetic data on bias and performance of FR systems. We generate balanced face dataset, FairFaceGen, using two state of the art text-to-image generators, Flux.1-dev and Stable Diffusion v3.5 (SD35), and combine them with several identity augmentation methods, including Arc2Face and four IP-Adapters. By maintaining equal identity count across synthetic and real datasets, we ensure fair comparisons when evaluating FR performance on standard (LFW, AgeDB-30, etc.) and challenging IJB-B/C benchmarks and FR bias on Racial Faces in-the-Wild (RFW) dataset. Our results demonstrate that although synthetic data still lags behind the real datasets in the generalization on IJB-B/C, demographically balanced synthetic datasets, especially those generated with SD35, show potential for bias mitigation. We also observe that the number and quality of intra-class augmentations significantly affect FR accuracy and fairness. These findings provide practical guidelines for constructing fairer FR systems using synthetic data.

cs.CV↗
arXiv2025

FantasyID: A dataset for detecting digital manipulations of ID-documents

Advancements in image generation led to the availability of easy-to-use tools for malicious actors to create forged images. These tools pose a serious threat to the widespread Know Your Customer (KYC) applications, requiring robust systems for detection of the forged Identity Documents (IDs). To facilitate the development of the detection algorithms, in this paper, we propose a novel publicly available (including commercial use) dataset, FantasyID, which mimics real-world IDs but without tampering with legal documents and, compared to previous public datasets, it does not contain generated faces or specimen watermarks. FantasyID contains ID cards with diverse design styles, languages, and faces of real people. To simulate a realistic KYC scenario, the cards from FantasyID were printed and captured with three different devices, constituting the bonafide class. We have emulated digital forgery/injection attacks that could be performed by a malicious actor to tamper the IDs using the existing generative tools. The current state-of-the-art forgery detection algorithms, such as TruFor, MMFusion, UniFD, and FatFormer, are challenged by FantasyID dataset. It especially evident, in the evaluation conditions close to practical, with the operational threshold set on validation set so that false positive rate is at 10%, leading to false negative rates close to 50% across the board on the test set. The evaluation experiments demonstrate that FantasyID dataset is complex enough to be used as an evaluation benchmark for detection algorithms.

cs.CV↗
arXiv2025

Second Competition on Presentation Attack Detection on ID Card

This work summarises and reports the results of the second Presentation Attack Detection competition on ID cards. This new version includes new elements compared to the previous one. (1) An automatic evaluation platform was enabled for automatic benchmarking; (2) Two tracks were proposed in order to evaluate algorithms and datasets, respectively; and (3) A new ID card dataset was shared with Track 1 teams to serve as the baseline dataset for the training and optimisation. The Hochschule Darmstadt, Fraunhofer-IGD, and Facephi company jointly organised this challenge. 20 teams were registered, and 74 submitted models were evaluated. For Track 1, the "Dragons" team reached first place with an Average Ranking and Equal Error rate (EER) of AV-Rank of 40.48% and 11.44% EER, respectively. For the more challenging approach in Track 2, the "Incode" team reached the best results with an AV-Rank of 14.76% and 6.36% EER, improving on the results of the first edition of 74.30% and 21.87% EER, respectively. These results suggest that PAD on ID cards is improving, but it is still a challenging problem related to the number of images, especially of bona fide images.

cs.CV↗
arXiv2025

Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms

We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the results of Eskin, Margulis and Mozes, we establish quantitative results regarding the distribution of values of an indefinite ternary quadratic form at integer points, giving in particular an effective and quantitative proof of the Oppenheim Conjecture.

math.DS↗
arXiv2025

Effective equidistribution of semisimple adelic periods and representations of quadratic forms

We prove an effective equidistribution theorem for semisimple closed orbits on compact adelic quotients. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. The proof uses dynamical arguments, property $(τ)$, Prasad's volume formula, an effective closing lemma, and a novel effective generation result for subgroups. The latter in turn relies on an effective version of Greenberg's theorem. We apply the above to the problem of establishing a local-global principle for representations of integral quadratic forms, improving the codimension assumptions and providing effective bounds in a theorem of Ellenberg and Venkatesh.

math.NT↗
arXiv2024

Spectral Independence

We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessary condition that the marginals posses a spectral gap. Furthermore, we give additional control on the spectral gap depending on certain specific properties of the given groups and marginals; in particular, we prove some new cases of the super-approximation conjecture. One ingredient of the proof is a local Ulam stability result which is introduced and proved in this paper. This result characterizes partially defined almost homomorphisms between two analytic compact groups with simple Lie algebras.

math.GR↗
arXiv2023

Trapping Ion Coulomb Crystals in an Optical Lattice

We report the optical trapping of multiple ions localized at individual lattice sites of a one-dimensional optical lattice. We observe a fivefold increase in robustness against axial DC-electric fields and an increase of the axial eigenfrequency by two orders of magnitude compared to an optical dipole trap without interference but similar intensity. Our findings motivate an alternative pathway to extend arrays of trapped ions in size and dimension, enabling quantum simulations with particles interacting at long range.

physics.atom-ph↗
arXiv2022

Isolations of geodesic planes in the frame bundle of a hyperbolic $3$-manifold

We present a quantitative isolation property of the lifts of properly immersed geodesic planes in the frame bundle of a geometrically finite hyperbolic $3$-manifold. Our estimates are polynomials in the tight areas and Bowen-Margulis-Sullivan densities of geodesic planes, with degree given by the modified critical exponents.

math.DS↗
arXiv2022

Quantitative behavior of unipotent flows and an effective avoidance principle

We give an effective bound on how much time orbits of a unipotent group $U$ on an arithmetic quotient $G/Γ$ can stay near homogeneous subvarieties of $G /Γ$ corresponding to $\mathbb Q$-subgroups of $G$. In particular, we show that if such a $U$-orbit is moderately near a proper homogeneous subvariety of $G/Γ$ for a long time it is very near a different homogeneous subvariety. Our work builds upon the linearization method of Dani and Margulis. Our motivation in developing these bounds is in order to prove quantitative density statements about unipotent orbits, which we plan to pursue in a subsequent paper. New qualitative implications of our effective bounds are also given.

math.DS↗
arXiv2022

Prepended Domain Transformer: Heterogeneous Face Recognition without Bells and Whistles

Heterogeneous Face Recognition (HFR) refers to matching face images captured in different domains, such as thermal to visible images (VIS), sketches to visible images, near-infrared to visible, and so on. This is particularly useful in matching visible spectrum images to images captured from other modalities. Though highly useful, HFR is challenging because of the domain gap between the source and target domain. Often, large-scale paired heterogeneous face image datasets are absent, preventing training models specifically for the heterogeneous task. In this work, we propose a surprisingly simple, yet, very effective method for matching face images across different sensing modalities. The core idea of the proposed approach is to add a novel neural network block called Prepended Domain Transformer (PDT) in front of a pre-trained face recognition (FR) model to address the domain gap. Retraining this new block with few paired samples in a contrastive learning setup was enough to achieve state-of-the-art performance in many HFR benchmarks. The PDT blocks can be retrained for several source-target combinations using the proposed general framework. The proposed approach is architecture agnostic, meaning they can be added to any pre-trained FR models. Further, the approach is modular and the new block can be trained with a minimal set of paired samples, making it much easier for practical deployment. The source code and protocols will be made available publicly.

cs.CV↗
arXiv2022

Closed geodesics and holonomies for Kleinian manifolds

For a rank one Lie group G and a Zariski dense and geometrically finite subgroup $Γ$ of G, we establish equidistribution of holonomy classes about closed geodesics for the associated locally symmetric space. Our result is given in a quantitative form for real hyperbolic geometrically finite manifolds whose critical exponents are big enough. In the case when G=PSL(2, C), our results can be interpreted as the equidistribution of eigenvalues of $Γ$ in the complex plane. When $Γ$ is a lattice, this result was proved by Sarnak and Wakayama in 1999.

math.DS↗
arXiv2022

Polynomial effective equidistribution

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

math.DS↗