Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the hypothesis space. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain approximation with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.

Effective models for analysing and predicting pedestrian flow are important to ensure the safety of both pedestrians and other road users. These tools also play a key role in optimising infrastructure design and geometry and supporting the economic utility of interconnected communities. The implementation of city-wide automatic pedestrian counting systems provides researchers with invaluable data, enabling the development and training of deep learning applications that offer better insights into traffic and crowd flows. Benefiting from real-world data provided by the City of Melbourne pedestrian counting system, this study presents a pedestrian flow prediction model, as an extension of Diffusion Convolutional Grated Recurrent Unit (DCGRU) with dynamic time warping, named DCGRU-DTW. This model captures the spatial dependencies of pedestrian flow through the diffusion process and the temporal dependency captured by Gated Recurrent Unit (GRU). Through extensive numerical experiments, we demonstrate that the proposed model outperforms the classic vector autoregressive model and the original DCGRU across multiple model accuracy metrics.