Deep　neural　networks　(DNNs)　have　shown　great　success　in　machine　learning　tasks　and　widely　used　in　many　fields.　However,　the　substantial　computational　and　storage　requirements　inherent　to　DNNs　are　usually　high,　which　poses　challenges　for　deploying　deep　learning　models　on　resource-limited　devices　and　hindering　further　applications.　To　address　this　issue,　the　lightweight　nature　of　neural　networks　has　garnered　significant　attention,　and　quantization　has　become　one　of　the　most　popular　approaches　to　compress　DNNs.　In　this　paper,　we　introduce　a　sparse　loss-aware　ternarization　(SLT)　model　for　training　ternary　neural　networks,　which　encodes　the　floating-point　parameters　into　{−1,0,1}.　Specifically,　we　abstract　the　ternarization　process　as　an　optimization　problem　with　discrete　constraints,　and　then　modify　it　by　applying　sparse　regularization　to　identify　insignificant　weights.　To　deal　with　the　challenges　brought　by　the　discreteness　of　the　model,　we　decouple　discrete　constraints　from　the　objective　function　and　design　a　new　algorithm　based　on　the　Alternating　Direction　Method　of　Multipliers　(ADMM).　Extensive　experiments　are　conducted　on　public　datasets　with　popular　network　architectures.　Comparisons　with　several　state-of-the-art　baselines　demonstrate　that　SLT　always　attains　comparable　accuracy　while　having　better　compression　performance.　©　2024　Elsevier　Inc.