SearcharxivSearch

arXiv subjects

Manish Kumar Pandey

Publications and source records attributed to Manish Kumar Pandey.

4 recordsLinked to original sources

Advancing Multimodal Fusion on Heterogeneous Medical Data with Hybrid Geometry Attention

Multimodal fusion learning (MFL) has shown great potential in the medical domain, where we are faced with disparate data modalities such as imaging, clinical records, and omics. However, existing MFL strategies face several major challenges. First, they struggle to capture complex cross-modal interactions effectively, which in turn limits performance improvements. Second, they incur high computational costs, restricting their applicability in resource-constrained healthcare AI applications. Finally, they are often designed and evaluated for narrow, fixed modality configurations (e.g., imaging-only, or specific pairs such as image and omics), which limits evidence of their adaptability and generalizability to broader collections of heterogeneous medical modalities. To address these challenges, we propose a novel MFL framework - Cascaded Unified Representation Learning for Efficient Fusion Network (CURE) - a lightweight and scalable framework that progressively integrates various modalities through a novel efficient Hybrid Geometry Aware Fusion layer (HyFuse), where each HyFuse layer is sequentially learned for each modality, making the framework adaptable and generalizable. Within HyFuse, an efficient residual convolution module captures rich multi-scale features to ensure cost-effective learning, while a hybrid-space aware attention mixer learns coarse-to-fine structural cues to better preserve cross-modal relationships. Complementary learnable late-fusion and shared information refinement modules are then employed to learn robust modality-order-invariant shared representations, which in turn yields consistent performance improvements. Extensive evaluations on 16 public datasets show that CURE outperforms leading multimodal fusion methods, boosting performance by up to 3.97% and lowering computational costs by up to 87.8%, ensuring more effective and reliable predictions.

cs.CV

Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticity

We introduce Hybrid Convolutions with Attention Stochasticity (HyCAS), an adversarial defense that narrows the long-standing gap between provable robustness under L2 certificates and empirical robustness against strong L attacks, while preserving strong generalization across diverse imaging benchmarks. HyCAS unifies deterministic and randomized principles by coupling 1-Lipschitz, spectrally normalized convolutions with two stochastic components, spectral normalized random, projection filters and a randomized attention-noise mechanism, to realize a randomized defense. Injecting smoothing randomness inside the architecture yields an overall <= 2-Lipschitz network with formal certificates. Exten-sive experiments on diverse imaging benchmarks, including CIFAR-10/100, ImageNet-1k, NIH Chest X-ray, HAM10000, show that HyCAS surpasses prior leading certified and empirical defenses, boosting certified accuracy by up to 7.3% (on NIH Chest X-ray) and empirical robustness by up to 3.1% (on HAM10000), without sacrificing clean accuracy. These results show that a randomized Lipschitz constrained architecture can simultaneously improve both certified L2 and empirical L adversarial robustness, thereby supporting safer deployment of deep models in high-stakes applications. Code: https://github.com/misti1203/HyCAS

cs.CV

First moment of Hecke eigenvalues at the integers represented by binary quadratic forms

In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; \begin{equation*} \begin{split} S(f, \mathcal{Q}; X ) &:= \sideset{}{^{\flat }}\sum_{n= \mathcal{Q}(\underline{x}) \le X \atop \gcd(n,N) =1 } \lambda_{f}(n), \end{split}\end{equation*} where $\flat$ means that sum runs over the square-free positive integers, $\lambda_{f}(n)$ denotes the normalised $n^{\rm th}$ Fourier coefficients of a Hecke eigenform $f$ of integral weight $k$ for the congruence subgroup $\Gamma_{0}(N)$ and $\mathcal{Q}$ is a primitive integral positive-definite binary quadratic forms of fixed discriminant $D<0$ with the class number $h(D)=1$. As a consequence, we determine the size, in terms of conductor of associated $L$-function, for the first sign change of Hecke eigenvalues indexed by the integers which are represented by $\mathcal{Q}$. This work is an improvement and generalisation of the previous results.

math.NT

Distinguishing pure representations by normalized traces

Given two pure representations of the absolute Galois group of an $\ell$-adic number field with coefficients in $\overline{\mathbb{Q}}_p$ (with $\ell\neq p$), we show that the Frobenius-semisimplifications of the associated Weil--Deligne representations are twists of each other by an integral power of certain unramified character if they have equal normalized traces. This is an analogue of a recent result of Patankar and Rajan in the context of local Galois representations.

math.NT