<p>We report that an autoencoder-based neuromorphic architecture, combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. We show that these machines can consistently produce state-of-the-art solutions with high reliability and with competitive time-to-solution metrics. The autoencoder captures higher-order interactions by decomposing Ising clauses and Ising spins into encoder-decoder layers of spiking neurons, thereby keeping the resource complexity independent of the interaction order for sparse problems. An annealing process based on the dynamics of Fowler-Nordheim quantum mechanical tunneling extrapolates between an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${{\mathcal{O}}}(1/t)$</EquationSource> <EquationSource Format="MATHML"><math> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>/</mo> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> annealing schedule and an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${{\mathcal{O}}}(1/\log (t))$</EquationSource> <EquationSource Format="MATHML"><math> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>/</mo> <mi>log</mi> <mrow> <mo>(</mo> <mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> annealing schedule. This not only ensures fast convergence towards high-quality solutions but also guarantees asymptotic convergence to the Ising ground state. To demonstrate the advantages of the proposed higher-order neuromorphic Ising machine, we systematically solved benchmark combinatorial optimization problems such as MAX-CUT and MAX-SAT, comparing the results to those obtained using a second-order Ising machine employing the same annealing process.</p>

Higher-order neuromorphic Ising machines—autoencoders and Fowler-Nordheim annealers are all you need for scalability

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2026年4月16日

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Faiek Ahsan,
Saptarshi Maiti,
Zihao Chen,
Jakob Kaiser,
Ankita Nandi,
Madhuvanthi Srivatsav,
Johannes Schemmel,
Andreas G. Andreou,
Jason Eshraghian,
Chetan Singh Thakur,
Shantanu Chakrabartty

摘要

We report that an autoencoder-based neuromorphic architecture, combined with Fowler-Nordheim annealing, is sufficient to implement scalable higher-order Ising machines. We show that these machines can consistently produce state-of-the-art solutions with high reliability and with competitive time-to-solution metrics. The autoencoder captures higher-order interactions by decomposing Ising clauses and Ising spins into encoder-decoder layers of spiking neurons, thereby keeping the resource complexity independent of the interaction order for sparse problems. An annealing process based on the dynamics of Fowler-Nordheim quantum mechanical tunneling extrapolates between an ${{\mathcal{O}}}(1/t)$ $O (1 / t)$ annealing schedule and an ${{\mathcal{O}}}(1/\log (t))$ $O (1 / \log (t))$ annealing schedule. This not only ensures fast convergence towards high-quality solutions but also guarantees asymptotic convergence to the Ising ground state. To demonstrate the advantages of the proposed higher-order neuromorphic Ising machine, we systematically solved benchmark combinatorial optimization problems such as MAX-CUT and MAX-SAT, comparing the results to those obtained using a second-order Ising machine employing the same annealing process.