Combine sugar, milk, butter, and salt in a 2-quart saucepan. Cook over low heat, stirring until sugar dissolves. Wash off sugar crystals that have formed on sides of pan, using a brush dipped in cold water.
Continue to cook, stirring occasionally, until mixture reaches firm ball stage (244°). Remove from heat; cool to lukewarm (110°). Add sweet potatoes; beat at medium speed of an electric mixer until mixture thickens. Stir in pecans. Pour candy into a well-buttered large serving platter. Cool and cut into 1-inch squares.