As the advent of large-scale quantum computing threatens classical encryption, Quasi-Cyclic Moderate Density Parity-Check (QC-MDPC) codes have emerged as a foundational element of Post-Quantum Cryptography (PQC). However, decoding these relatively dense codes using classical Belief Propagation algorithms often leads to failures caused by short graph cycles that stall the decoder. In cryptographic applications, these failures are severe security vulnerabilities that leak secret key information. To address this, this paper proposes a Recurrent Bipartite Graph Neural Network (R-BGNN) as proof of concept. By integrating Gated Recurrent Units (GRUs) into the message-passing framework and employing a multi-topology curriculum training strategy, the R-BGNN actively learns to break limit-cycle oscillations. Evaluated across 20 unseen matrix topologies, the proposed architecture significantly outperforms classical Bit-Flipping and Min-Sum baselines, reducing the Decoding Failure Rate (DFR) by 63.7\% at moderate noise levels ($t=10$) while converging in fewer iterations.
Self-attention mechanisms have established the Transformer as the dominant backbone across natural language processing, source code intelligence, and automated theorem proving. However, all-to-all pairwise token comparison enforces a quadratic $\mathcal{O}(N^2)$ compute and memory barrier alongside severe softmax attention dilution as sequence length $N$ scales beyond the training horizon. Inspired by recent advances in algebraic graph learning (\textbf{WPNet}), this work introduces \textbf{GTFormer}, a syntax-free hierarchical Graph Neural Network (GNN) that replaces flat self-attention for general long-context sequence modeling. GTFormer organizes raw token streams into a bounded-degree hierarchy combining a balanced binary reduction tree ($\lceil \log_2 N \rceil$ depth), horizontal boundary-bridging shift edges, random expander shortcuts, multi-channel convex highway gating, and a top-down broadcast pass. Across eight long-context code, log, and multi-hop retrieval benchmarks trained exclusively on sequences of length $N \le 512$, GTFormer extrapolates zero-shot to $N = 4{,}194{,}304$ ($8192\times$) on a single commodity GPU in linear $\mathcal{O}(N)$ memory, maintaining near-perfect accuracy where standard and RoPE Transformers suffer from out-of-distribution attention collapse and out-of-memory exhaustion.