arXiv subjects

Sourav Bhattacharya

Publications and source records attributed to Sourav Bhattacharya.

At least 19 recordsLinked to original sources

arXiv2026

Yukawa scalar self energy at two loop and $\langle ϕ^2 \rangle$ in the inflationary de Sitter spacetime

We have considered the Yukawa theory at two loop in the inflationary de Sitter spacetime, for a massless minimally coupled scalar and a massless fermion. The one loop computation for the same has been investigated in detail in the earlier literatures. The chief motivation behind this study is the fact that at one loop, the scalar self energy contains only fermions, which are conformally invariant. At two loop, there are two diagrams, each containing one internal scalar line, thereby breaking the conformal invariance. This should result in the appearance of infrared secular logarithms in the scalar self energy. The renormalisation of this two loop self energy has been performed. We next compute the loop corrected coincident two point correlation function, $\langle ϕ^2\rangle$, due to the self energies. The expectation value has been taken with respect to the initial Bunch-Davies vacuum. We argue that the late time secular contribution from the local or UV self energy must dominate the non-local or IR ones in the present case, from the point of view of the powers of these large logarithms of the scale factor. This corresponds to the fact that fermion lines do not show any IR secular effect. The leading behaviour of $\langle ϕ^2\rangle$ at one and two loop are respectively found to be $\ln^3 a$ and $\ln^4 a$. These are hybrids of UV and IR logarithms, where the latter originate from the massless and minimal two external scalar lines. A resummed expression for $\langle ϕ^2\rangle$ has also been computed. The same is found to be bounded and decreasing monotonically with the increasing magnitude of the Yukawa coupling. Accordingly, the dynamically generated scalar mass increases with the increasing coupling.

hep-th↗

arXiv2026

Effect of $ξRϕ^2$ non-minimal coupling on gravitational light bending

We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar $\sqrt{-g}ξR ϕ^2$ non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar $ϕ$, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both $ξ$ and the bending angle to be small, we use the eikonal approximation to compute the angle up to ${\cal O}(ξG^2)$. At tree level $({\cal O}(ξG))$ we find no bending, and hence the ${\cal O}(ξG^2)$ result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{μν} T^{μν}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like $\sim b^{-7}$, where $b$ is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.

hep-th↗

arXiv2026

Scattering of massive spin-2 field via graviton exchanges with different spin fields and the long range gravitational potential

In this work, we compute the graviton mediated scattering amplitude of a massive spin-2 Fierz-Pauli field with various other massive spin fields, and in the non-relativistic limit, find out the corresponding two-body gravitational potentials. The massive spin-2 field does not represent gravity here. The theory of gravity is taken to be the usual massless general relativity, and the massive spin-2 field is taken as a test quantum field coupled to gravity via the standard minimal prescription. We first compute the tree level 2-2 scattering of a massive spin-2 field with massive scalar, spin-1, and spin-1/2 fields with one graviton exchanges. Leading Newton potential, as well as the subleading spin or polarisation dependent terms at ${\cal O}(G)$ have been computed. We also consider the next to the leading order (${\cal O}(G^2)$) scattering of the massive spin-2 field with a massive scalar, and demonstrate the spin independent, spherically symmetric leading part of the two body gravitational potential. The present paper can be considered as an attempt to compute the gravitational potential in the context of a higher spin field theory.

hep-th↗

arXiv2026

$ξRϕ^2$ non-minimal coupling, and the long range gravitational potential for different spin fields from 2-2 scattering amplitudes

In this paper we investigate the long range gravitational effect of curvature-scalar field non-minimal coupling, in the form of $ξR ϕ^2$, in the perturbative quantum gravity framework. Such coupling is most naturally motivated from the renormalisation of a scalar field theory with a quartic self interaction in a curved spacetime background. This coupling results in two scalar-$n$ graviton vertices which contain no explicit momenta of the scalar, qualitatively different from the usual, e.g. $κh^{μν}T_{μν}$-type minimal matter-graviton vertices. Assuming the dimensionless coupling parameter $ξ$ to be small, we compute the 2-2 scattering Feynman amplitudes between such scalars up to ${\cal O}(G^2 ξ)$. From the non-relativistic limit of these amplitudes, we compute the corresponding long range gravitational potential. There exists no tree level contribution $({\cal O}(ξG))$ here, and hence the one loop ${\cal O}(G^2 ξ)$ result is leading. Recently, the effect of a cosmological constant in such non-minimal interaction and the subsequent gravitational potential was computed. In this work we take the cosmological constant to be vanishing. The resulting potential is found to have $r^{-4}$ leading behaviour. We further extend these results for scalar-massive spin-1 and massive spin-1/2 scattering. Spin and polarisation dependence of the two body potential have been explicitly demonstrated. We discuss some possible physical implications of these results.

hep-th↗

arXiv2026

HierarchicalPrune: Position-Aware Compression for Large-Scale Diffusion Models

State-of-the-art text-to-image diffusion models (DMs) achieve remarkable quality, yet their massive parameter scale (8-11B) poses significant challenges for inferences on resource-constrained devices. In this paper, we present HierarchicalPrune, a novel compression framework grounded in a key observation: DM blocks exhibit distinct functional hierarchies, where early blocks establish semantic structures while later blocks handle texture refinements. HierarchicalPrune synergistically combines three techniques: (1) Hierarchical Position Pruning, which identifies and removes less essential later blocks based on position hierarchy; (2) Positional Weight Preservation, which systematically protects early model portions that are essential for semantic structural integrity; and (3) Sensitivity-Guided Distillation, which adjusts knowledge-transfer intensity based on our discovery of block-wise sensitivity variations. As a result, our framework brings billion-scale diffusion models into a range more suitable for on-device inference, while preserving the quality of the output images. Specifically, combined with INT4 weight quantisation, HierarchicalPrune achieves 77.5-80.4% memory footprint reduction (e.g., from 15.8 GB to 3.2 GB) and 27.9-38.0% latency reduction, measured on server and consumer grade GPUs, with the minimum drop of 2.6% in GenEval score and 7% in HPSv2 score compared to the original model. Finally, our comprehensive user study with 85 participants demonstrates that HierarchicalPrune maintains perceptual quality comparable to the original model while significantly outperforming prior works.

cs.CV↗

arXiv2026

$ξR ϕ^2$ coupling, cosmological constant and quantum gravitational correction to Newton's potential

This letter investigates the contribution of the $\sqrt{-g}ξRϕ^2$ interaction to the long range gravitational potential for massive scalar fields, from the non-relativistic limit of the 2-2 scattering amplitude with graviton exchanges. Such coupling is naturally motivated from the renormalisation of a scalar field theory with quartic self interaction in a curved spacetime. This is qualitatively different from the minimal ones like $ \sqrt{G} h^{μν}T_{μν}$, as the vertices corresponding to the former do not explicitly contain any scalar momenta, but instead explicitly contains the momentum carried by graviton line. For the minimal vertex, the long range gravitational potential up to one loop $({\cal O}(G), {\cal O}(G^2))$ was obtained earlier from the terms non-analytic in the transfer momentum, $q^{-2},\ q^{-1},\ \ln q^2 $, yielding potentials respectively like $r^{-1}$, $r^{-2}$, $r^{-3}$. However owing to the aforesaid explicit appearance of transfer momentum for the non-minimal vertices, the leading contribution in this case comes at ${\cal O}(ξG^2)$, and turns out to be subleading compared to even $r^{-3}$. To complement this `screening' effect, we consider the three graviton vertex generated by the $\sim Λ\sqrt{-g}/G$ term in the action, where $Λ$ is the cosmological constant. This vertex does not explicitly contain any graviton momentum. With this vertex, and assuming short scale scattering much small compared to the Hubble horizon, we compute the seagull, the vacuum polarisation and the fish diagrams and obtain the 2-2 scattering amplitudes. The leading gravitational potential at ${\cal O}(ξΛG^2 )$ behaves like $ r^{-1}$, even though it is much subleading compared to Newton's potential due to the appearance of $Λ$. We also discuss the scenario where this potential dominates the aforesaid ${\cal O}(ξG^2)$ one.

hep-th↗

arXiv2025

Triod twist cycles and circle rotations

We study the problem of relating cycles on a \emph{triod} $Y$ to \emph{circle rotations}. We prove that the simplest cycles on a \emph{triod}~$Y$ with a given \emph{rotation number}~$ρ$, called \emph{triod--twist cycles} are conjugate, via a piece-wise monotone map of \emph{modality} at most~$m + 3$, where~$m$ is the \emph{modality} of~$P$ to the rotation on~$S^1$ by angle~$ρ$, restricted to one of its cycles.

math.DS↗

arXiv2025

Forcing among exact patterns of triods

We obtain a complete characterization of \emph{topologically exact patterns} on \emph{triods}. Based on their \emph{rotation number} $ρ$, these \emph{exact patterns} are grouped into three classes: \emph{slow} ($ρ< \frac{1}{3}$), \emph{fast} ($ρ> \frac{1}{3}$) and \emph{ternary} ($ρ= \frac{1}{3}$). For each category, we derive a \emph{linear ordering} of the set of natural numbers, $\mathbb{N}$ that captures \emph{forcing} between the \emph{patterns}. We also show that each of these orderings is \emph{stable} under perturbations.

math.DS↗

arXiv2025

Effective action for $ϕ^4$-Yukawa theory via 2PI formalism in the inflationary de Sitter spacetime

We consider a scalar field theory with quartic self interaction, Yukawa coupled to fermions in the inflationary de Sitter spacetime background. The scalar has a classical background plus quantum fluctuations, whereas the fermions are taken to be quantum. We derive for this system the effective action and the effective potential via the two particle irreducible (2PI) formalism. This formalism provides an opportunity to find out resummed or non-perturbative expressions for some series of diagrams. We have considered the two loop vacuum graphs and have computed the local part of the effective action. The various resummed counterterms corresponding to self energies, vertex functions and the tadpole have been explicitly found out. The variation of the renormalised effective potential for massless fields has been investigated numerically. We show that for the potential to be bounded from below, we must have $λ\gtrsim 16 g^2$, where $λ$ and $g$ are respectively the quartic and Yukawa couplings. We emphasise the qualitative differences of this non-perturbative calculation with that of the standard 1PI perturbative ones in de Sitter. The qualitative differences of our result with that of the flat spacetime has also been pointed out.

hep-th↗

arXiv2025

FraQAT: Quantization Aware Training with Fractional bits

State-of-the-art (SOTA) generative models have demonstrated impressive capabilities in image synthesis or text generation, often with a large capacity model. However, these large models cannot be deployed on smartphones due to the limited availability of on-board memory and computations. Quantization methods lower the precision of the model parameters, allowing for efficient computations, \eg, in \INT{8}. Although aggressive quantization addresses efficiency and memory constraints, preserving the quality of the model remains a challenge. To retain quality in previous aggressive quantization, we propose a new fractional bits quantization (\short) approach. The novelty is a simple yet effective idea: we progressively reduce the model's precision from 32 to 4 bits per parameter, and exploit the fractional bits during optimization to maintain high generation quality. We show that the \short{} yields improved quality on a variety of diffusion models, including SD3.5-Medium, Sana, \pixart, and FLUX.1-schnell, while achieving $4-7\%$ lower FiD than standard QAT. Finally, we deploy and run Sana on a Samsung S25U, which runs on the Qualcomm SM8750-AB Snapdragon 8 Elite Hexagon Tensor Processor (HTP).

cs.CV↗

arXiv2025

Efficient High-Resolution Image Editing with Hallucination-Aware Loss and Adaptive Tiling

High-resolution (4K) image-to-image synthesis has become increasingly important for mobile applications. Existing diffusion models for image editing face significant challenges, in terms of memory and image quality, when deployed on resource-constrained devices. In this paper, we present MobilePicasso, a novel system that enables efficient image editing at high resolutions, while minimising computational cost and memory usage. MobilePicasso comprises three stages: (i) performing image editing at a standard resolution with hallucination-aware loss, (ii) applying latent projection to overcome going to the pixel space, and (iii) upscaling the edited image latent to a higher resolution with adaptive context-preserving tiling. Our user study with 46 participants reveals that MobilePicasso not only improves image quality by 18-48% but reduces hallucinations by 14-51% over existing methods. MobilePicasso demonstrates significantly lower latency, e.g., up to 55.8$\times$ speed-up, yet with a small increase in runtime memory, e.g., a mere 9% increase over prior work. Surprisingly, the on-device runtime of MobilePicasso is observed to be faster than a server-based high-resolution image editing model running on an A100 GPU.

cs.CV↗

arXiv2025

Yukawa coupling, and inflationary correlation functions for a spectator scalar via stochastic spectral expansion

We consider a stochastic spectator scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. We consider the fermion to be massless, and take the one loop effective potential found earlier by using the exact fermion propagator in de Sitter spacetime. We take the potential for the spectator scalar to be quintessence-like, $V(ϕ)=α|ϕ|^p$ ($α\ensuremath{>} 0,\ p\ensuremath{>} 4$), so that the total effective potential is generically bounded from below for all values of the parameters and couplings, and a late time equilibrium state is allowed. Using next the stochastic spectral expansion method, we numerically investigate the two point correlation function, as well as the density fluctuations corresponding to the spectator field, with respect to the three parameters of the total effective potential, $α,\ p$ and the Yukawa coupling, $g$. In particular, we find that the power spectrum and the spectral index corresponds to blue tilt with increasing $g$. The three point correlation function and non-Gaussianity corresponding to the density fluctuation has also been investigated. The increasing Yukawa coupling is shown to flatten the peak of the shape function in the squeezed limit. Also in this limit, the increase in the same is shown to increase the local non-Gaussianity parameter.

gr-qc↗

arXiv2025

Self interacting scalar field theory in general curved spacetimes at zero and finite temperature revisited

We revisit the problem of spontaneous symmetry breaking (SSB), its restoration, and phase transition for a self interacting quantum scalar field in a general curved background, at zero and finite temperature. To the best of our knowledge, most of the earlier computations in this context have been done in the linear order in curvature, which may not be very suitable for the Ricci flat spacetimes. One of our objectives is to see whether the higher order terms can bring in qualitatively new physical effects, and thereby attempting to fill in this gap in the literature. We use Bunch and Parker's local momentum space representation of the Schwinger-DeWitt expansion of the Feynman propagator. Such expansion, being based upon the local Lorentz symmetry of spacetime, essentially probes the leading curvature correction to short scale, ultraviolet quantum processes. We compute the renormalised, background spacetime curvature (up to quadratic order) and temperature dependent one loop effective potential for $ϕ^4$ plus $ϕ^3$ self interaction. In particular for the de Sitter spacetime, we have shown for the $ϕ^4$-theory that we can have SSB even with a positive rest mass squared and positive non-minimal coupling, at zero temperature. This cannot be achieved by the linear curvature term alone and the result remains valid for a very large range of renormalisation scale. Such SSB will generate a field mass that depends upon the spacetime curvature as well as the non-minimal coupling. For a phase transition, we have computed the leading curvature correction to the critical temperature. At finite temperature, symmetry restoration is demonstrated. We also extend some of the above results to two loop level. The symmetry breaking in de Sitter at two loop remains present. We have further motivated the necessity of treating this problem non-perturbatively in some instances.

gr-qc↗

arXiv2025

EDiT: Efficient Diffusion Transformers with Linear Compressed Attention

Diffusion Transformers (DiTs) have emerged as a leading architecture for text-to-image synthesis, producing high-quality and photorealistic images. However, the quadratic scaling properties of the attention in DiTs hinder image generation with higher resolution or on devices with limited resources. This work introduces an efficient diffusion transformer (EDiT) to alleviate these efficiency bottlenecks in conventional DiTs and Multimodal DiTs (MM-DiTs). First, we present a novel linear compressed attention method that uses a multi-layer convolutional network to modulate queries with local information while keys and values are aggregated spatially. Second, we formulate a hybrid attention scheme for multimodal inputs that combines linear attention for image-to-image interactions and standard scaled dot-product attention for interactions involving prompts. Merging these two approaches leads to an expressive, linear-time Multimodal Efficient Diffusion Transformer (MM-EDiT). We demonstrate the effectiveness of the EDiT and MM-EDiT architectures by integrating them into PixArt-Sigma (conventional DiT) and Stable Diffusion 3.5-Medium (MM-DiT), achieving up to 2.2x speedup with comparable image quality after distillation.

cs.CV↗

arXiv2025

Spontaneous symmetry breaking induced by curvature : Analysis via non-perturbative 2PI Hartree approximation

In this work we investigate the spontaneous symmetry breaking (SSB) induced by a classical background spacetime's curvature, via the 2 particle irreducible (2PI) non-perturbative effective action formalism. We use the standard Schwinger-DeWitt local expansion of the Feynman propagator, appropriate to probe the effect of spacetime curvature on the local or short scale physics. Recently it was shown using perturbative computations that such SSB is possible with a scalar with a quartic self interaction, positive rest mass squared and positive non-minimal coupling. Here we confirm in the two loop Hartree approximation that curvature can indeed induce SSB for such a theory. SSB for such a model is not possible in a flat spacetime. The 2PI technique does not only resum the self energy resulting in mass generation, but also resums, as we have discussed, curvature terms through such mass generation. We have explicitly discussed our results in the context of the de Sitter spacetime, although our calculations are valid for any non-singular curved spacetime. We show that, in contrast to the perturbative results, SSB is possible with a vanishing non-minimal coupling. These results are further extended to the case of an $O(N)$ symmetric scalar field theory. Restoration of the broken symmetry in the thermal case is also briefly discussed.

gr-qc↗

arXiv2025

Entanglement generation between Unruh-DeWitt detectors in the de Sitter spacetime-analysis with complex scalar fields

We investigate the entanglement generation or harvesting between two identical, comoving Unruh-DeWitt detectors in the cosmological de Sitter spacetime. The detectors are assumed to be unentangled initially. They are individually coupled to a complex scalar field, which eventually leads to coupling between themselves. Two kinds of complex scalar fields are investigated here-conformally invariant and massless minimally coupled. By tracing out the degrees of freedom corresponding to the scalar, we construct the reduced density matrix for the two detectors, whose eigenvalues characterise transition probabilities between the energy levels of the detectors. We have computed the negativity, quantifying the degree of entanglement generated at late times between the two detectors. The similarities and differences of these results between the aforementioned two kinds of scalar fields have been discussed. We also compare our results with the existing result of the real scalar field, and point out the qualitative differences. In particular, we emphasise that entanglement harvesting is more resilient in scenarios involving complex fields and nonlinear couplings.

gr-qc↗

arXiv2025

Benchmarking Rotary Position Embeddings for Automatic Speech Recognition

Self-attention relies on positional embeddings to encode input order. Relative Position (RelPos) embeddings are widely used in Automatic Speech Recognition (ASR). However, RelPos has quadratic time complexity to input length and is often incompatible with fast GPU implementations of attention. In contrast, Rotary Positional Embedding (RoPE) rotates each input vector based on its absolute position, taking linear time to sequence length, implicitly encoding relative distances through self-attention dot products. Thus, it is usually compatible with efficient attention. However, its use in ASR remains underexplored. This work evaluates RoPE across diverse ASR tasks with training data ranging from 100 to 50,000 hours, covering various speech types (read, spontaneous, clean, noisy) and different accents in both streaming and non-streaming settings. ASR error rates are similar or better than RelPos, while training time is reduced by up to 21%. Code is available via the SpeechBrain toolkit.

cs.CL↗

arXiv2025

Robust Unsupervised Adaptation of a Speech Recogniser Using Entropy Minimisation and Speaker Codes

Speech recognisers usually perform optimally only in a specific environment and need to be adapted to work well in another. For adaptation to a new speaker, there is often too little data for fine-tuning to be robust, and that data is usually unlabelled. This paper proposes a combination of approaches to make adaptation to a single minute of data robust. First, instead of estimating the adaptation parameters with cross-entropy on a single error-prone hypothesis or "pseudo-label", this paper proposes a novel loss function, the conditional entropy over complete hypotheses. Using multiple hypotheses makes adaptation more robust to errors in the initial recognition. Second, a "speaker code" characterises a speaker in a vector short enough that it requires little data to estimate. On a far-field noise-augmented version of Common Voice, the proposed scheme yields a 20% relative improvement in word error rate on one minute of adaptation data, increasing on 10 minutes to 29%.

eess.AS↗