My research leverages inverse problem as a framework for devising efficient, interpretable, and generalizable deep learning methods across science and engineering. The vision is inspired by probabilistic modelling in signal processing and by the hypothesis that the brain, as an efficient and robust intelligence, is an inference machine solving inverse problems to perceive the world. Specifically, my research bridges between inverse problems and representation learning, and intends to address three fundamental questions, i.e., "what to learn" as representations from data, "how to learn" meaningful representations, and "how to use" representations to solve inverse problems.

Interested about knowing what inverse problems are? They refer to the process of estimating a latent representation (cause) that explains the data observations (effect) in a physical system via a likelihood model. Inverse problems are ill-posed, meaning that the sole observations are inadequate, and additional priors are required for successful recovery. Understanding of how biological networks leverage and combine the prior and likelihood plays a crucial role in advancing artificial intelligent systems to solve inverse problems.

My postdoctoral research have focused on foundational deep learning with applications to vision, brain imaging, and computational neuroscience. My research develops generalizable and robust methods for inverse problems and investigates how the brain solves inverse problems, such as recognizing scenes robustly from corrupted information. I lead three distinct research projects as follows:

• Generative models for inverse problems: Deep generative AI has revolutionized image generation from text prompts, but its impact on solving inverse problems in science and engineering has been limited. A key challenge is determining how much the neural network should rely on generative priors relative to observed data, and whether this reliance should increase over time—similar to how the brain builds confidence in a visual scene. In my recent project, I addressed this by focusing on vision inverse problems, such as deblurring. I developed a diffusion-based generative prior inverse solver using subspace optimization to minimize interference between observations and the prior, improving both performance and robustness. This research track now seeks to further enhance inverse problem-solving under uncertainty.
• Brain's generative models: A central question in vision neuroscience is how the brain integrates prior knowledge with sensory data to perceive the world. The Bayesian brain hypothesis suggests that the brain performs posterior inference using an internal model to explain stimuli. I explore this via diffusion-based generative networks to explain how the brain solves inverse problems by using feedback mechanisms to remove visual degradations. This track establishes the foundation for using generative, rather than discriminative, networks in brain studies.
• Neural operators for inverse problems: This track focuses on improving and accelerating the solution of inverse problems in brain imaging. I have developed neural operators for functional ultrasound imaging, significantly reducing the data acquisition and processing time needed to construct high-quality images. By leveraging the functional mapping of neural operators, my approach captures a temporally global physical intuition of ultrasound signals. It generalizes remarkably well across species. This method accelerates real-time brain-computer interfaces, reducing latency by 90% and transforming behavioral studies in neuroscience and healthcare.

My PhD research focused on sparse inverse problems to improve deep learning efficiency, interpretability, and performance. I developed methods based on sparse representation and statistical generative models to incorporate domain knowledge into deep learning. My PhD research is related to a class of machine learning algorithms referred to as unrolled learning in the literature.

• Deep learning for engineering: Inverse problems are traditionally solved by slow, unscalable optimization techniques. While deep learning offers scalability, it struggles to generalize in data-limited scenarios. My research integrated forward models and domain knowledge as priors into deep networks, achieving superior performance with accelerated inference in radar sensing and image denoising.
• Representations for computational neuroscience: While deep learning can capture neural dynamics, its black-box nature limits the identification of factors driving neural activity. My research integrated sparse priors into deep networks to recover interpretable, locally low-rank structures characterizing impulse responses. This versatile approach enabled the deconvolution of neural signals across various brain areas and data modalities.
• Learning theory and interpretability: I theoretically demonstrated that deep networks can be designed to learn world models for inverse problems, hence, improving interpretability. I also showed that backpropagation, compared to analytic gradients, accelerates learning and enhances model recovery.

During my two research internship experiences, I worked on speech enhancement. Here, I proposed channel-attention to improve multichannel speech enhancement. In another publication, a joint work with Kazuhito Koishida from Microsoft, I proposed a training framework for perceptual enhancement of stereo speech.