A major goal in the area of exact exponential algorithms is to solve the (worst-case) $n$-input Subset Sum problem in time $2^{(1/2 - c)n}$ for some constant $c \ge 0$. In this paper we give a Subset Sum algorithm with worst-case running time $O(2^{n/2} \cdot n^{-\gamma})$ for a constant $\gamma \ge 0.5023$ in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical ``meet-in-the-middle'' algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time $O(2^{n/2})$ in these memory models \cite{horowitz1974computing}.
Our algorithm combines several techniques, including the ``representation method'' introduced by Howgrave-Graham and Joux \cite{howgrave2010new} and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof~\cite{austrin2016dense}, and Nederlof and Wegrzycki \cite{NederlofW21}, and ``bit-packing'' techniques used in the work of Baran, Demaine, and P\v{a}tra\c{s}cu \cite{baran2005subquadratic} on subquadratic algorithms for 3SUM.