A semiconductor memory device according to one embodiment of the present invention includes a dielectric film configured to store information depending on presence or absence of a conductive path therein, and a plurality of electrodes provided to contact a first surface of the dielectric film. The conductive path can be formed between two electrodes arbitrarily selected form the plurality of electrodes. The conductive path has a rectifying property of allowing a current to flow more easily in a first direction connecting arbitrary two electrodes than in a second direction opposite to the first direction. The largest possible number of the conductive paths that may be formed is larger than the number of the plurality of electrodes.