# QINA: Quantum-Inspired Nonlinear Adapters for Pretrained Vision Models

arXiv: https://arxiv.org/abs/2609.29592 · HTML: https://mlsanity.com/paper/2609.29592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdaptFormer: Adapting Vision Transformers for Scalable Visual Recognition](https://mlsanity.com/paper/2205.13535/) (2022)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [A Large-scale Study of Representation Learning with the Visual Task Adaptation Benchmark](https://mlsanity.com/paper/1910.04867/) (2019)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [Parameter-Efficient Fine-Tuning with Discrete Fourier Transform](https://mlsanity.com/paper/2405.03003/) (2024)
- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [Skin Lesion Classification Using Ensembles of Multi-Resolution EfficientNets with Meta Data](https://mlsanity.com/paper/1910.03910/) (2019)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)
- [Efficient Learning With Sine-Activated Low-rank Matrices](https://mlsanity.com/paper/2403.19243/) (2024)
- [BRISC: Annotated Dataset for Brain Tumor Segmentation and Classification](https://mlsanity.com/paper/2506.14318/) (2025)
- [Q-Seg: Quantum Annealing-Based Unsupervised Image Segmentation](https://mlsanity.com/paper/2311.12912/) (2023)
- [DiTASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations](https://mlsanity.com/paper/2502.06029/) (2025)
- [HQViT: Hybrid Quantum Vision Transformer for Image Classification](https://mlsanity.com/paper/2504.02730/) (2025)
- [Qubit-efficient Variational Quantum Algorithms for Image Segmentation](https://mlsanity.com/paper/2405.14405/) (2024)
- [Quantum-enhanced unsupervised image segmentation for medical images analysis](https://mlsanity.com/paper/2411.15086/) (2024)
- [Enhancing Low-Rank Adaptation with Structured Nonlinear Transformations](https://mlsanity.com/paper/2509.21870/) (2025)

## Abstract (arXiv)

Adapting large pretrained vision models under limited data and frozen-backbone constraints remains a central challenge in transfer learning. While lightweight adapters and parameter-efficient fine-tuning methods are widely adopted, most rely on generic multilayer perceptrons or low-rank linear updates, offering limited control over the spectral and geometric structure of feature transformations. We investigate whether structured nonlinear feature lifting can improve representational alignment in frozen regimes. We introduce Quantum-Inspired Nonlinear Adapters (QINA), compact modules that perform learnable trigonometric feature lifting followed by bounded nonlinear aggregation. The design induces structured oscillatory basis functions with an explicit norm-dependent Lipschitz bound, enabling spectral reshaping of pretrained representations without increasing the receptive field or significantly expanding parameter count. Importantly, the method operates entirely within standard deep learning frameworks and does not require quantum hardware. Through systematic experiments across natural and medical imaging datasets, classification and segmentation tasks, multiple adapters and placements, and varying training budgets, we show that performance in frozen regimes is primarily representation-limited. Nonlinear lifting improves adaptation, and the proposed structured trigonometric formulation consistently outperforms identity baselines, fixed Fourier feature mappings, and parameter-matched baseline adapters. Within the evaluated frozen-backbone settings, structured spectral parameterization provides a more effective inductive bias than generic nonlinear adapters. This work highlights the importance of geometry- and spectrum-aware adaptation mechanisms for large pretrained vision models.