Recurrence Strikes Back: Efficient Neural Decoding Beyond Transformers

Recent work has made attention-based neural decoders substantially more efficient, yet it leaves a more fundamental question open: is attention the right computational primitive for error correction at all? Error correction is naturally expressed as repeated constraint resolution over a sparse code graph, suggesting recurrence rather than token interaction. We introduce Neural Syndrome Flow (NSF), a recurrent neural decoder that replaces attention with sparse message passing over the Tanner graph. NSF maintains persistent variable- and check-node states and repeatedly applies a shared, state-conditioned transition across decoding iterations. Lightweight edge gating, syndrome feedback, and adaptive solver control further refine this recurrent process. We evaluate NSF across a range of LDPC codes, including MacKay constructions, with particular emphasis on long blocks up to length 2304. NSF outperforms EfficientMPT, the previous state-of-the-art attention-based neural decoder for long LDPC codes; at $4$ $\mathrm{dB}$, it reduces BER by $2.77\times$ on the $(1920,1600)$ code and by $2.74\times$ on the $(2304,1920)$ code. Across the long-code suite, NSF uses $2.20$-$2.98\times$ fewer FLOPs and $3.63$-$6.84\times$ lower peak inference memory than EfficientMPT even at the full step budget, while syndrome-based early stopping at $4$ $\mathrm{dB}$ increases the FLOP reduction to $8.01$-$11.00\times$. A length-invariant shared-initialization variant uses only 152k trainable parameters, $12.0\times$ fewer than EfficientMPT, while retaining most of the decoding gain. These results show that structured recurrence can simultaneously improve decoding accuracy and computational efficiency for long-block neural decoding.