SubQuad: Near-Quadratic-Free Structure Inference with Distribution-Balanced Objectives in Adaptive Receptor framework

Technical Deep Dive: SubQuad - Near-Quadratic-Free Structure Inference with Distribution-Balanced Objectives in Adaptive Receptor Framework

Overview

SubQuad is an end-to-end pipeline for scalable, antigen-aware, and equity-preserving analysis of large immune repertoires. It addresses two key challenges in comparative analysis of adaptive immune repertoires at population scale:

1. The near-quadratic cost of pairwise affinity evaluations
2. Dataset imbalances that obscure clinically important minority clonotypes

The pipeline integrates three key innovations:

1. An antigen-aligned MinHash retrieval module for near-subquadratic candidate reduction
2. A multimodal fusion backbone with a differentiable gating controller to capture both fine-grained edits and higher-level biochemical structure
3. A fairness-aware spectral clustering objective with automated equity calibration to ensure proportional representation of rare antigen-specific clonotypes

Problem & Context

• Immune repertoires commonly comprise millions to hundreds of millions of distinct receptor sequences
• Comparing repertoires across individuals or clinical states can reveal antigen-specific response patterns that inform vaccine design, guide cancer immunotherapy, and support autoimmune disease monitoring
• However, pairwise affinity evaluations grow quadratically with the number of sequences, and naive comparison becomes infeasible for modern datasets
• Many scalable pipelines process receptor sequences as generic strings, discarding antigen-relevant signals important for epitope binding
• Subgroup representation has received limited consideration, risking systematic omission of low-prevalence but clinically consequential clonotypes

Methodology

Scalable Preprocessing

• Raw sequences $\mathcal{S}$ are processed via MinHash-based Indexing to generate a sparse candidate list $\mathcal{CAND}$ and optimized using hardware-aware batching $\mathcal{B}$

Representation Learning

• A Dual-Phase Meta-Encoder utilizes ImmunoBERT-style pretraining followed by MetaNet fine-tuning
• The Meta-Controller dynamically adjusts gating weights $\alpha_{m}$ for multi-paradigm fusion

Graph Construction

• Multi-channel affinities are integrated via Dynamic Affinity Fusion to produce $\widetilde{a}_{ij}$
• This similarity matrix is refined through RMT-based Thresholding (eigenvalue spectrum analysis) to produce a sparse weighted graph $G=(V, E, W)$

Fairness-Constrained Clustering

• The graph is partitioned into clusters $\mathcal{C}$ by optimizing a joint objective of spatial cohesion and Jensen-Shannon Equity
• An Automated Fairness Tuner dynamically calibrates the trade-off weight $\lambda$ to meet target disparity $\delta_{\max}$

Data & Experimental Setup

• Datasets: VDJdb, McPAS-TCR, NEPdb
• Evaluation metrics: Throughput, Recall, Memory, Purity, Equity Score
• Hardware: Single-node GPU (dual A100s), Distributed cluster (8 T4 nodes), Heterogeneous CPU-GPU-FPGA

Results

Optimized Indexing Mechanism

• Antigen-aware MinHash LSH index with block-aligned storage achieves 58% reduction in memory consumption compared to FAISS

Query Processing Efficiency

• Sub-millisecond median latencies under high concurrency through NUMA-conscious memory partitioning, lock-free coordination, and multiversion isolation

Component Impact Analysis

• GPU parallelism yields 67% throughput gains
• Equity-aware objectives improve cluster purity by ~16% compared to fairness-excluded variants
• Embedding-only pipelines trade memory efficiency for lower throughput and reduced purity

Immunological Performance and Robustness

• Enforcing fairness via Demographic Parity reduced subgroup representation bias from 20% to 12% in the tumor neoantigen setting
• Equalized Odds improved subgroup-balanced recall in viral epitope classification

Scalability Evaluation

• Processing 1 million sequences in under 40 minutes on a single node
• At 1 million sequences, SubQuad achieves recall@100 ≥ 0.96 vs. 0.92 for the MinHash-only baseline

Interpretation

• SubQuad provides a scalable and biologically valid graph-learning platform for epitope prioritization, biomarker discovery, and vaccine design
• The fairness constraints are grounded in immunological principles, ensuring that rare but clinically significant clonotypes are not overlooked
• By aligning computational objectives with biological realities, SubQuad offers a principled approach to large-scale immunoinformatics

Limitations & Uncertainties

• Verification of runtime and memory claims depends on complete reporting of index and kernel configuration details
• Long-term evaluation of the framework's clinical impact requires further validation in translational studies

What Comes Next

• Extend SubQuad to model longitudinal repertoire dynamics
• Incorporate epitope- and phenotype-supervised representations
• Evaluate privacy-preserving federated learning across multi-center cohorts