arXiv subjects

Arijit Ghosh

Publications and source records attributed to Arijit Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Balancing Frequencies and Pixels in Flow Matching

Natural images follow a $1/f^2$ spectral distribution: most signal energy lies in the low spatial frequencies, while the perceptually important structures such as textures and edges occupy sparse high-frequency bands. Pixel-space reconstruction objectives, however, treat all spatial errors uniformly, causing low frequencies to dominate the optimization signal and delaying the learning of fine-scale details. In this work, we identify this objective-level spectral imbalance as a key inefficiency in training pixel-space flow models. To address it, we propose a Focal Log-Frequency Loss (f-loss), a spectrally balanced objective that equalizes the learning signal across frequencies, emphasizing high-frequency components that are otherwise underrepresented in pixel-space objectives. Building on this, we introduce a simple training strategy that combines frequency and pixel supervision: we first emphasize frequency-domain learning early to capture all frequencies, and then transition to standard pixel-space v-loss for spatial refinement. This balancing mitigates the low-frequency bias of pixel losses and aligns the training signal with the evolving needs of the model. Our approach is conceptually simple, requires no architectural changes, and acts as a drop-in replacement for flow matching losses. Across multiple model scales, it accelerates convergence by up to 40% while consistently improving FID and perceptual fidelity. We will release code and models.

cs.CV↗

arXiv2026

Unlocking Fractional Moments in Delphic Set Streams

We consider estimation of non-integer frequency moments $F_k$ and related Bernstein-type statistics in the Delphic set stream model under a bounded-frequency assumption: every universe element appears at most $\tau$ times. The main challenge of this model is to keep space low while also keeping update time low, which is not trivial because the sets can be exponential in size compared to their representations. Our core insight is that by sampling the stream at different rates and observing the resulting distinct-counts, we can 'probe' the frequency distribution and numerically integrate these probes to reconstruct a broad class of statistics. Building on that, we crucially observe that the distinct-count of a randomly sampled substream, viewed as a function of the sampling rate, is a single analytic object whose evaluations determine a broad class of statistics via a complementary Laplace-type integral. Algorithmically we exploit this by: 1. estimating those evaluations using only standard $F_0$ (distinct-count) algorithms on sampled substreams and 2. recovering target statistics by controlled numerical integration on a judiciously chosen grid. For $F_k$ with $k\in (0,1)$ we obtain the first one-pass streaming algorithms for Delphic set streams whose space and per-set update time are $\mathrm{poly}(\log|\Omega|,\log m,\varepsilon^{-1},\log(1/\delta))$ in the practically relevant regime $\tau=\mathrm{polylog}(|\Omega|,m)$; in general the bounds are polynomial in $\tau$ and $\varepsilon^{-1}$ and logarithmic in $\delta^{-1}$. We also give a complexity-theoretic barrier explaining why lower bounds for removing the bounded-frequency assumption appear difficult: ruling out polylogarithmic algorithms for unrestricted Delphic $F_k$ would imply a linear-space threshold-counting separation.

cs.DS↗

arXiv2026

From Decision to Random Certificates: Exponential Separation for Edge Estimation with Independent Set Queries

We study the problem of estimating the number of edges in an undirected, unweighted graph using sublinear query access. We consider a query model that preserves the structure of Independent Set (IS) queries, but augments their output with a random certificate: given a vertex subset, the oracle returns a uniformly random edge from the induced subgraph if one exists, and returns null otherwise. Using this access, we give a randomized algorithm that outputs a $(1 \pm \varepsilon)$-approximation to the number of edges with constant success probability using $\widetilde{O}(\log^{2} m)$ queries. This implies an exponential separation from both standard IS queries and global random edge-sampling models: estimating the number of edges using standard IS queries require $\widetilde{\Theta}\!\left(\min\left\{\sqrt{m},\, \frac{n}{\sqrt{m}}\right\}\right)$ queries, while direct random edge-sample access requires $\widetilde{\Theta}(\sqrt{m})$ samples. Beyond separation in query complexity, our algorithm is output-sensitive: its query complexity is polylogarithmic in the number of edges in the graph. This aligns with the classical objective in group testing, where one seeks algorithms that are both worst-case optimal and instance-adaptive. Conceptually, our model connects group testing, the decision-versus-counting dichotomy, graph property testing, and the "power of a random certificate", and can be viewed as a structured form of conditional sampling of edges in graphs.

cs.DS↗

arXiv2026

Simplicial subdivision of simplices of arbitrary dimension in spaces of constant curvature with bounded quality

In 1942, Freudenthal showed that a simplex in Euclidean space can be subdivided such that the quality (well-shapedness of the simplex, quantified in terms of e.g. fatness) of the simplices in the subdivision is lower bounded. This answered a question of Brouwer. Recently, Brunck discussed the same problem for simplices in two-dimensional spaces of constant curvature and provided a closely related construction. In this paper we generalize Brunck's result to arbitrary dimensional spaces of constant curvature by combining Freudenthal's construction and radial projection. We contrast this approach with Brunck's construction.

cs.CG↗

arXiv2026

RE-TRIANGLE: Does TRIANGLE Enable Multimodal Alignment Beyond Cosine Similarity in Retrieval?

Multimodal alignment is critical for bridging the semantic gap in information retrieval. However, traditional pairwise strategies introduce a geometric blind spot: while they align anchor modalities (e.g., text) with others, they lack constraints to enforce mutual consistency between peripheral modalities (e.g., video and audio). The TRIANGLE framework addresses this by minimizing the area of modality triplets on a hypersphere to enforce holistic alignment. In this reproducibility study, we verify the robustness of this geometric objective for retrieval tasks. We confirm that TRIANGLE outperforms pairwise baselines in zero-shot settings, achieving Recall@1 gains of up to +8.7 points, though benefits are domain-dependent. However, we fail to reproduce the reported learning-from-scratch results. Analysis using a synthetic toy dataset attributes this to instability when jointly optimizing geometric alignment with Data-Text Matching (DTM) loss. Furthermore, we find that cosine regularization primarily stabilizes text-to-video retrieval, and fine-tuning with domain supervision amplifies geometric benefits but reduces cross-dataset generalization. Our findings support the efficacy of geometric alignment while highlighting critical optimization sensitivities. Code available at https://github.com/ARIJIT00171/RE-TRIANGLE.

cs.IR↗

arXiv2026

PoM: A Linear-Time Replacement for Attention with the Polynomial Mixer

This paper introduces the Polynomial Mixer (PoM), a novel token mixing mechanism with linear complexity that serves as a drop-in replacement for self-attention. PoM aggregates input tokens into a compact representation through a learned polynomial function, from which each token retrieves contextual information. We prove that PoM satisfies the contextual mapping property, ensuring that transformers equipped with PoM remain universal sequence-to-sequence approximators. We replace standard self-attention with PoM across five diverse domains: text generation, handwritten text recognition, image generation, 3D modeling, and Earth observation. PoM matches the performance of attention-based models while drastically reducing computational cost when working with long sequences. The code is available at https://github.com/davidpicard/pom.

cs.CV↗

arXiv2026

Spectral Shadows: When Communication Complexity Meets Linear Invariance Testing

In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g : \mathbb{F}_2^n \to \{-1, +1\}$, Alice and Bob are tasked with determining whether $f$ and $g$ are equivalent up to a nonsingular linear transformation of the input variables, or far from being so. This problem has been extensively investigated in several models of computation, including standard algorithmic and property testing frameworks, owing to its fundamental connections with combinatorial circuit design, complexity theory, and cryptography. However, despite its broad relevance, it has remained unexplored in the context of communication complexity, a gap we address in this work. Our main results demonstrate that the approximate spectral norm of the input functions plays a central role in governing the communication complexity of this problem. We design a simple deterministic protocol whose communication cost is polynomial in the approximate spectral norm, and complement it with nearly matching lower bounds (up to a quadratic gap). In the randomised setting with private coins, we present an even more efficient protocol, though equally simple, that achieves a quadratically improved dependence on the approximate spectral norm compared to the deterministic case, and we prove that such a dependence is essentially unavoidable. These results identify the approximate spectral norm as a key complexity measure for testing linear invariance in the communication complexity framework. As a core technical ingredient, we establish new junta theorems for Boolean functions with small approximate spectral norm, which may be of independent interest in Fourier analysis and learning theory.

cs.DS↗

arXiv2025

Optimal non-adaptive algorithm for edge estimation

We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph, our method requires only $\widetilde{O}(\sqrt{n})$ queries, achieving sublinear query complexity. The algorithm independently samples a set of vertices and queries their degrees, and also independently samples a set of edges, using the answers to these queries to estimate the total number of edges in the graph. We further prove a matching lower bound, establishing the optimality of our algorithm and resolving the non-adaptive query complexity of this problem with respect to degree and random-edge queries.

cs.DS↗

arXiv2025

MIRO: MultI-Reward cOnditioned pretraining improves T2I quality and efficiency

The default paradigm of post-training text-to-image generators includes post-hoc selection of generated images, and subsequent training with one reward model to align the generator to the reward, typically user preference. This discards informative data as well as optimizes only for a single reward, hence harming diversity, semantic fidelity and efficiency. Instead, we propose MIRO, a method that conditions the model on multiple rewards during training, thus letting the model learn user preferences directly. MIRO pre-training both improves the visual quality of the generated images and speeds up the training, achieving state of the art on the GenEval compositional benchmark and user-preference scores (PickAScore, ImageReward, HPSv2).

cs.CV↗

arXiv2025

No Infinite $(p,q)$-Theorem for Piercing Compact Convex Sets with Lines in $\mathbb{R}^3$

An infinite $(p,q)$-theorem, or an $(\aleph_0,q)$-theorem, involving two families $\mathcal{F}$ and $\mathcal{G}$ of sets, states that if in every infinite subset of $\mathcal{F}$, there are $q$ sets that are intersected by some set in $\mathcal{G}$, then there is a finite set $S_{\mathcal{F}}\subseteq\mathcal{G}$ such that for every $C\in\mathcal{F}$, there is a $B\in S_{\mathcal{F}}$ with $C\cap B\neq\emptyset$. We provide an example demonstrating that there is no $(\aleph_0,q)$-theorem for piercing compact convex sets in $\mathbb{R}^3$ with lines by constructing a family $\mathcal{F}$ of compact convex sets such that it does not have a finite line transversal, but for any $t\in\mathbb{N}$, every infinite subset of $\mathcal{F}$ contains $t$ sets that are pierced by a line.

math.CO↗

arXiv2025

Dimension Agnostic Testing of Survey Data Credibility through the Lens of Regression

Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional distributions, which typically requires a number of samples that grows exponentially with the dimension. However, depending on the model used for data analysis, the conclusions drawn from the data may remain consistent across different underlying distributions. In this context, we propose a task-based approach to assess the credibility of sampled surveys. Specifically, we introduce a model-specific distance metric to quantify this notion of credibility. We also design an algorithm to verify the credibility of survey data in the context of regression models. Notably, the sample complexity of our algorithm is independent of the data dimension. This efficiency stems from the fact that the algorithm focuses on verifying the credibility of the survey data rather than reconstructing the underlying regression model. Furthermore, we show that if one attempts to verify credibility by reconstructing the regression model, the sample complexity scales linearly with the dimensionality of the data. We prove the theoretical correctness of our algorithm and numerically demonstrate our algorithm's performance.

cs.LG↗

arXiv2025

Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Let $f$ and $g$ be Boolean functions over a finite Abelian group $\mathcal{G}$, where $g$ is fully known, and we have {\em query access} to $f$, that is, given any $x \in \mathcal{G}$ we can get the value $f(x)$. We study the tolerant isomorphism testing problem: given $\epsilon \geq 0$ and $\tau > 0$, we seek to determine, with minimal queries, whether there exists an automorphism $\sigma$ of $\mathcal{G}$ such that the fractional Hamming distance between $f \circ \sigma$ and $g$ is at most $\epsilon$, or whether for all automorphisms $\sigma$, the distance is at least $\epsilon + \tau$. We design an efficient tolerant testing algorithm for this problem, with query complexity $\mathrm{poly}\left( s, 1/\tau \right)$, where $s$ bounds the spectral norm of $g$. Additionally, we present an improved algorithm when $g$ is Fourier sparse. Our approach uses key concepts from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner-product for finite Abelian groups. We believe these techniques will find further applications in property testing.

cs.CC↗

arXiv2024

Testing vs Estimation for Index-Invariant Properties in the Huge Object Model

The Huge Object model of property testing [Goldreich and Ron, TheoretiCS 23] concerns properties of distributions supported on $\{0,1\}^n$, where $n$ is so large that even reading a single sampled string is unrealistic. Instead, query access is provided to the samples, and the efficiency of the algorithm is measured by the total number of queries that were made to them. Index-invariant properties under this model were defined in [Chakraborty et al., COLT 23], as a compromise between enduring the full intricacies of string testing when considering unconstrained properties, and giving up completely on the string structure when considering label-invariant properties. Index-invariant properties are those that are invariant through a consistent reordering of the bits of the involved strings. Here we provide an adaptation of Szemer\'edi's regularity method for this setting, and in particular show that if an index-invariant property admits an $\epsilon$-test with a number of queries depending only on the proximity parameter $\epsilon$, then it also admits a distance estimation algorithm whose number of queries depends only on the approximation parameter.

cs.DS↗

arXiv2024

Testing Credibility of Public and Private Surveys through the Lens of Regression

Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

cs.LG↗

arXiv2024

About almost covering subsets of the hypercube

Let $\mathbb{F}$ be a field, and consider the hypercube $\{ 0, 1 \}^{n}$ in $\mathbb{F}^{n}$. Sziklai and Weiner (Journal of Combinatorial Theory, Series A 2022) showed that if a polynomial $P ( X_{1}, \dots, X_{n} ) \in \mathbb{F}[ X_{1}, \dots, X_{n}]$ vanishes on every point of the hypercube $\{0,1\}^{n}$ except those with at most $r$ many ones then the degree of the polynomial will be at least $n-r$. This is a generalization of Alon and F\"uredi's fundamental result (European Journal of Combinatorics 1993) about polynomials vanishing on every point of the hypercube except at the origin (point with all zero coordinates). Sziklai and Weiner proved their interesting result using M\"{o}bius inversion formula and the Zeilberger method for proving binomial equalities. In this short note, we show that a stronger version of Sziklai and Weiner's result can be derived directly from Alon and F\"{u}redi's result.

math.CO↗

arXiv2024

Structure of sparse Boolean functions over Abelian groups, and its application to testing

We study Fourier-sparse Boolean functions over general finite Abelian groups. A Boolean function $f : G \to \{-1,+1\}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. We introduce a general notion of granularity of Fourier coefficients and prove that every non-zero coefficient of an $s$-sparse Boolean function has magnitude at least \begin{equation*} \frac{1}{2^{\varphi(\Delta)/2} \, s^{\varphi(\Delta)/2}}, \end{equation*} where $\Delta$ denotes the exponent of the group $G$ (that is, the maximum order of an element in $G$) and $\varphi$ is the Euler's totient function. This generalizes the celebrated result of Gopalan et al. (SICOMP 2011) for $\mathbb{Z}_2^n$, extending it to all finite Abelian groups via new techniques from group theory and algebraic number theory. Using our new structural results on the Fourier coefficients of sparse functions, we design an efficient sparsity testing algorithm for Boolean functions. The tester distinguishes whether a given function is $s$-sparse or $\epsilon$-far from every $s$-sparse Boolean function, with query complexity $poly\left((2s)^{\varphi(\Delta)},1/\epsilon \right)$. In addition, we generalize the classical notion of Boolean degree to arbitrary Abelian groups and establish an $\Omega(\sqrt{s})$ lower bound for adaptive sparsity testing.

cs.CC↗

arXiv2024

EchoNet-Synthetic: Privacy-preserving Video Generation for Safe Medical Data Sharing

To make medical datasets accessible without sharing sensitive patient information, we introduce a novel end-to-end approach for generative de-identification of dynamic medical imaging data. Until now, generative methods have faced constraints in terms of fidelity, spatio-temporal coherence, and the length of generation, failing to capture the complete details of dataset distributions. We present a model designed to produce high-fidelity, long and complete data samples with near-real-time efficiency and explore our approach on a challenging task: generating echocardiogram videos. We develop our generation method based on diffusion models and introduce a protocol for medical video dataset anonymization. As an exemplar, we present EchoNet-Synthetic, a fully synthetic, privacy-compliant echocardiogram dataset with paired ejection fraction labels. As part of our de-identification protocol, we evaluate the quality of the generated dataset and propose to use clinical downstream tasks as a measurement on top of widely used but potentially biased image quality metrics. Experimental outcomes demonstrate that EchoNet-Synthetic achieves comparable dataset fidelity to the actual dataset, effectively supporting the ejection fraction regression task. Code, weights and dataset are available at https://github.com/HReynaud/EchoNet-Synthetic.

cs.CV↗

arXiv2024

A Hanani-Tutte Theorem for Cycles

Given a drawing $D$ of a graph $G$, we define the crossing number between any two cycles $C_{1}$ and $C_{2}$ in $D$ to be the number of crossings that involve at least one edge from each of $C_1$ and $C_2$ except the crossings between edges that are common to both cycles. We show that if the crossing number between every two cycles in $G$ is even in a drawing of $G$ on the plane, then there is a planar drawing of $G$. This result can be extended to arbitrary surfaces. We also establish an equivalence between our result and a fundamental result due to Cairns-Nikolayevsky and Pelsmajer-Schaefer-\v{S}tefankovi\v{c}, about drawing graphs on surfaces, and derive the Loebl-Masbaum theorem from it.

math.CO↗