Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital documents. In the post-quantum era, classical public key-based signature schemes become vulnerable to brute-force and key-recovery attacks due to the computational power of quantum algorithms. Multivariate polynomial based signature schemes are among the one of the cryptographic constructions that offers strong security guarantees against such quantum threats. With the growing capabilities of neural networks, it is natural to explore their potential application in the design of cryptographic primitives. Neural networks inherently captures the non-linear relationships within the data, which are encoded in their synaptic weight matrices and bias vectors. In this paper, we propose a novel construction of a multivariate polynomial based digital signature scheme that leverages neural network architectures. A neural network with binary weights is employed to define the central structure of the signature scheme. The design introduces a recurrent random vector, functionally analogous to an attention mechanism, which contributes dynamic randomness based on the previous state, thereby enhancing the scheme's security. It is demonstrated that the proposed signature scheme provide security against Existential Unforgeability under adaptive Chosen-Message Attacks (EUF-CMA). Furthermore, it is proven that direct attacks aimed to recover the private keys are computationally infeasible within polynomial time, even in the presence of quantum computing abilities. The operational characteristics of the proposed scheme are also evaluated, with results indicating notable efficiency and practical viability in post-quantum cryptographic applications.