Paper 2025/1688 Original: eprint.iacr.org/2025/1688 ↗

SUMMER: Recursive Zero-Knowledge Proofs for Scalable RNN Training

Abstract

Zero-knowledge proofs of training (zkPoT) enable a prover to certify that a model was trained on a committed dataset under a prescribed algorithm without revealing the model or data. Proving recurrent neural network (RNN) training is challenging due to hidden-state recurrence and cross-step weight sharing, which require proofs to enforce recurrence, gradients, and nonlinear activations across time. We present SUMMER (SUMcheck and MERkle tree), a recursive zkPoT for scalable RNNs. SUMMER generates sumcheck-based proofs that backpropagation through time (BPTT) was computed correctly over a quantized finite field, while nonlinearities such as $\tanh$ and softmax are validated by lookup arguments. Per-step commitments and proofs are folded with Merkle trees, yielding a final commitment and a succinct proof whose size and verification time are independent of the number of iterations. SUMMER offers (i) the first end-to-end zkPoT for RNN training, including forward, backward, and parameter updates; (ii) the first use of LogUp for nonlinear operations with a batched interface; and (iii) efficient recursive composition of lookup and sumcheck proofs. On a Mini-Char-RNN with 12M parameters, the prover runs in 70.1 seconds per iteration, $8.5\times$ faster and $11.6\times$ more memory efficient than the IVC baseline, with 165 kilobyte proofs verified in 20 milliseconds.