# Research Plan: Non-Commutative Spectral Geometry for Adaptive Quantum-Classical Drug-Target Interaction Prediction

## Problem

We aim to address fundamental limitations in current drug-target interaction (DTI) prediction methods that struggle to capture the intricate, multiscale nature of molecular interactions and fail to generalize across diverse chemical and biological domains. Traditional machine learning approaches, including deep learning methods with graph neural networks and attention mechanisms, are constrained by their adherence to classical probability theory and Euclidean geometry. These limitations become particularly apparent when attempting to model quantum mechanical aspects of molecular interactions or when dealing with high-dimensional, non-Euclidean spaces characteristic of chemical compound libraries and protein structures.

Our hypothesis is that by leveraging advanced concepts from non-commutative geometry, optimal transport theory, and quantum information science, we can develop a unified framework that seamlessly integrates classical and quantum perspectives for DTI prediction. We propose that reframing the DTI prediction problem within the context of a non-commutative pharmacological manifold will enable more accurate modeling of molecular interactions and better domain adaptation capabilities.

## Method

We will develop the Non-Commutative Geometric Adaptation for Molecular Interactions (NCGAMI) framework, which integrates several advanced mathematical concepts:

**Non-Commutative Geometric Foundation**: We will formulate DTI prediction within a non-commutative pharmacological manifold defined as a triple (A, H, D), where A is a C*-algebra of observables on molecular configurations, H is a Hilbert space, and D is an unbounded self-adjoint Dirac operator.

**Spectral Action Principle**: We will apply the spectral action principle from non-commutative geometry to develop a novel domain adaptation technique. This will involve defining a geometrically motivated functional that, when minimized, yields optimal transport maps between pharmacological domains.

**Unified Variational Objective**: Using geometric quantization, we will formulate a unified variational objective that incorporates quantum relative entropy and Liouville volume forms, bridging information-theoretic and geometric aspects of the problem.

**Quantum Adiabatic Optimization**: We will develop a quantum adiabatic optimization algorithm inspired by adiabatic quantum computation to solve the proposed objective function, designed to guarantee convergence to optimal solutions under specified conditions.

**Statistical Manifold Framework**: We will model the problem using a pharmacological statistical manifold M = {P_θ : θ ∈ Θ} equipped with the Fisher-Rao metric, enabling Riemannian optimization techniques.

## Experiment Design

**Datasets**: We will evaluate our framework using two primary datasets: the DrugBank database and the Human dataset (containing 6,728 positive interactions between 2,726 unique compounds and 2,001 unique proteins). We will partition datasets into source and target domains in a 6:4 ratio, with further subdivision of target domains into training and testing sets.

**Baseline Comparisons**: We will benchmark NCGAMI against established methods including DeepDTA, DeepConv-DTI, MolTrans, and TransformerCPI to demonstrate performance improvements.

**Evaluation Metrics**: We will assess performance using AUC (Area Under the Curve) and AUPR (Area Under the Precision-Recall Curve) metrics to evaluate both classification accuracy and precision-recall trade-offs.

**Ablation Studies**: We will conduct systematic ablation experiments to validate the necessity of each framework component, including comparisons with variants that remove the UDA (Unsupervised Domain Adaptation) component or replace key modules with alternative architectures.

**Theoretical Validation**: We will empirically validate our theoretical results, including the spectral action principle for domain adaptation, the fluctuation theorem for non-equilibrium statistical mechanics, and the convergence properties of our quantum adiabatic optimization algorithm.

**Computational Implementation**: We will implement our framework using distributed computing resources (eight A100 GPUs with 40GB memory each) with carefully tuned hyperparameters including learning rates, batch sizes, and regularization parameters.

**Interpretability Analysis**: We will develop interpretability mechanisms rooted in the spectral properties of the Dirac operator to provide insights into the fundamental principles governing drug-target interactions and validate the biological relevance of our learned representations.