Add files using upload-large-folder tool

.gitattributes

@@ -13712,3 +13712,316 @@ pdf/train/SJlPOCEKvH.pdf filter=lfs diff=lfs merge=lfs -text
 pdf/train/rkKCdAdgx.pdf filter=lfs diff=lfs merge=lfs -text
 pdf/train/S1xBioR5KX.pdf filter=lfs diff=lfs merge=lfs -text
 pdf/train/ogciCC6fmBl.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ry3iBFqgl/ry3iBFqgl_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ByOExmWAb/ByOExmWAb_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ByOExmWAb/ByOExmWAb_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ByOExmWAb/ByOExmWAb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgs0oAqFQ/rkgs0oAqFQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgs0oAqFQ/rkgs0oAqFQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgs0oAqFQ/rkgs0oAqFQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lUOzWCW/r1lUOzWCW_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lUOzWCW/r1lUOzWCW_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lUOzWCW/r1lUOzWCW_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bkgq9ANKvB/Bkgq9ANKvB_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bkgq9ANKvB/Bkgq9ANKvB_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bkgq9ANKvB/Bkgq9ANKvB_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJyEH91A-/SJyEH91A-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJyEH91A-/SJyEH91A-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJyEH91A-/SJyEH91A-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJl7DsR5YQ/SJl7DsR5YQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJl7DsR5YQ/SJl7DsR5YQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJl7DsR5YQ/SJl7DsR5YQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJQRKzbA-/BJQRKzbA-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJQRKzbA-/BJQRKzbA-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJQRKzbA-/BJQRKzbA-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bk6qQGWRb/Bk6qQGWRb_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bk6qQGWRb/Bk6qQGWRb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bk6qQGWRb/Bk6qQGWRb_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lyTjAqYX/r1lyTjAqYX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lyTjAqYX/r1lyTjAqYX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1lyTjAqYX/r1lyTjAqYX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-uUGPbIjD/0-uUGPbIjD_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-uUGPbIjD/0-uUGPbIjD_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-uUGPbIjD/0-uUGPbIjD_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Kh0SVodY/B1Kh0SVodY_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Kh0SVodY/B1Kh0SVodY_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Kh0SVodY/B1Kh0SVodY_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/1Jv6b0Zq3qi/1Jv6b0Zq3qi_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/1Jv6b0Zq3qi/1Jv6b0Zq3qi_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/1Jv6b0Zq3qi/1Jv6b0Zq3qi_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkbd5xZRb/Hkbd5xZRb_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkbd5xZRb/Hkbd5xZRb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkbd5xZRb/Hkbd5xZRb_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/5vShUEyjmm/5vShUEyjmm_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/5vShUEyjmm/5vShUEyjmm_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/5vShUEyjmm/5vShUEyjmm_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/D7bPRxNt_AP/D7bPRxNt_AP_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/D7bPRxNt_AP/D7bPRxNt_AP_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/D7bPRxNt_AP/D7bPRxNt_AP_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1eK3i09YQ/S1eK3i09YQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1eK3i09YQ/S1eK3i09YQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1eK3i09YQ/S1eK3i09YQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/7_eLEvFjCi3/7_eLEvFjCi3_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/7_eLEvFjCi3/7_eLEvFjCi3_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/7_eLEvFjCi3/7_eLEvFjCi3_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJlkgaNKvr/BJlkgaNKvr_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJlkgaNKvr/BJlkgaNKvr_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJlkgaNKvr/BJlkgaNKvr_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/uDeDDoFOEpj/uDeDDoFOEpj_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/uDeDDoFOEpj/uDeDDoFOEpj_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jrA5GAccy_/jrA5GAccy__layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jrA5GAccy_/jrA5GAccy__origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/b9PoimzZFJ/b9PoimzZFJ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/b9PoimzZFJ/b9PoimzZFJ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/b9PoimzZFJ/b9PoimzZFJ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyL9u-WA-/SyL9u-WA-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyL9u-WA-/SyL9u-WA-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyL9u-WA-/SyL9u-WA-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgKO0EtvS/SkgKO0EtvS_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgKO0EtvS/SkgKO0EtvS_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgKO0EtvS/SkgKO0EtvS_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgbwsAcYm/rkgbwsAcYm_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgbwsAcYm/rkgbwsAcYm_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkgbwsAcYm/rkgbwsAcYm_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyxBxCNFwr/SyxBxCNFwr_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyxBxCNFwr/SyxBxCNFwr_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyxBxCNFwr/SyxBxCNFwr_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/fpJX0O5bWKJ/fpJX0O5bWKJ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/fpJX0O5bWKJ/fpJX0O5bWKJ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/fpJX0O5bWKJ/fpJX0O5bWKJ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkBsEQYll/SkBsEQYll_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkBsEQYll/SkBsEQYll_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkBsEQYll/SkBsEQYll_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy2fzU9gl/Sy2fzU9gl_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy2fzU9gl/Sy2fzU9gl_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy2fzU9gl/Sy2fzU9gl_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/m7QWxKp2Xqd/m7QWxKp2Xqd_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/m7QWxKp2Xqd/m7QWxKp2Xqd_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/m7QWxKp2Xqd/m7QWxKp2Xqd_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KCzRX9N8BIH/KCzRX9N8BIH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KCzRX9N8BIH/KCzRX9N8BIH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KCzRX9N8BIH/KCzRX9N8BIH_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Syx7A3NFvH/Syx7A3NFvH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Syx7A3NFvH/Syx7A3NFvH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Svfh1_hYEtF/Svfh1_hYEtF_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Svfh1_hYEtF/Svfh1_hYEtF_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Svfh1_hYEtF/Svfh1_hYEtF_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkFEGHx0Z/SkFEGHx0Z_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkFEGHx0Z/SkFEGHx0Z_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkFEGHx0Z/SkFEGHx0Z_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/519VBzfEaKW/519VBzfEaKW_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/519VBzfEaKW/519VBzfEaKW_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/519VBzfEaKW/519VBzfEaKW_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/mEdwVCRJuX4/mEdwVCRJuX4_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/mEdwVCRJuX4/mEdwVCRJuX4_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/mEdwVCRJuX4/mEdwVCRJuX4_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJVorjCcKQ/rJVorjCcKQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJVorjCcKQ/rJVorjCcKQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJVorjCcKQ/rJVorjCcKQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1X7nhsxl/S1X7nhsxl_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1X7nhsxl/S1X7nhsxl_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1X7nhsxl/S1X7nhsxl_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkxoh24FPH/rkxoh24FPH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkxoh24FPH/rkxoh24FPH_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkxoh24FPH/rkxoh24FPH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hke12T4KPS/Hke12T4KPS_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hke12T4KPS/Hke12T4KPS_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hke12T4KPS/Hke12T4KPS_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1kGbydxg/r1kGbydxg_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1kGbydxg/r1kGbydxg_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1kGbydxg/r1kGbydxg_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HwGNkx1WcIs/HwGNkx1WcIs_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HwGNkx1WcIs/HwGNkx1WcIs_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HwGNkx1WcIs/HwGNkx1WcIs_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1xwcyHFDr/B1xwcyHFDr_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1xwcyHFDr/B1xwcyHFDr_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1xwcyHFDr/B1xwcyHFDr_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ryxhB3CcK7/ryxhB3CcK7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ryxhB3CcK7/ryxhB3CcK7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ryxhB3CcK7/ryxhB3CcK7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/iktA2PtTRsK/iktA2PtTRsK_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/iktA2PtTRsK/iktA2PtTRsK_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/iktA2PtTRsK/iktA2PtTRsK_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/6xHJ37MVxxp/6xHJ37MVxxp_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/6xHJ37MVxxp/6xHJ37MVxxp_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/6xHJ37MVxxp/6xHJ37MVxxp_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyMDXnCcF7/SyMDXnCcF7_middle.json filter=lfs diff=lfs merge=lfs -text
+parse/train/SyMDXnCcF7/SyMDXnCcF7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyMDXnCcF7/SyMDXnCcF7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyMDXnCcF7/SyMDXnCcF7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/3SV-ZePhnZM/3SV-ZePhnZM_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/3SV-ZePhnZM/3SV-ZePhnZM_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/3SV-ZePhnZM/3SV-ZePhnZM_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkxStoC5F7/HkxStoC5F7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkxStoC5F7/HkxStoC5F7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkxStoC5F7/HkxStoC5F7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hyewf3AqYX/Hyewf3AqYX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hyewf3AqYX/Hyewf3AqYX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hyewf3AqYX/Hyewf3AqYX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkla1eHFvS/Hkla1eHFvS_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkla1eHFvS/Hkla1eHFvS_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hkla1eHFvS/Hkla1eHFvS_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rqfq0CYIekd/rqfq0CYIekd_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rqfq0CYIekd/rqfq0CYIekd_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rqfq0CYIekd/rqfq0CYIekd_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/DHSNrGhAY7W/DHSNrGhAY7W_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/DHSNrGhAY7W/DHSNrGhAY7W_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/DHSNrGhAY7W/DHSNrGhAY7W_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KJSC_AsN14/KJSC_AsN14_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KJSC_AsN14/KJSC_AsN14_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/KJSC_AsN14/KJSC_AsN14_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1gR2sC9FX/r1gR2sC9FX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1gR2sC9FX/r1gR2sC9FX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1gR2sC9FX/r1gR2sC9FX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyGjjsC5tQ/SyGjjsC5tQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyGjjsC5tQ/SyGjjsC5tQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SyGjjsC5tQ/SyGjjsC5tQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzfuiA9F7/rkzfuiA9F7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzfuiA9F7/rkzfuiA9F7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzfuiA9F7/rkzfuiA9F7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/vQTYEUtSUr/vQTYEUtSUr_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/vQTYEUtSUr/vQTYEUtSUr_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/vQTYEUtSUr/vQTYEUtSUr_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy4lojC9tm/Sy4lojC9tm_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy4lojC9tm/Sy4lojC9tm_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Sy4lojC9tm/Sy4lojC9tm_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1xh5sYgx/S1xh5sYgx_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1xh5sYgx/S1xh5sYgx_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/S1xh5sYgx/S1xh5sYgx_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1xwKoR9Y7/r1xwKoR9Y7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1xwKoR9Y7/r1xwKoR9Y7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1xwKoR9Y7/r1xwKoR9Y7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AYAgKFl78z/AYAgKFl78z_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AYAgKFl78z/AYAgKFl78z_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AYAgKFl78z/AYAgKFl78z_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgPCveAW/BJgPCveAW_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgPCveAW/BJgPCveAW_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgPCveAW/BJgPCveAW_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1gDNyrKDS/H1gDNyrKDS_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1gDNyrKDS/H1gDNyrKDS_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1gDNyrKDS/H1gDNyrKDS_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jQSBcVURlpW/jQSBcVURlpW_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jQSBcVURlpW/jQSBcVURlpW_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jQSBcVURlpW/jQSBcVURlpW_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AAes_3W-2z/AAes_3W-2z_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AAes_3W-2z/AAes_3W-2z_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/AAes_3W-2z/AAes_3W-2z_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-EYBhgw80y/0-EYBhgw80y_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-EYBhgw80y/0-EYBhgw80y_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/0-EYBhgw80y/0-EYBhgw80y_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jLHWRxwc7_f/jLHWRxwc7_f_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jLHWRxwc7_f/jLHWRxwc7_f_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/jLHWRxwc7_f/jLHWRxwc7_f_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B14rPj0qY7/B14rPj0qY7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B14rPj0qY7/B14rPj0qY7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B14rPj0qY7/B14rPj0qY7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/dvSExzhjG9D/dvSExzhjG9D_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/dvSExzhjG9D/dvSExzhjG9D_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/dvSExzhjG9D/dvSExzhjG9D_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzjUoAcFX/rkzjUoAcFX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzjUoAcFX/rkzjUoAcFX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rkzjUoAcFX/rkzjUoAcFX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJbbOLcex/rJbbOLcex_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJbbOLcex/rJbbOLcex_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJbbOLcex/rJbbOLcex_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1xQSjCqFQ/H1xQSjCqFQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1xQSjCqFQ/H1xQSjCqFQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1xQSjCqFQ/H1xQSjCqFQ_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1ldzA4tPr/H1ldzA4tPr_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1ldzA4tPr/H1ldzA4tPr_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H1ldzA4tPr/H1ldzA4tPr_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/MQQeeDiO5vv/MQQeeDiO5vv_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/MQQeeDiO5vv/MQQeeDiO5vv_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/MQQeeDiO5vv/MQQeeDiO5vv_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hye9lnCct7/Hye9lnCct7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hye9lnCct7/Hye9lnCct7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hye9lnCct7/Hye9lnCct7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c1EiEvivpx/4c1EiEvivpx_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c1EiEvivpx/4c1EiEvivpx_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c1EiEvivpx/4c1EiEvivpx_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G1jmxFOtY_/G1jmxFOtY__layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G1jmxFOtY_/G1jmxFOtY__span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G1jmxFOtY_/G1jmxFOtY__origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bke4KsA5FX/Bke4KsA5FX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bke4KsA5FX/Bke4KsA5FX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Bke4KsA5FX/Bke4KsA5FX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1eiu2VtwH/r1eiu2VtwH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1eiu2VtwH/r1eiu2VtwH_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1eiu2VtwH/r1eiu2VtwH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BylyV1BtDB/BylyV1BtDB_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BylyV1BtDB/BylyV1BtDB_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BylyV1BtDB/BylyV1BtDB_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgzYiRqtX/SkgzYiRqtX_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgzYiRqtX/SkgzYiRqtX_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkgzYiRqtX/SkgzYiRqtX_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/bMLeGGwptZk/bMLeGGwptZk_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/bMLeGGwptZk/bMLeGGwptZk_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/bMLeGGwptZk/bMLeGGwptZk_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/nIL7Q-p7-Sh/nIL7Q-p7-Sh_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/nIL7Q-p7-Sh/nIL7Q-p7-Sh_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/nIL7Q-p7-Sh/nIL7Q-p7-Sh_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgQ4lSFPH/BJgQ4lSFPH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgQ4lSFPH/BJgQ4lSFPH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJgQ4lSFPH/BJgQ4lSFPH_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkLXCE9lx/HkLXCE9lx_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkLXCE9lx/HkLXCE9lx_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HkLXCE9lx/HkLXCE9lx_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Igu2ogg/B1Igu2ogg_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Igu2ogg/B1Igu2ogg_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/B1Igu2ogg/B1Igu2ogg_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c0J6lwQ4_/4c0J6lwQ4__layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c0J6lwQ4_/4c0J6lwQ4__span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/4c0J6lwQ4_/4c0J6lwQ4__origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/XWYJ25-yTRS/XWYJ25-yTRS_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/XWYJ25-yTRS/XWYJ25-yTRS_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/XWYJ25-yTRS/XWYJ25-yTRS_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJe1334YDH/BJe1334YDH_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJe1334YDH/BJe1334YDH_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJe1334YDH/BJe1334YDH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJgf6Z-0W/SJgf6Z-0W_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJgf6Z-0W/SJgf6Z-0W_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJgf6Z-0W/SJgf6Z-0W_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SknC0bW0-/SknC0bW0-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SknC0bW0-/SknC0bW0-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SknC0bW0-/SknC0bW0-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hk6WhagRW/Hk6WhagRW_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hk6WhagRW/Hk6WhagRW_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hk6WhagRW/Hk6WhagRW_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/eNdiU_DbM9/eNdiU_DbM9_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/eNdiU_DbM9/eNdiU_DbM9_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/eNdiU_DbM9/eNdiU_DbM9_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H135uzZ0-/H135uzZ0-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H135uzZ0-/H135uzZ0-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/H135uzZ0-/H135uzZ0-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1genAVKPB/r1genAVKPB_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1genAVKPB/r1genAVKPB_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/r1genAVKPB/r1genAVKPB_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HyEi7bWR-/HyEi7bWR-_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HyEi7bWR-/HyEi7bWR-_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HyEi7bWR-/HyEi7bWR-_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/CmI7NqBR4Ua/CmI7NqBR4Ua_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/CmI7NqBR4Ua/CmI7NqBR4Ua_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/CmI7NqBR4Ua/CmI7NqBR4Ua_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hy1d-ebAb/Hy1d-ebAb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hy1d-ebAb/Hy1d-ebAb_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/Hy1d-ebAb/Hy1d-ebAb_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ZyugLlWzdO/ZyugLlWzdO_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ZyugLlWzdO/ZyugLlWzdO_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/ZyugLlWzdO/ZyugLlWzdO_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJaP_-xAb/SJaP_-xAb_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJaP_-xAb/SJaP_-xAb_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SJaP_-xAb/SJaP_-xAb_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJl3yM-Ab/rJl3yM-Ab_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJl3yM-Ab/rJl3yM-Ab_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/rJl3yM-Ab/rJl3yM-Ab_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G8A_Nl0yim6/G8A_Nl0yim6_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G8A_Nl0yim6/G8A_Nl0yim6_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/G8A_Nl0yim6/G8A_Nl0yim6_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJl2_nVFPB/BJl2_nVFPB_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJl2_nVFPB/BJl2_nVFPB_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/BJl2_nVFPB/BJl2_nVFPB_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkMwpiR9Y7/SkMwpiR9Y7_layout.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkMwpiR9Y7/SkMwpiR9Y7_origin.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/SkMwpiR9Y7/SkMwpiR9Y7_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HygegyrYwH/HygegyrYwH_span.pdf filter=lfs diff=lfs merge=lfs -text
+parse/train/HygegyrYwH/HygegyrYwH_origin.pdf filter=lfs diff=lfs merge=lfs -text

parse/dev/1sx0Drq4jfT/1sx0Drq4jfT.md

@@ -0,0 +1,613 @@
+# TRAINING META-SURROGATE MODEL FOR TRANS-FERABLE ADVERSARIAL ATTACK.
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+We consider adversarial attacks to a black-box model when no queries are allowed. In this setting, many methods directly attack surrogate models and transfer the obtained adversarial examples to fool the target model. Plenty of previous works investigated what kind of attacks to the surrogate model can generate more transferable adversarial examples, but their performances are still limited due to the mismatches between surrogate models and the target model. In this paper, we tackle this problem from a novel angle—instead of using the original surrogate models, can we obtain a Meta-Surrogate Model (MSM) such that attacks to this model can be easier transferred to other models? We show that this goal can be mathematically formulated as a well-posed (bi-level-like) optimization problem and design a differentiable attacker to make training feasible. Given one or a set of surrogate models, our method can thus obtain an MSM such that adversarial examples generated on MSM enjoy eximious transferability. Comprehensive experiments on Cifar-10 and ImageNet demonstrate that by attacking the MSM, we can obtain stronger transferable adversarial examples to fool black-box models including adversarially trained ones, with much higher success rates than existing methods.
+
+# 1 INTRODUCTION
+
+The developments of Convolutional Neural Network (CNN) (LeCun et al., 1995; Krizhevsky et al., 2012) have greatly promoted the advancements in Computer Vision (Ren et al., 2016). However, previous works (Goodfellow et al., 2014; Carlini & Wagner, 2017; Croce & Hein, 2020a; Ganeshan et al., 2019) have shown a critical robustness issue that CNN models are vulnerable to humanimperceptible perturbations of input images, also known as adversarial examples (AEs). The design of AEs is useful for revealing the security threats on machine learning systems (Croce & Hein, 2020b) and for understanding the representations learned by CNN models (Ilyas et al., 2019).
+
+In this paper, we consider the problem of black-box attack, where the target victim model is entirely hidden from the attacker. In this setting, standard white-box attacks (Moosavi-Dezfooli et al., 2016; Carlini & Wagner, 2017) or even query-based black-box attacks (Ilyas et al., 2018; Cheng et al., 2018; 2020; 2019) cannot be used, and the prevailing way to attack the victim is through transfer attack (Papernot et al., 2017; Wu et al., 2018). In transfer attack (Demontis et al., 2019; Dong et al., 2018), the attackers commonly generate AEs by attacking one or an ensemble of surrogate models and hope the obtained AEs can also successfully fool the victim black-box model.
+
+Although great efforts have been made to improve the transferability of adversarial attacks (Tramer\` et al., 2017; Xie et al., 2019; Wu et al., 2020a), the transfer attack-based methods still encounter poor success rates, especially when attacking adversarially trained target models. This is caused by a fundamental limitation of current approaches—they all leverage the surrogate models trained by standard learning tasks (e.g., classification, object detection), while it is not always the case that attacks fooling such models can be easily transferred. We thus pose the following important question on transfer attack that has not been well studied in the literature: Instead of using standard (naturally trained) models as surrogate, can we artificially construct another Meta-Surrogate Model (MSM) such that attacks to this model can be easier transferred to other models?
+
+We answer this question in the affirmative by developing a novel black-box attack pipeline called Meta-Transfer Attack (MTA). Assume a set of source models (standard surrogate models) are given, instead of directly attacking these source models, our algorithm aims to obtain a “meta-surrogate model (MSM)”, which is designed in the way that attacks to this model can be easier transferred to fool other models, and conduct attacks on the MSM to obtain transferable AEs. We show that this goal can be mathematically formulated as a well-posed (bi-level-like) training objective by unrolling the attacks on the MSM and defining a loss to measure the transferability of the resulting AEs. To avoid discrete operations in the white-box attack, we propose a Customized PGD attacker that enables back-propagation through the whole procedure. With this bi-level-like optimization (Finn et al., 2017; Qin et al., 2020), the source models supervise the MSM to improve the transferability of the AEs created on it. Through extensive experiments on various models and datasets, we show that the proposed MTA method leads to significantly improved transfer attacks, demonstrating the effectiveness of the MSM.
+
+We summarize the main contributions of our work as follows. 1) We propose a novel MTA framework to train an MSM to improve the transferability of AEs. To the best of our knowledge, our work is the first attempt to explore a better surrogate model for producing stronger transferable AEs. 2) We compare MTA with state-of-the-art transfer attack methods (e.g., MI (Dong et al., 2018), DI (Xie et al., 2019), TI (Dong et al., 2019), SGM (Wu et al., 2020a), AEG (Bose et al., 2020), IR (Wang et al., 2021a), SI-NI (Lin et al., 2020)) on Cifar-10 (Krizhevsky et al., 2009) and Imagenet (Deng et al., 2009). The comparisons demonstrate the effectiveness of the proposed MTA—the AEs generated by attacking MSM significantly outperform previous methods, in attacking both naturally trained and adversarially trained black-box target models.
+
+# 2 BACKGROUND
+
+Adversarial attacks. Szegedy et al. (2014) reveals the interesting phenomenon that CNN models are vunerable to adversarial attacks. After that, many attacks have been developed (Gao et al., 2020; Zhou et al., 2018; Wu et al., 2020b; Li et al., 2020b; Kaidi et al., 2019; Sriramanan et al., 2020). Adversarial attacks can be mainly classified into white-box and black-box attacks (Maksym et al., 2020) according to how much information about the target model is exposed to the attacker. Whitebox attacks (Kurakin et al., 2016) are often more effective than than black-box attacks (Brendel et al., 2017; Cheng et al., 2018; 2020) as they can leverage full knowledge of the target model including the model weights and architecture. For example, Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2014) uses 1-step gradient ascent to produce adversarial examples that enlarge the model’s loss. Projected gradient descent (PGD) attack can be viewed as a multi-step FGSM attack (Madry et al., 2018). Many other white-box attacks have also been developed by leveraging full information of the target model (Moosavi-Dezfooli et al., 2016; Croce & Hein, 2020a). In the black-box setting, query-based black-box attacks (Huang & Zhang, 2020; Du et al., 2020) assume model information is hidden but attackers can query the model and observe the corresponding hard-label or soft-label predictions. Among them, (Chen et al., 2017; Ilyas et al., 2018) considered soft-label probability predictions and (Chen et al., 2020; Huang & Zhang, 2020; Cheng et al., 2018) considered hard-label decision-based predictions. Considering that using a large number of queries to attack an image is impractical, several works try to further reduce the query counts (Li et al., 2020a; Wang et al., 2020).
+
+Transferability of adversarial examples. In this paper, we consider the black-box attack scenario when the attacker cannot make any query to the target model (Lin et al., 2020; Huang et al., 2019; Wang et al., 2021b). In this case, the common attack method is based on transfer attack—the attacker generates AEs by attacking one or few surrogate models and hopes the AEs can also fool the target model (Papernot et al., 2016; Liu et al., 2017; Yuan et al., 2021; Zhou et al., 2018). Compared with query-based attacks, crafting AEs from the surrogate model consumes less computational resources and is more realistic in practice. Along this direction, subsequent works have made attempts to improve the transferability of AEs (Guo et al., 2020; Wu et al., 2020c; Naseer et al., 2019; Li et al., $2 0 2 0 \mathrm { c }$ ; Wang & He, 2021). For instance, Dong et al. (2018) boosted the transferability by integrating the momentum term into the iterative process. Other techniques like data augmentations (Xie et al., 2019), exploiting gradients of skip-connection (Wu et al., 2020a), and negative interaction between pixels (Wang et al., 2021a) also contribute to stronger transferable attacks. In addition to using the original surrogate models, AEG (Bose et al., 2020) adversarially trains a robust classifier together with an encoder-decoder-based transferable perturbation generator. After the training, AEG uses the generator to generate transferable AEs to attack a set of classifiers. Compared to all the existing works, our method is the first that meta-trains a new meta-surrogate model (MSM) such that attacks on MSM can be easier transferred to other models. This not only differs from all the previous methods that attack standard surrogate models but also differs from the encoder-decoder based method such as AEG (Bose et al., 2020).
+
+# 3 METHODOLOGY
+
+We consider the black-box attack setting where the target model is hidden to the attacker and queries are not allowed. This setting is also known as the transfer attack setting (Dong et al., 2018; 2019; Xie et al., 2019; Wang et al., 2021a) and the attacker 1) cannot access the weight, the architecture, and the gradient of the target model; and 2) cannot querying the target model. The attacker can access 1) the dataset used by the target model; and 2) a single or a set of surrogate models (also known as source models) that may share the dataset with the target model. For example, it is common to assume that the attacker can access one or multiple well-performed (pretrained) image classification models. Existing transferable adversarial attack methods conduct various attacks to these models and hope to get transferable AEs that can fool an unknown target model. Instead of proposing another attack method on surrogate models, we propose a novel framework MTA to train a Meta-Surrogate Model (MSM) with the goal that attacking the MSM can generate stronger transferable AEs than directly attacking the original surrogate models. When evaluating, the transferable AEs are generated by attacking the MSM with standard white-box attack methods (e.g., PGD attack). In the following, we will first review exiting attacks and then show how to form a bi-level optimization objective to train the MSM model.
+
+# 3.1 REVIEWS OF FGSM AND PGD
+
+We follow the settings of existing works (Dong et al., 2018; Xie et al., 2019; Wu et al., 2020a; Wang et al., 2021a) to focus on untargeted attack, where the attack is considered successful as long as the perturbed image is wrongly predicted.
+
+FGSM (Goodfellow et al., 2014) conducts one-step gradient ascent to generate AEs to enlarge the prediction loss. The formulation can be written as
+
+$$
+\begin{array} { r } { x _ { a d v } = \mathbf { C l i p } \big ( x + \epsilon \cdot \mathrm { s i g n } \big ( \nabla _ { x } L ( f ( x ) , y ) \big ) \big ) , } \end{array}
+$$
+
+where $x$ is a clean image and $y$ is the corresponding label; $\epsilon$ is the attack step size that determines the maximum $L _ { \infty }$ perturbation of each pixel; $f$ is the victim model that is transparent to the FGSM attacker; Clip is the function that clipping the values of $x _ { a d v }$ to the legal range (e.g., clipping the RGB AEs to the range of $[ 0 , 2 5 5 ] ,$ ); $L$ is usually the cross-entropy loss.
+
+PGD (Kurakin et al., 2016), also known as I-FGSM attack, is a multi-step extension of FGSM. The formulation of PGD is
+
+$$
+\boldsymbol { x } _ { a d v } ^ { k } = \mathrm { C l i p } \big ( \boldsymbol { x } _ { a d v } ^ { k - 1 } + \frac { \epsilon } { T } \cdot \mathrm { s i g n } \big ( \nabla _ { \boldsymbol { x } _ { a d v } ^ { k - 1 } } L \big ( f \big ( \boldsymbol { x } _ { a d v } ^ { k - 1 } \big ) , y \big ) \big ) \big ) .
+$$
+
+$x _ { a d v } ^ { k }$ is the AEs generated in the $k$ -th gradient ascent step. Note that $x _ { a d v } ^ { 0 }$ is the clean image equals to $x$ . Eq 2 will be run for iterations to obtain $x _ { a d v } ^ { T }$ with perturbation size $\epsilon$ .
+
+# 3.2 META-TRANSFER ATTACK
+
+How to train the MSM where attacks to this model can be easier transferred to other models? We show this can be formulated as a bi-level training objective. Let $\mathcal { A }$ denote an attack algorithm (e.g., FGSM or PGD) and $\mathcal { M } _ { \theta }$ denote the MSM parameterized by $\theta$ . For a given image $x$ , the AE generated by attacking $\mathcal { M } _ { \theta }$ can be denoted as $\bar { \boldsymbol { A } } ( \mathcal { M } _ { \theta } , x , y )$ . For example, if $\mathcal { A }$ is FGSM, then $\begin{array} { r } { \mathcal { A } ( \mathcal { M } _ { \theta } , x , y ) = x _ { a d v } = \mathbf { C } \mathrm { l i p } \big ( x + \epsilon \cdot \mathrm { s i g n } \big ( \nabla _ { x } L ( \mathcal { M } _ { \theta } ( x ) , y ) ) \big ) } \end{array}$ . Since in the attack time we only have access to a set of source models $\mathcal { F } _ { 1 } , \ldots , \mathcal { F } _ { N }$ , we can evaluate the transferability of the adversarial example $\mathcal { A } ( \mathcal { M } _ { \theta } , x , y )$ on the source models and optimize the MSM via maximizing the adversarial losses of those $N$ source models, leading to the following training objective:
+
+$$
+\underset { \ b { \theta } } { \arg \operatorname* { m a x } } \mathbb { E } _ { ( \boldsymbol { x } , \boldsymbol { y } ) \sim D } \big [ \sum _ { i = 1 } ^ { N } L ( \underset { \mathcal { F } _ { i } ^ { \prime } s \mathrm { ~ p r e d i c t i o n ~ f o r ~ A E } }  \overbrace { \mathcal { F } _ { i } ( \overbrace { A ( \mathcal { M } _ { \theta } , \boldsymbol { x } , \boldsymbol { y } ) } ) } , \boldsymbol { y } ) \big ] ,
+$$
+
+where $D$ is the distribution of training data. The structure of this objective and the training procedure can be illustrated in Figure 1, where we can view it as a meta-learning or bi-level optimization method. At the lower level, the AE is generated by a white-box attack (usually gradient ascent) on MSM, while at the higher level, we feed the AE to the source models to compute the robust loss. Solving Eq 3 will find an MSM where attacking it leads to stronger transferable AEs. The optimization steps of $\operatorname { E q } 3$ are detailed below.
+
+First, $\mathcal { A }$ should be some strong white-box attacks, such as FGSM or PGD. However, directly using those attacks will make the gradient of meta training objective Eq 3 ill-defined since the sign function in both FGSM and PGD introduce a discrete operation. This results in that the gradient back-propagating through sign be zero and further prohibits the training of the MSM.
+
+To overcome this challenge, we design $\mathcal { A }$ as an approximation of PGD and denote it as Customized PGD. Section 3.3 will show more explanation about how the sign function in PGD prohibits backpropagation and how Customized PGD enables the back-propagation. The crucial difference between PGD and the Customized PGD is the operation to the gradient $\nabla _ { x _ { a d v } ^ { k - 1 } } L ( \mathcal { M } _ { \theta } ( x _ { a d v } ^ { \bar { k } - 1 } ) , y )$ , where $L$ is the cross entropy loss. For simplicity, we denote the vanilla gradient $\mathrm { \dot { \nabla } } _ { x _ { a d v } ^ { k } } \dot { L } ( \mathcal { M } _ { \theta } ( x _ { a d v } ^ { k } ) , y )$ at the $k$ -th step as $g ^ { k }$ , and generate another map $g _ { e n s } ^ { k }$ via Eq 4:
+
+$$
+\left\{ \begin{array} { l l } { g _ { 1 } ^ { k } = \frac { g ^ { k } } { \mathrm { s u m } ( \mathrm { a b s } ( g ^ { k } ) ) } } \\ { g _ { t } ^ { k } = \frac { 2 } { \pi } \cdot \arctan ( \frac { g ^ { k } } { \mathrm { m e a n } ( \mathrm { a b s } ( g ^ { k } ) ) } ) } \\ { g _ { s } ^ { k } = \mathrm { s i g n } ( g ^ { k } ) } \\ { g _ { e n s } ^ { k } = g _ { 1 } ^ { k } + \gamma _ { 1 } \cdot g _ { t } ^ { k } + \gamma _ { 2 } \cdot g _ { s } ^ { k } } \end{array} \right.
+$$
+
+![](images/8428e7ac823ab1dc2d285fe8dfad7603251a7b1a1e7fee0e2a64addb41e7763c.jpg)  
+Figure 1: The framework of the proposed MTA when T = 1 and A(Mθ(x)) = x1adv. The clean image $x$ is first feed into the MSM $\mathcal { M } _ { \theta }$ and obtain the loss $L ( \mathcal { M } _ { \theta } ( x ) , y )$ . Next we back-propagate the loss and use Eq 4 to obtain the noise g0ens. Then, via $\operatorname { E q } 5$ , we obtain the adversarial example x1adv which will be feed into the source models $\mathcal { F } _ { 1 }$ $\mathbf { \Phi } _ { 1 } , \mathcal { F } _ { 2 } , \mathbf { \Phi } .$ .., and $\mathcal { F } _ { N }$ . Finally, by maximizing the source models’ loss, we can optimize the MSM to learn a particular weight so that the adversarial example $x _ { a d v } ^ { 1 }$ attacking it can fool source models.
+
+Note that we set $\gamma _ { 1 } = \gamma _ { 2 } = 0 . 0 1$ as default
+
+for all the experiments. Both $g _ { 1 } ^ { k }$ and $g _ { t } ^ { k }$ ensure the objective in $\operatorname { E q } 3$ be differentiable with respect to the MSM’s weight $\theta$ ; arctan $( \cdot )$ is a smooth approximation of sign and mean(abs(gk)) prevents arctan from falling into the saturation or linear region. The item $\gamma _ { 2 } \cdot g _ { s } ^ { k }$ provides the lower-bound for each pixel’s perturbation in $g _ { e n s } ^ { k }$ . The experiments in Section 4.3 will demonstrate the importances of $\mathbf { \bar { { g } } } _ { t } ^ { k }$ and $\overset { \cdot } { g } _ { s } ^ { k }$ for Customized PGD. With Eq 4, the Customized PGD conducts the following update to generate AE:
+
+$$
+x _ { a d v } ^ { k } = \mathrm { C l i p } ( x _ { a d v } ^ { k - 1 } + \frac { \epsilon _ { c } } { T } \cdot g _ { e n s } ^ { k - 1 } ) .
+$$
+
+Note that $\epsilon _ { c }$ differs from the perturbation $\epsilon$ in FGSM and PGD because $g _ { e n s } ^ { k - 1 }$ in our update is not a sign vector and its size will depend on the magnitude of the original gradient. Finally, we get $x _ { a d v } ^ { T }$ after $T$ iterations of $\operatorname { E q } 5$ .
+
+Second, we feed $x _ { a d v } ^ { T }$ into $N$ source models and calculate the corresponding adversarial losses $L ( \mathcal { F } _ { i } ( x _ { a d v } ^ { T } ) , y )$ for all $i = 1 , \ldots , N$ . Larger losses of the $N$ source models indicate a higher advlikelihood that $x _ { a d v } ^ { T }$ fooling the MSM can transfer to other models.
+
+Third, we optimize the MSM by maximizing the objective function defined in Eq 3. The update rule can be written as
+
+$$
+\begin{array} { r } { \boldsymbol { \theta } ^ { ' } = \boldsymbol { \theta } + \alpha \cdot \sum _ { i = 1 } ^ { N } \nabla _ { \boldsymbol { \theta } } L ( \mathcal { F } _ { i } ( x _ { a d v } ^ { T } ) , y ) , } \end{array}
+$$
+
+where xTadv can be written as a function of $\theta$ by unrolling the attack update rule $\mathrm { E q } 5 T$ times. We will show how to explicitly compute the gradient in Section 3.3. With this training procedure, the MSM is trained to learn a particular weight with which the white-box AEs fooling it can also fool other models. We summarize the training and testing of MTA in Algorithm 1 and Section A.1, respectively. Each capitalized notation represents a batch of the variable denoted with lower case. For example, $X$ denotes a batch of $x$ . Note that Customized PGD is just a continuous approximation of PGD used to train the MSM. In the inference phase, we use standard attacks such as PGD to craft AEs on the MSM.
+
+# 3.3 GRADIENT CALCULATION
+
+In the calculation we set both $N$ and $T$ in $\operatorname { E q } 6$ to 1, so the gradient in $\operatorname { E q } 6$ is $\nabla _ { \theta } L ( \mathcal { F } _ { 1 } ( x _ { a d v } ^ { 1 } ) , y )$ According to $\operatorname { E q } 5$ , we can replace $x _ { a d v } ^ { 1 }$ in Eq 6 with $\mathrm { C l i p } ( \bar { x } _ { a d v } ^ { 0 } + \epsilon _ { c } \cdot g _ { e n s } ^ { \bar { 0 } } )$ , where $x _ { a d v } ^ { 0 }$ equals to $x$ . For simplicity, we ignore the clip function in the analysis and simplify the derivation as $\nabla _ { \boldsymbol { \theta } } L ( \mathcal { F } _ { 1 } ( \boldsymbol { x } + \dot { \epsilon _ { c } } \cdot \boldsymbol { g } _ { e n s } ^ { 0 } ) , y )$ . By chain rule and since $x$ is independent to $\theta$ , we can further rewrite this
+
+as
+
+$$
+\frac { \partial L ( \mathcal { F } _ { 1 } ( x + \epsilon _ { c } \cdot g _ { e n s } ^ { 0 } ) , y ) } { \partial g _ { e n s } ^ { 0 } } \cdot \frac { \partial g _ { e n s } ^ { 0 } } { \partial \theta } .
+$$
+
+By replacing $g _ { e n s } ^ { 0 }$ with $\mathrm { E q } 4$ , the second term of $\operatorname { E q } 7$ can be expanded as
+
+$$
+\nabla _ { \boldsymbol { \theta } } g _ { e n s } ^ { 0 } = \nabla _ { \boldsymbol { \theta } } g _ { 1 } ^ { 0 } + \gamma _ { 1 } \cdot \nabla _ { \boldsymbol { \theta } } g _ { t } ^ { 0 } + \gamma _ { 2 } \cdot \nabla _ { \boldsymbol { \theta } } g _ { s } ^ { 0 } .
+$$
+
+Note that $g _ { s } ^ { 0 }$ equals to $\mathrm { s i g n } ( g ^ { 0 } )$ and the sign function introduces discrete operation so that the gradient of $g _ { s } ^ { 0 }$ with respect to $\theta$ becomes 0 (unless $g ^ { 0 } = 0 \array$ ). Therefore, $\nabla _ { \theta } g _ { e n s } ^ { 0 }$ can be further written as
+
+$$
+\begin{array} { r l r } {  { \nabla _ { \theta } g _ { e n s } ^ { 0 } = \nabla _ { \theta } g _ { 1 } ^ { 0 } + \gamma _ { 1 } \cdot \nabla _ { \theta } g _ { t } ^ { 0 } } } \\ & { } & { = \nabla _ { \theta } ( \frac { \nabla _ { x } L ( M _ { \theta } ( x ) , y ) } { \operatorname { s u m } ( \mathrm { a b s } ( \nabla _ { x } L ( M _ { \theta } ( x ) , Y ) ) ) } ) + \gamma _ { 1 } \cdot \nabla _ { \theta } ( \arctan ( \frac { \nabla _ { x } L ( M _ { \theta } ( x ) , y ) } { \operatorname { m e a n } ( \mathrm { a b s } ( \nabla _ { x } L ( M _ { \theta } ( x ) , y ) ) ) } ) ) . } \end{array}
+$$
+
+In this formulation, $\nabla _ { x } L ( \mathcal { M } _ { \theta } ( x ) , y )$ depends on $\theta$ and the second-order derivative of $\nabla _ { x } L ( \mathcal { M } _ { \theta } ( x ) , y )$ $w . r . t \theta$ can be obtained with lots of deep learning libraries (Abadi et al., 2016; Paszke et al., 2017). In summary, by integrating Eqs.6-9, the MSM can be optimized by an SGD-based optimizer.
+
+# 4 EXPERIMENT
+
+We conduct experiments to show that the proposed method, under the same set of source models, can generate stronger transferable AEs than existing transfer attack methods.
+
+We first present our general experimental settings. 1) We conduct experiments on both Cifar10 (Krizhevsky et al., 2009) and ImageNet (Deng et al., 2009). 2) We compare the proposed MTA with seven state-of-the-art transferable adversarial attack methods, including MI (Dong et al., 2018), DI (Xie et al., 2019), TI (Dong et al., 2019), SGM (Wu et al., 2020a), SI-NI (Lin et al., 2020), AEG (Bose et al.,
+
+# Algorithm 1 Training of Meta-Transfer Attack
+
+input: $N$ source models $\mathcal { F } _ { 1 } , \ldots , \mathcal { F } _ { N }$ , Training set $\mathbb { D }$ , batch size $b$ , initialized MSM $\mathcal { M } _ { \theta }$ .   
+output: Optimized weight $\theta$ .   
+$\textbf { 1 : }$ while not done do   
+2 : sample data $( X = [ x _ { 1 } , \dots , x _ { b } ] , Y = [ y _ { 1 } , \dots , y _ { b } ] ) \in \mathbb { D }$ 3 : X0adv = X   
+4 : for $\mathrm { k }$ in [1, 2, ..., T]:   
+5 : 0 $G ^ { k } = \mathsf { \bar { V } } _ { X _ { a d v } ^ { k - 1 } } L ( \mathcal { M } _ { \theta } ( X _ { a d v } ^ { k - 1 } ) , Y )$   
+6 : advobtain Gkens v ia Eq 4   
+7 : obtain $X _ { a d v } ^ { k ^ { - } }$ via Eq 5   
+$\mathbf { 8 : }$ end for   
+9 : for each source model $\mathcal { F } _ { i } \in [ \mathcal { F } _ { 1 } , \mathcal { F } _ { 2 } , \ldots , \mathcal { F } _ { N } ]$ , do 10: evaluate XT on ${ \mathcal { F } } _ { i }$ and obtain $L ( \mathcal { F } _ { i } ( X _ { a d v } ^ { T } ) , Y )$ 11: end for   
+12: $\theta = \theta + \alpha \cdot \nabla _ { \theta } \sum _ { i } ^ { N } L ( \mathcal { F } _ { i } ( X _ { a d v } ^ { T } ) , Y )$   
+13: return θ
+
+2020), IR (Wang et al., 2021a), and FIA (Wang et al., 2021b). Note that since SGM is based on enlarging the gradient of skip connections, we only include this method on ImageNet experiments when the source models have sufficient skip connections. AEG is compared only on Cifar-10 because the official AEG is evaluated only on small scale datasets (Mnist and Cifar-10), and it is computational costly to train the perturbation generator on large-scale datasets. FIA is implemented only on ImageNet using the same intermediate feature layers introduces in (Wang et al., 2021b). 3) Since the number of attack iterations $T$ is different between training and testing, we denote it as $T _ { t }$ in training and $T _ { v }$ in testing respectively to avoid confusion. 4) When training the MSM, we use the Customized PGD with $\gamma _ { 1 } = \gamma _ { 2 } = 0 . 0 1$ to attack the MSM. When evaluating, we use PGD with ${ \mathit { T } } _ { v } { = } 1 0$ and $\epsilon { = } 1 5$ to attack the MSM. 5) When using the baseline methods to generate AEs on multiple source models, we follow Dong et al. (2018) to ensemble the logits of the source models before loss calculation. 6) We use source and target models to train and to evaluate the MSM, respectively. 7) For fair comparisons between MTA and baselines, we implement baselines with the number of iterations $T { = } 1 0$ and $\epsilon { = } 1 5$ , and other hyper-parameters are tuned for their best possible performances (implementations are detailed in Section A.8). 8) More experiments (e.g., targeted transfer attack, attacks with smaller $\epsilon$ , more comparisons between MTA and baselines) will be shown in Section A.3.
+
+# 4.1 EXPERIMENTS ON CIFAR-10
+
+# 4.1.1 EXPERIMENTAL CONFIGURATIONS
+
+On Cifar-10, we use 8 source models including ResNet-10, -18, -34 (He et al., 2016), SeResNet-14, -26, -50 (Hu et al., 2018), MobileNet-V1 (Howard et al., 2017), and -V2 (Sandler et al., 2018) to train the MSM. To ensure mismatches between the source and target models and to avoid saturated transfer attack performances (i.e., attack success rates close to $100 \%$ ), we select the 8 target models including MobileNet-V3 (Howard et al., 2019), ShuffleNet-V1, -V2 (Zhang et al., 2018), SqueezeNetA, -B (Iandola et al., 2016), and adversarially trained ResNet-18, -34, and SeResNet-50. The network architectures of all 16 models are defined on public GitHub repositories1,2,3. We train all the source and target models and describe the training details of these models in Section A.2. The trained models and the code will be released to the community for reproducibility.
+
+Table 1: Transfer attack success rates on eight target networks on Cifar-10. The MSM is trained with eight source models. From left to right, the eight target models are MobileNet-V3 (MN-V3), ShuffleNet-V1 (SN-V1), -V2 (SN-V2), SqueezeNet-A (SN-A), -B (SN-B), and adversarially trained ResNet-18 $( \mathrm { R e s - } 1 8 _ { a d v } )$ ), ResNet-34 $( \mathsf { R e s } - 3 4 _ { a d v } )$ , and SeResNet-50 $( \mathrm { S e R e s }  – \mathsf { I } 0 _ { a d v } )$ .   
+
+<table><tr><td>Method</td><td>MN-V3</td><td>SN-V1</td><td>SN-V2</td><td>SN-A</td><td>SN-B</td><td>Res-18adu</td><td>Res-34adu</td><td>SE-50adu</td></tr><tr><td>PGD</td><td>51.8%</td><td>64.1%</td><td>49.4%</td><td>57.2%</td><td>56.3%</td><td>67.7%</td><td>63.9%</td><td>63.4%</td></tr><tr><td>DI</td><td>57.8%</td><td>72.5%</td><td>56.4%</td><td>65.7%</td><td>64.6%</td><td>80.7%</td><td>73.1%</td><td>71.0%</td></tr><tr><td>MI</td><td>70.2%</td><td>85.6%</td><td>72.6%</td><td>83.7%</td><td>83.0%</td><td>92.9%</td><td>90.9%</td><td>89.1%</td></tr><tr><td>A-PGD</td><td>74.1%</td><td>88.9%</td><td>75.8%</td><td>84.2%</td><td>83.6%</td><td>90.7%</td><td>89.3%</td><td>89.1%</td></tr><tr><td>TI</td><td>54.5%</td><td>59.9%</td><td>54.2%</td><td>71.8%</td><td>71.4%</td><td>57.6%</td><td>46.3%</td><td>46.6%</td></tr><tr><td>AEG</td><td>90.8%</td><td>92.5%</td><td>85.8%</td><td>91.3%</td><td>91.0%</td><td>96.1%</td><td>93.6%</td><td>93.1%</td></tr><tr><td>IR</td><td>59.3%</td><td>77.9%</td><td>62.5%</td><td>71.6%</td><td>69.1%</td><td>79.8%</td><td>73.7%</td><td>72.1%</td></tr><tr><td>MTA</td><td>91.8%</td><td>98.4%</td><td>90.9%</td><td>94.9%</td><td>93.8%</td><td>98.4%</td><td>96.5%</td><td>97.1%</td></tr><tr><td>MTAγ1=0</td><td>70.0%</td><td>80.9%</td><td>68.5%</td><td>58.5%</td><td>59.4%</td><td>67.7%</td><td>59.2%</td><td>68.9%</td></tr><tr><td>MTAγ2=0</td><td>90.0%</td><td>98.2%</td><td>90.5%</td><td>93.9%</td><td>93.1%</td><td>97.6%</td><td>96.0%</td><td>96.3%</td></tr><tr><td>MTAdense</td><td>86.9%</td><td>96.2%</td><td>87.1%</td><td>89.0%</td><td>87.6%</td><td>96.2%</td><td>91.3%</td><td>93.6%</td></tr></table>
+
+![](images/39ac7fe8f9e261e1db855162b6660542b13843cf18af6ccb682c26d2b0acda40.jpg)  
+Figure 2: (a) The structures of ResNet-13 and -19. ResNet-13 contains the top four blocks in the solid-line box and the classifier. ResNet-19 contains all the six blocks and the classifier. The parameter $M *$ of each block denotes the number of filters of its convolution layers. (b) The detailed structure of residual block. The orange cube is the convolution layer and the number on it denotes its number of filters. Pool in the sixth block is global-average pooling while all the other pool is max-pooling with both stride and kernel size of $2 \times 2$ . The convolution layer in the shortcut path uses $1 \times 1$ kernel size while all the other convolution layers use $3 \times 3$ .
+
+Training the MSM. The default network architecture of the MSM is ResNet-13 shown in Figure 2, with $M 1$ , $M 2$ , $M 3$ , and $M 4$ set to 64, 128, 256, and 512, respectively. We use the 8 source models to train the MSM for 60 epochs with the number of attack steps $T _ { t }$ of 7. $\epsilon _ { c }$ of the Customized PGD is initialized to 1,600 and is exponentially decayed by $0 . 9 \times$ for every 4,000 iterations. The learning rate $\alpha$ and the batch size are set to 0.001 and 64, respectively.
+
+Evaluating the MSM. On each target model, we only attack the correctly classified test images because attacking wrongly classified clean images is less meaningful.
+
+# 4.1.2 EXPERIMENTAL RESULTS
+
+Table 1 shows the experimental results. The recently proposed white-box attack method APGD (Croce & Hein, 2020b) is also treated as a compared method here. Apparently, MTA performs much better than all the previous methods with significantly increased transfer attack success rates. For example, compared with IR (Wang et al., 2021a), MTA improves the success rates by $5 4 . 8 \%$ , $2 6 . 3 \%$ , $4 5 . 4 \%$ , $3 2 . 5 \%$ , $3 5 . 7 \%$ , $2 3 . 3 \%$ , $3 0 . 9 \%$ , and $3 4 . 7 \%$ on the eight target models. The results of $\mathrm { M T A } _ { \gamma _ { 1 } = 0 }$ , $\mathrm { M T A } _ { \gamma _ { 2 } = 0 }$ , and $\mathbf { M T A } _ { d e n s e }$ will be discussed in ablation study (Section 4.3).
+
+Table 2: Transfer attack results on seven black-box networks when using one source model.   
+
+<table><tr><td>Source</td><td>Method</td><td>Inc-V3</td><td>Inc-V4</td><td>IncRes-V2</td><td>Res-152</td><td>Inc-V3 ens3</td><td>Inc-V3 ens4</td><td>IncRes-V2 ens</td></tr><tr><td rowspan="8">Inc-V3</td><td>DI</td><td>/</td><td>35.2%</td><td>28.2%</td><td>22.3%</td><td>5.1%</td><td>4.3%</td><td>2.5%</td></tr><tr><td>MI</td><td>/</td><td>38.1%</td><td>35.8%</td><td>29.6%</td><td>9.1%</td><td>8.8%</td><td>4.5%</td></tr><tr><td>MI-DI</td><td>/</td><td>61.7%</td><td>57.3%</td><td>48.0%</td><td>13.6%</td><td>12.0%</td><td>6.5%</td></tr><tr><td>SI-NI</td><td>/</td><td>63.8%</td><td>62.0%</td><td>51.7%</td><td>25.5%</td><td>25.2%</td><td>12.4%</td></tr><tr><td>IR</td><td>/</td><td>33.6%</td><td>28.1%</td><td>15.9%</td><td>5.1%</td><td>5.5%</td><td>3.0%</td></tr><tr><td>FIA</td><td>/</td><td>69.0%</td><td>66.8%</td><td>52.5%</td><td>29.3%</td><td>27.7%</td><td>14.9%</td></tr><tr><td>MTA</td><td>99.9%</td><td>90.9%</td><td>87.3%</td><td>74.1%</td><td>67.7%</td><td>39.3%</td><td>26.1%</td></tr><tr><td>MTA-IR</td><td>/</td><td>95.5%</td><td>93.2%</td><td>85.0%</td><td>83.5%</td><td>56.9%</td><td>40.7%</td></tr><tr><td rowspan="7">Inc-V4</td><td>DI</td><td>44.9%</td><td>/</td><td>30.5%</td><td>26.7%</td><td>5.9%</td><td>5.5%</td><td>3.3%</td></tr><tr><td>MI</td><td>52.7%</td><td>/</td><td>41.8%</td><td>37.3%</td><td>12.4%</td><td>11.0%</td><td>5.8%</td></tr><tr><td>MI-DI</td><td>69.1%</td><td>/</td><td>58.7%</td><td>49.3%</td><td>16.6%</td><td>14.1%</td><td>8.2%</td></tr><tr><td>SI-NI</td><td>74.6%</td><td>/</td><td>67.3%</td><td>61.6%</td><td>39.2%</td><td>35.9%</td><td>22.0%</td></tr><tr><td>IR</td><td>46.5%</td><td>/</td><td>33.2%</td><td>18.9%</td><td>8.1%</td><td>8.8%</td><td>4.9%</td></tr><tr><td>FIA</td><td>63.6%</td><td>/</td><td>55.2%</td><td>45.9%</td><td>28.5%</td><td>26.1%</td><td>16.8%</td></tr><tr><td>MTA</td><td>87.3%</td><td>99.9%</td><td>84.7%</td><td>73.1%</td><td>61.7%</td><td>38.2%</td><td>29.0%</td></tr><tr><td rowspan="8">IncRes-V2</td><td>MTA-IR</td><td>93.3%</td><td>/</td><td>90.5%</td><td>82.0%</td><td>77.2%</td><td>57.7%</td><td>44.9%</td></tr><tr><td>DI</td><td>46.9%</td><td>42.0%</td><td>/</td><td>29.5%</td><td>8.6%</td><td>6.5%</td><td>5.5%</td></tr><tr><td>MI</td><td>53.2%</td><td>45.2%</td><td>/</td><td>38.8%</td><td>16.2%</td><td>13.3%</td><td>9.7%</td></tr><tr><td>MI-DI</td><td>64.7%</td><td>61.7%</td><td>/</td><td>50.6%</td><td>23.7%</td><td>18.6%</td><td>13.6%</td></tr><tr><td>SI-NI</td><td>78.2%</td><td>70.7%</td><td>/</td><td>63.8%</td><td>45.2%</td><td>38.8%</td><td>32.9%</td></tr><tr><td>IR</td><td>49.7%</td><td>44.9%</td><td>/</td><td>25.2%</td><td>13.6%</td><td>11.2%</td><td>10.9%</td></tr><tr><td>FIA</td><td>63.2%</td><td>57.8%</td><td>/</td><td>51.3%</td><td>35.1%</td><td>30.3%</td><td>25.0%</td></tr><tr><td>MTA</td><td>44.7%</td><td>41.7%</td><td>98.0%</td><td>57.9%</td><td>23.5%</td><td>19.4%</td><td>17.5%</td></tr><tr><td></td><td>MTAInc</td><td>64.3%</td><td>51.7%</td><td>/</td><td>76.0%</td><td>46.2%</td><td>39.3%</td><td>27.5%</td></tr><tr><td rowspan="11">Res-152</td><td>MTA-IRInc</td><td>66.2%</td><td>52.3%</td><td>/</td><td>78.3%</td><td>49.0%</td><td>42.2%</td><td>31.7%</td></tr><tr><td>DI</td><td>51.8%</td><td>48.1%</td><td>40.6%</td><td>/</td><td>9.7%</td><td>8.3%</td><td>6.2%</td></tr><tr><td>MI</td><td>50.2%</td><td>44.9%</td><td>39.4%</td><td>/</td><td>13.9%</td><td>12.0%</td><td>7.8%</td></tr><tr><td>MI-DI</td><td>76.2%</td><td>73.3%</td><td>69.5%</td><td>/</td><td>24.6%</td><td>21.1%</td><td>12.7%</td></tr><tr><td>SI-NI</td><td>59.6%</td><td>50.1%</td><td>51.3%</td><td>/</td><td>37.9%</td><td>34.0%</td><td>20.7%</td></tr><tr><td>IR</td><td>42.3%</td><td>33.8%</td><td>34.1%</td><td>/</td><td>22.0%</td><td>20.6%</td><td>16.2%</td></tr><tr><td>FIA</td><td>73.8%</td><td>67.2%</td><td>67.9%</td><td>/</td><td>48.0%</td><td>43.7%</td><td>30.4%</td></tr><tr><td>MTA</td><td>70.7%</td><td>77.5%</td><td>62.8%</td><td>99.1%</td><td>53.0%</td><td>59.2%</td><td>56.3%</td></tr><tr><td>MTA-IR</td><td>72.8%</td><td>78.0%</td><td>64.3%</td><td>/</td><td>54.9%</td><td>63.0%</td><td>59.3%</td></tr><tr><td>SGM=16</td><td>57.2%</td><td>48.6%</td><td>45.4%</td><td>/</td><td>31.6%</td><td>27.8%</td><td>20.0%</td></tr><tr><td>IR=16</td><td>53.6%</td><td>50.6%</td><td>46.0%</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td></td><td>MTAe=16</td><td>76.0%</td><td>80.5%</td><td>67.6%</td><td>/</td><td>60.5%</td><td>68.4%</td><td>62.6%</td></tr></table>
+
+# 4.2 EXPERIMENTS ON IMAGENET
+
+# 4.2.1 EXPERIMENTAL CONFIGURATIONS
+
+We directly use the public trained ImageNet models4,5,6 including ResNet-50, -101, -152 (He et al., 2016), DenseNet-121, -161 (Huang et al., 2017), Inception-V3 (Szegedy et al., 2016), -V4 (Szegedy et al., 2017), Inception-ResNet-V2, Inception- $\mathrm { V } 3 _ { e n s 3 }$ , Inception- $. \mathrm { V } 3 _ { e n s 4 }$ , and Inception-ResNet$\mathrm { V } 2 _ { e n s }$ . The former eight models are normally trained models while the latter three are secure models trained by ensemble adversarial training (Tramer et al., 2017). We shorten these models as Res-50,\` Res-101, Res-152, DN-121, DN-161, Inc-V3, Inc-V4, IncRes-V2, Inc- $\mathrm { V } 3 _ { e n s 3 }$ , Inc- $\mathbf { V } 3 _ { e n s 4 }$ , and IncRes- $. \mathrm { V } 3 _ { e n s }$ .
+
+Training the MSM. The default network architecture of the MSM is ResNet-19 shown in Figure 2, with $M 1$ , $M 2$ , $M 3$ , and $M 4$ set to 32, 80, 200, and 500, respectively. We follow previous works (Dong et al., 2018; Wu et al., 2020a) to evaluate the transferability of AEs in two settings: using a single source model and using multiple source models. We set the input resolution of the MSM to $2 2 4 \times 2 2 4$ . Note that, when the resolution of the source model differs from that of the MSM, we resize the AE $x _ { a d v } ^ { T }$ to the resolution of the source model before feeding it into the source model. More details about training the MSM will be shown in Section A.4.
+
+Evaluating the MSM. Following the official testing data settings in the papers of DI (Xie et al., 2019) and SGM (Wu et al., 2020a), we also randomly choose 5,000 validation images from ImageNet that are correctly classified by all models for evaluation. Note that, when the resolutions of the MSM and the target model are different, we resize the AE $x _ { a d v } ^ { T }$ to the resolution of the target model. For instance, when attacking Inc-V3 whose resolution is $2 9 9 \times 2 9 9$ , we first resize $x _ { a d v } ^ { T }$ from $2 2 4 \times 2 2 4$ to $2 9 9 \times 2 9 9$ and then use the resized $x _ { a d v } ^ { T }$ to attack Inc-V3.
+
+Table 3: Transfer attack results on seven black-box models when using multiple source models.   
+
+<table><tr><td>Source</td><td>Method</td><td>Inc-V3</td><td>Inc-V4</td><td>IncRes-V2</td><td>Res-101</td><td>Inc-V3ens3</td><td>Inc-V3ens4</td><td>IncRes-V2ens</td></tr><tr><td rowspan="6">Res-50 + Res-152 + DN-161</td><td>DI MI</td><td>86.9% 82.0%</td><td>84.3%</td><td>81.8%</td><td>96.7%</td><td>59.7%</td><td>55.1%</td><td>41.9%</td></tr><tr><td></td><td></td><td>76.1%</td><td>76.0%</td><td>98.0%</td><td>63.6%</td><td>60.3%</td><td>49.6%</td></tr><tr><td>TI-DI</td><td>60.6%</td><td>59.2%</td><td>50.2%</td><td>86.8%</td><td>54.9%</td><td>56.2%</td><td>46.9%</td></tr><tr><td>SGM</td><td>81.8%</td><td>74.7%</td><td>73.9%</td><td>98.7%</td><td>54.9%</td><td>50.1%</td><td>38.7%</td></tr><tr><td>SGM-DI</td><td>86.2%</td><td>83.9%</td><td>81.6%</td><td>98.3%</td><td>69.8%</td><td>64.9%</td><td>54.4%</td></tr><tr><td>SGM-MI</td><td>86.5%</td><td>84.3%</td><td>82.7%</td><td>98.2%</td><td>71.1%</td><td>67.4%</td><td>60.8%</td></tr><tr><td>IR</td><td>75.2%</td><td>70.3%</td><td>67.9%</td><td>90.6%</td><td>51.7%</td><td>49.1%</td><td>37.5%</td></tr><tr><td>MTA</td><td>90.4%</td><td>94.3%</td><td>87.6%</td><td>97.5%</td><td>75.5%</td><td>79.7%</td><td>79.0%</td></tr><tr><td>MTA-IR</td><td>93.1%</td><td>95.8%</td><td>90.5%</td><td>98.3%</td><td>83.6%</td><td>87.2%</td><td>85.0%</td></tr><tr><td>DI</td><td>84.1%</td><td>82.3%</td><td>79.4%</td><td>93.9%</td><td>56.3%</td><td>50.1%</td><td>35.2%</td></tr><tr><td rowspan="8">Res-50 + Inc-V1 + DN-121</td><td>MI</td><td>79.9%</td><td>73.6%</td><td>72.3%</td><td>93.7%</td><td>59.3%</td><td>56.0%</td><td>42.7%</td></tr><tr><td>TI-DI</td><td>61.9%</td><td>58.5%</td><td>49.0%</td><td>79.7%</td><td>53.1%</td><td>54.1%</td><td>41.9%</td></tr><tr><td>SGM</td><td>62.7%</td><td>53.5%</td><td>50.9%</td><td>89.1%</td><td>33.8%</td><td>30.4%</td><td>19.3%</td></tr><tr><td>SGM-DI</td><td>87.2%</td><td>83.6%</td><td>79.5%</td><td>95.1%</td><td>59.6%</td><td>54.9%</td><td>37.9%</td></tr><tr><td>SGM-MI</td><td>82.8%</td><td>76.0%</td><td>74.3%</td><td>95.9%</td><td>62.2%</td><td>59.7%</td><td>45.3%</td></tr><tr><td>IR</td><td>76.5%</td><td>70.9%</td><td>64.0%</td><td>92.1%</td><td>51.3%</td><td>44.9%</td><td>31.5%</td></tr><tr><td>MTA</td><td>91.7%</td><td>86.4%</td><td>76.0%</td><td>93.6%</td><td>81.7%</td><td>79.6%</td><td>61.6%</td></tr><tr><td>MTA-IR</td><td>92.8%</td><td>87.9%</td><td>77.2%</td><td>93.8%</td><td>82.6%</td><td>79.3%</td><td>61.5%</td></tr><tr><td rowspan="8">Res-50 + Inc-V1</td><td>DI</td><td>76.1%</td><td>69.3%</td><td>66.3%</td><td>90.0%</td><td>43.5%</td><td>39.2%</td><td>25.5%</td></tr><tr><td>MI</td><td>69.5%</td><td>60.1%</td><td>59.5%</td><td>91.5%</td><td>47.1%</td><td>44.7%</td><td>32.5%</td></tr><tr><td>TI-DI</td><td>51.6%</td><td>46.9%</td><td>38.4%</td><td>73.4%</td><td>43.4%</td><td>44.2%</td><td>32.8%</td></tr><tr><td>SGM</td><td>46.1%</td><td>35.6%</td><td>33.3%</td><td>82.0%</td><td>22.1%</td><td>19.5%</td><td>12.3%</td></tr><tr><td>SGM-DI</td><td>79.2%</td><td>70.6%</td><td>68.7%</td><td>91.9%</td><td>47.9%</td><td>42.0%</td><td>28.1%</td></tr><tr><td>SGM-MI</td><td>71.9%</td><td>62.0%</td><td>61.3%</td><td>94.3%</td><td>49.6%</td><td>47.2%</td><td>33.8%</td></tr><tr><td>IR</td><td>60.2%</td><td>49.0%</td><td>46.2%</td><td>93.0%</td><td>36.5%</td><td>30.6%</td><td>21.0%</td></tr><tr><td>MTA</td><td>84.1%</td><td>88.8%</td><td>78.4%</td><td>93.9%</td><td>60.6%</td><td>61.1%</td><td>55.1%</td></tr><tr><td>MTA-IR</td><td>87.6%</td><td>91.8%</td><td>83.9%</td><td>95.2%</td><td></td><td>71.5%</td><td>72.6%</td><td>63.7%</td></tr></table>
+
+# 4.2.2 USING ONE SOURCE MODEL
+
+Table 2 reports the experimental results of using one source model. Note that, in this work, we only focus on the transfer attack testing scene and neglect the white-box attack testing scene. So we left the results of the testing scenes where the target model is the source model itself to $/$ . MI-DI is a combination of MI and DI. IR is our re-implementation with $\epsilon { = } 1 5$ and the implementation details will be shown in Section A.8. Obviously, MTA outperforms the baselines on almost all testing scenes with great margins, especially when attacking adversarially trained models. For example, compared with FIA, MTA improves the transfer attack success rates by about $3 1 . 7 \%$ , $3 0 . 7 \%$ , $4 1 . 1 \%$ , $1 3 1 . 1 \%$ , $4 1 . 9 \%$ , and $7 5 . 2 \%$ when using the Inc-V3 source model and attacking the target models (Inc-V4, IncRes-152, Res-152, Inc- $. \mathrm { V } 3 _ { e n s 3 }$ , Inc- $. \mathrm { V } 3 _ { e n s 4 }$ , IncRes- $. \mathrm { V } 2 _ { e n s }$ ). MTA-IR combines MTA with IR. Instead of attacking the MSM using PGD, MTA-IR generates AEs by attacking the MSM using IR. Compared with MTA, MTA-IR improves the attack success rates by about $5 . 1 \%$ , $6 . 8 \%$ , $1 4 . 7 \%$ , $2 3 . 3 \%$ , $4 4 . 8 \%$ , and $5 5 . 9 \%$ when using the Inc-V3 source model and attacking the target models, indicating that existing transferable attack methods can further improve MTA.
+
+Recall that SGM only works for source models with lots of skip connections (e.g., ResNet). And the original paper sets $\epsilon$ to 16, which differs from most of the other methods. The official IR also sets $\epsilon$ to 16. Therefore, we copy their results with $\epsilon = 1 6$ from their official paper to Table 2 and denote them as $\mathbf { S G M } _ { \epsilon = 1 6 } ^ { * }$ and $\mathrm { I R } _ { \epsilon = 1 6 } ^ { \ast }$ , respectively. To compare MTA with them, we further set $\epsilon$ to 16 for MTA and denote the new result as $\mathbf { M T A } _ { \epsilon = 1 6 }$ . The comparisons show that $\mathbf { M T A } _ { \epsilon = 1 6 }$ outperforms $\mathbf { S G M } _ { \epsilon = 1 6 } ^ { * }$ and $\mathrm { I R } _ { \epsilon = 1 6 } ^ { \ast }$ significantly.
+
+When using IncRes-V2 source model, MTA sometimes performs slightly worse than MI-DI, possibly because the MSM with ResNet-19 backbone is not suitable to be trained to attack IncRes-V2. We then replace the backbone from ResNet-19 with another simplified Inception network (the architecture will be shown in Section A.6) and retrain the MSM. The newly trained MSM is denoted as $\mathbf { M T A } _ { I n c }$ Compared with ResNet-19, the simplified Inception backbone is more similar to IncRes-V2 so that $\mathbf { M T A } _ { I n c }$ turns to be easier to generate adversarial attacks to fool IncRes-V2 than MTA, leading to easier convergence of $\mathbf { M T A } _ { I n c }$ . The experimental results show that $\mathbf { M T A } _ { I n c }$ outperforms not only MTA but also the compared methods in most testing scenes, indicating 1) the advantage of the proposed MTA framework and 2) MTA can be further improved by using more suitable backbones.
+
+# 4.2.3 USING MULTIPLE SOURCE MODELS
+
+The experimental results of using multiple source models are reported in Table 3. We use three source model groups $( \mathrm { R e s } { - } 5 0 { + } \mathrm { R e s } { - } 1 5 2 { + } \mathrm { D N } 1 6 1$ , Res-50+Inc-V1+DN-121, Res-50+Inc-V1) to train the MSM, respectively, and use seven target models (Inc-V3, Inc-V4, InvRes-V2, Res-101, Inc- $\mathrm { V } 3 _ { e n s 3 }$
+
+Inc- $\mathbf { V } 3 _ { e n s 4 }$ , IncRes- $\mathrm { V } 2 _ { e n s }$ ) to evaluate the transferability of the attacks to the MSM. SGM-X is the combination of SGM and X $\mathrm { X = D I }$ or MI). TI-DI is the combination of TI and DI, which is also known as TI-DIM (Dong et al., 2019). The results show that MTA outperforms the baselines in almost all testing scenes, especially when attacking defensive models. For instance, compared with SGM-DI, MTA improves the transfer attack success rates by $6 . 2 \%$ , $2 5 . 8 \%$ , $1 4 . 1 \%$ , $2 . 2 \%$ , $2 6 . 5 \%$ , $4 5 . 5 \%$ , and $9 6 . 1 \%$ on the seven target models when using Res-50 and Inc-V1 source models. Besides, MTA-IR outperforms MTA.
+
+# 4.3 ABLATION STUDY
+
+Network structure The comparison between MTA and $\mathbf { M T A } _ { I n c }$ shown in Table 2 has validated the effect of backbone on the MSM. Here we conduct another experiment on Cifar-10 to further verify the effect of backbone by replacing the backbone from ResNet-13 to DenseNet-22BC (the structure of DenseNet-22BC will be shown in Section A.6). We denote the MSM using DenseNet-22BC backbone as $\mathbf { M T A } _ { d e n s e }$ and report its experimental results in Table 1. The comparisons among MTA, $\mathbf { M T A } _ { d e n s e }$ , and the other compared methods indicate that 1) the backbone affects the performance of MTA; 2) MTA outperforms the compared methods with various backbones. This also inspires us to design more suitable backbones to improve MTA as future work.
+
+Number of attack iterations We perform several experiments on Cifar-10 to validate how the number of attack iterations $T _ { t }$ affects the performance. $T _ { t }$ is set to 7 by default on Cifar-10. Here we set $T _ { t }$ to 1, 3, 5, 9, and 11 and keep all the other settings be consistent with the default settings. Figure 3 shows the corresponding performances of MTA. It is observed that when $T _ { t } < 7$ , the performances of MTA will be improved with the increase of $T _ { t }$ while when $T _ { t } > 7$ , the performance tends to drop. We think this is due to the difficulty of unrolling too many attack steps when training the MSM. We also verify how $T _ { v }$ affects the performance by changing $T _ { v }$ . $T _ { v }$ is default set to 10 in all our experiments. Figure 3 shows the experimental results using different numbers of $T _ { v }$ . When $T _ { v } = 1$ , the performances can be denoted as MTA-FGSM (one-step PGD). With the increase of $T _ { v }$ , the transfer attack success rates are clearly increased.
+
+The effects of $\gamma _ { 1 }$ and $\gamma _ { 2 }$ We perform two experiments on Cifar-10 to verify how the parameters $\gamma _ { 1 }$ and $\gamma _ { 2 }$ in Eq 5 affect the transfer attack performance. In the two experiments, we set $\gamma _ { 1 }$ and $\gamma _ { 2 }$ to zero respectively, and amplify $\epsilon _ { c }$ appropriately to offset the decrease of the training perturbation size caused by zeroing $\gamma _ { 1 }$ or $\gamma _ { 2 }$ . We denote the two newly performed MTA as $\mathrm { M T A } _ { \gamma _ { 1 } = 0 }$ and $\mathrm { M T A } _ { \gamma _ { 2 } = 0 }$ . Table 1 shows the experimental results. The results show that by setting $\gamma _ { 1 }$
+
+![](images/d60090523363ad6df108d4eb9dbc616aae91d5e96f96a4f57e2382d28e5731e5.jpg)  
+Figure 3: Transfer attack performances of MTA on the eight target models of Cifar-10. Left: Attack success rates with different $T _ { t }$ . Right: Attack success rates with different $T _ { v }$ . yaxis denotes the attack success rate.
+
+to zero, the performances of MTA are greatly damaged on all target models, indicating the indispensability of the arctan component in the Customized PGD. Setting $\gamma _ { 2 }$ to zero also decreases MTA’s performances, but the effect is much smaller than that of $\gamma _ { 1 }$ . Overall, the two experiments demonstrate the indispensability of Customized PGD for the proposed MTA framework. Further, both the arctan and sign components in Customized PGD are important to train the MSM, especially arctan.
+
+# 5 CONCLUSION
+
+Existing query free black-box adversarial attack methods directly use image classification models as surrogate models to generate transferable adversarial attacks to attack black-box models neglecting the study of surrogate models. In this paper, we propose a novel framework called meta-transfer attack (MTA) to improve the transferability of adversarial attacks via training an MSM using these surrogate models. The MSM is a particular model trained to learn how to make the adversarial attacks to it can fool the surrogate models. To enable and improve the training of the MSM, a novel Customized PGD is also developed. Through extensive experiments, we validate that by attacking the trained MSM, we can get transferable adversarial attacks that are generalizable to attack black-box target models with much higher success rates than existing methods, demonstrating the effectiveness of the proposed MTA framework.
+
+# 6 ETHICS STATEMENT
+
+Our work is promising to evaluate and improve the security of deep models, and has no potential negative societal impacts.
+
+# 7 REPRODUCIBILITY STATEMENT
+
+We provide our code in supplemental material and describe all the experimental settings in Sections 4.1.1, 4.2.1, and Appendix. The hyperparameter settings and the network structure are clear. The training details of source and target models used on Cifar-10 are described in Section A.2, and the network architecture descriptions of these models can be found in Section 4.1.1 and our code. The source and target models used on ImageNet can be found in the repositories described in Section 4.2.1. We include a very simple code example of our method at the end of Appendix, which also helps readers to understand and to reproduce our results. Overall, our work is easy to reproduce and follow.
+
+# REFERENCES
+
+Mart´ın Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, et al. Tensorflow: A system for large-scale machine learning. In 12th {USENIX} symposium on operating systems design and implementation ({OSDI} 16), pp. 265–283, 2016.
+
+Avishek Joey Bose, Gauthier Gidel, Hugo Berrard, Andre Cianflone, Pascal Vincent, Simon LacosteJulien, and William L Hamilton. Adversarial example games. Advances in neural information processing systems, 2020.
+
+Wieland Brendel, Jonas Rauber, and Matthias Bethge. Decision-based adversarial attacks: Reliable attacks against black-box machine learning models. arXiv preprint arXiv:1712.04248, 2017.
+
+Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 ieee symposium on security and privacy (sp), pp. 39–57. IEEE, 2017.
+
+Jianbo Chen, Michael I Jordan, and Martin J Wainwright. HopSkipJumpAttack: a query-efficient decision-based adversarial attack. In 2020 IEEE Symposium on Security and Privacy (SP). IEEE, 2020.
+
+Pin-Yu Chen, Huan Zhang, Yash Sharma, Jinfeng Yi, and Cho-Jui Hsieh. Zoo: Zeroth order optimization based black-box attacks to deep neural networks without training substitute models. In Proceedings of the 10th ACM workshop on artificial intelligence and security, pp. 15–26, 2017.
+
+Minhao Cheng, Thong Le, Pin-Yu Chen, Jinfeng Yi, Huan Zhang, and Cho-Jui Hsieh. Query-efficient hard-label black-box attack: An optimization-based approach. arXiv preprint arXiv:1807.04457, 2018.
+
+Minhao Cheng, Simranjit Singh, Patrick H. Chen, Pin-Yu Chen, Sijia Liu, and Cho-Jui Hsieh. Sign-opt: A query-efficient hard-label adversarial attack. In international conference on learning representations, 2020.
+
+Shuyu Cheng, Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu. Improving black-box adversarial attacks with a transfer-based prior. pp. 10932–10942, 2019.
+
+Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive boundary attack. In International Conference on Machine Learning, pp. 2196–2205. PMLR, 2020a.
+
+Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In International Conference on Machine Learning, pp. 2206–2216. PMLR, 2020b.
+
+Ambra Demontis, Marco Melis, Maura Pintor, Matthew Jagielski, Battista Biggio, Alina Oprea, Cristina Nita-Rotaru, and Fabio Roli. Why do adversarial attacks transfer? explaining transferability of evasion and poisoning attacks. USENIX Security Symposium, pp. 321–338, 2019.
+
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pp. 248–255. Ieee, 2009.
+
+Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boosting adversarial attacks with momentum. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 9185–9193, 2018.
+
+Yinpeng Dong, Tianyu Pang, Hang Su, and Jun Zhu. Evading defenses to transferable adversarial examples by translation-invariant attacks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4312–4321, 2019.
+
+Jiawei Du, Hu Zhang, Tianyi Joey Zhou, Yi Yang, and Jiashi Feng. Query-efficient meta attack to deep neural networks. International Conference on Learning Representations, 2020.
+
+Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. In International Conference on Machine Learning, pp. 1126–1135. PMLR, 2017.
+
+Aditya Ganeshan, Vivek BS, and R Venkatesh Babu. Fda: Feature disruptive attack. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 8069–8079, 2019.
+
+Lianli Gao, Qilong Zhang, Jingkuan Song, Xianglong Liu, and Heng Tao Shen. Patch-wise attack for fooling deep neural network. In European Conference on Computer Vision, pp. 307–322. Springer, 2020.
+
+Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. international conference on learning representations, 2014.
+
+Yiwen Guo, Qizhang Li, and Hao Chen. Backpropagating linearly improves transferability of adversarial examples. In Advances in neural information processing systems 33 (NIPS 2020), 2020.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
+
+Andrew Howard, Mark Sandler, Grace Chu, Liang-Chieh Chen, Bo Chen, Mingxing Tan, Weijun Wang, Yukun Zhu, Ruoming Pang, Vijay Vasudevan, et al. Searching for mobilenetv3. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1314–1324, 2019.
+
+Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861, 2017.
+
+Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 7132–7141, 2018.
+
+Gao Huang, Zhuang Liu, Laurens Van Der Maaten, and Kilian Q Weinberger. Densely connected convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708, 2017.
+
+Qian Huang, Isay Katsman, Horace He, Zeqi Gu, Serge Belongie, and Ser-Nam Lim. Enhancing adversarial example transferability with an intermediate level attack. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 4733–4742, 2019.
+
+Zhichao Huang and Tong Zhang. Black-box adversarial attack with transferable model-based embedding. International Conference on Learning Representations, 2020.
+
+Forrest N Iandola, Song Han, Matthew W Moskewicz, Khalid Ashraf, William J Dally, and Kurt Keutzer. Squeezenet: Alexnet-level accuracy with 50x fewer parameters and¡ $0 . 5 \mathrm { m b }$ model size. arXiv preprint arXiv:1602.07360, 2016.
+
+Andrew Ilyas, Logan Engstrom, Anish Athalye, and Jessy Lin. Black-box adversarial attacks with limited queries and information. In International Conference on Machine Learning, pp. 2137–2146. PMLR, 2018.
+
+Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Logan Engstrom, Brandon Tran, and Aleksander Madry. Adversarial examples are not bugs, they are features. arXiv preprint arXiv:1905.02175, 2019.
+
+Xu Kaidi, Liu Sijia, Zhao Pu, Chen Pin-Yu, Zhang Huan, Fan Quanfu, Erdogmus Deniz, Wang Yanzhi, and Lin Xue. Structured adversarial attack: Towards general implementation and better interpretability. International Conference on Learning Representations, 2019.
+
+Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25:1097–1105, 2012.
+
+Alexey Kurakin, Ian Goodfellow, Samy Bengio, et al. Adversarial examples in the physical world, 2016.
+
+Yann LeCun, Yoshua Bengio, et al. Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 3361(10):1995, 1995.
+
+Huichen Li, Xiaojun Xu, Xiaolu Zhang, Shuang Yang, and Bo Li. Qeba: Query-efficient boundarybased blackbox attack. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1221–1230, 2020a.
+
+Qizhang Li, Yiwen Guo, and Hao Chen. Practical no-box adversarial attacks against dnns. Advances In Neural Information Processing Systems 2020, 2020b.
+
+Yingwei Li, Song Bai, Yuyin Zhou, Cihang Xie, Zhishuai Zhang, and Alan Yuille. Learning transferable adversarial examples via ghost networks. AAAI, pp. 11458–11465, 2020c.
+
+Jiadong Lin, Chuanbiao Song, Kun He, Liwei Wang, and John E Hopcroft. Nesterov accelerated gradient and scale invariance for adversarial attacks. International Conference on Learning Representations, 2020.
+
+Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. international conference on learning representations, 2017.
+
+Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. international conference on learning representations, 2018.
+
+Andriushchenko Maksym, Croce Francesco, Flammarion Nicolas, and Hein Matthias. Square attack: a query-efficient black-box adversarial attack via random search. european conference on computer vision, pp. 484–501, 2020.
+
+Seyed-Mohsen Moosavi-Dezfooli, Alhussein Fawzi, and Pascal Frossard. Deepfool: a simple and accurate method to fool deep neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2574–2582, 2016.
+
+Muhammad Muzammal Naseer, Salman H Khan, Muhammad Haris Khan, Fahad Shahbaz Khan, and Fatih Porikli. Cross-domain transferability of adversarial perturbations. Advances in Neural Information Processing Systems, 32:12905–12915, 2019.
+
+Nicolas Papernot, Patrick McDaniel, and Ian Goodfellow. Transferability in machine learning: from phenomena to black-box attacks using adversarial samples. arXiv preprint arXiv:1605.07277, 2016.
+
+Nicolas Papernot, Patrick McDaniel, Ian Goodfellow, Somesh Jha, Z Berkay Celik, and Ananthram Swami. Practical black-box attacks against machine learning. In Proceedings of the 2017 ACM on Asia conference on computer and communications security, pp. 506–519, 2017.
+
+Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017.
+
+Yunxiao Qin, Weiguo Zhang, Zezheng Wang, Chenxu Zhao, and Jingping Shi. Layer-wise adaptive updating for few-shot image classification. IEEE Signal Processing Letters, 27:2044–2048, 2020.
+
+Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: towards real-time object detection with region proposal networks. IEEE transactions on pattern analysis and machine intelligence, 39(6):1137–1149, 2016.
+
+Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh Chen. Mobilenetv2: Inverted residuals and linear bottlenecks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4510–4520, 2018.
+
+Gaurang Sriramanan, Sravanti Addepalli, Arya Baburaj, and Venkatesh R. Babu. Guided adversarial attack for evaluating and enhancing adversarial defenses. Advances In Neural Information Processing Systems, 2020.
+
+Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, J. Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. international conference on learning representations, 2014.
+
+Christian Szegedy, Vincent Vanhoucke, Sergey Ioffe, Jon Shlens, and Zbigniew Wojna. Rethinking the inception architecture for computer vision. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2818–2826, 2016.
+
+Christian Szegedy, Sergey Ioffe, Vincent Vanhoucke, and Alexander Alemi. Inception-v4, inceptionresnet and the impact of residual connections on learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 31, 2017.
+
+Florian Tramer, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick Mc- \` Daniel. Ensemble adversarial training: Attacks and defenses. arXiv preprint arXiv:1705.07204, 2017.
+
+Lu Wang, Huan Zhang, Jinfeng Yi, Cho-Jui Hsieh, and Yuan Jiang. Spanning attack: reinforce black-box attacks with unlabeled data. Machine Learning, 109(12):2349–2368, 2020.
+
+Xiaosen Wang and Kun He. Enhancing the transferability of adversarial attacks through variance tuning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1924–1933, 2021.
+
+Xin Wang, Jie Ren, Shuyun Lin, Xiangming Zhu, Yisen Wang, and Quanshi Zhang. A unified approach to interpreting and boosting adversarial transferability. International Conference on Learning Representations, 2021a.
+
+Zhibo Wang, Hengchang Guo, Zhifei Zhang, Wenxin Liu, Zhan Qin, and Kui Ren. Feature importanceaware transferable adversarial attacks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021b.
+
+Dongxian Wu, Yisen Wang, Shu-Tao Xia, James Bailey, and Xingjun Ma. Skip connections matter: On the transferability of adversarial examples generated with resnets. international conference on learning representations, 2020a.
+
+Kaiwen Wu, Allen Wang, and Yaoliang Yu. Stronger and faster wasserstein adversarial attacks. International Conference on Machine Learning, pp. 10377–10387, 2020b.
+
+Lei Wu, Zhanxing Zhu, Cheng Tai, et al. Understanding and enhancing the transferability of adversarial examples. arXiv preprint arXiv:1802.09707, 2018.
+
+Weibin Wu, Yuxin Su, Xixian Chen, Shenglin Zhao, Irwin King, R. Michael Lyu, and Yu-Wing Tai. Boosting the transferability of adversarial samples via attention. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1158–1167, 2020c.
+
+Cihang Xie, Zhishuai Zhang, Yuyin Zhou, Song Bai, Jianyu Wang, Zhou Ren, and Alan L Yuille. Improving transferability of adversarial examples with input diversity. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 2730–2739, 2019.
+
+Zheng Yuan, Jie Zhang, Yunpei Jia, Chuanqi Tan, Tao Xue, and Shiguang Shan. Meta gradient adversarial attack. In Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021.
+
+Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, and Jian Sun. Shufflenet: An extremely efficient convolutional neural network for mobile devices. computer vision and pattern recognition, 2018.
+
+Wen Zhou, Xin Hou, Yongjun Chen, Mengyun Tang, Xiangqi Huang, Xiang Gan, and Yong Yang. Transferable adversarial perturbations. In Proceedings of the European Conference on Computer Vision (ECCV), pp. 452–467, 2018.
+
+# A APPENDIX
+
+# A.1 TESTING PSEUDO CODE OF MTA
+
+We summarize the testing pseudo code of MTA in Algorithm.2, where $\hat { \mathcal { F } }$ is the target model and $\tilde { y }$ is the target model’s prediction for the adversarial example $x _ { a d v } ^ { T }$ . Note that all the clean examples in $\hat { \mathbb { D } }$ are correctly classified by the target model. Len $( \hat { \mathbb { D } } )$ denotes the number of examples in $\hat { \mathbb { D } }$ .
+
+# A.2 TRAINING THE SOURCE AND TARGET MODELS ON CIFAR-10
+
+On Cifar-10, we use 16 source and target models to train and test the metasurrogate model (MSM). The 8 source models are ResNet-10, -18, -34, SeResNet-14, -26, -50, MobileNetV1, and -V2. The 8 target models are MobileNet-V3, ShuffleNet-V1, -V2, SqueezeNet-A, -B, and adversarially trained ResNet-18, -34 and SeResNet50. It is not easy to collect the 16 trained Cifar-10 models on the internet. Therefore, before the experiments of MTA, we first use consistent hyperparameters to train the 16 models on Cifar-10 for 200 epochs. The learning rate, L2 weight decay, and batch size are set to 0.01, 1e-5, and 128, respectively. For each adversarially trained model, we first use FGSM and the normally trained model to generate one
+
+# Algorithm 2 Testing of Meta-Transfer Attack
+
+input: Black-box target model $\hat { \mathcal { F } }$ , Testing examples $\hat { \mathbb { D } }$ that are correctly classified by the target model, Optimized metasurrogate model $\mathcal { M } _ { \theta }$ .   
+output: Transfer attack success rate.   
+$\mathbf { 1 } : P = 0$   
+2 : for $( x , y ) \in { \hat { \mathbb { D } } }$ do   
+3 : $x _ { a d v } ^ { 0 } = x$   
+4 : for $\mathrm { k }$ in [1, 2, ..., T] do   
+5 : $g ^ { k } = \bar { \nabla } _ { x _ { a d v } ^ { k - 1 } } L ( \bar { \mathcal { M } } _ { \theta } ( x _ { a d v } ^ { k - 1 } ) , y )$   
+xadv   
+6 : $\scriptstyle x _ { a d v } ^ { k } = \mathrm { C l i p } \left( x _ { a d v } ^ { k - 1 } + { \frac { \epsilon } { T } } \cdot \mathrm { s i g n } ( g ^ { k } ) \right)$   
+7 :8 : end forevaluate $x _ { a d v } ^ { T }$ on $\hat { \mathcal { F } }$ and obtain $\tilde { y } = \hat { \mathcal { F } } ( x _ { a d v } ^ { T } )$   
+9 : if $y \ne \tilde { y }$ do   
+10: P+ = 1   
+11: end if   
+12: return Len(Dˆ) P
+
+adversarial example for each training image with $\epsilon = 3$ , and then train the model on both clean and adversarial images. The 8 source models obtain $9 0 . 0 \%$ , $9 1 . 8 \%$ , $9 2 . 6 \%$ , $8 5 . 6 \%$ , $8 8 . 3 \%$ , $9 0 . 5 \%$ , $8 2 . 0 \%$ , and $8 1 . 8 \%$ accuracies on the test set, and the 8 target models obtain $8 0 . 0 \%$ , $8 2 . 5 \%$ , $7 6 . 4 \%$ , $8 6 . 4 \%$ , $8 6 . 9 \%$ , $8 8 . 9 \%$ , $9 0 . 5 \%$ , and $8 7 . 5 \%$ accuracies.
+
+# A.3 MORE EXPERIMENTS ON CIFAR-10
+
+Here we show more experiments on Cifar-10.
+
+# A.3.1 TARGETED TRANSFER ATTACK
+
+We conduct targeted transfer attack and show the experimental results in Table 4. MTA has a great advantage over the compared methods in the targeted transfer attack setting.
+
+# A.3.2 TRANSFER ATTACK WITH SMALLER $\epsilon$
+
+We set $\epsilon$ to 8 to evaluate how does MTA perform with smaller $\epsilon$ . The results shown in Table 5 indicate that MTA outperforms the compared methods no matter the value of $\epsilon$ .
+
+# A.3.3 COMPARISON BETWEEN MTA AND METAATTACK
+
+MetaAttack[14] is developed for query-based black-box adversarial attack but not for transfer attack. We implement MetaAttack in the transfer attack scene on Cifar-10 and compare it with MTA in Table 6. The comparison indicates that MTA greatly outperforms MetaAttack in transfer attack.
+
+# A.3.4 MORE EXPERIMENTS ABOUT THE CUSTOMIZED PGD
+
+As introduced in Section 3, the sign function in the vanilla PGD with $\mathrm { L } _ { \infty }$ constraint introduces a discrete operation. This results in that the gradient back-propagating through sign be zero and further prohibits the training of the MSM. We propose the Customized PGD to enable the training of the MSM. Here we conduct other four experiments to validate the indispensability and the effect of the Customized PGD on the proposed MTA framework.
+
+Table 4: Targeted transfer attack results on Cifar-10.   
+
+<table><tr><td>Method</td><td>MN-V3</td><td>SN-V1</td><td>SN-V2</td><td>SN-A</td><td>SN-B</td></tr><tr><td>DI</td><td>16.3%</td><td>26.4%</td><td>17.2%</td><td>22.3%</td><td>21.6%</td></tr><tr><td>MI</td><td>29.6%</td><td>43.6%</td><td>29.8%</td><td>37.1%</td><td>35.4%</td></tr><tr><td>TI</td><td>17.6%</td><td>21.1%</td><td>16.5%</td><td>26.1%</td><td>25.8%</td></tr><tr><td>IR</td><td>10.8%</td><td>19.6%</td><td>9.5%</td><td>13.7%</td><td>12.5%</td></tr><tr><td>AEG</td><td>47.2%</td><td>53.8%</td><td>36.5%</td><td>42.6%</td><td>41.0%</td></tr><tr><td>MTA</td><td>49.0%</td><td>70.3%</td><td>47.7%</td><td>60.3%</td><td>58.5%</td></tr></table>
+
+Table 5: Transfer attack results with $\epsilon = 8 / 2 5 5$ on Cifar-10.   
+
+<table><tr><td>Method</td><td>MN-V3</td><td>SN-V1</td><td>SN-V2</td><td>SN-A</td><td>SN-B</td></tr><tr><td>DI</td><td>31.5%</td><td>42.1%</td><td>30.0%</td><td>38.2%</td><td>36.9%</td></tr><tr><td>MI</td><td>44.2%</td><td>59.8%</td><td>43.2%</td><td>55.7%</td><td>54.9%</td></tr><tr><td>TI</td><td>29.5%</td><td>31.3%</td><td>29.6%</td><td>37.7%</td><td>36.8%</td></tr><tr><td>IR</td><td>29.2%</td><td>51.1%</td><td>35.3%</td><td>38.5%</td><td>37.4%</td></tr><tr><td>AEG</td><td>58.0%</td><td>66.5%</td><td>50.4%</td><td>61.9%</td><td>59.6%</td></tr><tr><td>MTA</td><td>62.5%</td><td>79.6%</td><td>58.2%</td><td>70.5%</td><td>69.3%</td></tr></table>
+
+As PGD with L2 constraint contains no sign, in the first experiment, we use PGD with L2 constraint $( P G D _ { L 2 } )$ instead of the Customized PGD to attack the MSM in the training phase and denote the trained MSM as MTAP GDL2.
+
+PGD with L1 constraint also contains no sign. In the second experiment, we use PGD with L1 constraint $( P G D _ { L 1 } )$ to attack the MSM in the training phase and denote the trained MSM as MTAP GDL1.
+
+Both $\gamma _ { 1 }$ and $\gamma _ { 2 }$ of the Customized PGD are set to 0.01 by default. In the third experiment, we set $\gamma _ { 1 }$ to 0.05. Note that we decrease $\epsilon _ { c }$ appropriately to offset the increase of the training perturbation size caused by setting $\gamma _ { 1 }$ to 0.05. All the other experimental settings are consistent with the default settings. We denote the MSM trained in this experiment as $\mathrm { M T A } _ { \gamma _ { 1 } = 0 . 0 5 }$ .
+
+In the fourth experiment, we set $\gamma _ { 2 }$ to 0.05 and denote the trained MSM as $\mathrm { M T A } _ { \gamma _ { 2 } = 0 . 0 5 }$
+
+Table 6 reports all the four experimental results. We can get three conclusions. First, directly using $P G D _ { L 1 }$ or $P G D _ { L 2 }$ in MTA’s training stage is also effective to train the MSM but leads to limited performance. Second, the proposed Customized PGD is important for the proposed MTA framework to achieve superior performance. Third, larger $\gamma _ { 1 }$ or $\gamma _ { 2 }$ damages the performances of MTA.
+
+# A.3.5 MORE EXPERIMENTS ABOUT SOURCE AND TARGET MODELS
+
+Here we change the setting of source and target models, and evaluate MTA under this new setting. In this setting, the source models are MobileNet-V2, ShuffleNet-V1, ShuffleNet-V2, SqueezeNet-A, and SqueezeNet-B, and the target models are ResNet-10, ResNet-18, ResNet-34, SeResNet-14, SeResNet-26, SeResNet-50, MobileNet-V1, and MobileNet-V2. All the other experimental settings are consistent with those introduced before. The experimental results are summarized in Table 7, where MTA still shows its advantage in the transfer attack problem.
+
+A.3.6 THE EXPERIMENT WHERE SOURCE MODELS DO NOT SHARE TRAINING SAMPLES WITHTARGET MODELS.
+
+In our previous experiment, the source and target models are all trained on the same training set. Here we conduct a new experiment, where we train the source and target models on different training samples, and use the new trained models to perform transfer attack. This experiment is performed on Cifar-10, which contains 10 categories and each category in the training set contains 5000 images.
+
+Table 6: More transfer attack experimental results on Cifar-10.   
+
+<table><tr><td>Method</td><td>MN-V3</td><td>SN-V1</td><td>SN-V2</td><td>SN-A</td><td>SN-B</td></tr><tr><td>MetaAttack</td><td>39.2%</td><td>43.9%</td><td>32.1%</td><td>38.6%</td><td>37.8%</td></tr><tr><td>MTAPGD L2</td><td>80.8%</td><td>92.7%</td><td>83.5%</td><td>89.0%</td><td>86.8%</td></tr><tr><td>MTAPGD L1</td><td>81.5%</td><td>91.3%</td><td>82.4%</td><td>85.3%</td><td>83.7%</td></tr><tr><td>MTAγ1=0.05</td><td>90.5%</td><td>98.0%</td><td>90.2%</td><td>94.5%</td><td>93.1%</td></tr><tr><td>MTAγ2=0.05</td><td>86.7%</td><td>95.3%</td><td>85.8%</td><td>89.5%</td><td>88.4%</td></tr><tr><td>MTA</td><td>91.8%</td><td>98.4%</td><td>90.9%</td><td>94.9%</td><td>93.8%</td></tr></table>
+
+Table 7: The MSM is trained with source models MobileNet-V3, ShuffleNet-V1, ShuffleNet-V2, SqueezeNet-A, and SqueezeNet-B. From left to right, the target models are ResNet-10 (Res-10), ResNet-18 (Res-18), ResNet-34 (Res-34), SeResNet-14 (SE-14), SeResNet-26 (SE-26), SeResNet-50 (Res-18), MobileNet-V1 (MB-V1), and MobileNet-V2 (MB-V2).   
+
+<table><tr><td>Method</td><td>Res-10</td><td>Res-18</td><td>Res-34</td><td>SE-14</td><td>SE-26</td><td>SE-50</td><td>MB-V1</td><td>MB-V2</td></tr><tr><td>PGD</td><td>46.9%</td><td>42.5%</td><td>50.1%</td><td>49.6%</td><td>50.2%</td><td>45.9%</td><td>47.9%</td><td>54.5%</td></tr><tr><td>DI</td><td>65.2%</td><td>56.9%</td><td>69.6%</td><td>70.2%</td><td>71.5%</td><td>65.7%</td><td>69.5%</td><td>71.2%</td></tr><tr><td>MI</td><td>89.5%</td><td>86.1%</td><td>90.7%</td><td>88.3%</td><td>91.0%</td><td>89.1%</td><td>86.6%</td><td>88.8%</td></tr><tr><td>TI</td><td>48.1%</td><td>39.2%</td><td>49.9%</td><td>53.8%</td><td>55.6%</td><td>47.8%</td><td>63.9%</td><td>60.8%</td></tr><tr><td>MTA</td><td>96.7%</td><td>94.6%</td><td>98.3%</td><td>98.7%</td><td>98.8%</td><td>97.5%</td><td>96.7%</td><td>98.7%</td></tr></table>
+
+In this experiment, we split the training set into two sub-training sets and each of the sub-training set contains all the 10 categories. Every category in the first sub-training set contains 2500 images and every category in the second sub-training set contains the remaining 2500 images. Therefore, there is no overlapping samples between the two sub-training sets, and the two sub-training sets share only the label set. We use the first sub-training set to train the source models and the meta-surrogate model, and use the second sub-training set to train the target models. Thus the source models and the meta-surrogate model does not use the training images of the target models. The source models are ResNet-10, ResNet-18, ResNet-34, SeResNet-14, SeResNet-26, SeResNet-50, MobileNet-V1, MobileNet-V2 with testing accuracies of $8 6 . 8 \%$ , $8 6 . 7 \%$ , $8 7 . 2 \%$ , $8 4 . 2 \%$ , $8 5 . 4 \%$ , $8 7 . 7 \%$ , $8 0 . 7 \%$ , and $8 0 . 9 \%$ , respectively. The target models are MobileNet-V3, ShuffleNet-V1, ShuffleNet-V2, SqueezeNet-A, and SqueezeNet-B with testing accuracies of $7 3 . 9 \%$ , $8 1 . 1 \%$ , $7 2 . 6 \%$ , $8 2 . 3 \%$ , and $8 3 . 0 \%$ , respectively. Then we use the source models and the trained meta-surrogate model to attack the target models. The experimental results are reported in Table 8. It is clear that when we know the label set but do not know the training images of the target models, MTA still outperforms the baselines with clear margins.
+
+# A.4 THE SUPPLEMENTAL EXPERIMENTAL SETTINGS OF MTA ON IMAGENET.
+
+In our experiment on ImageNet, we found that the MSM directly trained on the resolution of $2 2 4 \times 2 2 4$ often suffers from slow and unstable convergence due to the high dimensionality. Therefore, we develop a three-stage training strategy for gradually and stably training the MSM. The first training stage only trains the top 4 blocks and the classifier of the MSM. The input data $x _ { a d v } ^ { k - 1 }$ is down-sampled by $4 \times$ and is fed into the 3rd block skipping the 1st and 2nd blocks. The perturbation $g _ { e n s } ^ { k - 1 }$ is first up-sampled by $4 \times$ and is then added to $x _ { a d v } ^ { k - 1 }$ to obtain $x _ { a d v } ^ { k }$ . The second stage trains the top 5 blocks and the classifier. The input $x _ { a d v } ^ { k - 1 }$ is down-sampled by $2 \times$ and is fed into the 2nd block skipping the 1st block. The third stage trains all layers. Note that, except for the newly added block in the second or third stage and the layers directly connected with the newly added block, all the other layers inherit the weights trained in the previous stage. Due to memory limitation, we set $T _ { t }$ to a small number of 2.
+
+The first, second, and third training stages take 100,000, 50,000, and 50,000 iterations, with the batch size of 50, 36, and 24, respectively. Both the second and the third stages train the newly added blocks and the layers directly connected with them in the first 20,000 iterations and fine-tune all the blocks in the later 30,000 iterations. The learning rate $\alpha$ and the number of iterations $T _ { t }$ are set to 0.001 and 2, respectively. In the first, second, and third training stages, $\epsilon _ { c }$ is initialized to 3, 000, 1, 200, and 1, 200 respectively, and is exponentially decayed by $0 . 9 \times$ for every $4 , 0 0 0 , 3 , 0 0 0$ , and 3, 000 iterations, respectively.
+
+![](images/45fa236b3deaa279be1b0a8deb3250cfb09b9280a17edefa31677aef610e74db.jpg)  
+Figure 4: (a) DenseNet-22-BC. Orange cube is convolution layer with $3 \times 3$ kernel size. Pink cube is convolution layer with $1 \times 1$ kernel size. ‘Bottle Neck $( M _ { 2 }$ ) $\ast 3 ^ { \ast }$ denotes three cascaded ‘Bottle Neck $( M _ { 2 } ) '$ . The number (e.g., $M _ { 1 }$ , $4 * M , M )$ on each convolution layer denotes its number of filters. ‘Pool’ in the Transition block is Max Pooling with both stride and kernel size of $2 \times 2$ , and the last ‘Pool’ before the classifier is Global Average Pooling. (b) The detailed structure of Bottle Neck. (c) The detailed structure of Transition.
+
+We refer to the data pre-processing methods in the repository7 on GitHub to pre-process the data used in our experiments on ImageNet. When the resolution of the source model is $2 2 4 \times 2 2 4$ , we refer to ‘vgg preprocessing.py’ while when the resolution is $2 9 9 \times 2 9 9$ , we refer to ‘inception preprocessing.py’.
+
+# A.5 ATTACKING TRANSFORMER
+
+We also conduct an experiment on ImageNet to evaluate how the proposed MTA performs in attacking Vision Transformer (ViT). In this experiment, the source model is Inception-V3, and the target model is Vit base patch $1 6 . 2 2 4 ^ { 8 }$ . Experimental results are reported in Table 9. It is clear that MTA performs the best in attacking ViT.
+
+# A.6 THE NETWORK ARCHITECTURE
+
+Table 8: The transfer attack results on Cifar-10 when the source models do not share training images with target models. The source models are ResNet-10 (Res-10), ResNet-18 (Res-18), ResNet-34 (Res34), SeResNet-14 (SE-14), SeResNet-26 (SE-26), SeResNet-50 (Res-18), MobileNet-V1 (MB-V1), and MobileNet-V2 (MB-V2). The target models are MobileNet-V2, ShuffleNet-V1, ShuffleNet-V2, SqueezeNet-A, and SqueezeNet-B.   
+Table 9: Transfer attack performances of MTA on ViT.   
+
+<table><tr><td>Method</td><td>PGD</td><td>TI</td><td>DI</td><td>MI</td><td>MTA</td></tr><tr><td>Success Rate</td><td>5.5%</td><td>8.6%</td><td>7.0%</td><td>15.6%</td><td>21.3%</td></tr></table>
+
+DenseNet-22BC is shown in Figure 4. $M _ { 1 }$ , $M _ { 2 }$ , $M _ { 3 }$ , and $M _ { 4 }$ are set to 80, 40, 100, and 110, respectively. We denote MTA with DenseNet-22BC backbone as $\mathbf { M T A } _ { d e n s e }$ and show its performances in Table 1 of the main-body.
+
+The simplified Inception network is a much shallower and thinner version of the official InceptionResNet-V2. Figure 5 shows the structure of the simplified Inception. The official Inception-ResNet
+
+Figure 5: The simplified Inception network. All the blocks have the same inner structures with those of Inception-ResNet-V2.
+
+![](images/e8875fc6574a2f9d76ed945c62390b81f2c98b71f19f43c9f5db3be3cb04af3e.jpg)  
+Figure 6: Transfer attack success rates of MTA on the eight black-box Cifar-10 models, across the training process.
+
+V2 repeats each Indeption-resnet1-A, -B, or -C block for several times while the simplified Inception does not repeat them. We denote MTA with this backbone as $\mathbf { M T A } _ { I n c }$ and show its performances in Table 2 of the main-body.
+
+# A.7 DEFINITION OF ATTACK SUCCESS RATE.
+
+The formulation of attack success rate is $\begin{array} { r } { R a t e \mathrm { ~ = ~ } \frac { C a r d ( \{ x \| x \in D _ { t } , M ( x ) = y \neq M ( x _ { a d v } ) \} ) } { C a r d ( \{ x \| x \in D _ { t } , M ( x ) = y \} ) } } \end{array}$ , where $D _ { t }$ is the test set, $x$ is a test image and $x _ { a d v }$ is the adversarial image generated for $x$ , $y$ is the groundtruth label for $x$ , $M$ is the target model and $M ( x )$ is the prediction of the target model for $x$ . $\{ x \| x \in D _ { t } , M ( x ) = y \}$ is the set containing all clean images that are correctly classified by model $M$ . $\{ x \| x \in D _ { t } , M ( x ) = y \neq M ( x _ { a d v } ) \}$ is the set containing all clean images that not only are correctly classified by model $M$ but also the corresponding adversarial images are misclassified by model $M$ . $C a r d ( \{ x \| x \in D _ { t } , M ( x ) = y \}$ ) denotes the number of elements in the set $\{ x \| x \in D _ { t } , M ( x ) = y \}$ .
+
+# A.8 IMPLEMENTATIONS OF THE COMPARED METHODS.
+
+For fair comparisons between MTA and the compared methods, we tune the compared methods for their best possible performances in our re-implementation. $\epsilon$ is set to 15 by default for all methods and $T _ { v }$ is set to 10 for all PGD-based methods.
+
+MI utilizes gradient momentum to make the generated adversarial examples more transferable. The most important hyper-parameter of MI is $\mu$ . In our implementation, we found that setting $\mu$ to 1 can achieve the best transfer attack performance.
+
+DI. We follow the available public code9 of DI to implement it in Tables 1, 2, and 3. As to the experiments on ImageNet, we set ’FLAGS.image width’ and ’FLAGS.image resize’ (two parameters of the input diversity function in the official code9) to 224 and 256 respectively. On Cifar-10, we set ’FLAGS.image width’ and ’FLAGS.image resize’ to 32 and 36, respectively. For all experiments, we set $p$ to 0.8.
+
+TI. We directly utilize the public code10 to implement TI and TI-DI in Tables 1, and 3, respectively.
+
+SGM uses a parameter $\gamma$ to reduce the gradient from all residual modules of ResNet or DenseNet. We utilize grid search to tune $\gamma$ for each ResNet and DenseNet source model shown in Table 3. We denote $\gamma$ for the source model of Res-50, Res-152, DN-161, and DN-121 as $\gamma _ { r e s 5 0 }$ , γres152, γdn161, and $\gamma _ { d n 1 2 1 }$ , respectively. The tuned best $\gamma _ { r e s 5 0 }$ , $\gamma _ { r e s 1 5 2 }$ , and $\gamma _ { d e n s e }$ for the source model group $\mathrm { R e s } { - } 5 0 { + } \mathrm { R e s } { - } 1 5 2 { + } \mathrm { D N } { - } 1 6 1$ are 0.20, 0.45, and 0.70, respectively. The tuned best $\gamma _ { r e s 5 0 }$ and $\gamma _ { d n 1 2 1 }$ for the source model group Res-50+Inc-V1+DN-121 are 0.60 and 0.85, respectively. The tuned best $\gamma _ { r e s 5 0 }$ for the source model group Res-50+Inc-V1 is 0.65.
+
+A-PGD. We directly utilize the public public code11 of A-PGD to implement it in Table 1.
+
+AEG. By referring to the AEG’s paper and code12, we re-implement AEG on Cifar-10 and train the generator and the critic for 500 epochs with the learning rate of 0.001. The architecture of the generator is the encoder-decoder defined in Tab.7 of AEG’s paper. We do not implement AEG on ImageNet because training the generator and critic is expensive on ImageNet.
+
+IR. We directly utilize the public code13 of IR to implement it on ImageNet. When implementing IR on Cifar-10, we set the hyper-parameter ‘args.grid scale’ to 1.
+
+# A.9 TRAINING CURVES
+
+In the training process of the MSM, we evaluate MTA’s transfer attack performances on the target models for every 250 iterations. Figure 6 visualizes the performance curves on eight Cifar-10 target models. It is observed that with the training going on, the transfer attack success rates on the target models rise gradually. The periodic fluctuations of the performances are caused by the periodic decay of the hyper-parameter $\epsilon _ { c }$ described in Section 4.1.1.
+
+# A.10 COMPUTATIONAL COST
+
+We conduct all experiments on Tesla P40 GPU. The computational cost can be summarized into training cost and inference cost happened in the training and the inference phases, respectively. The training cost of the proposed MTA depends mainly on the backbone of MSM, the used source models, the dataset, the batch size, $T _ { t }$ , and etc.. On Cifar-10, the default backbone of the MSM is ResNet-13, the batch size is 64, $T _ { t } = 7$ , and we use 8 source models to train the MSM. The training costs one P40 GPU and approximately $2 . 5 \mathrm { T }$ FLOPs per iteration. On ImageNet, the default backbone of the MSM is ResNet-19, $T _ { t } = 2$ , the batch size is 24 in the third training stage. When using the Inc-V3 source model to train the MSM, the third training stage costs one P40 and approximately 3.2T FLOPs per iteration. When using the Res-152, Res-50, and DN-161 source models to train the MSM, the third training stage costs three P40 GPUs and approximately 6.5T FLOPs per iteration.
+
+In the inference phase (generating adversarial examples and attack the target models), the cost of MTA depends mainly on the backbone of MSM and $T _ { v }$ . The inference cost of baselines depend on the source models and $T _ { v }$ . On ImageNet, when using the Res-152, Res-50, and DN-161 source models, the PGD-based baselines (DI, MI, TI, SGM) cost about 124.1 GFLOPs per gradient ascent step per image, and cost about 109.1M parameters. As a comparison, the inference cost of MTA is only 11.3 GFLOPs per gradient ascent step per image and the parameter the MTA needed is only 6.77M. Obviously, both the inference cost and the parameter the MTA used is much smaller than those of the PGD-based baselines, and this is another advantage of the proposed MTA over the PGD-based baselines.
+
+# A.11 VISUALIZATION OF ADVERSARIAL EXAMPLES
+
+Figure 7 visualizes the adversarial examples and the noises generated for the corresponding clean images via MI, DI, TI, SGM, IR, and MTA. All the clean images are sampled from the testing set of ImageNet.
+
+# A.12 THE TENSORFLOW CODE
+
+We show the simplified core code of MTA on the last two pages for a better understanding of our work. Note that the showed code is used for the experiments on Cifar-10 but not on ImageNet. The code used on ImageNet differs slightly from the showed code.
+
+![](images/3f1413f838ac21701f0b98dec38f25fe345a7b3f385c8f69f013066ec3f94363.jpg)  
+Figure 7: The adversarial examples and the noises generated via MI, DI, TI, SGM, IR, and MTA. The corresponding clean images are shown in the left most column. The source model is Res-152.
+
+1 import tensorflow as tf   
+2   
+3 class Meta_Transfer_Attack:   
+4 def _init__(self):   
+5 # Define some hyperparameters   
+6 self.lr $=$ tf.placeholder_with_default(0.001, ())   
+7 self.epsilon_c $=$ tf.placeholder_with_default(1, ())   
+8 # Define the meta-surrogate model   
+9 self.MSM $=$ ResNet13()   
+10 # Define the source models   
+11 self.source_models $=$ [ResNet(10), ..., MobileNet_V2()]   
+12 # Define the input data and the label   
+13 self.image $=$ tf.placeholder(tf.float32, shape $=$ [None, 32, 32, 3])   
+14 self.label $=$ tf.placeholder(tf.float32, shape $=$ [None, 10])   
+15   
+16 def build_training_graph(self, T):   
+17 # The initial adversarial examples are the clean images   
+18 attack $=$ self.image   
+19 with tf.variable_scope('surrogate', reuse $=$ tf.AUTO_REUSE):   
+20 for k in range(T):   
+21 # Predict the adversarial examples   
+22 surrogate_logits $=$ self.MSM.predict(attack)   
+23   
+24 # meta-surrogate models' loss on the adversarial examples.   
+25 surrogate_loss $=$ Cross_entropy(logits $=$ surrogate_logits,   
+26 labels $=$ self.label)   
+27   
+28 # calculate Gˆk   
+29 grad $=$ tf.gradients(surrogate_loss, attack)[0]   
+30   
+31 # calculate Gˆk_1   
+32 grad_1 $=$ grad / tf.reduce_sum(tf.abs(grad), axis $=$ [1,2,3],   
+33 keep_dims $=$ True)   
+34   
+35 # calculate Gˆk_t   
+36 mean_abs_grad $=$ tf.reduce_mean(tf.abs(grad), axis $=$ [1,2,3],   
+37 keep_dims $=$ True)   
+38 norm_one_grad $=$ grad / mean_abs_grad   
+39 grad_atan $=$ tf.atan(norm_one_grad) $\star$ (2 / 3.1415926)   
+40   
+41 # calculate Gˆk_s   
+42 grad_sign $=$ tf.sign(grad)   
+43   
+44 # calculate Gˆk_ens   
+45 grad_ens $=$ grad_1 $^ +$ 0.01 $\star$ grad_sign $^ +$ 0.01 $\star$ grad_atan   
+46   
+47 # Obtain the adversarial examples Xˆk_adv   
+48 attack_temp $=$ attack $^ +$ (self.epsilon_c / T) $\star$ grad_ens   
+49 attack $=$ tf.clip_by_value(attack, 0.0, 1.0)   
+50   
+51 # Evaluate the adversarial examples $X ^ { \wedge }$ T_adv on the source models   
+52 with tf.variable_scope('Source', reuse $: =$ tf.AUTO_REUSE):   
+53 for model in self.source_models:   
+54 logits $=$ model.predict(attack)   
+55 loss $=$ Cross_entropy(logits $=$ logits, labels $=$ self.label)   
+56 self.source_loss $+ =$ tf.reduce_mean(loss)/len(self.source_models)   
+57   
+58   
+59 def build_optimizing_graph(self):   
+60 opt $=$ tf.train.AdamOptimizer(self.lr)   
+61 $\#$ Optimize the MSM via maximizing the source models' loss.   
+62 gvs $=$ opt.compute_gradients(-self.source_loss, self.MSM.weight)   
+63 gvs $=$ [(tf.clip_by_value(grad, -15, 15), var) for grad, var in gvs]   
+64 self.train_op $=$ optimizer.apply_gradients(gvs)   
+65   
+66 def main():   
+67 # Initialize the settings.   
+68 Batch_size $=$ 64   
+69 Init_eps_c $=$ 1600 / 255   
+70   
+71 # Define the graph   
+72 MTA $=$ Meta_Transfer_Attack()   
+73 MTA.build_training_graph(7)   
+74 MTA.build_optimizing_graph()   
+75   
+76 # Define the data loader   
+77 Cifar10_dataloader $=$ DataSet('Cifar10')   
+78   
+79 sess $=$ tf.InteractiveSession()   
+80 tf.global_variables_initializer().run()   
+81   
+82 # Restore the weights of all source models   
+83 restore_source_weights(MTA.source_models, sess)   
+84   
+85 for iter in range(47000):   
+86 # Exponentially decay eps_c by 0. $9 \times$ for every 4000 iterations.   
+87 eps_c $=$ Init_eps_c $\star$ ( 0.9 \*\* int(iter / 4000) )   
+88   
+89 images, labels $=$ Cifar10_dataloader.get_data(Batch_size)   
+90   
+91 feed_dict $\begin{array} { r l } { = } &  { } \left\{ \begin{array} { l } { \right\} } \end{array} \end{array}$   
+92 feed_dict[MTA.image] $=$ images   
+93 feed_dict[MTA.label] $=$ labels   
+94 feed_dict[MTA.lr] $=$ 0.001   
+95 feed_dict[MTA.epsilon_c] $=$ eps_c   
+96   
+97 # Train the MSM   
+98 sess.run(MTA.train_op, feed_dict)

parse/dev/IfFZr1gl0b/IfFZr1gl0b.md

@@ -0,0 +1,523 @@
+# Uni-Mol: A Universal 3D Molecular Representation Learning Framework
+
+Anonymous Author(s)   
+Affiliation   
+Address   
+email
+
+# Abstract
+
+Molecular representation learning (MRL) has gained tremendous attention due to its critical role in learning from limited supervised data for applications like drug design. In most MRL methods, molecules are treated as 1D sequential tokens or 2D topology graphs, limiting their ability to incorporate 3D information for downstream tasks and, in particular, making it almost impossible for 3D geometry prediction or generation. Herein, we propose Uni-Mol, a universal MRL framework that significantly enlarges the representation ability and application scope of MRL schemes. Uni-Mol is composed of two models with the same SE(3)-equivariant transformer architecture: a molecular pretraining model trained by 209M molecular conformations; a pocket pretraining model trained by 3M candidate protein pocket data. The two models are used independently for separate tasks, and are combined when used in protein-ligand binding tasks. By properly incorporating 3D information, Uni-Mol outperforms SOTA in 14/15 molecular property prediction tasks. Moreover, Uni-Mol achieves superior performance in 3D spatial tasks, including protein-ligand binding pose prediction, molecular conformation generation, etc. Finally, we show that Uni-Mol can be successfully applied to the tasks with few-shot data like pocket druggability prediction. The model and data will be made publicly available at https://github.com/dptech-corp/Uni-Mol.
+
+# 19 1 Introduction
+
+20 Recently, representation learning (or pretraining, self-supervised learning) [1, 2, 3] has been prevailing   
+21 in many applications, such as BERT [4] and GPT [5, 6, 7] in Natural Language Processing (NLP),   
+22 ViT [8] in Computer Vision (CV), etc. These applications have a common characteristic: unlabeled   
+23 data is abundant, while labeled data is limited. As a solution, in a typical representation learning   
+24 method, one first adopts a pretraining procedure to learn a good representation from large-scale   
+25 unlabeled data, and then a finetuning scheme is followed to extract more information from limited   
+26 supervised data.   
+27 Applications in the field of drug design share the characteristic that calls for representation learning   
+28 schemes. The chemical space that a drug candidate lies in is vast, while drug-related labeled data is   
+29 limited. Not surprisingly, compared with traditional molecular fingerprint based models [9, 10], recent   
+30 molecular representation learning (MRL) models perform much better in most property prediction   
+31 tasks [11, 12, 13]. However, to further improve the performance and extend the application scope   
+32 of existing MRL models, one is faced with a critical issue. From the perspective of life science, the   
+33 properties of molecules and the effects of drugs are mostly determined by their 3D structures [14,   
+34 15]. In most current MRL methods, one starts with representing molecules as 1D sequential strings,   
+35 such as SMILES [16, 17, 18] and InChI [19, 20, 21], or 2D graphs [22, 11, 23, 12, 24]. This may   
+36 limit their ability to incorporate 3D information for downstream tasks. In particular, this makes it   
+37 almost impossible for 3D geometry prediction or generation, such as, e.g., the prediction of protein  
+38 ligand binding pose [25]. Even though there have been some recent attempts trying to leverage 3D   
+39 information in MRL [26, 27], the performance is less than optimal, possibly due to the small size of   
+40 3D datasets, and 3D positions can not be used as inputs/outputs during finetuning, since they only   
+41 serve as auxiliary information.   
+42 In this work, we propose Uni-Mol, to our best knowledge, the first universal 3D molecular pretraining   
+43 framework, which is derived from large-scale unlabeled data and is able to directly take 3D positions   
+44 as both inputs and outputs. Uni-Mol consists of 3 parts. 1) Backbone. Based on Transformer, the   
+45 invariant spatial positional encoding and pair level representation are added to better capture the 3D   
+46 information. Moreover, an equivariant head is used to directly predict 3D positions. 2) Pretraining.   
+47 We create two large-scale datasets, a 209M molecular conformation dataset and a 3M candidate   
+48 protein pocket dataset, for pretraining 2 models on molecules and protein pockets, respectively.   
+49 For the pretraining tasks, besides masked atom prediction, a 3D position denoising task is used   
+50 for learning 3D spatial representation. 3) Finetuning. According to specific downstream tasks, the   
+51 used pretraining models are different. For example, in molecular property prediction tasks, only the   
+52 molecular pretraining model is used; in protein-ligand binding pose prediction, both two pretraining   
+53 models are used. We refer to Fig. 1 for an overall schematic illustration of the Uni-Mol framework.   
+54 To demonstrate the effectiveness of Uni-Mol, we conduct experiments on a series of downstream   
+55 tasks. In the molecular property prediction tasks, Uni-Mol outperforms SOTA on 14/15 datasets on   
+56 the MoleculeNet benchmark. In 3D geometric tasks, Uni-Mol also achieves superior performance.   
+57 For the pose prediction of protein-ligand complexes, Uni-Mol predicts $8 8 . 0 7 \%$ binding poses with   
+58 $\mathrm { R M S D } < = 2 \bar { \mathring { \mathrm { A } } } .$ , $2 2 . 8 1 \%$ more than popular docking methods, and ranks 1st in the docking power test   
+59 on CASF-2016 [28] benchmark. Regarding molecular conformation generation, Uni-Mol achieves   
+60 SOTA for both Coverage and Matching metrics on GEOM-QM9 and GEOM-Drugs [29]. Moreover,   
+61 Uni-Mol can be successfully applied to tasks with very limited data like pocket druggability prediction.   
+62
+
+![](images/7472f8a9be38c66e92230f52e6fcee71f0744478f8fec8fc9c6cfce93c1913d7.jpg)  
+Figure 1: Schematic illustration of the Uni-Mol framework. Uni-Mol is composed of two models: a molecular pretraining model trained by 209M molecular 3D conformations; a pocket pretraining model trained by 3M candidate protein pocket data. The two models are used independently for separate tasks, and are combined when used in protein-ligand binding tasks.
+
+# 63 2 Uni-Mol Framework
+
+64 In this section, we introduce the Uni-Mol framework by showing the details of the backbone, the   
+65 pretraining scheme, and the finetuning scheme. We refer to Fig. 2 for a schematic illustration of the   
+66 model architecture.
+
+![](images/8af14cb1d3c8b880c00008808226d9becf5945578ca9e11487e2d9b74adb8b77.jpg)  
+Figure 2: Left: the overall pretraining architecture. Middle: the model inputs, including atoms and spatial positional encoding created by pair Euclidean distance. Right: pair representation and its update process.
+
+# 67 2.1 Backbone
+
+68 Transformer [30] is widely used as a backbone model in representation learning. However, Trans  
+69 former was originally designed for NLP tasks and cannot handle 3D spatial data directly. To tackle   
+70 this, based on the standard Transformer with Pre-LayerNorm [31] backbone, we introduce several   
+71 modifications.   
+72 Invariant spatial positional encoding Due to its permutationally invariant property, Transformer   
+73 cannot distinguish the positions of inputs without positional encoding. Different with the discrete   
+74 (ordinal) positions used in NLP/CV [32, 33], the positions in 3D space, i.e. coordinates, are continuous   
+75 values. Besides, the positional encoding procedure needs to be invariant under global rotation and   
+76 translation. To achieve that, similar to the relative positional encoding, we simply use Euclidean   
+77 distances of all atom pairs, as well as pair-type aware Gaussian kernels [34]. Formally, the $D$ -channel   
+78 positional encoding of atom pair $i j$ is denoted as
+
+$$
+\pmb { p } _ { i j } = \{ \mathcal { G } ( A ( d _ { i j } , t _ { i j } ; \pmb { a } , \pmb { b } ) , \mu ^ { k } , \sigma ^ { k } ) | k \in [ 1 , D ] \} , \quad \pmb { \mathcal { A } } ( d , r ; \pmb { a } , \pmb { b } ) = a _ { r } d + b _ { r } ,
+$$
+
+79 where $\begin{array} { r } { \mathcal { G } ( d , \mu , \sigma ) = \frac { 1 } { \sigma \sqrt { 2 \pi } } e ^ { - \frac { ( d - \mu ) ^ { 2 } } { 2 \sigma ^ { 2 } } } } \end{array}$ is a Gaussian density function with parameters $\mu$ and $\sigma , d _ { i j }$ is the   
+80 Euclidean distance of atom pair $i j$ , and $t _ { i j }$ is the pair-type of atom pair $i j$ . Please note the pair-type   
+81 here is not the chemical bond, and it is determined by the atom types of pair $i j$ . $\mathcal { A } ( d _ { i j } , t _ { i j } ; \pmb { a } , \pmb { b } )$ is   
+82 the affine transformation with parameters $\textbf { \em a }$ and $^ { b }$ , it affines $d _ { i j }$ corresponding to its pair-type $t _ { i j }$   
+83 Except $d _ { i j }$ and $t _ { i j }$ , all remaining parameters are trainable and randomly initialized.   
+84 Pair representation By default, Transformer maintains the token(atom) level representation, which   
+85 is later used in finetuning downstream tasks. Nevertheless, as the spatial positions are encoded at   
+86 pair-level, we also maintain the pair-level representation, to better learn the 3D spatial representation.   
+87 Specifically, the pair representation is initialized as the aforementioned spatial positional encoding.   
+88 Then, to update pair representation, we use the atom-to-pair communication via the multi-head Query  
+89 Key product results in self-attention. Formally, the update of $i j$ pair representation is denoted as
+
+$$
+\pmb { q } _ { i j } ^ { 0 } = { \pmb { p } } _ { i j } M , \quad \pmb { q } _ { i j } ^ { l + 1 } = \pmb { q } _ { i j } ^ { l } + \{ \frac { { \pmb { Q } } _ { i } ^ { l , h } ( \pmb { K } _ { j } ^ { l , h } ) ^ { T } } { \sqrt { d } } | h \in [ 1 , H ] \} ,
+$$
+
+where 90 $\pmb { q } _ { i j } ^ { l }$ is the pair representation of atom pair $i j$ in $l$ -th layer, $H$ is the number of attention heads, 91 $d$ is the dimension of hidden representations, $Q _ { i } ^ { l , h } ( K _ { j } ^ { l , h } )$ is the Query (Key) of the $i$ -th ( $j$ -th) atom 92 in the $l$ -th layer $h$ -th head, and $M \in \mathbb { R } ^ { D \times H }$ is the projection matrix to make the representation the 93 same shape as multi-head Query-Key product results.
+
+94 Besides, to leverage 3D information in the atom representation, we also introduce the pair-to-atom   
+95 communication, by using the pair representation as the bias term in self-attention. Formally, the
+
+$$
+\mathrm { A t t e n t i o n } ( Q _ { i } ^ { l , h } , { \bf K } _ { j } ^ { l , h } , { \bf V } _ { j } ^ { l , h } ) = \mathrm { s o f t m a x } ( \frac { Q _ { i } ^ { l , h } ( { \bf K } _ { j } ^ { l , h } ) ^ { T } } { \sqrt { d } } + { \bf q } _ { i j } ^ { l - 1 , h } ) { \bf V } _ { j } ^ { l , h } ,
+$$
+
+97 where $V _ { . j } ^ { l , h }$ is the Value of the $j$ -th atom in the $l$ -th layer $h$ -th head. The pair representation and   
+98 atom-pair communication are firstly proposed in the Evoformer in AlphaFold [35], but the cost of   
+99 Evoformer is extremely large. In Uni-Mol, as we keep them as simple as possible, the extra cost of   
+100 maintaining pair representation is negligible.   
+101 SE(3)-Equivariance coordinate head With 3D spatial positional encoding and pair representation,   
+102 the model can learn a good 3D representation. However, it still lacks the ability to directly output co  
+103 ordinates, which is essential in 3D spatial tasks. To this end, we add a simple SE(3)-equivariance head   
+104 to Uni-Mol. Following the idea of EGNN [36], the design of SE(3)-equivariance head is denoted as
+
+$$
+\hat { \pmb x } _ { i } = { \pmb x } _ { i } + \sum _ { j = 1 } ^ { n } \frac { ( { \pmb x } _ { i } - { \pmb x } _ { j } ) c _ { i j } } { n } , \quad c _ { i j } = \mathrm { R e L U } ( ( { \pmb q } _ { i j } ^ { L } - { \pmb q } _ { i j } ^ { 0 } ) U ) W ,
+$$
+
+105 where $n$ is the number of total atoms, $L$ is the number of layers in model, $\pmb { x } _ { i } \in \mathbb { R } ^ { 3 }$ is the input   
+106 coordinate of $i$ -th atom, and $\hat { \pmb { x } } _ { i } \in \mathbb { R } ^ { 3 }$ is the output coordinate of $i$ -th atom, $\mathrm { R e L U } ( y ) = \operatorname* { m a x } ( 0 , y )$   
+107 is Rectified Linear Unit [37], $U \in \mathbb { R } ^ { H \times H }$ and $\dot { \boldsymbol { W } } \in \mathbb { R } ^ { H \times 1 }$ are the projection matrices to convert   
+108 pair representation to scalar.
+
+# 09 2.2 Pretraining
+
+110 For the purpose of pretraining, we generate two large-scale datasets, one composed of 3D structures   
+111 of organic molecules, and another composed of 3D structures of candidate protein pockets. Then,   
+112 two models are pretrained using these two datasets, respectively. As pockets are directly involved   
+113 in many drug design tasks, intuitively, the pretraining on candidate protein pockets can boost the   
+114 performance of tasks related to protein-ligand structures and interactions.   
+115 The molecular pretraining dataset is based on multiple public datasets (See Appendix ?? for more   
+116 information). After normalizing and deduplicating, it contains about 19M molecules. To generate   
+117 3D conformations, we use ETKGD [38] with Merck Molecular Force Field [39] optimization   
+118 in RDKit [40] to randomly generate 10 conformations for each molecule. We also generate an   
+119 additional 2D conformation (based on the molecular graph), to avoid some rare cases that fail to   
+120 generate 3D conformations.   
+121 The protein pocket pretraining dataset is derived from the Protein Data Bank (RCSB PDB 1) [41], a   
+122 collection of 180K 3D structures of proteins. To extract candidate pockets, we first clean the data   
+123 by adding the missing side chains and hydrogen atoms; then we use Fpocket [42] to detect possible   
+124 binding pockets of the proteins; and finally, we filter pockets by the number of residues in contact   
+125 with and retains water molecules in the pocket. In this way, We collect a dataset composed of 3.2M   
+126 candidate pockets for pretraining.   
+127 Self-supervised task is vitally important for effective learning from large-scale unlabeled data.   
+128 For example, the masked token prediction task in BERT [4] encourages the model to learn the   
+129 contextual information. Similar to BERT, the masked atom prediction task is used in Uni-Mol.   
+130 For each molecule/pocket, we add a special atom [CLS], whose coordinate is the center of all   
+131 atoms, to represent the whole molecule/pocket. However, as 3D spatial positional encoding leaks   
+132 chemical bonds, atom types could be inferred easily, and therefore, the masked atom prediction   
+133 cannot encourage the model to learn useful information. To tackle this, as well as learning from 3D   
+134 information, we design a 3D position denoising task. Particularly, uniform noises of $[ - 1 \bar { \mathrm { \bf A } } , 1 \bar { \mathrm { \bf A } } ]$ are   
+135 added to the random $15 \%$ atom coordinates, then the spatial positional encoding is calculated based   
+136 on corrupted coordinates. In this way, the masked atom prediction task becomes non-trivial. Besides,   
+137 two additional heads are used to recover the correct spatial positions. 1) Pair-distance prediction.   
+138 Based on pair-representation, the model needs to predict the correct Euclidean distances of the atoms   
+139 pairs with corrupted coordinates. 2) Coordinate prediction. Based on SE(3)-Equivariance coordinate   
+140 head, the model needs to predict the correct coordinates for the atoms with corrupted coordinates.   
+141 Both 2 pretraining models use the same self-supervised tasks described above, and Figure 2 is the   
+142 illustration of the overall pretraining framework. For the detailed configurations of pretraining, please   
+143 refer to Appendix ??.
+
+# 2.3 Finetuning
+
+145 To be consistent with pretraining, we use the same data prepossessing pipeline during finetuning.   
+146 For molecules, as multiple random conformations can be generated in a short time, we can use them   
+147 as data augmentation in finetuning to improve performance and robustness. Some molecules may fail   
+148 to generate 3D conformations, and we use their molecular graph as 2D conformation. For tasks that   
+149 provide atom coordinates, we use them directly and skip the 3D conformation generation process.   
+150 As there are 2 pretraining models and several types of downstream tasks, we should properly use   
+151 them in the finetuning stage. According to the task types, and the involvement of protein or ligand,   
+152 we can categorize them as follow.   
+153 Non-3D prediction tasks These tasks do not need to output 3D conformations. Examples include   
+154 molecular property prediction, molecule similarity, pocket druggability prediction, protein-ligand   
+155 binding affinity prediction, etc. Similar to NLP/CV, we can simply use the representation of [CLS]   
+156 which represents the whole molecule/pocket, or the mean representation of all atoms, with a linear   
+157 head to finetune on downstream tasks. In the tasks with pocket-molecule pair, we can concatenate   
+158 their [CLS] representations, and then finetune with linear head.
+
+3D prediction tasks of molecules or pockets These tasks need to predict a 3D conformation of the input, such as molecular conformation generation. Different with the fast conformation generation method used in Uni-Mol, molecular conformation generation task usually requires running advanced sampling and semi-empirical density functional theory (DFT) to account for the ensemble of 3D conformers that are accessible to a molecule, and this is very time-consuming. Therefore, there are many recent works that train the model to fast generate conformations from molecular graph [43, 44, 45, 46]. While in Uni-Mol, this task straightforwardly becomes a conformation optimization task: generate a new conformation based on a different input conformation. Specifically, in finetuning, the model supervised learns the mapping from Uni-Mol generated conformations to the labeled conformations. Moreover, the optimized conformations can be generated end-to-end by SE(3)-Equivariance coordinate head.
+
+170 3D prediction tasks of protein-ligand pairs This is one of the most important tasks in structure  
+171 based drug design. The task is to predict the complex structure of a protein binding site and a   
+172 molecular ligand. Besides the conformation changes of the pocket and the molecule themselves, we   
+173 also need to consider how the molecule lays in the pocket, that is, the additional 6 degrees (3 rotations   
+174 and 3 translations) of freedom of a rigid movement. In principle, with Uni-Mol, we can predict the   
+175 complex conformation by the SE(3)-Equivariant coordinate head in an end-to-end fashion. However,   
+176 this is unstable as it is very sensitive to the initial docking positions of molecular ligand. Herein, to   
+177 get rid of the initial positions, we use a scoring function based optimization method in this paper. In   
+178 particular, the molecular representation and pocket representation are firstly obtained from their own   
+179 pretraining models by their own conformations; then, their representations are concatenated as the   
+180 input of an additional 4-layer Uni-Mol decoder, which is finetuned to learn the pair distances of all   
+181 atoms in molecule and pocket. With the predicted pair-distance matrix as the scoring function, we   
+182 use a simple differential evolution algorithm [47] to sample and optimize the complex conformations.   
+183 More details can be found in Appendix ??.
+
+# 184 3 Experiments
+
+To verify the effectiveness of our proposed Uni-Mol model, we conduct extensive experiments on multiple downstream tasks, including molecular property prediction, molecular conformation generation, pocket property prediction, and protein-ligand binding pose prediction. Besides, we also conduct several ablation studies. Due to space restrictions, we leave the detailed experimental settings and ablation studies to Appendix ??.
+
+# 3.1 Molecular property prediction
+
+191 Datasets and setup MoleculeNet [48] is a widely used benchmark for molecular property   
+192 prediction, including datasets focusing on different levels of properties of molecules, from quantum   
+193 mechanics and physical chemistry to biophysics and physiology. Following previous work GEM [13],   
+194 we use scaffold splitting for the dataset and report the mean and standard deviation of the results   
+195 for three random seeds.   
+196 Baselines We compare Uni-Mol with multiple baselines, including supervised and pretraining   
+197 baselines. D-MPNN [49] and AttentiveFP [50] are supervised GNNs methods. N-gram [51],   
+198 PretrainGNN [22], GROVER [11], GraphMVP [26], MolCLR [12], and GEM [13] are pretraining   
+199 methods. N-gram embeds the nodes in the graph and assembles them in short walks as the graph   
+200 representation. Random Forest and XGBoost [52] are used as the predictor for downstream tasks.
+
+Table 1: Uni-Mol performance on molecular property prediction classification tasks   
+
+<table><tr><td colspan="11">Classification (ROC-AUC %,higher is better ↑)</td></tr><tr><td>Datasets #Molecules # Tasks</td><td>BBBP 2039 1</td><td>BACE 1513 1</td><td>ClinTox 1478 2</td><td>Tox21 7831 12</td><td>ToxCast 8575 617</td><td>SIDER 1427 27</td><td>HIV 41127 1</td><td>PCBA 437929 128</td><td>MUV 93087 17</td></tr><tr><td>D-MPNN</td><td>71.0(0.3)</td><td>80.9(0.6)</td><td>90.6(0.6)</td><td>75.9(0.7)</td><td>65.5(0.3)</td><td>57.0(0.7)</td><td>77.1(0.5)</td><td>86.2(0.1)</td><td>78.6(1.4)</td></tr><tr><td>Attentive FP</td><td>64.3(1.8)</td><td>78.4(0.022)</td><td>84.7(0.3)</td><td>76.1(0.5)</td><td>63.7(0.2)</td><td>60.6(3.2)</td><td>75.7(1.4)</td><td>80.1(1.4)</td><td>76.6(1.5)</td></tr><tr><td>N-GramRF</td><td>69.7(0.6)</td><td>77.9(1.5)</td><td>77.5(4.0)</td><td>74.3(0.4)</td><td></td><td>66.8(0.7)</td><td>77.2(0.1)</td><td></td><td>76.9(0.7)</td></tr><tr><td>N-GramxGB</td><td>69.1(0.8)</td><td>79.1(1.3)</td><td>87.5(2.7)</td><td>75.8(0.9)</td><td></td><td>65.5(0.7)</td><td>78.7(0.4)</td><td></td><td>74.8(0.2)</td></tr><tr><td>PretrainGNN</td><td>68.7(1.3)</td><td>84.5(0.7)</td><td>72.6(1.5)</td><td>78.1(0.6)</td><td>65.7(0.6)</td><td>62.7(0.8)</td><td>79.9(0.7)</td><td>86.0(0.1)</td><td>81.3(2.1)</td></tr><tr><td>GROVERbase</td><td>70.0(0.1)</td><td>82.6(0.7)</td><td>81.2(3.0)</td><td>74.3(0.1)</td><td>65.4(0.4)</td><td>64.8(0.6) 65.4(0.1)</td><td>62.5(0.9) 68.2(1.1)</td><td>76.5(2.1)</td><td>67.3(1.8)</td></tr><tr><td>GROVERlarge</td><td>69.5(0.1) 72.4(1.6)</td><td>81.0(1.4)</td><td>76.2(3.7)</td><td>73.5(0.1)</td><td>65.3(0.5) 63.1(0.4)</td><td></td><td></td><td>83.0(0.4)</td><td>67.3(1.8)</td></tr><tr><td>GraphMVP</td><td>72.2(2.1)</td><td>81.2(0.9) 82.4(0.9)</td><td>79.1(2.8) 91.2(3.5)</td><td>75.9(0.5) 75.0(0.2)</td><td></td><td>63.9(1.2) 58.9(1.4)</td><td>77.0(1.2) 78.1(0.5)</td><td></td><td>77.7(0.6)</td></tr><tr><td>MolCLR GEM</td><td>72.4(0.4)</td><td>85.6(1.1)</td><td>90.1(1.3)</td><td>78.1(0.1)</td><td>69.2(0.4)</td><td>67.2(0.4)</td><td>80.6(0.9)</td><td>86.6(0.1)</td><td>79.6(1.9) 81.7(0.5)</td></tr><tr><td>Uni-Mol</td><td>72.9(0.6)</td><td>85.7(0.2)</td><td>91.9(1.8)</td><td>79.6(0.5)</td><td>69.6(0.1)</td><td>65.9(1.3)</td><td>80.8(0.3)</td><td>88.5(0.1)</td><td>82.1(1.3)</td></tr></table>
+
+Table 2: Uni-Mol performance on molecular property prediction regression tasks   
+
+<table><tr><td colspan="6">Regression (lower is better ↓)</td></tr><tr><td colspan="3">RMSE</td><td colspan="3">MAE</td></tr><tr><td>Datasets # Molecules</td><td>ESOL 1128</td><td>FreeSolv 642</td><td>Lipo 4200</td><td>QM7 6830</td><td>QM8 21786</td><td>QM9 133885</td></tr><tr><td>#Tasks D-MPNN</td><td>1</td><td>1</td><td>1</td><td>1</td><td>12</td><td>3</td></tr><tr><td></td><td>1.050(0.008)</td><td>2.082(0.082)</td><td>0.683(0.016)</td><td>103.5(8.6)</td><td>0.0190(0.0001)</td><td>0.00814(0.00001)</td></tr><tr><td>Attentive FP</td><td>0.877(0.029)</td><td>2.073(0.183)</td><td>0.721(0.001)</td><td>72.0(2.7)</td><td>0.0179(0.001)</td><td>0.00812(0.00001)</td></tr><tr><td>N-GramRF</td><td>1.074(0.107)</td><td>2.688(0.085)</td><td>0.812(0.028)</td><td>92.8(4.0)</td><td>0.0236(0.0006)</td><td>0.01037(0.00016)</td></tr><tr><td>N-GramxGB</td><td>1.083(0.082)</td><td>5.061(0.744)</td><td>2.072(0.030)</td><td>81.9(1.9)</td><td>0.0215(0.0005)</td><td>0.00964(0.00031)</td></tr><tr><td>PretrainGNN</td><td>1.100(0.006)</td><td>2.764(0.002)</td><td>0.739(0.003)</td><td>113.2(0.6)</td><td>0.0200(0.0001)</td><td>0.00922(0.00004)</td></tr><tr><td>GROVERbase</td><td>0.983(0.090)</td><td>2.176(0.052)</td><td>0.817(0.008)</td><td>94.5(3.8)</td><td>0.0218(0.0004)</td><td>0.00984(0.00055)</td></tr><tr><td>GROVERlarge</td><td>0.895(0.017)</td><td>2.272(0.051)</td><td>0.823(0.010)</td><td>92.0(0.9)</td><td>0.0224(0.0003)</td><td>0.00986(0.00025)</td></tr><tr><td>GraphMVP</td><td>1.029(0.033)</td><td></td><td>0.681(0.010)</td><td></td><td></td><td></td></tr><tr><td>MoiCLR</td><td>1.271(0.040)</td><td>2.594(0.249)</td><td>0.691(0.004)</td><td>66.8(2.3)</td><td>0.0178(0.0003)</td><td></td></tr><tr><td>GEM</td><td>0.798(0.029)</td><td>1.877(0.094)</td><td>0.660(0.008)</td><td>58.9(0.8)</td><td>0.0171(0.0001)</td><td>0.00746(0.00001)</td></tr><tr><td>Uni-Mol</td><td>0.788(0.029)</td><td>1.620(0.035)</td><td>0.603(0.010)</td><td>41.8(0.2)</td><td>0.0156(0.0001)</td><td>0.00467(0.00004)</td></tr></table>
+
+Results Table 1 and Table 2 show the experiment results of Uni-Mol and competitive baselines, where the best results are marked in bold. Most baseline results are from the paper of GEM, except for the recent works GraphMVP and MolCLR. The results of GraphMVP are from its paper. As MolCLR uses a different data split setting (without considering chirality), we rerun it with the same data split setting as other baselines. From the results, we can summarize them as follows: 1) overall, Uni-Mol outperforms baselines on almost all downstream datasets. 2) In solubility (ESOL, Lipo), free energy (FreeSolv), and quantum mechanical (QM7, QM8, QM9) properties prediction tasks, Uni-Mol is significantly better than baselines. As 3D information is critical in these properties, it indicates that Uni-Mol can learn a better 3D representation than other baselines. 3) Uni-Mol fails to beat SOTA on the SIDER dataset. After investigation, we find Uni-Mol fails to generate 3D conformations (and rollbacks to 2D graphs) for many molecules (like natural products and peptides) in SIDER. Therefore, due to the missing 3D information, it is reasonable that Uni-Mol cannot outperform others.
+
+213 In summary, by better utilizing 3D information in pretraining, Uni-Mol outperforms all previous   
+214 MRL models in almost all property prediction tasks.
+
+Table 3: Uni-Mol performance on molecular conformation generation   
+
+<table><tr><td rowspan="3">Dataset Methods</td><td colspan="4">QM9</td><td colspan="4">Drugs</td></tr><tr><td colspan="2">COV(↑, %)</td><td colspan="2">MAT(↓, A)</td><td colspan="2">COV(↑,%)</td><td colspan="2">MAT(↓,A)</td></tr><tr><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td></tr><tr><td>RDKit</td><td>83.26</td><td>90.78</td><td>0.3447</td><td>0.2935</td><td>60.91</td><td>65.70</td><td>1.2026</td><td>1.1252</td></tr><tr><td>CVGAE</td><td>0.09</td><td>0.00</td><td>1.6713</td><td>1.6088</td><td>0.00</td><td>0.00</td><td>3.0702</td><td>2.9937</td></tr><tr><td>GraphDG</td><td>73.33</td><td>84.21</td><td>0.4245</td><td>0.3973</td><td>8.27</td><td>0.00</td><td>1.9722</td><td>1.9845</td></tr><tr><td>CGCF</td><td>78.05</td><td>82.48</td><td>0.4219</td><td>0.3900</td><td>53.96</td><td>57.06</td><td>1.2487</td><td>1.2247</td></tr><tr><td>ConfVAE</td><td>80.42</td><td>85.31</td><td>0.4066</td><td>0.3891</td><td>53.14</td><td>53.98</td><td>1.2392</td><td>1.2447</td></tr><tr><td>ConfGF</td><td>88.49</td><td>94.13</td><td>0.2673</td><td>0.2685</td><td>62.15</td><td>70.93</td><td>1.1629</td><td>1.1596</td></tr><tr><td>GeoMol</td><td>71.26</td><td>72.00</td><td>0.3731</td><td>0.3731</td><td>67.16</td><td>71.71</td><td>1.0875</td><td>1.0586</td></tr><tr><td>DGSM</td><td>91.49</td><td>95.92</td><td>0.2139</td><td>0.2137</td><td>78.73</td><td>94.39</td><td>1.0154</td><td>0.9980</td></tr><tr><td>DMCG</td><td>96.34</td><td>99.53</td><td>0.2065</td><td>0.2003</td><td>96.69</td><td>100.00</td><td>0.7223</td><td>0.7236</td></tr><tr><td>GeoDiff</td><td>90.07</td><td>93.39</td><td>0.2090</td><td>0.1988</td><td>89.13</td><td>97.88</td><td>0.8629</td><td>0.8529</td></tr><tr><td>Uni-Mol</td><td>98.68</td><td>100.00</td><td>0.1806</td><td>0.1510</td><td>92.69</td><td>100.00</td><td>0.6596</td><td>0.6215</td></tr></table>
+
+# 15 3.2 Molecular conformation generation
+
+Datasets and setup Following the settings in previous works [44, 53], we use GEOM-QM9 and GEOM-Drugs [54] dataset to perform conformation generation experiments. As described in Sec. 2.3, in this task, Uni-Mol optimizes its generative conformations to the labeled ones. To construct the finetuning data, we first randomly generate 10 conformations. Then, for each of them, we calculate the RMSD between it and labeled conformations, and choose the one with minimal RMSD as its optimizing target. For the inference in the test set, we generate the same number of conformations (twice the number of labeled conformations) as previous works do. And we use the same metrics, Coverage (COV) and Matching (MAT). Higher COV means better diversity, while lower MAT means higher accuracy.
+
+Baselines We compare Uni-Mol with 10 competitive baselines. RDKit [38] is a traditional conformation generation method based on distance geometry. The rest baseline can be categorized into two classes. GraphDG [43], CGCF[44], ConfVAE [55], ConfGF [53], and DGSM [56] combine generative models with distance geometry, which first generates interatomic distance matrices and then iteratively generates atomic coordinates. CVGAE [45], GeoMol [46], DMCG [57], and GeoDiff [58] directly generate atomic coordinates.
+
+Results The results are shown in Table 3. We report the mean and median of COV and MAT on GEOM-QM9 and GEOM-Drugs datasets. ConfVAE [55], GeoMol[46], DGSM [56], DMCG [57], GeoDiff’s [58] results are from their papers, respectively. Other baseline results are from ConfGF’s paper. As shown in Table 3, Uni-Mol exceeds existing baselines in both COV and MAT metrics on both datasets. Although Uni-Mol outperforms SOTA, we suspect that the above benchmark cannot satisfy the real-world demand of conformation generation tasks in the field of drug design. Since the ensemble of molecular conformations in biological systems is different from that in a vacuum or general solution environment, the ensemble of bioactive conformation must be considered in order to apply the conformation generation model in the context of drug design, while the GEOM dataset just ignores this. Establishing a reasonable benchmark will be crucial in this research direction.
+
+# 3.3 Pocket property prediction
+
+Datasets and setup Druggability, the ability of a candidate protein pocket to produce stable binding to a specific molecular ligand, is one of the most critical properties of a candidate protein pocket. However, this task is very challenging due to the very limited supervised data. For example, NRDLD [59], a commonly used dataset, only contains 113 data samples. Therefore, besides NRDLD, we construct a regression dataset for benchmarking pocket property prediction performance. Specifically, based on Fpocket tool, we calculate Fpocket Score, Druggability Score, Total SASA, and Hydrophobicity Score for the selected 164,586 candidate pockets. Model is trained to predict these scores. To avoid leaking, the selected pockets are not overlapped with the candidate protein pocket dataset used in Uni-Mol pretraining.
+
+251 Baselines On the NRDLD dataset, we compare Uni-Mol with 6 previous methods evaluated in [60].   
+252 Accuracy, recall, precision, and F1-score are used as metrics for this classification task. On our   
+253 created benchmark dataset, as there are no appropriate baselines, we use an additional Uni-Mol model
+
+Table 4: Uni-Mol performance on pocket property prediction   
+
+<table><tr><td colspan="8">Classification (higher is better ↑)</td><td colspan="2">Regression (lower is better ↓) Fpocket Scores</td></tr><tr><td></td><td>Methods |Cavity-DrugScore</td><td>Volsite DrugPred PockDrug</td><td></td><td></td><td></td><td></td><td>TRAPP-CNN Uni-Mol|Methods</td><td>Uni-Molrandom</td><td>Uni-Mol</td></tr><tr><td>Accuracy</td><td>0.82</td><td>0.89</td><td>0.89</td><td>0.865</td><td>0.946</td><td>0.946</td><td>|MSEFpocket</td><td>[0.621(0.004)</td><td>0.551(0.008)</td></tr><tr><td>Recall</td><td></td><td></td><td></td><td>0.957</td><td>0.913</td><td>1.000</td><td>MSEDrggability</td><td>0.601(0.02)</td><td>0.499(0.007)</td></tr><tr><td>Precision</td><td></td><td>=</td><td></td><td>0.846</td><td>1.000</td><td>0.920</td><td>MSETotal SASA</td><td>0.197(0.008)</td><td>0.129(0.005)</td></tr><tr><td>F1-score</td><td></td><td></td><td></td><td>0.898</td><td>0.955</td><td>0.958</td><td>MSEHydrophobicity</td><td>0.0357(0.017)</td><td>0.0127(0.0005)</td></tr></table>
+
+without pretraining, denoted as $\mathrm { U n i - M o l _ { r a n d o m } }$ , to check the performance brought by pretraining on pocket property prediction. MSE (mean square error) is used as the metric.
+
+Results As shown in Table 4, Uni-Mol shows the best accuracy, recall, and F1-score on NRDLD, the few-show dataset. In our created benchmark dataset, the pretraining Uni-Mol model largely outperforms the non-pretraining one on all four scores. This indicates that pretraining on candidate protein pockets indeed brings improvement in pocket property prediction tasks.
+
+Unlike Molecular property prediction, due to the very limited supervised data, pocket property prediction gained much less attention. Therefore, we also plan to release our created benchmark dataset, and hopefully, it can help future research.
+
+# 3.4 Protein-ligand binding pose prediction
+
+Datasets and setup As mentioned above, protein-ligand binding pose prediction is one of the most important tasks in drug design. And Uni-Mol combines both the molecular and pocket pretraining models to learn a distance matrix based scoring function, and then sample and optimize the complex conformations. For the benchmark dataset, referring to the previous works [28, 61], we use CASF2016 as the test set. For the training data used in finetuning, we use PDBbind General set v.2020 [62] (19,443 protein-ligand complexes), excluding complexes that already exist in the CASF-2016.
+
+Two benchmarks are conducted: 1) Docking power, the default metric to benchmark the ability of a scoring function in CASF-2016. Specifically, it tests whether a scoring function can distinguish the ground truth binding pose from a set of decoys or not. For each ground truth, CASF-2016 provides 50 100 decoy conformations of the same ligand. Scoring functions are applied to rank them, and the ground truth binding pose is expected to be the top 1. 2) Binding pose accuracy. Specifically, we use the semi-flexible docking setting: keep the pocket conformation fixed, while the conformation of the ligand is fully flexible. We evaluate the RMSD between the predicted binding pose and the ground truth. Following previous works, we use the percentage of results that are below predefined RMSD thresholds as metrics.
+
+Baselines For docking power benchmark, the baselines are DeepDock [61] and the top 10 scoring functions reported in [28], including both conventional scoring functions and machine learningbased ones. For the binding pose accuracy, the baselines are Autodock Vina [63, 64], Vinardo [65], Smina [66], and AutoDock4 [67].
+
+Results From the docking power benchmark results shown in Figure 3, Uni-Mol ranks the 1st, with the top 1 success rate of $9 1 . 6 \%$ . For comparison, the previous top scoring function AutoDock Vina [63, 64] achieves $9 0 . 2 \%$ of the top 1 success rate in this benchmark. From the binding pose accuracy results shown in Table 5, Uni-Mol also surpasses all other baselines. Notably, Uni-Mol outperforms the second best method by $2 2 . 8 1 \%$ under the threshold of $2 \mathring \mathrm { A }$ . This result indicates that Uni-Mol can effectively learn the 3D information from both molecules and pockets, as well as the interaction in 3D space of them. Even without pretraining, Uni-Mol (denoted as Uni-Mol random) is also better than other baselines. This demonstrates the effectiveness of Uni-Mol backbone, as it effectively learns the 3D information by limited data.
+
+In summary, by combining molecular and pocket pretraining models, Uni-Mol significantly outperforms the widely used docking tools in the protein-ligand binding tasks.
+
+# 4 Related work
+
+Molecular representation learning Representation learning on large-scale unlabeled molecules attracts much attention recently. SMILES-BERT [18] is pretrained on SMILES strings of molecules using BERT [4]. Subsequent works are mostly pretraining on 2D molecular topological graphs [23, 11]. MolCLR [12] applies data augmentation to molecular graphs at both node and graph levels, using
+
+![](images/15e0d1258867cc24a58381b54a0cbb8e0fb8bc0c4da37581b2a673b8c05c6c0f.jpg)  
+Figure 3: Docking power evaluation on CASF-2016 (Top 10 methods)
+
+<table><tr><td colspan="3">Ligand RMSD % Below Threshold 个</td></tr><tr><td>Methods</td><td>0.5A 1.0A 1.5A 2.0A 3.0A 5.0A</td></tr><tr><td>Autodock Vina</td><td>23.86 44.21 57.54 64.56 73.68 84.56</td></tr><tr><td>Vinardo 23.51</td><td>41.75 57.54 62.81 69.82 76.84</td></tr><tr><td>Smina 23.51</td><td>47.37 59.65 65.26 74.39 82.11</td></tr><tr><td>Autodock4 7.02</td><td>21.75 31.58 35.44 47.02 64.56</td></tr><tr><td>Uni-Molrandom 14.04 Uni-Mol 24.91</td><td>49.47 65.26 75.44 87.02 98.60 70.53 84.21 88.07 94.74 98.95</td></tr></table>
+
+Table 5: Uni-Mol performance on binding pose prediction
+
+299 a self-supervised contrastive learning strategy to learn molecular representations. Further, several   
+300 recent works try to leverage the 3D spatial information of molecules, and focus on contrastive or   
+301 transfer learning between 2D topology and 3D geometry of molecules. For example, GraphMVP [26]   
+302 proposes a contrastive learning GNN-based framework between 2D topology and 3D geometry.   
+303 GEM [13] uses bond angles and bond length as additional edge attributes to enhance 3D information.   
+304 As aforementioned, due to the inability of handling 3D information, most previous representation   
+305 learning models cannot be used in the important 3D prediction tasks.   
+306 SE(3)-Equivariant models In many-body scenarios such as potential energy surface fitting, SE-(3)   
+307 equivariance is usually required. A series of SE(3) models are proposed, such as SchNet [68], tensor   
+308 field networks [69], SE(3) Transformer [70], DimmNet [71], equivariant graph neural networks   
+309 (EGNN) [36], GemNet [72] and SphereNet [73]. Most of these models are used in supervised   
+310 learning with energy and force. In Uni-Mol, based on the standard Transformer, we introduce several   
+311 minor changes to make the model SE(3)-Equivariant.
+
+Pocket druggability prediction Druggability prediction of protein binding pockets is crucial for drug discovery as druggable pockets need to be identified at the beginning. Since proteins undergo conformation changes that might alter the druggability of pockets, it is necessary to utilize 3D spatial data beyond sequential information. Early methods, such as Volsite [74], DrugPred [59], and PockDrug [75], predict druggability based on the predefined descriptors of pockets’ static structures. Later, TRAPP-CNN [60], based on 3D-CNN, proposes the analysis of proteins’ conformation changes and the use of such information for druggability prediction.
+
+Protein-ligand binding pose prediction In structure-based drug design, it is crucial to understand the interactions between protein targets and ligands. The in vitro estimation of the binding pose and affinity, such as docking, allows for lead identification and guides molecular optimization. In particular, docking is one of the most important approaches in structure-based drug design and has been developed for the past decades. Tools such as AutoDock4 [67], AutoDock Vina [63, 64], and Smina [66] are among the most used docking programs. Also, machine learning-based docking methods, such as $\Delta _ { V i n a } \mathrm { R F _ { 2 0 } }$ [76], DeepDock [61] and Equibind [77], have also been developed to predict protein-ligand binding poses and assess protein-ligand binding affinity.
+
+# 5 Conclusion
+
+In this paper, to enlarge the application scope and representation ability of molecular representation learning (MRL), we propose Uni-Mol, the first universal large-scale 3D MRL framework. Uni-Mol consists of 3 parts: a Transformer based backbone to handle 3D data; two large-scale pretraining models to learn molecular and pocket representations respectively; finetuning strategies for all kinds of downstream tasks. Experiments demonstrate that Uni-Mol can outperform existing SOTA in various downstream tasks, especially in 3D spatial tasks.
+
+334 There are 3 potential future directions. 1) Better interaction mechanisms for finetuning two pretraining   
+335 models together. As the interaction between the pretraining pocket model and the pretraining   
+336 molecular model is simple in the current version of Uni-Mol, we believe there is a large room for   
+337 further improvement. 2) Large Uni-Mol models. As larger pretraining models often perform better, it   
+338 is worthy of training a large Uni-Mol model on a bigger dataset. 3) More high-quality benchmarks.   
+339 Although there have been many applications in the field of drug design, high-quality public datasets   
+340 have been lacking. Many public datasets cannot satisfy real-world demand due to the low data quality.   
+341 We believe the high-quality benchmarks will be the lighthouse of the entire field, and will significantly   
+342 accelerate the development of drug design.
+
+# 343 References
+
+344 [1] Yoshua Bengio, Aaron Courville, and Pascal Vincent. “Representation learning: A review and new   
+345 perspectives”. In: IEEE transactions on pattern analysis and machine intelligence 35.8 (2013), pp. 1798–   
+346 1828.   
+347 [2] William L. Hamilton, Rex Ying, and Jure Leskovec. “Representation Learning on Graphs: Methods and   
+348 Applications”. In: IEEE Data Eng. Bull. 40.3 (2017), pp. 52–74. URL: http://sites.computer.org/   
+349 debull/A17sept/p52.pdf.   
+350 [3] Daokun Zhang et al. “Network representation learning: A survey”. In: IEEE transactions on Big Data   
+351 6.1 (2018), pp. 3–28.   
+352 [4] Jacob Devlin et al. “BERT: Pre-training of Deep Bidirectional Transformers for Language Under  
+353 standing”. In: Proceedings of the 2019 Conference of the North American Chapter of the Association   
+354 for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers).   
+355 Minneapolis, Minnesota: Association for Computational Linguistics, June 2019, pp. 4171–4186. DOI:   
+356 10.18653/v1/N19-1423. URL: https://aclanthology.org/N19-1423.   
+357 [5] Alec Radford et al. “Improving language understanding by generative pre-training”. In: (2018).   
+358 [6] Alec Radford et al. “Language models are unsupervised multitask learners”. In: OpenAI blog 1.8 (2019),   
+359 p. 9.   
+360 [7] Tom Brown et al. “Language models are few-shot learners”. In: Advances in neural information process  
+361 ing systems 33 (2020), pp. 1877–1901.   
+362 [8] Alexey Dosovitskiy et al. “An Image is Worth 16x16 Words: Transformers for Image Recognition at   
+363 Scale”. In: International Conference on Learning Representations. 2021. URL: https://openreview.   
+364 net/forum?id=YicbFdNTTy.   
+365 [9] Qingda Zang et al. “In silico prediction of physicochemical properties of environmental chemicals using   
+366 molecular fingerprints and machine learning”. In: Journal of chemical information and modeling 57.1   
+367 (2017), pp. 36–49.   
+368 [10] Minjian Yang et al. “Machine learning models based on molecular fingerprints and an extreme gradient   
+369 boosting method lead to the discovery of JAK2 inhibitors”. In: Journal of Chemical Information and   
+370 Modeling 59.12 (2019), pp. 5002–5012.   
+371 [11] Yu Rong et al. “Self-Supervised Graph Transformer on Large-Scale Molecular Data”. In: Advances in   
+372 Neural Information Processing Systems 33 (2020).   
+373 [12] Yuyang Wang et al. “Molecular contrastive learning of representations via graph neural networks”. In:   
+374 Nature Machine Intelligence (2022), pp. 1–9. DOI: 10.1038/s42256-022-00447-x.   
+375 [13] Xiaomin Fang et al. “Geometry-enhanced molecular representation learning for property prediction”. In:   
+376 Nature Machine Intelligence (2022), pp. 1–8. DOI: 10.1038/s42256-021-00438-4.   
+377 [14] A Crum-Brown and TR Fraser. “The connection of chemical constitution and physiological action”. In:   
+378 Trans R Soc Edinb 25.1968-1969 (1865), p. 257.   
+379 [15] Corwin Hansch and Toshio Fujita. “p-σ-π Analysis. A Method for the Correlation of Biological Activity   
+380 and Chemical Structure”. In: Journal of the American Chemical Society 86.8 (1964), pp. 1616–1626.   
+381 [16] David Weininger. “SMILES, a chemical language and information system. 1. Introduction to methodology   
+382 and encoding rules”. In: Journal of chemical information and computer sciences 28.1 (1988), pp. 31–36.   
+383 [17] Zheng Xu et al. “Seq2seq fingerprint: An unsupervised deep molecular embedding for drug discovery”.   
+384 In: Proceedings of the 8th ACM international conference on bioinformatics, computational biology, and   
+385 health informatics. 2017, pp. 285–294.   
+386 [18] Sheng Wang et al. “Smiles-bert: large scale unsupervised pre-training for molecular property prediction”.   
+387 In: Proceedings of the 10th ACM international conference on bioinformatics, computational biology and   
+388 health informatics. 2019, pp. 429–436.   
+389 [19] Stephen R Heller et al. “InChI, the IUPAC international chemical identifier”. In: Journal of cheminfor  
+390 matics 7.1 (2015), pp. 1–34.   
+391 [20] Robin Winter et al. “Learning continuous and data-driven molecular descriptors by translating equivalent   
+392 chemical representations”. In: Chemical science 10.6 (2019), pp. 1692–1701.   
+393 [21] Jennifer Handsel et al. “Translating the InChI: adapting neural machine translation to predict IUPAC   
+394 names from a chemical identifier”. In: Journal of cheminformatics 13.1 (2021), pp. 1–11.   
+395 [22] Weihua $\mathrm { H u ^ { * } }$ et al. “Strategies for Pre-training Graph Neural Networks”. In: International Conference on   
+396 Learning Representations. 2020. URL: https://openreview.net/forum?id=HJlWWJSFDH.   
+397 [23] Pengyong Li et al. “An effective self-supervised framework for learning expressive molecular global   
+398 representations to drug discovery”. In: Briefings in Bioinformatics 22.6 (2021), bbab109.   
+399 [24] Chengxuan Ying et al. “Do Transformers Really Perform Badly for Graph Representation?” In: Advances   
+400 in Neural Information Processing Systems 34 (2021).   
+401 [25] Panagiotis I Koukos, Li C Xue, and Alexandre MJJ Bonvin. “Protein–ligand pose and affinity prediction:   
+402 Lessons from D3R Grand Challenge 3”. In: Journal of computer-aided molecular design 33.1 (2019),   
+403 pp. 83–91.   
+404 [26] Shengchao Liu et al. “Pre-training Molecular Graph Representation with 3D Geometry”. In: International   
+405 Conference on Learning Representations. 2022. URL: https : / / openreview . net / forum ? id $=$   
+406 xQUe1pOKPam.   
+407 [27] Hannes Stärk et al. “3D Infomax improves GNNs for Molecular Property Prediction”. In: arXiv preprint   
+408 arXiv:2110.04126 (2021).   
+409 [28] Minyi Su et al. “Comparative assessment of scoring functions: the CASF-2016 update”. In: Journal of   
+410 chemical information and modeling 59.2 (2018), pp. 895–913.   
+411 [29] Andrew L Hopkins, Colin R Groom, and Alexander Alex. “Ligand efficiency: a useful metric for lead   
+412 selection.” In: Drug discovery today 9.10 (2004), pp. 430–431.   
+413 [30] Ashish Vaswani et al. “Attention is all you need”. In: Advances in neural information processing systems   
+414 30 (2017).   
+415 [31] Ruibin Xiong et al. “On Layer Normalization in the Transformer Architecture”. In: Proceedings of the   
+416 37th International Conference on Machine Learning. Ed. by Hal Daumé III and Aarti Singh. Vol. 119.   
+417 Proceedings of Machine Learning Research. PMLR, July 2020, pp. 10524–10533.   
+418 [32] Guolin Ke, Di He, and Tie-Yan Liu. “Rethinking Positional Encoding in Language Pre-training”. In:   
+419 International Conference on Learning Representations. 2020.   
+420 [33] Philipp Dufter, Martin Schmitt, and Hinrich Schütze. “Position information in transformers: An overview”.   
+421 In: arXiv preprint arXiv:2102.11090 (2021).   
+422 [34] Muhammed Shuaibi et al. “Rotation invariant graph neural networks using spin convolutions”. In: arXiv   
+423 preprint arXiv:2106.09575 (2021).   
+424 [35] John Jumper et al. “Highly accurate protein structure prediction with AlphaFold”. In: Nature 596.7873   
+425 (2021), pp. 583–589.   
+426 [36] Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. “E (n) equivariant graph neural networks”.   
+427 In: International Conference on Machine Learning. PMLR. 2021, pp. 9323–9332.   
+428 [37] Abien Fred Agarap. “Deep learning using rectified linear units (relu)”. In: arXiv preprint   
+429 arXiv:1803.08375 (2018).   
+430 [38] Sereina Riniker and Gregory A Landrum. “Better informed distance geometry: using what we know   
+431 to improve conformation generation”. In: Journal of chemical information and modeling 55.12 (2015),   
+432 pp. 2562–2574.   
+433 [39] Thomas A Halgren. “Merck molecular force field. I. Basis, form, scope, parameterization, and perfor  
+434 mance of MMFF94”. In: Journal of computational chemistry 17.5-6 (1996), pp. 490–519.   
+435 [40] Greg Landrum et al. RDKit: A software suite for cheminformatics, computational chemistry, and predictive   
+436 modeling. 2013.   
+437 [41] Helen M Berman et al. “The protein data bank”. In: Nucleic acids research 28.1 (2000), pp. 235–242.   
+438 [42] Vincent Le Guilloux, Peter Schmidtke, and Pierre Tuffery. “Fpocket: an open source platform for ligand   
+439 pocket detection”. In: BMC bioinformatics 10.1 (2009), pp. 1–11.   
+440 [43] Gregor Simm and Jose Miguel Hernandez-Lobato. “A Generative Model for Molecular Distance Geome  
+441 try”. In: International Conference on Machine Learning. PMLR. 2020, pp. 8949–8958.   
+442 [44] Minkai Xu et al. “Learning Neural Generative Dynamics for Molecular Conformation Generation”. In:   
+443 International Conference on Learning Representations. 2020.   
+444 [45] Elman Mansimov et al. “Molecular geometry prediction using a deep generative graph neural network”.   
+445 In: Scientific reports 9.1 (2019), pp. 1–13.   
+446 [46] Octavian Ganea et al. “Geomol: Torsional geometric generation of molecular 3d conformer ensembles”.   
+447 In: Advances in Neural Information Processing Systems 34 (2021).   
+448 [47] Rainer Storn and Kenneth Price. “Differential evolution–a simple and efficient heuristic for global   
+449 optimization over continuous spaces”. In: Journal of global optimization 11.4 (1997), pp. 341–359.   
+450 [48] Zhenqin Wu et al. “MoleculeNet: a benchmark for molecular machine learning”. In: Chemical science   
+451 9.2 (2018), pp. 513–530.   
+452 [49] Kevin Yang et al. “Analyzing learned molecular representations for property prediction”. In: Journal of   
+453 chemical information and modeling 59.8 (2019), pp. 3370–3388.   
+454 [50] Zhaoping Xiong et al. “Pushing the boundaries of molecular representation for drug discovery with the   
+455 graph attention mechanism”. In: Journal of medicinal chemistry 63.16 (2019), pp. 8749–8760.   
+456 [51] Shengchao Liu, Mehmet F Demirel, and Yingyu Liang. “N-gram graph: Simple unsupervised representa  
+457 tion for graphs, with applications to molecules”. In: Advances in neural information processing systems   
+458 32 (2019).   
+459 [52] Tianqi Chen and Carlos Guestrin. “Xgboost: A scalable tree boosting system”. In: Proceedings of the   
+460 22nd acm sigkdd international conference on knowledge discovery and data mining. 2016, pp. 785–794.   
+[53] g   
+462 Conference on Machine Learning. PMLR. 2021, pp. 9558–9568.   
+463 [54] Simon Axelrod and Rafael Gomez-Bombarelli. “GEOM, energy-annotated molecular conformations for   
+464 property prediction and molecular generation”. In: Scientific Data 9.1 (2022), pp. 1–14.   
+465 [55] Minkai Xu et al. “An end-to-end framework for molecular conformation generation via bilevel program  
+466 ming”. In: International Conference on Machine Learning. PMLR. 2021, pp. 11537–11547.   
+467 [56] Shitong Luo et al. “Predicting Molecular Conformation via Dynamic Graph Score Matching”. In:   
+468 Advances in Neural Information Processing Systems 34 (2021).   
+469 [57] Jinhua Zhu et al. “Direct molecular conformation generation”. In: arXiv preprint arXiv:2202.01356   
+470 (2022).   
+471 [58] Minkai Xu et al. “GeoDiff: A Geometric Diffusion Model for Molecular Conformation Generation”. In:   
+472 International Conference on Learning Representations. 2022.   
+473 [59] Agata Krasowski et al. “DrugPred: a structure-based approach to predict protein druggability developed   
+474 using an extensive nonredundant data set”. In: Journal of chemical information and modeling 51.11   
+475 (2011), pp. 2829–2842.   
+476 [60] Jui-Hung Yuan et al. “Druggability assessment in TRAPP using machine learning approaches”. In:   
+477 Journal of Chemical Information and Modeling 60.3 (2020), pp. 1685–1699.   
+478 [61] Oscar Méndez-Lucio et al. “A geometric deep learning approach to predict binding conformations of   
+479 bioactive molecules”. In: Nature Machine Intelligence 3.12 (2021), pp. 1033–1039.   
+480 [62] Zhihai Liu et al. “PDB-wide collection of binding data: current status of the PDBbind database”. In:   
+481 Bioinformatics 31.3 (2015), pp. 405–412.   
+482 [63] Oleg Trott and Arthur J Olson. “AutoDock Vina: improving the speed and accuracy of docking with a   
+483 new scoring function, efficient optimization, and multithreading”. In: Journal of computational chemistry   
+484 31.2 (2010), pp. 455–461.   
+485 [64] Jerome Eberhardt et al. “AutoDock Vina 1.2. 0: New docking methods, expanded force field, and python   
+486 bindings”. In: Journal of Chemical Information and Modeling 61.8 (2021), pp. 3891–3898.   
+487 [65] Rodrigo Quiroga and Marcos A Villarreal. “Vinardo: A scoring function based on autodock vina improves   
+488 scoring, docking, and virtual screening”. In: PloS one 11.5 (2016), e0155183.   
+489 [66] David Ryan Koes, Matthew P Baumgartner, and Carlos J Camacho. “Lessons learned in empirical scoring   
+490 with smina from the CSAR 2011 benchmarking exercise”. In: Journal of chemical information and   
+491 modeling 53.8 (2013), pp. 1893–1904.   
+492 [67] Garrett M Morris et al. “AutoDock4 and AutoDockTools4: Automated docking with selective receptor   
+493 flexibility”. In: Journal of computational chemistry 30.16 (2009), pp. 2785–2791.   
+494 [68] Kristof Schütt et al. “Schnet: A continuous-filter convolutional neural network for modeling quantum   
+495 interactions”. In: Advances in neural information processing systems 30 (2017).   
+496 [69] Nathaniel Thomas et al. “Tensor field networks: Rotation-and translation-equivariant neural networks for   
+497 3d point clouds”. In: arXiv preprint arXiv:1802.08219 (2018).   
+498 [70] Fabian Fuchs et al. “Se (3)-transformers: 3d roto-translation equivariant attention networks”. In: Advances   
+499 in Neural Information Processing Systems 33 (2020), pp. 1970–1981.   
+500 [71] Johannes Gasteiger, Janek Groß, and Stephan Günnemann. “Directional Message Passing for Molecular   
+501 Graphs”. In: International Conference on Learning Representations (ICLR). 2020.   
+502 [72] Johannes Klicpera, Florian Becker, and Stephan Günnemann. “GemNet: Universal Directional Graph   
+503 Neural Networks for Molecules”. In: Advances in Neural Information Processing Systems. 2021.   
+504 [73] Yi Liu et al. “Spherical Message Passing for 3D Molecular Graphs”. In: International Conference on   
+505 Learning Representations. 2022. URL: https://openreview.net/forum?id=givsRXsOt9r.   
+506 [74] Jérémy Desaphy et al. Comparison and druggability prediction of protein–ligand binding sites from   
+507 pharmacophore-annotated cavity shapes. 2012.   
+508 [75] Alexandre Borrel et al. “PockDrug: A model for predicting pocket druggability that overcomes pocket   
+509 estimation uncertainties”. In: Journal of chemical information and modeling 55.4 (2015), pp. 882–895.   
+510 [76] Cheng Wang and Yingkai Zhang. “Improving scoring-docking-screening powers of protein–ligand   
+511 scoring functions using random forest”. In: Journal of computational chemistry 38.3 (2017), pp. 169–   
+512 177.   
+513 [77] Hannes Stärk et al. EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. 2022.
+
+# 514 Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
+
+(b) Did you describe the limitations of your work? [Yes]   
+(c) Did you discuss any potential negative societal impacts of your work? [N/A]   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] The data we used are all from public databases and details in data processing are explained in Appendix. The data, code, and instructions will be made public upon the acceptance of the paper.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] We report all the training details for the experiemnt in Appendix.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We report the mean and std for different runs of experiments in Table 1, Table 2 and Table 4.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] We report the detailed computing resources used for the experiment in Appendix.
+
+38 4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] We discuss all the used datasets in the experiment section 3, datasets and setup part.   
+(b) Did you mention the license of the assets? [Yes] We mention the license for the datasets used in Appendix.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/dev/IfFZr1gl0b/IfFZr1gl0b_content_list.json

@@ -0,0 +1,1097 @@
+[
+    {
+        "type": "text",
+        "text": "Uni-Mol: A Universal 3D Molecular Representation Learning Framework ",
+        "text_level": 1,
+        "bbox": [
+            186,
+            122,
+            813,
+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous Author(s)   \nAffiliation   \nAddress   \nemail ",
+        "bbox": [
+            423,
+            226,
+            578,
+            281
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            318,
+            535,
+            334
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Molecular representation learning (MRL) has gained tremendous attention due to its critical role in learning from limited supervised data for applications like drug design. In most MRL methods, molecules are treated as 1D sequential tokens or 2D topology graphs, limiting their ability to incorporate 3D information for downstream tasks and, in particular, making it almost impossible for 3D geometry prediction or generation. Herein, we propose Uni-Mol, a universal MRL framework that significantly enlarges the representation ability and application scope of MRL schemes. Uni-Mol is composed of two models with the same SE(3)-equivariant transformer architecture: a molecular pretraining model trained by 209M molecular conformations; a pocket pretraining model trained by 3M candidate protein pocket data. The two models are used independently for separate tasks, and are combined when used in protein-ligand binding tasks. By properly incorporating 3D information, Uni-Mol outperforms SOTA in 14/15 molecular property prediction tasks. Moreover, Uni-Mol achieves superior performance in 3D spatial tasks, including protein-ligand binding pose prediction, molecular conformation generation, etc. Finally, we show that Uni-Mol can be successfully applied to the tasks with few-shot data like pocket druggability prediction. The model and data will be made publicly available at https://github.com/dptech-corp/Uni-Mol. ",
+        "bbox": [
+            148,
+            348,
+            766,
+            597
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "19 1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            148,
+            616,
+            310,
+            633
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "20 Recently, representation learning (or pretraining, self-supervised learning) [1, 2, 3] has been prevailing   \n21 in many applications, such as BERT [4] and GPT [5, 6, 7] in Natural Language Processing (NLP),   \n22 ViT [8] in Computer Vision (CV), etc. These applications have a common characteristic: unlabeled   \n23 data is abundant, while labeled data is limited. As a solution, in a typical representation learning   \n24 method, one first adopts a pretraining procedure to learn a good representation from large-scale   \n25 unlabeled data, and then a finetuning scheme is followed to extract more information from limited   \n26 supervised data.   \n27 Applications in the field of drug design share the characteristic that calls for representation learning   \n28 schemes. The chemical space that a drug candidate lies in is vast, while drug-related labeled data is   \n29 limited. Not surprisingly, compared with traditional molecular fingerprint based models [9, 10], recent   \n30 molecular representation learning (MRL) models perform much better in most property prediction   \n31 tasks [11, 12, 13]. However, to further improve the performance and extend the application scope   \n32 of existing MRL models, one is faced with a critical issue. From the perspective of life science, the   \n33 properties of molecules and the effects of drugs are mostly determined by their 3D structures [14,   \n34 15]. In most current MRL methods, one starts with representing molecules as 1D sequential strings,   \n35 such as SMILES [16, 17, 18] and InChI [19, 20, 21], or 2D graphs [22, 11, 23, 12, 24]. This may   \n36 limit their ability to incorporate 3D information for downstream tasks. In particular, this makes it   \n37 almost impossible for 3D geometry prediction or generation, such as, e.g., the prediction of protein  \n38 ligand binding pose [25]. Even though there have been some recent attempts trying to leverage 3D   \n39 information in MRL [26, 27], the performance is less than optimal, possibly due to the small size of   \n40 3D datasets, and 3D positions can not be used as inputs/outputs during finetuning, since they only   \n41 serve as auxiliary information.   \n42 In this work, we propose Uni-Mol, to our best knowledge, the first universal 3D molecular pretraining   \n43 framework, which is derived from large-scale unlabeled data and is able to directly take 3D positions   \n44 as both inputs and outputs. Uni-Mol consists of 3 parts. 1) Backbone. Based on Transformer, the   \n45 invariant spatial positional encoding and pair level representation are added to better capture the 3D   \n46 information. Moreover, an equivariant head is used to directly predict 3D positions. 2) Pretraining.   \n47 We create two large-scale datasets, a 209M molecular conformation dataset and a 3M candidate   \n48 protein pocket dataset, for pretraining 2 models on molecules and protein pockets, respectively.   \n49 For the pretraining tasks, besides masked atom prediction, a 3D position denoising task is used   \n50 for learning 3D spatial representation. 3) Finetuning. According to specific downstream tasks, the   \n51 used pretraining models are different. For example, in molecular property prediction tasks, only the   \n52 molecular pretraining model is used; in protein-ligand binding pose prediction, both two pretraining   \n53 models are used. We refer to Fig. 1 for an overall schematic illustration of the Uni-Mol framework.   \n54 To demonstrate the effectiveness of Uni-Mol, we conduct experiments on a series of downstream   \n55 tasks. In the molecular property prediction tasks, Uni-Mol outperforms SOTA on 14/15 datasets on   \n56 the MoleculeNet benchmark. In 3D geometric tasks, Uni-Mol also achieves superior performance.   \n57 For the pose prediction of protein-ligand complexes, Uni-Mol predicts $8 8 . 0 7 \\%$ binding poses with   \n58 $\\mathrm { R M S D } < = 2 \\bar { \\mathring { \\mathrm { A } } } .$ , $2 2 . 8 1 \\%$ more than popular docking methods, and ranks 1st in the docking power test   \n59 on CASF-2016 [28] benchmark. Regarding molecular conformation generation, Uni-Mol achieves   \n60 SOTA for both Coverage and Matching metrics on GEOM-QM9 and GEOM-Drugs [29]. Moreover,   \n61 Uni-Mol can be successfully applied to tasks with very limited data like pocket druggability prediction.   \n62 ",
+        "bbox": [
+            147,
+            647,
+            825,
+            744
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            145,
+            751,
+            825,
+            902
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7472f8a9be38c66e92230f52e6fcee71f0744478f8fec8fc9c6cfce93c1913d7.jpg",
+        "image_caption": [
+            "Figure 1: Schematic illustration of the Uni-Mol framework. Uni-Mol is composed of two models: a molecular pretraining model trained by 209M molecular 3D conformations; a pocket pretraining model trained by 3M candidate protein pocket data. The two models are used independently for separate tasks, and are combined when used in protein-ligand binding tasks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            215,
+            88,
+            767,
+            332
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            147,
+            430,
+            825,
+            486
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            145,
+            492,
+            825,
+            659
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            147,
+            665,
+            826,
+            790
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "63 2 Uni-Mol Framework ",
+        "text_level": 1,
+        "bbox": [
+            148,
+            824,
+            379,
+            842
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "64 In this section, we introduce the Uni-Mol framework by showing the details of the backbone, the   \n65 pretraining scheme, and the finetuning scheme. We refer to Fig. 2 for a schematic illustration of the   \n66 model architecture. ",
+        "bbox": [
+            147,
+            869,
+            823,
+            911
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/8af14cb1d3c8b880c00008808226d9becf5945578ca9e11487e2d9b74adb8b77.jpg",
+        "image_caption": [
+            "Figure 2: Left: the overall pretraining architecture. Middle: the model inputs, including atoms and spatial positional encoding created by pair Euclidean distance. Right: pair representation and its update process. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            199,
+            99,
+            795,
+            296
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "67 2.1 Backbone ",
+        "text_level": 1,
+        "bbox": [
+            148,
+            378,
+            281,
+            393
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "68 Transformer [30] is widely used as a backbone model in representation learning. However, Trans  \n69 former was originally designed for NLP tasks and cannot handle 3D spatial data directly. To tackle   \n70 this, based on the standard Transformer with Pre-LayerNorm [31] backbone, we introduce several   \n71 modifications.   \n72 Invariant spatial positional encoding Due to its permutationally invariant property, Transformer   \n73 cannot distinguish the positions of inputs without positional encoding. Different with the discrete   \n74 (ordinal) positions used in NLP/CV [32, 33], the positions in 3D space, i.e. coordinates, are continuous   \n75 values. Besides, the positional encoding procedure needs to be invariant under global rotation and   \n76 translation. To achieve that, similar to the relative positional encoding, we simply use Euclidean   \n77 distances of all atom pairs, as well as pair-type aware Gaussian kernels [34]. Formally, the $D$ -channel   \n78 positional encoding of atom pair $i j$ is denoted as ",
+        "bbox": [
+            148,
+            405,
+            825,
+            460
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            147,
+            468,
+            825,
+            565
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a49b9a61cd6a5306588d84fb0771250316d8f2a19e653354bede6db5d52088af.jpg",
+        "text": "$$\n\\pmb { p } _ { i j } = \\{ \\mathcal { G } ( A ( d _ { i j } , t _ { i j } ; \\pmb { a } , \\pmb { b } ) , \\mu ^ { k } , \\sigma ^ { k } ) | k \\in [ 1 , D ] \\} , \\quad \\pmb { \\mathcal { A } } ( d , r ; \\pmb { a } , \\pmb { b } ) = a _ { r } d + b _ { r } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            246,
+            569,
+            748,
+            589
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "79 where $\\begin{array} { r } { \\mathcal { G } ( d , \\mu , \\sigma ) = \\frac { 1 } { \\sigma \\sqrt { 2 \\pi } } e ^ { - \\frac { ( d - \\mu ) ^ { 2 } } { 2 \\sigma ^ { 2 } } } } \\end{array}$ is a Gaussian density function with parameters $\\mu$ and $\\sigma , d _ { i j }$ is the   \n80 Euclidean distance of atom pair $i j$ , and $t _ { i j }$ is the pair-type of atom pair $i j$ . Please note the pair-type   \n81 here is not the chemical bond, and it is determined by the atom types of pair $i j$ . $\\mathcal { A } ( d _ { i j } , t _ { i j } ; \\pmb { a } , \\pmb { b } )$ is   \n82 the affine transformation with parameters $\\textbf { \\em a }$ and $^ { b }$ , it affines $d _ { i j }$ corresponding to its pair-type $t _ { i j }$   \n83 Except $d _ { i j }$ and $t _ { i j }$ , all remaining parameters are trainable and randomly initialized.   \n84 Pair representation By default, Transformer maintains the token(atom) level representation, which   \n85 is later used in finetuning downstream tasks. Nevertheless, as the spatial positions are encoded at   \n86 pair-level, we also maintain the pair-level representation, to better learn the 3D spatial representation.   \n87 Specifically, the pair representation is initialized as the aforementioned spatial positional encoding.   \n88 Then, to update pair representation, we use the atom-to-pair communication via the multi-head Query  \n89 Key product results in self-attention. Formally, the update of $i j$ pair representation is denoted as ",
+        "bbox": [
+            145,
+            594,
+            825,
+            675
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            145,
+            681,
+            826,
+            766
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1f68cf863ece0e5d68c4d8e14d5238147e471b0362a6a60d2ad7abfb551fbf68.jpg",
+        "text": "$$\n\\pmb { q } _ { i j } ^ { 0 } = { \\pmb { p } } _ { i j } M , \\quad \\pmb { q } _ { i j } ^ { l + 1 } = \\pmb { q } _ { i j } ^ { l } + \\{ \\frac { { \\pmb { Q } } _ { i } ^ { l , h } ( \\pmb { K } _ { j } ^ { l , h } ) ^ { T } } { \\sqrt { d } } | h \\in [ 1 , H ] \\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
+            768,
+            692,
+            808
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where 90 $\\pmb { q } _ { i j } ^ { l }$ is the pair representation of atom pair $i j$ in $l$ -th layer, $H$ is the number of attention heads, 91 $d$ is the dimension of hidden representations, $Q _ { i } ^ { l , h } ( K _ { j } ^ { l , h } )$ is the Query (Key) of the $i$ -th ( $j$ -th) atom 92 in the $l$ -th layer $h$ -th head, and $M \\in \\mathbb { R } ^ { D \\times H }$ is the projection matrix to make the representation the 93 same shape as multi-head Query-Key product results. ",
+        "bbox": [
+            145,
+            813,
+            825,
+            877
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "94 Besides, to leverage 3D information in the atom representation, we also introduce the pair-to-atom   \n95 communication, by using the pair representation as the bias term in self-attention. Formally, the ",
+        "bbox": [
+            147,
+            882,
+            826,
+            912
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e7c63e8be8917ed8fedde2aebe4f2bf81f6cf8c779cd7540df4abd20b06a0334.jpg",
+        "text": "$$\n\\mathrm { A t t e n t i o n } ( Q _ { i } ^ { l , h } , { \\bf K } _ { j } ^ { l , h } , { \\bf V } _ { j } ^ { l , h } ) = \\mathrm { s o f t m a x } ( \\frac { Q _ { i } ^ { l , h } ( { \\bf K } _ { j } ^ { l , h } ) ^ { T } } { \\sqrt { d } } + { \\bf q } _ { i j } ^ { l - 1 , h } ) { \\bf V } _ { j } ^ { l , h } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            264,
+            112,
+            730,
+            151
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "97 where $V _ { . j } ^ { l , h }$ is the Value of the $j$ -th atom in the $l$ -th layer $h$ -th head. The pair representation and   \n98 atom-pair communication are firstly proposed in the Evoformer in AlphaFold [35], but the cost of   \n99 Evoformer is extremely large. In Uni-Mol, as we keep them as simple as possible, the extra cost of   \n100 maintaining pair representation is negligible.   \n101 SE(3)-Equivariance coordinate head With 3D spatial positional encoding and pair representation,   \n102 the model can learn a good 3D representation. However, it still lacks the ability to directly output co  \n103 ordinates, which is essential in 3D spatial tasks. To this end, we add a simple SE(3)-equivariance head   \n104 to Uni-Mol. Following the idea of EGNN [36], the design of SE(3)-equivariance head is denoted as ",
+        "bbox": [
+            143,
+            157,
+            825,
+            217
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            142,
+            224,
+            825,
+            281
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/21eeca16ff799e531078e12b63f20e2f89134c4425aa2f5101be9b60b80ded0f.jpg",
+        "text": "$$\n\\hat { \\pmb x } _ { i } = { \\pmb x } _ { i } + \\sum _ { j = 1 } ^ { n } \\frac { ( { \\pmb x } _ { i } - { \\pmb x } _ { j } ) c _ { i j } } { n } , \\quad c _ { i j } = \\mathrm { R e L U } ( ( { \\pmb q } _ { i j } ^ { L } - { \\pmb q } _ { i j } ^ { 0 } ) U ) W ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            287,
+            287,
+            710,
+            330
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "105 where $n$ is the number of total atoms, $L$ is the number of layers in model, $\\pmb { x } _ { i } \\in \\mathbb { R } ^ { 3 }$ is the input   \n106 coordinate of $i$ -th atom, and $\\hat { \\pmb { x } } _ { i } \\in \\mathbb { R } ^ { 3 }$ is the output coordinate of $i$ -th atom, $\\mathrm { R e L U } ( y ) = \\operatorname* { m a x } ( 0 , y )$   \n107 is Rectified Linear Unit [37], $U \\in \\mathbb { R } ^ { H \\times H }$ and $\\dot { \\boldsymbol { W } } \\in \\mathbb { R } ^ { H \\times 1 }$ are the projection matrices to convert   \n108 pair representation to scalar. ",
+        "bbox": [
+            142,
+            338,
+            826,
+            395
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "09 2.2 Pretraining ",
+        "text_level": 1,
+        "bbox": [
+            155,
+            411,
+            294,
+            426
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "110 For the purpose of pretraining, we generate two large-scale datasets, one composed of 3D structures   \n111 of organic molecules, and another composed of 3D structures of candidate protein pockets. Then,   \n112 two models are pretrained using these two datasets, respectively. As pockets are directly involved   \n113 in many drug design tasks, intuitively, the pretraining on candidate protein pockets can boost the   \n114 performance of tasks related to protein-ligand structures and interactions.   \n115 The molecular pretraining dataset is based on multiple public datasets (See Appendix ?? for more   \n116 information). After normalizing and deduplicating, it contains about 19M molecules. To generate   \n117 3D conformations, we use ETKGD [38] with Merck Molecular Force Field [39] optimization   \n118 in RDKit [40] to randomly generate 10 conformations for each molecule. We also generate an   \n119 additional 2D conformation (based on the molecular graph), to avoid some rare cases that fail to   \n120 generate 3D conformations.   \n121 The protein pocket pretraining dataset is derived from the Protein Data Bank (RCSB PDB 1) [41], a   \n122 collection of 180K 3D structures of proteins. To extract candidate pockets, we first clean the data   \n123 by adding the missing side chains and hydrogen atoms; then we use Fpocket [42] to detect possible   \n124 binding pockets of the proteins; and finally, we filter pockets by the number of residues in contact   \n125 with and retains water molecules in the pocket. In this way, We collect a dataset composed of 3.2M   \n126 candidate pockets for pretraining.   \n127 Self-supervised task is vitally important for effective learning from large-scale unlabeled data.   \n128 For example, the masked token prediction task in BERT [4] encourages the model to learn the   \n129 contextual information. Similar to BERT, the masked atom prediction task is used in Uni-Mol.   \n130 For each molecule/pocket, we add a special atom [CLS], whose coordinate is the center of all   \n131 atoms, to represent the whole molecule/pocket. However, as 3D spatial positional encoding leaks   \n132 chemical bonds, atom types could be inferred easily, and therefore, the masked atom prediction   \n133 cannot encourage the model to learn useful information. To tackle this, as well as learning from 3D   \n134 information, we design a 3D position denoising task. Particularly, uniform noises of $[ - 1 \\bar { \\mathrm { \\bf A } } , 1 \\bar { \\mathrm { \\bf A } } ]$ are   \n135 added to the random $15 \\%$ atom coordinates, then the spatial positional encoding is calculated based   \n136 on corrupted coordinates. In this way, the masked atom prediction task becomes non-trivial. Besides,   \n137 two additional heads are used to recover the correct spatial positions. 1) Pair-distance prediction.   \n138 Based on pair-representation, the model needs to predict the correct Euclidean distances of the atoms   \n139 pairs with corrupted coordinates. 2) Coordinate prediction. Based on SE(3)-Equivariance coordinate   \n140 head, the model needs to predict the correct coordinates for the atoms with corrupted coordinates.   \n141 Both 2 pretraining models use the same self-supervised tasks described above, and Figure 2 is the   \n142 illustration of the overall pretraining framework. For the detailed configurations of pretraining, please   \n143 refer to Appendix ??. ",
+        "bbox": [
+            140,
+            436,
+            825,
+            507
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            140,
+            512,
+            825,
+            595
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            140,
+            602,
+            825,
+            685
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            143,
+            691,
+            826,
+            887
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            142,
+            92,
+            825,
+            133
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2.3 Finetuning ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            150,
+            289,
+            165
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "145 To be consistent with pretraining, we use the same data prepossessing pipeline during finetuning.   \n146 For molecules, as multiple random conformations can be generated in a short time, we can use them   \n147 as data augmentation in finetuning to improve performance and robustness. Some molecules may fail   \n148 to generate 3D conformations, and we use their molecular graph as 2D conformation. For tasks that   \n149 provide atom coordinates, we use them directly and skip the 3D conformation generation process.   \n150 As there are 2 pretraining models and several types of downstream tasks, we should properly use   \n151 them in the finetuning stage. According to the task types, and the involvement of protein or ligand,   \n152 we can categorize them as follow.   \n153 Non-3D prediction tasks These tasks do not need to output 3D conformations. Examples include   \n154 molecular property prediction, molecule similarity, pocket druggability prediction, protein-ligand   \n155 binding affinity prediction, etc. Similar to NLP/CV, we can simply use the representation of [CLS]   \n156 which represents the whole molecule/pocket, or the mean representation of all atoms, with a linear   \n157 head to finetune on downstream tasks. In the tasks with pocket-molecule pair, we can concatenate   \n158 their [CLS] representations, and then finetune with linear head. ",
+        "bbox": [
+            140,
+            170,
+            825,
+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            140,
+            290,
+            825,
+            372
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3D prediction tasks of molecules or pockets These tasks need to predict a 3D conformation of the input, such as molecular conformation generation. Different with the fast conformation generation method used in Uni-Mol, molecular conformation generation task usually requires running advanced sampling and semi-empirical density functional theory (DFT) to account for the ensemble of 3D conformers that are accessible to a molecule, and this is very time-consuming. Therefore, there are many recent works that train the model to fast generate conformations from molecular graph [43, 44, 45, 46]. While in Uni-Mol, this task straightforwardly becomes a conformation optimization task: generate a new conformation based on a different input conformation. Specifically, in finetuning, the model supervised learns the mapping from Uni-Mol generated conformations to the labeled conformations. Moreover, the optimized conformations can be generated end-to-end by SE(3)-Equivariance coordinate head. ",
+        "bbox": [
+            166,
+            383,
+            825,
+            535
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "170 3D prediction tasks of protein-ligand pairs This is one of the most important tasks in structure  \n171 based drug design. The task is to predict the complex structure of a protein binding site and a   \n172 molecular ligand. Besides the conformation changes of the pocket and the molecule themselves, we   \n173 also need to consider how the molecule lays in the pocket, that is, the additional 6 degrees (3 rotations   \n174 and 3 translations) of freedom of a rigid movement. In principle, with Uni-Mol, we can predict the   \n175 complex conformation by the SE(3)-Equivariant coordinate head in an end-to-end fashion. However,   \n176 this is unstable as it is very sensitive to the initial docking positions of molecular ligand. Herein, to   \n177 get rid of the initial positions, we use a scoring function based optimization method in this paper. In   \n178 particular, the molecular representation and pocket representation are firstly obtained from their own   \n179 pretraining models by their own conformations; then, their representations are concatenated as the   \n180 input of an additional 4-layer Uni-Mol decoder, which is finetuned to learn the pair distances of all   \n181 atoms in molecule and pocket. With the predicted pair-distance matrix as the scoring function, we   \n182 use a simple differential evolution algorithm [47] to sample and optimize the complex conformations.   \n183 More details can be found in Appendix ??. ",
+        "bbox": [
+            140,
+            545,
+            826,
+            738
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "184 3 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            143,
+            758,
+            312,
+            775
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To verify the effectiveness of our proposed Uni-Mol model, we conduct extensive experiments on multiple downstream tasks, including molecular property prediction, molecular conformation generation, pocket property prediction, and protein-ligand binding pose prediction. Besides, we also conduct several ablation studies. Due to space restrictions, we leave the detailed experimental settings and ablation studies to Appendix ??. ",
+        "bbox": [
+            174,
+            784,
+            823,
+            853
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1 Molecular property prediction ",
+        "text_level": 1,
+        "bbox": [
+            171,
+            863,
+            424,
+            878
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "191 Datasets and setup MoleculeNet [48] is a widely used benchmark for molecular property   \n192 prediction, including datasets focusing on different levels of properties of molecules, from quantum   \n193 mechanics and physical chemistry to biophysics and physiology. Following previous work GEM [13],   \n194 we use scaffold splitting for the dataset and report the mean and standard deviation of the results   \n195 for three random seeds.   \n196 Baselines We compare Uni-Mol with multiple baselines, including supervised and pretraining   \n197 baselines. D-MPNN [49] and AttentiveFP [50] are supervised GNNs methods. N-gram [51],   \n198 PretrainGNN [22], GROVER [11], GraphMVP [26], MolCLR [12], and GEM [13] are pretraining   \n199 methods. N-gram embeds the nodes in the graph and assembles them in short walks as the graph   \n200 representation. Random Forest and XGBoost [52] are used as the predictor for downstream tasks. ",
+        "bbox": [
+            148,
+            883,
+            823,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/51ced12fcc504b10cc1314b13b9ca017f8a0e4116b98e8ef08c0699642948770.jpg",
+        "table_caption": [
+            "Table 1: Uni-Mol performance on molecular property prediction classification tasks "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"11\">Classification (ROC-AUC %,higher is better ↑)</td></tr><tr><td>Datasets #Molecules # Tasks</td><td>BBBP 2039 1</td><td>BACE 1513 1</td><td>ClinTox 1478 2</td><td>Tox21 7831 12</td><td>ToxCast 8575 617</td><td>SIDER 1427 27</td><td>HIV 41127 1</td><td>PCBA 437929 128</td><td>MUV 93087 17</td></tr><tr><td>D-MPNN</td><td>71.0(0.3)</td><td>80.9(0.6)</td><td>90.6(0.6)</td><td>75.9(0.7)</td><td>65.5(0.3)</td><td>57.0(0.7)</td><td>77.1(0.5)</td><td>86.2(0.1)</td><td>78.6(1.4)</td></tr><tr><td>Attentive FP</td><td>64.3(1.8)</td><td>78.4(0.022)</td><td>84.7(0.3)</td><td>76.1(0.5)</td><td>63.7(0.2)</td><td>60.6(3.2)</td><td>75.7(1.4)</td><td>80.1(1.4)</td><td>76.6(1.5)</td></tr><tr><td>N-GramRF</td><td>69.7(0.6)</td><td>77.9(1.5)</td><td>77.5(4.0)</td><td>74.3(0.4)</td><td></td><td>66.8(0.7)</td><td>77.2(0.1)</td><td></td><td>76.9(0.7)</td></tr><tr><td>N-GramxGB</td><td>69.1(0.8)</td><td>79.1(1.3)</td><td>87.5(2.7)</td><td>75.8(0.9)</td><td></td><td>65.5(0.7)</td><td>78.7(0.4)</td><td></td><td>74.8(0.2)</td></tr><tr><td>PretrainGNN</td><td>68.7(1.3)</td><td>84.5(0.7)</td><td>72.6(1.5)</td><td>78.1(0.6)</td><td>65.7(0.6)</td><td>62.7(0.8)</td><td>79.9(0.7)</td><td>86.0(0.1)</td><td>81.3(2.1)</td></tr><tr><td>GROVERbase</td><td>70.0(0.1)</td><td>82.6(0.7)</td><td>81.2(3.0)</td><td>74.3(0.1)</td><td>65.4(0.4)</td><td>64.8(0.6) 65.4(0.1)</td><td>62.5(0.9) 68.2(1.1)</td><td>76.5(2.1)</td><td>67.3(1.8)</td></tr><tr><td>GROVERlarge</td><td>69.5(0.1) 72.4(1.6)</td><td>81.0(1.4)</td><td>76.2(3.7)</td><td>73.5(0.1)</td><td>65.3(0.5) 63.1(0.4)</td><td></td><td></td><td>83.0(0.4)</td><td>67.3(1.8)</td></tr><tr><td>GraphMVP</td><td>72.2(2.1)</td><td>81.2(0.9) 82.4(0.9)</td><td>79.1(2.8) 91.2(3.5)</td><td>75.9(0.5) 75.0(0.2)</td><td></td><td>63.9(1.2) 58.9(1.4)</td><td>77.0(1.2) 78.1(0.5)</td><td></td><td>77.7(0.6)</td></tr><tr><td>MolCLR GEM</td><td>72.4(0.4)</td><td>85.6(1.1)</td><td>90.1(1.3)</td><td>78.1(0.1)</td><td>69.2(0.4)</td><td>67.2(0.4)</td><td>80.6(0.9)</td><td>86.6(0.1)</td><td>79.6(1.9) 81.7(0.5)</td></tr><tr><td>Uni-Mol</td><td>72.9(0.6)</td><td>85.7(0.2)</td><td>91.9(1.8)</td><td>79.6(0.5)</td><td>69.6(0.1)</td><td>65.9(1.3)</td><td>80.8(0.3)</td><td>88.5(0.1)</td><td>82.1(1.3)</td></tr></table>",
+        "bbox": [
+            173,
+            113,
+            825,
+            310
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3ff1e0f32dea04dbebbd3b676ebb7a80e6d3862a06856cf1a397fba6e8fcde18.jpg",
+        "table_caption": [
+            "Table 2: Uni-Mol performance on molecular property prediction regression tasks "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"6\">Regression (lower is better ↓)</td></tr><tr><td colspan=\"3\">RMSE</td><td colspan=\"3\">MAE</td></tr><tr><td>Datasets # Molecules</td><td>ESOL 1128</td><td>FreeSolv 642</td><td>Lipo 4200</td><td>QM7 6830</td><td>QM8 21786</td><td>QM9 133885</td></tr><tr><td>#Tasks D-MPNN</td><td>1</td><td>1</td><td>1</td><td>1</td><td>12</td><td>3</td></tr><tr><td></td><td>1.050(0.008)</td><td>2.082(0.082)</td><td>0.683(0.016)</td><td>103.5(8.6)</td><td>0.0190(0.0001)</td><td>0.00814(0.00001)</td></tr><tr><td>Attentive FP</td><td>0.877(0.029)</td><td>2.073(0.183)</td><td>0.721(0.001)</td><td>72.0(2.7)</td><td>0.0179(0.001)</td><td>0.00812(0.00001)</td></tr><tr><td>N-GramRF</td><td>1.074(0.107)</td><td>2.688(0.085)</td><td>0.812(0.028)</td><td>92.8(4.0)</td><td>0.0236(0.0006)</td><td>0.01037(0.00016)</td></tr><tr><td>N-GramxGB</td><td>1.083(0.082)</td><td>5.061(0.744)</td><td>2.072(0.030)</td><td>81.9(1.9)</td><td>0.0215(0.0005)</td><td>0.00964(0.00031)</td></tr><tr><td>PretrainGNN</td><td>1.100(0.006)</td><td>2.764(0.002)</td><td>0.739(0.003)</td><td>113.2(0.6)</td><td>0.0200(0.0001)</td><td>0.00922(0.00004)</td></tr><tr><td>GROVERbase</td><td>0.983(0.090)</td><td>2.176(0.052)</td><td>0.817(0.008)</td><td>94.5(3.8)</td><td>0.0218(0.0004)</td><td>0.00984(0.00055)</td></tr><tr><td>GROVERlarge</td><td>0.895(0.017)</td><td>2.272(0.051)</td><td>0.823(0.010)</td><td>92.0(0.9)</td><td>0.0224(0.0003)</td><td>0.00986(0.00025)</td></tr><tr><td>GraphMVP</td><td>1.029(0.033)</td><td></td><td>0.681(0.010)</td><td></td><td></td><td></td></tr><tr><td>MoiCLR</td><td>1.271(0.040)</td><td>2.594(0.249)</td><td>0.691(0.004)</td><td>66.8(2.3)</td><td>0.0178(0.0003)</td><td></td></tr><tr><td>GEM</td><td>0.798(0.029)</td><td>1.877(0.094)</td><td>0.660(0.008)</td><td>58.9(0.8)</td><td>0.0171(0.0001)</td><td>0.00746(0.00001)</td></tr><tr><td>Uni-Mol</td><td>0.788(0.029)</td><td>1.620(0.035)</td><td>0.603(0.010)</td><td>41.8(0.2)</td><td>0.0156(0.0001)</td><td>0.00467(0.00004)</td></tr></table>",
+        "bbox": [
+            173,
+            347,
+            825,
+            558
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            142,
+            587,
+            825,
+            628
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            143,
+            635,
+            825,
+            705
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results Table 1 and Table 2 show the experiment results of Uni-Mol and competitive baselines, where the best results are marked in bold. Most baseline results are from the paper of GEM, except for the recent works GraphMVP and MolCLR. The results of GraphMVP are from its paper. As MolCLR uses a different data split setting (without considering chirality), we rerun it with the same data split setting as other baselines. From the results, we can summarize them as follows: 1) overall, Uni-Mol outperforms baselines on almost all downstream datasets. 2) In solubility (ESOL, Lipo), free energy (FreeSolv), and quantum mechanical (QM7, QM8, QM9) properties prediction tasks, Uni-Mol is significantly better than baselines. As 3D information is critical in these properties, it indicates that Uni-Mol can learn a better 3D representation than other baselines. 3) Uni-Mol fails to beat SOTA on the SIDER dataset. After investigation, we find Uni-Mol fails to generate 3D conformations (and rollbacks to 2D graphs) for many molecules (like natural products and peptides) in SIDER. Therefore, due to the missing 3D information, it is reasonable that Uni-Mol cannot outperform others. ",
+        "bbox": [
+            166,
+            710,
+            825,
+            877
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "213 In summary, by better utilizing 3D information in pretraining, Uni-Mol outperforms all previous   \n214 MRL models in almost all property prediction tasks. ",
+        "bbox": [
+            145,
+            883,
+            825,
+            911
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/f5d8fc99db771b4f435f1d3b7cc46777ef93a93b26f893ec1912a9f2020a39e2.jpg",
+        "table_caption": [
+            "Table 3: Uni-Mol performance on molecular conformation generation "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Dataset Methods</td><td colspan=\"4\">QM9</td><td colspan=\"4\">Drugs</td></tr><tr><td colspan=\"2\">COV(↑, %)</td><td colspan=\"2\">MAT(↓, A)</td><td colspan=\"2\">COV(↑,%)</td><td colspan=\"2\">MAT(↓,A)</td></tr><tr><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td><td>Mean</td><td>Median</td></tr><tr><td>RDKit</td><td>83.26</td><td>90.78</td><td>0.3447</td><td>0.2935</td><td>60.91</td><td>65.70</td><td>1.2026</td><td>1.1252</td></tr><tr><td>CVGAE</td><td>0.09</td><td>0.00</td><td>1.6713</td><td>1.6088</td><td>0.00</td><td>0.00</td><td>3.0702</td><td>2.9937</td></tr><tr><td>GraphDG</td><td>73.33</td><td>84.21</td><td>0.4245</td><td>0.3973</td><td>8.27</td><td>0.00</td><td>1.9722</td><td>1.9845</td></tr><tr><td>CGCF</td><td>78.05</td><td>82.48</td><td>0.4219</td><td>0.3900</td><td>53.96</td><td>57.06</td><td>1.2487</td><td>1.2247</td></tr><tr><td>ConfVAE</td><td>80.42</td><td>85.31</td><td>0.4066</td><td>0.3891</td><td>53.14</td><td>53.98</td><td>1.2392</td><td>1.2447</td></tr><tr><td>ConfGF</td><td>88.49</td><td>94.13</td><td>0.2673</td><td>0.2685</td><td>62.15</td><td>70.93</td><td>1.1629</td><td>1.1596</td></tr><tr><td>GeoMol</td><td>71.26</td><td>72.00</td><td>0.3731</td><td>0.3731</td><td>67.16</td><td>71.71</td><td>1.0875</td><td>1.0586</td></tr><tr><td>DGSM</td><td>91.49</td><td>95.92</td><td>0.2139</td><td>0.2137</td><td>78.73</td><td>94.39</td><td>1.0154</td><td>0.9980</td></tr><tr><td>DMCG</td><td>96.34</td><td>99.53</td><td>0.2065</td><td>0.2003</td><td>96.69</td><td>100.00</td><td>0.7223</td><td>0.7236</td></tr><tr><td>GeoDiff</td><td>90.07</td><td>93.39</td><td>0.2090</td><td>0.1988</td><td>89.13</td><td>97.88</td><td>0.8629</td><td>0.8529</td></tr><tr><td>Uni-Mol</td><td>98.68</td><td>100.00</td><td>0.1806</td><td>0.1510</td><td>92.69</td><td>100.00</td><td>0.6596</td><td>0.6215</td></tr></table>",
+        "bbox": [
+            215,
+            112,
+            781,
+            311
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "15 3.2 Molecular conformation generation ",
+        "text_level": 1,
+        "bbox": [
+            156,
+            338,
+            460,
+            352
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets and setup Following the settings in previous works [44, 53], we use GEOM-QM9 and GEOM-Drugs [54] dataset to perform conformation generation experiments. As described in Sec. 2.3, in this task, Uni-Mol optimizes its generative conformations to the labeled ones. To construct the finetuning data, we first randomly generate 10 conformations. Then, for each of them, we calculate the RMSD between it and labeled conformations, and choose the one with minimal RMSD as its optimizing target. For the inference in the test set, we generate the same number of conformations (twice the number of labeled conformations) as previous works do. And we use the same metrics, Coverage (COV) and Matching (MAT). Higher COV means better diversity, while lower MAT means higher accuracy. ",
+        "bbox": [
+            173,
+            356,
+            825,
+            482
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines We compare Uni-Mol with 10 competitive baselines. RDKit [38] is a traditional conformation generation method based on distance geometry. The rest baseline can be categorized into two classes. GraphDG [43], CGCF[44], ConfVAE [55], ConfGF [53], and DGSM [56] combine generative models with distance geometry, which first generates interatomic distance matrices and then iteratively generates atomic coordinates. CVGAE [45], GeoMol [46], DMCG [57], and GeoDiff [58] directly generate atomic coordinates. ",
+        "bbox": [
+            174,
+            483,
+            825,
+            566
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results The results are shown in Table 3. We report the mean and median of COV and MAT on GEOM-QM9 and GEOM-Drugs datasets. ConfVAE [55], GeoMol[46], DGSM [56], DMCG [57], GeoDiff’s [58] results are from their papers, respectively. Other baseline results are from ConfGF’s paper. As shown in Table 3, Uni-Mol exceeds existing baselines in both COV and MAT metrics on both datasets. Although Uni-Mol outperforms SOTA, we suspect that the above benchmark cannot satisfy the real-world demand of conformation generation tasks in the field of drug design. Since the ensemble of molecular conformations in biological systems is different from that in a vacuum or general solution environment, the ensemble of bioactive conformation must be considered in order to apply the conformation generation model in the context of drug design, while the GEOM dataset just ignores this. Establishing a reasonable benchmark will be crucial in this research direction. ",
+        "bbox": [
+            171,
+            574,
+            825,
+            713
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3 Pocket property prediction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            723,
+            400,
+            738
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets and setup Druggability, the ability of a candidate protein pocket to produce stable binding to a specific molecular ligand, is one of the most critical properties of a candidate protein pocket. However, this task is very challenging due to the very limited supervised data. For example, NRDLD [59], a commonly used dataset, only contains 113 data samples. Therefore, besides NRDLD, we construct a regression dataset for benchmarking pocket property prediction performance. Specifically, based on Fpocket tool, we calculate Fpocket Score, Druggability Score, Total SASA, and Hydrophobicity Score for the selected 164,586 candidate pockets. Model is trained to predict these scores. To avoid leaking, the selected pockets are not overlapped with the candidate protein pocket dataset used in Uni-Mol pretraining. ",
+        "bbox": [
+            173,
+            742,
+            826,
+            867
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "251 Baselines On the NRDLD dataset, we compare Uni-Mol with 6 previous methods evaluated in [60].   \n252 Accuracy, recall, precision, and F1-score are used as metrics for this classification task. On our   \n253 created benchmark dataset, as there are no appropriate baselines, we use an additional Uni-Mol model ",
+        "bbox": [
+            143,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/763bef9dd96b32519e24f05b77183583061f3d986cae62b423c282f52d2a3dac.jpg",
+        "table_caption": [
+            "Table 4: Uni-Mol performance on pocket property prediction "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"8\">Classification (higher is better ↑)</td><td colspan=\"2\">Regression (lower is better ↓) Fpocket Scores</td></tr><tr><td></td><td>Methods |Cavity-DrugScore</td><td>Volsite DrugPred PockDrug</td><td></td><td></td><td></td><td></td><td>TRAPP-CNN Uni-Mol|Methods</td><td>Uni-Molrandom</td><td>Uni-Mol</td></tr><tr><td>Accuracy</td><td>0.82</td><td>0.89</td><td>0.89</td><td>0.865</td><td>0.946</td><td>0.946</td><td>|MSEFpocket</td><td>[0.621(0.004)</td><td>0.551(0.008)</td></tr><tr><td>Recall</td><td></td><td></td><td></td><td>0.957</td><td>0.913</td><td>1.000</td><td>MSEDrggability</td><td>0.601(0.02)</td><td>0.499(0.007)</td></tr><tr><td>Precision</td><td></td><td>=</td><td></td><td>0.846</td><td>1.000</td><td>0.920</td><td>MSETotal SASA</td><td>0.197(0.008)</td><td>0.129(0.005)</td></tr><tr><td>F1-score</td><td></td><td></td><td></td><td>0.898</td><td>0.955</td><td>0.958</td><td>MSEHydrophobicity</td><td>0.0357(0.017)</td><td>0.0127(0.0005)</td></tr></table>",
+        "bbox": [
+            176,
+            112,
+            821,
+            200
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "without pretraining, denoted as $\\mathrm { U n i - M o l _ { r a n d o m } }$ , to check the performance brought by pretraining on pocket property prediction. MSE (mean square error) is used as the metric. ",
+        "bbox": [
+            163,
+            226,
+            821,
+            253
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results As shown in Table 4, Uni-Mol shows the best accuracy, recall, and F1-score on NRDLD, the few-show dataset. In our created benchmark dataset, the pretraining Uni-Mol model largely outperforms the non-pretraining one on all four scores. This indicates that pretraining on candidate protein pockets indeed brings improvement in pocket property prediction tasks. ",
+        "bbox": [
+            173,
+            256,
+            825,
+            311
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Unlike Molecular property prediction, due to the very limited supervised data, pocket property prediction gained much less attention. Therefore, we also plan to release our created benchmark dataset, and hopefully, it can help future research. ",
+        "bbox": [
+            174,
+            318,
+            823,
+            359
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.4 Protein-ligand binding pose prediction ",
+        "text_level": 1,
+        "bbox": [
+            169,
+            369,
+            480,
+            385
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Datasets and setup As mentioned above, protein-ligand binding pose prediction is one of the most important tasks in drug design. And Uni-Mol combines both the molecular and pocket pretraining models to learn a distance matrix based scoring function, and then sample and optimize the complex conformations. For the benchmark dataset, referring to the previous works [28, 61], we use CASF2016 as the test set. For the training data used in finetuning, we use PDBbind General set v.2020 [62] (19,443 protein-ligand complexes), excluding complexes that already exist in the CASF-2016. ",
+        "bbox": [
+            174,
+            388,
+            825,
+            472
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Two benchmarks are conducted: 1) Docking power, the default metric to benchmark the ability of a scoring function in CASF-2016. Specifically, it tests whether a scoring function can distinguish the ground truth binding pose from a set of decoys or not. For each ground truth, CASF-2016 provides 50 100 decoy conformations of the same ligand. Scoring functions are applied to rank them, and the ground truth binding pose is expected to be the top 1. 2) Binding pose accuracy. Specifically, we use the semi-flexible docking setting: keep the pocket conformation fixed, while the conformation of the ligand is fully flexible. We evaluate the RMSD between the predicted binding pose and the ground truth. Following previous works, we use the percentage of results that are below predefined RMSD thresholds as metrics. ",
+        "bbox": [
+            173,
+            478,
+            825,
+            603
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Baselines For docking power benchmark, the baselines are DeepDock [61] and the top 10 scoring functions reported in [28], including both conventional scoring functions and machine learningbased ones. For the binding pose accuracy, the baselines are Autodock Vina [63, 64], Vinardo [65], Smina [66], and AutoDock4 [67]. ",
+        "bbox": [
+            174,
+            604,
+            825,
+            661
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results From the docking power benchmark results shown in Figure 3, Uni-Mol ranks the 1st, with the top 1 success rate of $9 1 . 6 \\%$ . For comparison, the previous top scoring function AutoDock Vina [63, 64] achieves $9 0 . 2 \\%$ of the top 1 success rate in this benchmark. From the binding pose accuracy results shown in Table 5, Uni-Mol also surpasses all other baselines. Notably, Uni-Mol outperforms the second best method by $2 2 . 8 1 \\%$ under the threshold of $2 \\mathring \\mathrm { A }$ . This result indicates that Uni-Mol can effectively learn the 3D information from both molecules and pockets, as well as the interaction in 3D space of them. Even without pretraining, Uni-Mol (denoted as Uni-Mol random) is also better than other baselines. This demonstrates the effectiveness of Uni-Mol backbone, as it effectively learns the 3D information by limited data. ",
+        "bbox": [
+            173,
+            662,
+            825,
+            790
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In summary, by combining molecular and pocket pretraining models, Uni-Mol significantly outperforms the widely used docking tools in the protein-ligand binding tasks. ",
+        "bbox": [
+            171,
+            795,
+            823,
+            824
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4 Related work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            837,
+            318,
+            853
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Molecular representation learning Representation learning on large-scale unlabeled molecules attracts much attention recently. SMILES-BERT [18] is pretrained on SMILES strings of molecules using BERT [4]. Subsequent works are mostly pretraining on 2D molecular topological graphs [23, 11]. MolCLR [12] applies data augmentation to molecular graphs at both node and graph levels, using ",
+        "bbox": [
+            174,
+            856,
+            825,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/15e0d1258867cc24a58381b54a0cbb8e0fb8bc0c4da37581b2a673b8c05c6c0f.jpg",
+        "image_caption": [
+            "Figure 3: Docking power evaluation on CASF-2016 (Top 10 methods) "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
+            88,
+            418,
+            190
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/eed740989a6ea7f15450da23d2d435bad1a6588a67d08187cf667e02f43a3dd0.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 5: Uni-Mol performance on binding pose prediction "
+        ],
+        "table_body": "<table><tr><td colspan=\"3\">Ligand RMSD % Below Threshold 个</td></tr><tr><td>Methods</td><td>0.5A 1.0A 1.5A 2.0A 3.0A 5.0A</td></tr><tr><td>Autodock Vina</td><td>23.86 44.21 57.54 64.56 73.68 84.56</td></tr><tr><td>Vinardo 23.51</td><td>41.75 57.54 62.81 69.82 76.84</td></tr><tr><td>Smina 23.51</td><td>47.37 59.65 65.26 74.39 82.11</td></tr><tr><td>Autodock4 7.02</td><td>21.75 31.58 35.44 47.02 64.56</td></tr><tr><td>Uni-Molrandom 14.04 Uni-Mol 24.91</td><td>49.47 65.26 75.44 87.02 98.60 70.53 84.21 88.07 94.74 98.95</td></tr></table>",
+        "bbox": [
+            447,
+            88,
+            816,
+            207
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "299 a self-supervised contrastive learning strategy to learn molecular representations. Further, several   \n300 recent works try to leverage the 3D spatial information of molecules, and focus on contrastive or   \n301 transfer learning between 2D topology and 3D geometry of molecules. For example, GraphMVP [26]   \n302 proposes a contrastive learning GNN-based framework between 2D topology and 3D geometry.   \n303 GEM [13] uses bond angles and bond length as additional edge attributes to enhance 3D information.   \n304 As aforementioned, due to the inability of handling 3D information, most previous representation   \n305 learning models cannot be used in the important 3D prediction tasks.   \n306 SE(3)-Equivariant models In many-body scenarios such as potential energy surface fitting, SE-(3)   \n307 equivariance is usually required. A series of SE(3) models are proposed, such as SchNet [68], tensor   \n308 field networks [69], SE(3) Transformer [70], DimmNet [71], equivariant graph neural networks   \n309 (EGNN) [36], GemNet [72] and SphereNet [73]. Most of these models are used in supervised   \n310 learning with energy and force. In Uni-Mol, based on the standard Transformer, we introduce several   \n311 minor changes to make the model SE(3)-Equivariant. ",
+        "bbox": [
+            140,
+            253,
+            825,
+            351
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            145,
+            356,
+            825,
+            438
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Pocket druggability prediction Druggability prediction of protein binding pockets is crucial for drug discovery as druggable pockets need to be identified at the beginning. Since proteins undergo conformation changes that might alter the druggability of pockets, it is necessary to utilize 3D spatial data beyond sequential information. Early methods, such as Volsite [74], DrugPred [59], and PockDrug [75], predict druggability based on the predefined descriptors of pockets’ static structures. Later, TRAPP-CNN [60], based on 3D-CNN, proposes the analysis of proteins’ conformation changes and the use of such information for druggability prediction. ",
+        "bbox": [
+            166,
+            443,
+            825,
+            540
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Protein-ligand binding pose prediction In structure-based drug design, it is crucial to understand the interactions between protein targets and ligands. The in vitro estimation of the binding pose and affinity, such as docking, allows for lead identification and guides molecular optimization. In particular, docking is one of the most important approaches in structure-based drug design and has been developed for the past decades. Tools such as AutoDock4 [67], AutoDock Vina [63, 64], and Smina [66] are among the most used docking programs. Also, machine learning-based docking methods, such as $\\Delta _ { V i n a } \\mathrm { R F _ { 2 0 } }$ [76], DeepDock [61] and Equibind [77], have also been developed to predict protein-ligand binding poses and assess protein-ligand binding affinity. ",
+        "bbox": [
+            173,
+            545,
+            825,
+            656
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            678,
+            299,
+            694
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this paper, to enlarge the application scope and representation ability of molecular representation learning (MRL), we propose Uni-Mol, the first universal large-scale 3D MRL framework. Uni-Mol consists of 3 parts: a Transformer based backbone to handle 3D data; two large-scale pretraining models to learn molecular and pocket representations respectively; finetuning strategies for all kinds of downstream tasks. Experiments demonstrate that Uni-Mol can outperform existing SOTA in various downstream tasks, especially in 3D spatial tasks. ",
+        "bbox": [
+            173,
+            698,
+            825,
+            780
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "334 There are 3 potential future directions. 1) Better interaction mechanisms for finetuning two pretraining   \n335 models together. As the interaction between the pretraining pocket model and the pretraining   \n336 molecular model is simple in the current version of Uni-Mol, we believe there is a large room for   \n337 further improvement. 2) Large Uni-Mol models. As larger pretraining models often perform better, it   \n338 is worthy of training a large Uni-Mol model on a bigger dataset. 3) More high-quality benchmarks.   \n339 Although there have been many applications in the field of drug design, high-quality public datasets   \n340 have been lacking. Many public datasets cannot satisfy real-world demand due to the low data quality.   \n341 We believe the high-quality benchmarks will be the lighthouse of the entire field, and will significantly   \n342 accelerate the development of drug design. ",
+        "bbox": [
+            140,
+            786,
+            825,
+            912
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "343 References ",
+        "text_level": 1,
+        "bbox": [
+            140,
+            90,
+            267,
+            106
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "344 [1] Yoshua Bengio, Aaron Courville, and Pascal Vincent. “Representation learning: A review and new   \n345 perspectives”. In: IEEE transactions on pattern analysis and machine intelligence 35.8 (2013), pp. 1798–   \n346 1828.   \n347 [2] William L. Hamilton, Rex Ying, and Jure Leskovec. “Representation Learning on Graphs: Methods and   \n348 Applications”. In: IEEE Data Eng. Bull. 40.3 (2017), pp. 52–74. URL: http://sites.computer.org/   \n349 debull/A17sept/p52.pdf.   \n350 [3] Daokun Zhang et al. “Network representation learning: A survey”. In: IEEE transactions on Big Data   \n351 6.1 (2018), pp. 3–28.   \n352 [4] Jacob Devlin et al. “BERT: Pre-training of Deep Bidirectional Transformers for Language Under  \n353 standing”. In: Proceedings of the 2019 Conference of the North American Chapter of the Association   \n354 for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers).   \n355 Minneapolis, Minnesota: Association for Computational Linguistics, June 2019, pp. 4171–4186. DOI:   \n356 10.18653/v1/N19-1423. URL: https://aclanthology.org/N19-1423.   \n357 [5] Alec Radford et al. “Improving language understanding by generative pre-training”. In: (2018).   \n358 [6] Alec Radford et al. “Language models are unsupervised multitask learners”. In: OpenAI blog 1.8 (2019),   \n359 p. 9.   \n360 [7] Tom Brown et al. “Language models are few-shot learners”. In: Advances in neural information process  \n361 ing systems 33 (2020), pp. 1877–1901.   \n362 [8] Alexey Dosovitskiy et al. “An Image is Worth 16x16 Words: Transformers for Image Recognition at   \n363 Scale”. In: International Conference on Learning Representations. 2021. URL: https://openreview.   \n364 net/forum?id=YicbFdNTTy.   \n365 [9] Qingda Zang et al. “In silico prediction of physicochemical properties of environmental chemicals using   \n366 molecular fingerprints and machine learning”. In: Journal of chemical information and modeling 57.1   \n367 (2017), pp. 36–49.   \n368 [10] Minjian Yang et al. “Machine learning models based on molecular fingerprints and an extreme gradient   \n369 boosting method lead to the discovery of JAK2 inhibitors”. In: Journal of Chemical Information and   \n370 Modeling 59.12 (2019), pp. 5002–5012.   \n371 [11] Yu Rong et al. “Self-Supervised Graph Transformer on Large-Scale Molecular Data”. In: Advances in   \n372 Neural Information Processing Systems 33 (2020).   \n373 [12] Yuyang Wang et al. “Molecular contrastive learning of representations via graph neural networks”. In:   \n374 Nature Machine Intelligence (2022), pp. 1–9. DOI: 10.1038/s42256-022-00447-x.   \n375 [13] Xiaomin Fang et al. “Geometry-enhanced molecular representation learning for property prediction”. In:   \n376 Nature Machine Intelligence (2022), pp. 1–8. DOI: 10.1038/s42256-021-00438-4.   \n377 [14] A Crum-Brown and TR Fraser. “The connection of chemical constitution and physiological action”. In:   \n378 Trans R Soc Edinb 25.1968-1969 (1865), p. 257.   \n379 [15] Corwin Hansch and Toshio Fujita. “p-σ-π Analysis. A Method for the Correlation of Biological Activity   \n380 and Chemical Structure”. In: Journal of the American Chemical Society 86.8 (1964), pp. 1616–1626.   \n381 [16] David Weininger. “SMILES, a chemical language and information system. 1. Introduction to methodology   \n382 and encoding rules”. In: Journal of chemical information and computer sciences 28.1 (1988), pp. 31–36.   \n383 [17] Zheng Xu et al. “Seq2seq fingerprint: An unsupervised deep molecular embedding for drug discovery”.   \n384 In: Proceedings of the 8th ACM international conference on bioinformatics, computational biology, and   \n385 health informatics. 2017, pp. 285–294.   \n386 [18] Sheng Wang et al. “Smiles-bert: large scale unsupervised pre-training for molecular property prediction”.   \n387 In: Proceedings of the 10th ACM international conference on bioinformatics, computational biology and   \n388 health informatics. 2019, pp. 429–436.   \n389 [19] Stephen R Heller et al. “InChI, the IUPAC international chemical identifier”. In: Journal of cheminfor  \n390 matics 7.1 (2015), pp. 1–34.   \n391 [20] Robin Winter et al. “Learning continuous and data-driven molecular descriptors by translating equivalent   \n392 chemical representations”. In: Chemical science 10.6 (2019), pp. 1692–1701.   \n393 [21] Jennifer Handsel et al. “Translating the InChI: adapting neural machine translation to predict IUPAC   \n394 names from a chemical identifier”. In: Journal of cheminformatics 13.1 (2021), pp. 1–11.   \n395 [22] Weihua $\\mathrm { H u ^ { * } }$ et al. “Strategies for Pre-training Graph Neural Networks”. In: International Conference on   \n396 Learning Representations. 2020. URL: https://openreview.net/forum?id=HJlWWJSFDH.   \n397 [23] Pengyong Li et al. “An effective self-supervised framework for learning expressive molecular global   \n398 representations to drug discovery”. In: Briefings in Bioinformatics 22.6 (2021), bbab109.   \n399 [24] Chengxuan Ying et al. “Do Transformers Really Perform Badly for Graph Representation?” In: Advances   \n400 in Neural Information Processing Systems 34 (2021).   \n401 [25] Panagiotis I Koukos, Li C Xue, and Alexandre MJJ Bonvin. “Protein–ligand pose and affinity prediction:   \n402 Lessons from D3R Grand Challenge 3”. In: Journal of computer-aided molecular design 33.1 (2019),   \n403 pp. 83–91.   \n404 [26] Shengchao Liu et al. “Pre-training Molecular Graph Representation with 3D Geometry”. In: International   \n405 Conference on Learning Representations. 2022. URL: https : / / openreview . net / forum ? id $=$   \n406 xQUe1pOKPam.   \n407 [27] Hannes Stärk et al. “3D Infomax improves GNNs for Molecular Property Prediction”. In: arXiv preprint   \n408 arXiv:2110.04126 (2021).   \n409 [28] Minyi Su et al. “Comparative assessment of scoring functions: the CASF-2016 update”. In: Journal of   \n410 chemical information and modeling 59.2 (2018), pp. 895–913.   \n411 [29] Andrew L Hopkins, Colin R Groom, and Alexander Alex. “Ligand efficiency: a useful metric for lead   \n412 selection.” In: Drug discovery today 9.10 (2004), pp. 430–431.   \n413 [30] Ashish Vaswani et al. “Attention is all you need”. In: Advances in neural information processing systems   \n414 30 (2017).   \n415 [31] Ruibin Xiong et al. “On Layer Normalization in the Transformer Architecture”. In: Proceedings of the   \n416 37th International Conference on Machine Learning. Ed. by Hal Daumé III and Aarti Singh. Vol. 119.   \n417 Proceedings of Machine Learning Research. PMLR, July 2020, pp. 10524–10533.   \n418 [32] Guolin Ke, Di He, and Tie-Yan Liu. “Rethinking Positional Encoding in Language Pre-training”. In:   \n419 International Conference on Learning Representations. 2020.   \n420 [33] Philipp Dufter, Martin Schmitt, and Hinrich Schütze. “Position information in transformers: An overview”.   \n421 In: arXiv preprint arXiv:2102.11090 (2021).   \n422 [34] Muhammed Shuaibi et al. “Rotation invariant graph neural networks using spin convolutions”. In: arXiv   \n423 preprint arXiv:2106.09575 (2021).   \n424 [35] John Jumper et al. “Highly accurate protein structure prediction with AlphaFold”. In: Nature 596.7873   \n425 (2021), pp. 583–589.   \n426 [36] Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. “E (n) equivariant graph neural networks”.   \n427 In: International Conference on Machine Learning. PMLR. 2021, pp. 9323–9332.   \n428 [37] Abien Fred Agarap. “Deep learning using rectified linear units (relu)”. In: arXiv preprint   \n429 arXiv:1803.08375 (2018).   \n430 [38] Sereina Riniker and Gregory A Landrum. “Better informed distance geometry: using what we know   \n431 to improve conformation generation”. In: Journal of chemical information and modeling 55.12 (2015),   \n432 pp. 2562–2574.   \n433 [39] Thomas A Halgren. “Merck molecular force field. I. Basis, form, scope, parameterization, and perfor  \n434 mance of MMFF94”. In: Journal of computational chemistry 17.5-6 (1996), pp. 490–519.   \n435 [40] Greg Landrum et al. RDKit: A software suite for cheminformatics, computational chemistry, and predictive   \n436 modeling. 2013.   \n437 [41] Helen M Berman et al. “The protein data bank”. In: Nucleic acids research 28.1 (2000), pp. 235–242.   \n438 [42] Vincent Le Guilloux, Peter Schmidtke, and Pierre Tuffery. “Fpocket: an open source platform for ligand   \n439 pocket detection”. In: BMC bioinformatics 10.1 (2009), pp. 1–11.   \n440 [43] Gregor Simm and Jose Miguel Hernandez-Lobato. “A Generative Model for Molecular Distance Geome  \n441 try”. In: International Conference on Machine Learning. PMLR. 2020, pp. 8949–8958.   \n442 [44] Minkai Xu et al. “Learning Neural Generative Dynamics for Molecular Conformation Generation”. In:   \n443 International Conference on Learning Representations. 2020.   \n444 [45] Elman Mansimov et al. “Molecular geometry prediction using a deep generative graph neural network”.   \n445 In: Scientific reports 9.1 (2019), pp. 1–13.   \n446 [46] Octavian Ganea et al. “Geomol: Torsional geometric generation of molecular 3d conformer ensembles”.   \n447 In: Advances in Neural Information Processing Systems 34 (2021).   \n448 [47] Rainer Storn and Kenneth Price. “Differential evolution–a simple and efficient heuristic for global   \n449 optimization over continuous spaces”. In: Journal of global optimization 11.4 (1997), pp. 341–359.   \n450 [48] Zhenqin Wu et al. “MoleculeNet: a benchmark for molecular machine learning”. In: Chemical science   \n451 9.2 (2018), pp. 513–530.   \n452 [49] Kevin Yang et al. “Analyzing learned molecular representations for property prediction”. In: Journal of   \n453 chemical information and modeling 59.8 (2019), pp. 3370–3388.   \n454 [50] Zhaoping Xiong et al. “Pushing the boundaries of molecular representation for drug discovery with the   \n455 graph attention mechanism”. In: Journal of medicinal chemistry 63.16 (2019), pp. 8749–8760.   \n456 [51] Shengchao Liu, Mehmet F Demirel, and Yingyu Liang. “N-gram graph: Simple unsupervised representa  \n457 tion for graphs, with applications to molecules”. In: Advances in neural information processing systems   \n458 32 (2019).   \n459 [52] Tianqi Chen and Carlos Guestrin. “Xgboost: A scalable tree boosting system”. In: Proceedings of the   \n460 22nd acm sigkdd international conference on knowledge discovery and data mining. 2016, pp. 785–794.   \n[53] g   \n462 Conference on Machine Learning. PMLR. 2021, pp. 9558–9568.   \n463 [54] Simon Axelrod and Rafael Gomez-Bombarelli. “GEOM, energy-annotated molecular conformations for   \n464 property prediction and molecular generation”. In: Scientific Data 9.1 (2022), pp. 1–14.   \n465 [55] Minkai Xu et al. “An end-to-end framework for molecular conformation generation via bilevel program  \n466 ming”. In: International Conference on Machine Learning. PMLR. 2021, pp. 11537–11547.   \n467 [56] Shitong Luo et al. “Predicting Molecular Conformation via Dynamic Graph Score Matching”. In:   \n468 Advances in Neural Information Processing Systems 34 (2021).   \n469 [57] Jinhua Zhu et al. “Direct molecular conformation generation”. In: arXiv preprint arXiv:2202.01356   \n470 (2022).   \n471 [58] Minkai Xu et al. “GeoDiff: A Geometric Diffusion Model for Molecular Conformation Generation”. In:   \n472 International Conference on Learning Representations. 2022.   \n473 [59] Agata Krasowski et al. “DrugPred: a structure-based approach to predict protein druggability developed   \n474 using an extensive nonredundant data set”. In: Journal of chemical information and modeling 51.11   \n475 (2011), pp. 2829–2842.   \n476 [60] Jui-Hung Yuan et al. “Druggability assessment in TRAPP using machine learning approaches”. In:   \n477 Journal of Chemical Information and Modeling 60.3 (2020), pp. 1685–1699.   \n478 [61] Oscar Méndez-Lucio et al. “A geometric deep learning approach to predict binding conformations of   \n479 bioactive molecules”. In: Nature Machine Intelligence 3.12 (2021), pp. 1033–1039.   \n480 [62] Zhihai Liu et al. “PDB-wide collection of binding data: current status of the PDBbind database”. In:   \n481 Bioinformatics 31.3 (2015), pp. 405–412.   \n482 [63] Oleg Trott and Arthur J Olson. “AutoDock Vina: improving the speed and accuracy of docking with a   \n483 new scoring function, efficient optimization, and multithreading”. In: Journal of computational chemistry   \n484 31.2 (2010), pp. 455–461.   \n485 [64] Jerome Eberhardt et al. “AutoDock Vina 1.2. 0: New docking methods, expanded force field, and python   \n486 bindings”. In: Journal of Chemical Information and Modeling 61.8 (2021), pp. 3891–3898.   \n487 [65] Rodrigo Quiroga and Marcos A Villarreal. “Vinardo: A scoring function based on autodock vina improves   \n488 scoring, docking, and virtual screening”. In: PloS one 11.5 (2016), e0155183.   \n489 [66] David Ryan Koes, Matthew P Baumgartner, and Carlos J Camacho. “Lessons learned in empirical scoring   \n490 with smina from the CSAR 2011 benchmarking exercise”. In: Journal of chemical information and   \n491 modeling 53.8 (2013), pp. 1893–1904.   \n492 [67] Garrett M Morris et al. “AutoDock4 and AutoDockTools4: Automated docking with selective receptor   \n493 flexibility”. In: Journal of computational chemistry 30.16 (2009), pp. 2785–2791.   \n494 [68] Kristof Schütt et al. “Schnet: A continuous-filter convolutional neural network for modeling quantum   \n495 interactions”. In: Advances in neural information processing systems 30 (2017).   \n496 [69] Nathaniel Thomas et al. “Tensor field networks: Rotation-and translation-equivariant neural networks for   \n497 3d point clouds”. In: arXiv preprint arXiv:1802.08219 (2018).   \n498 [70] Fabian Fuchs et al. “Se (3)-transformers: 3d roto-translation equivariant attention networks”. In: Advances   \n499 in Neural Information Processing Systems 33 (2020), pp. 1970–1981.   \n500 [71] Johannes Gasteiger, Janek Groß, and Stephan Günnemann. “Directional Message Passing for Molecular   \n501 Graphs”. In: International Conference on Learning Representations (ICLR). 2020.   \n502 [72] Johannes Klicpera, Florian Becker, and Stephan Günnemann. “GemNet: Universal Directional Graph   \n503 Neural Networks for Molecules”. In: Advances in Neural Information Processing Systems. 2021.   \n504 [73] Yi Liu et al. “Spherical Message Passing for 3D Molecular Graphs”. In: International Conference on   \n505 Learning Representations. 2022. URL: https://openreview.net/forum?id=givsRXsOt9r.   \n506 [74] Jérémy Desaphy et al. Comparison and druggability prediction of protein–ligand binding sites from   \n507 pharmacophore-annotated cavity shapes. 2012.   \n508 [75] Alexandre Borrel et al. “PockDrug: A model for predicting pocket druggability that overcomes pocket   \n509 estimation uncertainties”. In: Journal of chemical information and modeling 55.4 (2015), pp. 882–895.   \n510 [76] Cheng Wang and Yingkai Zhang. “Improving scoring-docking-screening powers of protein–ligand   \n511 scoring functions using random forest”. In: Journal of computational chemistry 38.3 (2017), pp. 169–   \n512 177.   \n513 [77] Hannes Stärk et al. EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction. 2022. ",
+        "bbox": [
+            137,
+            114,
+            826,
+            896
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            137,
+            93,
+            828,
+            915
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            137,
+            102,
+            826,
+            825
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "514 Checklist ",
+        "text_level": 1,
+        "bbox": [
+            142,
+            840,
+            254,
+            856
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "1. For all authors... ",
+        "bbox": [
+            174,
+            867,
+            302,
+            881
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] ",
+        "bbox": [
+            191,
+            868,
+            825,
+            911
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "(b) Did you describe the limitations of your work? [Yes]   \n(c) Did you discuss any potential negative societal impacts of your work? [N/A]   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
+        "bbox": [
+            148,
+            92,
+            826,
+            154
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "2. If you are including theoretical results... ",
+        "bbox": [
+            166,
+            156,
+            455,
+            171
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
+        "bbox": [
+            197,
+            172,
+            700,
+            204
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "3. If you ran experiments... ",
+        "bbox": [
+            174,
+            208,
+            354,
+            223
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] The data we used are all from public databases and details in data processing are explained in Appendix. The data, code, and instructions will be made public upon the acceptance of the paper.   \n(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] We report all the training details for the experiemnt in Appendix.   \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We report the mean and std for different runs of experiments in Table 1, Table 2 and Table 4.   \n(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] We report the detailed computing resources used for the experiment in Appendix. ",
+        "bbox": [
+            197,
+            224,
+            826,
+            397
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "38 4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... ",
+        "bbox": [
+            155,
+            401,
+            785,
+            416
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "(a) If your work uses existing assets, did you cite the creators? [Yes] We discuss all the used datasets in the experiment section 3, datasets and setup part.   \n(b) Did you mention the license of the assets? [Yes] We mention the license for the datasets used in Appendix.   \n(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]   \n(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   \n(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A] ",
+        "bbox": [
+            197,
+            419,
+            826,
+            554
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "5. If you used crowdsourcing or conducted research with human subjects... ",
+        "bbox": [
+            168,
+            558,
+            666,
+            571
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   \n(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   \n(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] ",
+        "bbox": [
+            197,
+            574,
+            826,
+            662
+        ],
+        "page_idx": 12
+    }
+]

parse/dev/KVljrqehulG/KVljrqehulG.md

@@ -0,0 +1,494 @@
+# EFFICIENT AUTOMATIC GRAPH LEARNING VIA DESIGN RELATIONS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Despite the success of automated machine learning (AutoML), which aims to find the best design, including the architecture of neural networks and hyper-parameters, conventional AutoML methods are computationally expensive and hardly provide insights into the relations of different model design choices. This work focus on the scope of AutoML on graph tasks. To tackle the challenges, we propose FALCON, an efficient sample-based method to search for the optimal model design on graph tasks. Our key insight is to model the design space of possible model designs as a design graph, where the nodes represent design choices, and the edges denote design similarities. FALCON features 1) a task-agnostic module, which performs message passing on the design graph via a Graph Neural Network (GNN), and 2) a task-specific module, which conducts label propagation of the known model performance information on the design graph. Both modules are combined to predict the design performances in the design space, navigating the search direction. We conduct extensive experiments on 27 node and graph classification tasks from various application domains. We empirically show that FALCON can efficiently obtain the well-performing designs for each task using only 30 explored nodes. Specifically, FALCON has a comparable time cost with the one-shot approaches while achieving an average improvement of $3 . 3 \%$ compared with the best baselines.
+
+# 1 INTRODUCTION
+
+Automated machine learning (AutoML) (Liu et al., 2019; Pham et al., 2018; Bender et al., 2018; Real et al., 2019; Zoph & Le, 2017; Cai et al., 2019; 2021; Gao et al., 2019; You et al., 2020b; Zhang et al., 2021) has demonstrated great success in various domains including computer vision (Chu et al., 2020; Ghiasi et al., 2019; Chen et al., 2019), language modeling (Zoph & Le, 2017; So et al., 2019), and recommender systems (Chen et al., 2022). It is an essential component for the state-of-the-art deep learning models (Liu et al., 2018; Baker et al., 2017; Xu et al., 2020; Chen et al., 2021).
+
+Given a graph learning task, e.g., a node/graph classification task on graphs, our goal of AutoML is to search for a model architecture and hyper-parameter setting from a design space that results in the best test performance on the task. Following previous works (You et al., 2020b), we define design as a set of architecture and hyper-parameter choices (e.g., 3 layer, 64 embedding dimensions, batch normalization, skip connection between consecutive layers), and define design space as the space of all possible designs for a given task.
+
+However, AutoML is very computationally intensive. The design space of interest often involves millions of possible designs (Elsken et al.; You et al., 2020a). Sample-based AutoML (Zoph & Le, 2017; Gao et al., 2019; Bergstra et al., 2011; Liu et al., 2017; Luo et al., 2018) has been used to perform search via sampling candidate designs from the design space to explore. One central challenge of existing sample-based AutoML solutions is its sample efficiency: it needs to train as few models as possible to identify the best-performing model in the vast design space. To improve the efficiency, existing research focuses on developing good search algorithms to navigate in the design space (White et al., 2021; Shi et al., 2020; Ma et al., 2019).
+
+However, these methods do not consider modeling the effect of model design choices, which provides strong inductive biases in searching for the best-performing model. By “inductive bias”, we refer to the patterns of multiple variables interacting together, which can happen in multiple parts of the design space. Thus, an efficient search strategy should rapidly rule out a large subset of the design space with potentially bad performance leveraging such learned inductive bias.
+
+![](images/04ee7fcbb2d6516a0a5aa8a9d70ab613ff804401fdf41ee9bf3f9558ac3993bf.jpg)  
+Figure 1: Overview of FALCON. (a) Design graph example. We present a small design graph on TU-COX2 graph classification dataset. The design choices are shown in the table, #pre, #mp, #post denotes the numbers of pre-processing, message passing, and post-processing layers, respectively. The better design performance, the darker node colors. (b) FALCON search strategy. Red: Explored nodes. Green: Candidate nodes to be sampled from. Blue: The best node. Gray: Other nodes. Locally, FALCON extends the design subgraph via a search strategy detailed in Section 3.3. Globally, FALCON approaches the optimal design navigated by the inductive bias of the design relations.
+
+Proposed approach. To overcome the limitations, we propose FALCON, an AutoML framework on graph tasks that achieves state-of-the-art sample efficiency and performance by leveraging model design insights. Our key insight is to build a design graph over the design space of architecture and hyper-parameter choices. FALCON extracts model design insights by learning a meta-model that captures the relation between the design graph and model performance and uses it to inform a sample-efficient search strategy. FALCON consists of the following two novel components.
+
+Design space as a graph. Previous works view the model design space as a high-dimensional space with isolated design choices (You et al., 2020b), which offer few insights regarding the relations between different design choices. For example, through trial runs if we find the models with more than 3 layers do not work well without batch normalization, this knowledge can help us reduce the search space by excluding all model designs of more than 3 layers with batch normalization set to false. While such insights are hardly obtained with existing AutoML algorithms (Liu et al., 2019; Pham et al., 2018; Gao et al., 2019; Zoph & Le, 2017; Cai et al., 2019), FALCON achieves it via constructing a graph representation, design graph, among all the design choices. Figure 1(a) shows a visualization of a design graph, where each node represents a candidate design, and edges denote the similarity between the designs. See Section 3.1 for details on the similarity and graph construction.
+
+Search by navigating on the design graph. Given the design graph, FALCON deploys a Graph Neural Network predictor, short for meta-GNN, which is supervised by the explored nodes’ performances and learns to predict the performance of a specific design given the corresponding node in the design graph. The meta-GNN is designed with 1) a task-agnostic module, which performs message passing on the design graph, and 2) a task-specific module, which conducts label propagation of the known model performance information on the design graph. Furthermore, we propose a search strategy that uses meta-GNN predictions to navigate the search in the design graph efficiently.
+
+Experiments. We conduct extensive experiments on 27 graph datasets, covering node- and graphlevel tasks with distinct distributions. Moreover, we demonstrate FALCON’ potential applicability on image datasets by conducting experiments on the CIFAR-10 image dataset. Our code is available at https://anonymous.4open.science/r/Falcon.
+
+# 2 RELATED WORK
+
+Automatic Machine Learning (AutoML) is the cornerstone of discovering state-of-the-art model designs without costing massive human efforts. We introduce four types of related works below.
+
+Sample-based AutoML methods. Existing sample-based approaches explore the search space via sampling candidate designs, which includes heuristic search algorithms, e.g., Simulated Annealing, Bayesian Optimization approaches (Bergstra et al., 2011; White et al., 2021; Ma et al., 2019), evolutionary- (Xie & Yuille, 2017; Real et al., 2017) and reinforcement-based methods (Zoph & Le, 2017; Zhou et al., 2019; Gao et al., 2019). However, they tend to train thousands of models from scratch, which results in the low sample efficiency. For example, (Zoph & Le, 2017; Gao et al., 2019) usually involve training hundreds of GPUs for several days, hindering the development of AutoML in real-world applications (Bender et al., 2018). Some hyper-parameter search methods aim to reduce the computational cost. For example, Successive Halving (Karnin et al., 2013) allocates the training resources to more potentially valuable models based on the early-stage training information. Li et al. (2017) further extend it using different budgets to find the best configurations to avoid the trade-off between selecting the configuration number and allocating the budget. Jaderberg et al. (2017) combine parallel search and sequential optimisation methods to conduct fast search. However, their selective mechanisms are only based on the model performance and lack of deep knowledge, which draws less insight into the relation of design variables and limits the sample efficiency.
+
+One-shot AutoML methods. The one-shot approaches (Liu et al., 2019; Pham et al., 2018; Xie et al., 2019; Bender et al., 2018; Qin et al., 2021) have been popular for the high search efficiency. Specifically, they involve training a super-net representing the design space, i.e., containing every candidate design, and shares the weights for the same computational cell. Nevertheless, weight sharing degrades the reliability of design ranking, as it fails to reflect the true performance of the candidate designs (Yu et al., 2020).
+
+Graph-based AutoML methods. The key insight of our work is to construct the design space as a design graph, where nodes are candidate designs and edges denote design similarities, and deploy a Graph Neural Network, i.e., meta-GNN, to predict the design performance. Graph HyperNetwork (Zhang et al., 2019a) directly generates weights for each node in a computation graph representation. You et al. (2020a) study network generators that output relational graphs and analyze the link between their predictive performance and the graph structure. Recently, Zhao et al. (2020) considers both the micro- (i.e., a single block) and macro-architecture (i.e., block connections) of each design in graph domain. AutoGML (Park et al., 2022) designs a meta-graph to capture the relations among models and graphs and take a meta-learning approach to estimate the relevance of models to different graphs. Notably, none of these works model the search space as a design graph.
+
+Design performance predictor. Previous works predict the performance of a design using the learning curves (Baker et al., 2018), layer-wise features (Deng et al., 2017), computational graph structure (Zhang et al., 2019a; White et al., 2021; Shi et al., 2019; Ma et al., 2019; Zhang et al., 2019b; Lee et al., 2021a), or combining dataset information (Lee et al., 2021a) via a dataset encoder. To highlight, FALCON explicitly models the relations among model designs. Moreover, it leverages the performance information on training instances to provide task-specific information besides the design features, which is differently motivated compared with Lee et al. (2021b) that employs meta-learning techniques and incorporate hardware features to rapidly adapt to unseen devices. Besides, meta-GNN is applicable for both images and graphs, compared with Lee et al. (2021a).
+
+# 3 PROPOSED METHOD
+
+This section introduces our proposed approach FALCON for sample-based AutoML. In Section 3.1, we introduce the construction of design graph, and formulate the AutoML goal as a search on the design graph for the node with the best task performance. In Section 3.2, we introduce our novel neural predictor consisting of a task-agnostic module and a task-specific module, which predicts the performances of unknown designs. Finally, we detail our search strategy in Section 3.3. We refer the reader to Figure 1 (b) for a high-level overview of FALCON.
+
+# 3.1 DESIGN SPACE AS A GRAPH
+
+Motivation. Previous works generally consider each design choice as isolated from other designs. However, it is often observed that some designs that share the same design features, e.g., graph neural networks (GNNs) that are more than 3 layers and have batch normalization layers, may have similar performances. Moreover, the inductive bias of the relations between design choices can provide valuable information for navigating the design space for the best design. For example, suppose we find that setting batch normalization of a 3-layer GCN (Kipf & Welling, 2017) and a 4-layer GIN (Xu et al., 2019) to false both degrade the performance. Then we can reasonably infer that a 3-layer GraphSAGE (Hamilton et al., 2017) with batch normalization outperforms the one without. We could leverage such knowledge and only search for the designs that are more likely to improve the task performance. To the best of our knowledge, FALCON is the first method to explicitly consider such relational information among model designs.
+
+Design graph. We denote the design graph as $\mathcal { G } ( \mathcal { N } , \mathcal { E } )$ , where the nodes $\mathcal { N }$ include the candidate designs, and edges $\mathcal { E }$ denote the similarities between the candidate designs. Specifically, we use the notion of design distance to decide the graph connectivity, and we elaborate on them below.
+
+Design distance. For each numerical design dimension, two design choices have a distance 1 if they are adjacent in the ordered list of design choices. For example, if the hidden dimension size can take values [16, 32, 64, 128], then the distance between 16 and 32 is 1, and the distance between 32 and 128 is 2. For each categorical design dimension, any two distinct design choices have a distance 1. We then define the connectivity of the design graph in terms of the design distance:
+
+Definition 1 (Design Graph Connectivity) The design graph can be expressed as $\mathscr { G } ( \mathcal { N } , \mathcal { E } )$ , where the nodes $\mathcal { N } = \{ d _ { 1 } , \ldots , d _ { n } \}$ are model designs, and $( d _ { i } , d _ { j } ) \in \mathcal { E }$ iff the design distance between $d _ { i }$ and $d _ { j }$ is 1.
+
+Structure of the design graph. The definition of edges implies that the design graph is highly structured, with the following properties: (1) All designs that are the same except for one categorical design dimension form a clique subgraph. (2) All designs that are the same except $k$ numerical design dimensions form a grid graph structure. Moreover, we use a special calculation for the design distance with a combination of design dimensions that have dependencies. For example, the design dimensions of pooling operations, pooling layers, and the number of layers can depend on each other, thus the design graph structure becomes more complex. See the details in Appendix A.2.
+
+Design subgraph. The design graph may contain millions of nodes. Therefore, directly applying the meta-model to the design graph is computationally intensive. Moreover, a reliable performance estimation for an unknown node depends on its similarity between the nodes already explored by the search algorithm. Therefore, we focus on using a meta-model to predict performance for a dynamic subgraph, i.e., design subgraph, containing the explored nodes in the current search stage and the candidate nodes to be sampled in the next step. The candidate set can be constructed by selecting the multi-hop neighbors of explored nodes on the design graph. The design subgraph is defined as:
+
+Definition 2 (Design Subgraph) During a search, suppose the explored node set is $\mathcal { N } _ { e }$ and the candidate set is $\mathcal { N } _ { c }$ . The design subgraph is formulated as $\mathcal { G } _ { s } ( \mathcal { N } _ { s } , \mathcal { E } _ { s } )$ , where $\mathcal { N } _ { s } = \mathcal { N } _ { e } \cup \mathcal { N } _ { c }$ are the nodes and $\mathcal { E } _ { s } = \{ ( u , v ) | u \in \mathrm { \bar { \mathcal { N } } } _ { s } , v \in \bar { \mathcal { N } } _ { s } , ( \bar { u } , v ) \in \mathcal { N } \}$ are the edges.
+
+Given the design subgraph, we formulate the AutoML problem as searching for the node, i.e., design choice, with the best task performance.
+
+# 3.2 META-GNN FOR PERFORMANCE PREDICTION
+
+Here we introduce a meta-model, named meta-GNN, to predict the performance of model designs, i.e., nodes of the design subgraph. The goal of meta-GNN is learning the inductive bias of design relations, which is used to navigate the search path on the design graph. As is illustrated in Figure 2, the meta-GNN comprises a task-agnostic module and a task-specific module, used to capture the knowledge of model design and task performance, respectively.
+
+Task-agnostic module. The task-agnostic module uses a design encoder to encode the design features on nodes of the design subgraph, and a relation encoder to capture the design similarities and differences on edges of the design subgraph. After that, it performs message passing on the design subgraph. We introduce each component below:
+
+• Design encoder: it computes the node features of design subgraph by the concatenation of the feature encoding of each design dimension. For numerical design dimensions,we conduct min-max normalization on their values as the node features. For categorical design dimensions such as aggregation operator which takes one of (SUM, MAX, MEAN), we encode it as a one-hot feature. • Relation encoder: it captures the similarity relationships between the connecting designs. For each $( d _ { i } , d _ { j } ) \in \mathcal { E }$ , we encode the design dimension where $d _ { i }$ and $d _ { j }$ differ by a one-hot encoding.
+
+![](images/ac51ffd0c96eb11829c7368c37bf457eedcaa96c4b47cc518cb26e0e783c39cd.jpg)  
+Figure 2: Meta-GNN Framework: Task-agnostic module generates the embedding given the design variables and their graphical structures. Task-specific module leverages performance information and conducts label propagation to generate the task-specific embeddings. The two embeddings are concatenated and input into an MLP for predicting the design performance.
+
+• Message passing module: a GNN model is used to take the design subgraph and the processed features to perform message passing and output node representations. This information will be combined with the task-specific module to predict the design’s performance.
+
+Task-specific module. The task-specific module takes into account the information of design performance on selected training instances and thus is specific for one dataset.
+
+The challenge of including such task-specific performance is that it is only available on a very limited set of explored nodes. To overcome the challenge, we use label propagation to propagate the performance information of explored nodes to the unexplored nodes. This is based on our observation that models trained with similar designs typically make similar predictions on instances. We provide an example in Figure 2 to illustrate the task-specific module.
+
+• Identifying critical instances: The first step is to identify critical training instances that result in different performances across different designs. Here we use a set of explored designs (anchors) to provide the instance-wise performances. Specifically, the $( i , j )$ element of the top left matrix of Figure 2 represents whether the $i$ -th design can correctly predict the label of $j$ -th instance. Then, we compute the entropy of each training instance’s performance over the anchors. Then we obtain the instance-wise probability via Softmax on the entropy vector, from which we sample instances that result in high variation across designs. The high variation implies that these instances can distinguish good designs from bad ones in the design subgraph, which are informative.
+
+• Label propagation and linear projection: Based on the inductive bias of smoothness, we perform label propagation to make the task-specific information available to all candidate designs. Concretely, label propagation can be written as
+
+$$
+\mathbf { Y } ^ { ( k + 1 ) } = \alpha \cdot D ^ { - 1 / 2 } A D ^ { - 1 / 2 } \mathbf { Y } ^ { ( k ) } + ( 1 - \alpha ) \mathbf { Y } ^ { ( k ) }
+$$
+
+where each row of $\mathbf { Y }$ is the performance vector of design $i$ (if explored) or a zero vector (for the unexplored designs). $D \in \bar { \mathbb { R } } ^ { | \mathcal { N } _ { s } | \times | \mathcal { N } _ { s } | }$ is the diagonal matrix of node degree, $A \in \mathbb { R } ^ { | \mathcal { N } _ { s } | \times | \mathcal { N } _ { s } | }$ is the adjacent matrix of the design subgraph, and $\alpha$ is a hyper-parameter. After label propagation, we use a linear layer to project the performance information to another high-dimensional space.
+
+Finally, as shown in Figure 2, we concatenate the output embeddings of the task-specific and taskagnostic modules and use an MLP to produce the performance predictions.
+
+Objective for Meta-GNN. The training of neural performance predictor is commonly formulated as a regression using mean square error (MSE), in order to predict how good the candidate designs are for the current task. However, the number of explored designs is usually small for sample-efficient AutoML, especially during the early stage of the search process. Thus, the deep predictor tends to overfit, degrading the reliability of performance prediction. To solve this problem, we incorporate a pair-wise rank loss (Burges et al., 2005; Hu et al., 2021) with the MSE objective, resulting in
+
+Require: $S$ : Design space. $K$ : Exploration size. $h _ { \theta }$ : Meta-GNN. $V / V ^ { \prime }$ : Warm-up / Full epoch. η:   
+Learning rate. $C$ : Number of start nodes.   
+1: $\Omega  \boldsymbol { \mathrm { S } }$ AMPLE-NODES $( S , C )$ // Initialize the exploration set   
+2: $\Gamma $ MULTI-HOP-NEIGHBORS $( \Omega )$ // Construct candidate set from multi-hop neighbors   
+3: $Y _ { \Omega } = \mathbf { G } \mathbf { E } \mathbf { T } \mathbf { \cdot }$ -VALIDATION-PERFORMANCE $( \Omega , V )$ // Explore the initial nodes (for $V$ epochs)   
+4: while $t = | \Omega | < K$ do   
+5: $\mathcal { G } _ { s } ^ { ( t ) } \gets ( \mathcal { N } _ { v } = \Omega \cup \Gamma , \mathcal { E } = \mathrm { S I M I L A R I T Y } ( \mathcal { N } _ { v } )$ // (1) Update the design subgraph   
+6: while not converge do   
+7: $\theta \gets \theta - \eta \cdot \partial \bar { \mathcal { L } } ( \hat { Y } _ { \Omega } , h _ { \theta } ( \mathcal { G } _ { s } ^ { ( t ) } ) _ { \Omega } ) / \partial \theta$ // (2) Compute Eq. 2 and conduct optimization   
+8: end while   
+9: // (3) Sample a candidate node with probability proportional to the meta-GNN’s prediction   
+10: $d ^ { ( t ) } = s$ AMPLE-WITH-PROBABILITY $( \Gamma , \mathrm { S o f t m a x } ( h _ { \theta } ( \mathcal { G } _ { s } ^ { ( t ) } ) _ { \Gamma } ) )$   
+11: $Y _ { t } = \mathbf { G } \mathbf { E } \mathbf { T } \mathbf { - }$ VALIDATION-PERFORMANCE $( d ^ { ( t ) } , V )$ // (2) Explore the current selected node   
+12: $\Omega  \Omega \cup \{ d ^ { ( t ) } \}$ , $\Gamma  \Gamma \cup$ MULTI-HOP-NEIGHBORS $( \{ d ^ { ( t ) } \} )$ )   
+13: end while   
+14: $D = \mathbf { S }$ ELECT-TOPK $\{ \Omega _ { i } : Y _ { i } \} _ { i = 1 } ^ { K }$ , $\mathrm { s i z e } = \mathbf { M I N } \big ( \big \lceil 1 0 \% \cdot K \big \rceil , 5 \big ) ,$ ) // Models to be fully trained   
+15: $Y ^ { \prime } = \mathbf { G } \mathbf { E } \mathbf { T } \mathbf { - }$ VALIDATION-PERFORMANCE $( D , V ^ { \prime } )$ // Obtain the final performance   
+16: $I = \mathrm { A R G M A X } ( Y ^ { \prime } )$ // Obtain best model   
+17: return $D _ { I } , Y _ { I } ^ { \prime }$
+
+a quadratic number of training pairs, thus reducing overfitting. Furthermore, predicting relative performance is more robust across datasets than predicting absolute performance. Overall, the objective is formulated as follows:
+
+$$
+\begin{array} { l } { { \displaystyle { \mathcal { L } } ( \hat { Y } , Y ) = \sum _ { i = 1 } ^ { N } ( \hat { Y } _ { i } - Y _ { i } ) ^ { 2 } + \lambda { \mathcal { L } } _ { r a n k } ( \hat { Y } , Y ) , \mathrm { ~ w h e r e ~ } } } \\ { ~ } \\ { { \displaystyle { \mathcal { L } } _ { r a n k } ( \hat { Y } , Y ) = \sum _ { i = 1 } ^ { N } \sum _ { j = i } ^ { N } ( - 1 ) ^ { \mathbb { I } ( Y _ { i } > Y _ { j } ) } \cdot \sigma \left( \frac { \hat { Y } _ { i } - \hat { Y } _ { j } } { \tau } \right) } } \end{array}
+$$
+
+where $\lambda$ is the trade-off hyper-parameter, $\tau$ is the temperature controlling the minimal performance gap that will be highly penalized, and $\sigma$ is the Sigmoid function. Thus, the meta-GNN is trained to predict the node performance on the design subgraph supervised by the explored node performance.
+
+# 3.3 SEARCH STRATEGY
+
+Equipped with the meta-GNN, we propose a sequential search strategy to search for the best design in the design graph. The core idea is to leverage meta-GNN to perform fast inference on the dynamic design subgraph, and decide what would be the next node to explore, thus navigating the search. We summarize our search strategy in Algorithm 1. Concretely, our search strategy consists of the following three steps:
+
+• Initialization: As shown in Figure 1 (b), FALCON randomly samples multiple nodes on the design graph. The motivation of sampling multiple nodes in the initial step is to enlarge the receptive field on the design graph to avoid the local optima and bad performance, which is empirically verified in Appendix D. Then, FALCON explore the initialized nodes by training designs on the tasks and construct the instance mask for the task-specific module. • Meta-GNN training: Following Figure 2, meta-GNN predicts the performance of the explored nodes. The loss is computed via Equation 2 and back-propagated to optimize the meta-GNN. • Exploration via inference: Meta-GNN is then used to make predictions for the performances of all candidate nodes. Then we apply Softmax on the predictions as the probability distribution of candidate designs, from which FALCON samples a new node and updates the design subgraph.
+
+At every iteration, FALCON extends the design subgraph through the last two steps. After several iterations, it selects and retrains a few designs in the search trajectory with top performances. Overall,
+
+FALCON approaches the optimal design navigated by the relational inductive bias learned by metaGNN, as shown in Figure 1 (b).
+
+# 4 EXPERIMENTS
+
+We conduct extensive experiments on 27 graph datasets and an image dataset. The goal is twofold: (1) to show FALCON’s sample efficiency over the existing AutoML methods (cf. Section 4.2) and (2) to provide insights into how the inductive bias of design relartions navigate the search on design graph (cf. Section 4.3).
+
+# 4.1 EXPERIMENTAL SETTINGS
+
+We consider the following tasks in our evaluation and we leave the details including dataset split, evaluation metrics, and hyper-parameters in Appendix A.
+
+Node classification. We use 6 benchmarks ranging from citation networks to product or social networks: Cora, CiteSeer, PubMed (Sen et al., 2008), ogbn-arxiv (Hu et al., 2020), AmazonComputers (Shchur et al., 2018), and Reddit (Zeng et al., 2020).
+
+Graph classification. We use 21 benchmark binary classification tasks in TUDataset (Morris et al., 2020), which are to predict certain properties for molecule datasets with various distribution.
+
+Image classification. We use CIFAR-10 (Krizhevsky, 2009). See details in Appendix C.
+
+Baselines. We compare FALCON with three types of baselines:
+
+• Simple search strategies: Random, Simulated Annealing (SA), Bayesian Optimization (BO) (Bergstra et al., 2011).   
+• AutoML approaches: DARTS (Liu et al., 2019), ENAS (Pham et al., 2018), GraphNAS (Gao et al., 2019), AutoAttend (Guan et al., 2021), GASSO (Qin et al., 2021), where the last three methods are specifically designed for graph tasks.   
+• Ablation models: FALCON-G and FALCON-LP, where FALCON-G discards the design graph and predicts the design performance using an MLP, and FALCON-LP removes the task-specific module and predicts design performance using only the task-agnostic module.
+
+We also include a naive method, BRUTEFORCE, which trains $5 \%$ designs from scratch and returns the best design among them. The result of BRUTEFORCE is regarded as the approximated ground truth performance. We compare FALCON and the simple search baselines under sample size controlled search, where we limit the number of explored designs. We set the exploration size as 30 by default.
+
+Design Space. We use different design spaces on node- and graph-level tasks. Specifically, The design variables include common hyper-parameters, e.g., dropout ratio, and architecture choices, e.g., layer connectivity and batch normalization. Moreover, we consider node pooling choices for the graph classification datasets, which is less studied in the previous works (Cai et al., 2021; Gao et al., 2019; Zhou et al., 2019). Besides, we follow You et al. (2020b) and control the number of parameters for all the candidate designs to ensure a fair comparison. See Appendix A.2 for the details.
+
+# 4.2 MAIN RESULTS
+
+Node classification tasks. Table 1 summarizes the performance of FALCON and the baselines.
+
+![](images/c4740e4a9b914698454235ed1796f3a5ed7c866e6eba861d099ca6748a66837e.jpg)  
+Figure 3: Accuracy v.s. the number of explored nodes on ogbn-arxiv.
+
+Notably, FALCON takes comparable search cost as the oneshot methods and is $1 5 \mathrm { x }$ less expensive than GraphNAS. Moreover, FALCON achieves the best performances over the baselines with sufficient margins in the most datasets, using only 30 explored designs. For example, FALCON outperforms ENAS by $1 . 8 \%$ in CiteSeer and GASSO by $1 . 6 \%$ in AmazonComputers. Also, the removal of the design graph and task-specific module decreases the performance constantly, which validates their effectiveness. It is worth mentioning that FALCON is competitive with BRUTEFORCE, demonstrating the excellence of FALCON in searching for globally bestperforming designs.
+
+Table 1: Search results on five node classification tasks, where Time stands for the search cost (GPU·hours). We conduct t-test to compute p-value on our method with the best AutoML baselines.   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Cora</td><td colspan="2">CiteSeer</td><td colspan="2">Pubmed</td><td colspan="2">AmazonComputers</td><td colspan="2">Reddit</td></tr><tr><td>ACC</td><td>Time</td><td>ACC</td><td>Time</td><td>ACC</td><td>Time</td><td>ACC</td><td>Time</td><td>F1</td><td>Time</td></tr><tr><td>Random</td><td>80.8±1.7</td><td>0.20</td><td>71.2±0.8</td><td>0.22</td><td>86.0±3.5</td><td>0.24</td><td>81.6±3.0</td><td>0.16</td><td>94.3±0.1</td><td>0.97</td></tr><tr><td>BO</td><td>85.1±0.3</td><td>0.28</td><td>72.6±0.9</td><td>0.30</td><td>88.5±0.3</td><td>0.31</td><td>82.3±6.3</td><td>0.16</td><td>94.2±0.2</td><td>0.94</td></tr><tr><td>SA</td><td>81.1±0.8</td><td>0.24</td><td>74.7±0.2</td><td>0.25</td><td>88.9±0.1</td><td>0.29</td><td>81.2±6.9</td><td>0.23</td><td>94.3±0.5</td><td>0.97</td></tr><tr><td>ENAS</td><td>85.8±0.4</td><td>0.27</td><td>74.9±0.2</td><td>0.39</td><td>88.6±0.8</td><td>2.06</td><td>74.5±1.2</td><td>0.83</td><td>92.3±1.0</td><td>1.98</td></tr><tr><td>DARTS</td><td>85.8±0.2</td><td>0.25</td><td>75.2±0.3</td><td>0.25</td><td>89.1±0.1</td><td>0.35</td><td>84.1±1.9</td><td>0.35</td><td>[OoM]</td><td>-</td></tr><tr><td>GraphNAS</td><td>82.2±3.6</td><td>3.12</td><td>74.9±0.6</td><td>3.99</td><td>89.2±0.3</td><td>5.37</td><td>88.5±2.4</td><td>2.53</td><td>89.1±2.9</td><td>3.03</td></tr><tr><td>AutoAttend</td><td>84.6±0.2</td><td>1.23</td><td>73.9±0.2</td><td>1.25</td><td>84.4±0.7</td><td>1.55</td><td>87.3±1.1</td><td>2.62</td><td>[OoM]</td><td>-</td></tr><tr><td>GASSO</td><td>86.8±1.1</td><td>0.38</td><td>75.3±0.7</td><td>0.33</td><td>86.3±0.4</td><td>0.41</td><td>89.8±0.1</td><td>0.73</td><td>[OoM]</td><td>-</td></tr><tr><td>FALCON-G</td><td>84.5±0.8</td><td>0.23</td><td>74.3±1.7</td><td>0.24</td><td>89.2±0.1</td><td>0.26</td><td>87.6±0.9</td><td>0.27</td><td>93.7±0.4</td><td>1.11</td></tr><tr><td>FALCON-LP</td><td>85.5±1.0</td><td>0.26</td><td>74.6±0.1</td><td>0.26</td><td>89.0±0.2</td><td>0.29</td><td>90.7±0.6</td><td>0.30</td><td>94.9±0.2</td><td>1.00</td></tr><tr><td>FALCON</td><td>86.4±0.5</td><td>0.26</td><td>76.2±0.4</td><td>0.28</td><td>89.3±0.5</td><td>0.32</td><td>91.2±0.5</td><td>0.30</td><td>95.2±0.2</td><td>1.15</td></tr><tr><td>BRUTEFORCE</td><td>87.0</td><td>52.5</td><td>76.0</td><td>59.7</td><td>90.0</td><td>63.0</td><td>91.4</td><td>81.5</td><td>95.5</td><td>&gt;200</td></tr><tr><td>p-value</td><td></td><td>-</td><td>0.051</td><td>-</td><td>0.145</td><td>-</td><td>0.017</td><td>-</td><td>0002</td><td>-</td></tr></table>
+
+We further investigate the speed-performance trade-off of FALCON and other sample-based approaches in ogbn-arxiv. We run several search trials under different sample sizes. As shown in Figure 3, FALCON reaches the approximated ground truth result with very few explored nodes. In contrast, SA and Random require more samples to converge, while BO performs bad even with a large number of explored nodes, potentially due to its inability in dealing with high-dimensional design features.
+
+Graph classification tasks. The graph classification datasets cover a wide range of graph distributions. In Table 2, we report the selected performance results for graph classification tasks and leave other results including the search costs in Appendix B. We highlight three observations:
+
+• On average, the state-of-the-art AutoML baselines algorithms perform close to the simple search methods, indicating the potentially unreliable search, as similarly concluded by Yu et al. (2020). • FALCON surpasses the best AutoML baselines with an average improvement of $3 . 3 \%$ . The sufficient and consistent improvement greatly validates our sample efficiency under a controlled sample size. where FALCON can explore the designs that are more likely to perform well through the relational inference based on the relations of previously explored designs and their performances. • In the second block, we attribute the high sample efficiency of FALCON to the exhibition of design relations and the performance information from the training instances. Specifically, FALCON outperforms FALCON-LP by $4 . 8 7 \%$ on average, indicating that the task-specific module provides more task information that aids the representation learning of model designs, enabling a fast adaption on a certain task. Moreover, FALCON gains an average improvement of $6 . 4 3 \%$ compared to FALCON-G, which justifies our motivation that the design relations promote the learning of relational inductive bias and guide the search on the design graph.
+
+We also conduct experiments similar to Figure 3 to investigate how FALCON converges with the increasing sample size ( $\mathrm { { } } ^ { c f . }$ Appendix B.1) and report the best designs found by FALCON for each dataset (cf. Appendix B.2). Besides, we provide sensitivity analysis on FALCON’s hyper-parameters, e.g., number of random start nodes $C$ (cf. Appendix D).
+
+Image classification task. We demonstrate the potential of FALCON in image domain. Due to space limitation, we leave the results of CIFAR-10 to Appendix C. We found FALCON can search for designs that are best-performing, compared with the baselines. Specifically, it gains average improvements of $1 . 4 \%$ over the simple search baselines and $0 . 3 \%$ over the one-shot baselines on the architecture design space, with search cost comparable to the one-shot based baselines.
+
+# 4.3 CASE STUDIES OF FALCON
+
+We study FALCON in two dimensions: (1) Search process: we probe FALCON’s inference process through the explanations of meta-GNN on a design graph, and (2) Design representations: we visualize the node representations output by the meta-GNN to examine the effect of design choices.
+
+Search process. We use GNNExplainer (Ying et al., 2019) to explain the node prediction of metaGNN and shed light on the working mechanism of FALCON. Here we consider the importance of each design dimension for each node’s prediction. We demonstrate on a real case when searching on CIFAR-10 (cf. Table 12 for the design space). For conciseness, we focus on two design dimensions: (Weight Decay, Batch Size). Then, given a node of interest $n ^ { \prime } = ( 0 . 9 , 1 2 8 )$ , we observe the change in its predictions and dimension importance during the search process.
+
+Table 2: Selected results for the graph classification tasks. The average task performance (ROC-AUC) of the architectures searched by FALCON is $3 . 3 \%$ over the best AutoML baselines.   
+
+<table><tr><td></td><td>ER-MD</td><td>AIDS</td><td>OVCAR-8</td><td>MCF-7</td><td>SN12C</td><td>NCI109</td><td>Tox21-AhR</td><td>Avg.</td></tr><tr><td>Random</td><td>77.5±1.6</td><td>97.0±1.4</td><td>56.2±0.0</td><td>58.2±0.3</td><td>57.4±1.0</td><td>73.4±0.9</td><td>75.7±2.0</td><td>70.8</td></tr><tr><td>BO</td><td>77.6±3.5</td><td>96.1±1.0</td><td>63.6±0.7</td><td>60.7±0.0</td><td>54.8±1.1</td><td>73.6±1.2</td><td>75.5±1.1</td><td>71.7</td></tr><tr><td>SA</td><td>75.9±4.2</td><td>95.4±0.9</td><td>59.5±3.2</td><td>56.7±0.8</td><td>60.4±1.7</td><td>76.6±5.6</td><td>76.5±3.0</td><td>71.6</td></tr><tr><td>ENAS</td><td>76.0±2.2</td><td>97.1±0.4</td><td>56.0±1.3</td><td>59.7±0.8</td><td>66.4±0.6</td><td>71.2±1.0</td><td>73.6±0.9</td><td>71.4</td></tr><tr><td>DARTS</td><td>75.0±0.7</td><td>98.0±0.0</td><td>56.8±0.3</td><td>60.2±0.7</td><td>66.0±0.4</td><td>73.5±0.2</td><td>76.0±1.1</td><td>72.2</td></tr><tr><td>GraphNAS</td><td>76.9±3.6</td><td>95.9±0.8</td><td>58.7±0.8</td><td>61.3±5.2</td><td>60.7±1.5</td><td>73.6±2.9</td><td>70.6±4.3</td><td>71.1</td></tr><tr><td>AutoAttend</td><td>73.1±0.8</td><td>97.4±0.3</td><td>59.8±0.8</td><td>64.4±0.2</td><td>71.8±0.3</td><td>75.9±1.8</td><td>74.1±0.9</td><td>73.8</td></tr><tr><td>GASSO</td><td>73.2±0.4</td><td>95.2±0.7</td><td>62.3±0.3</td><td>62.5±0.4</td><td>70.9±2.3</td><td>73.9±0.4</td><td>70.2±3.5</td><td>72.6</td></tr><tr><td>FALCON-G</td><td>78.3±3.0</td><td>96.3±1.4</td><td>56.4±1.1</td><td>62.3±4.5</td><td>69.8±2.2</td><td>70.3±6.4</td><td>72.5±2.8</td><td>72.3</td></tr><tr><td>FALCON-LP</td><td>76.7±2.4</td><td>96.0±0.2</td><td>61.5±4.9</td><td>59.5±5.7</td><td>70.3±3.8</td><td>73.1±0.3</td><td>76.5±2.5</td><td>73.3</td></tr><tr><td>FALCON</td><td>78.4±0.2</td><td>97.5±1.1</td><td>66.7±3.4</td><td>65.5±2.5</td><td>73.3±0.0</td><td>78.4±2.3</td><td>78.5±1.1</td><td>76.9</td></tr><tr><td>BRUTEFORCE</td><td>83.3</td><td>96.0</td><td>67.4</td><td>70.6</td><td>73.7</td><td>81.8</td><td>82.0</td><td>79.3</td></tr><tr><td>p-value</td><td>0.155</td><td>1</td><td>0.008</td><td>0.035</td><td>&lt;0.001</td><td>0.096</td><td>0.018</td><td>-</td></tr></table>
+
+<table><tr><td>Explored node nt:</td><td>·</td><td>(0.99, 64)</td><td>(0.9, 64)</td><td>(0.99, 128)</td><td></td></tr><tr><td>Performance of nt:</td><td>…</td><td>++</td><td>：</td><td>+</td><td>：</td></tr><tr><td>Prediction on n&#x27;:</td><td>：</td><td>0.90</td><td>0.77 …</td><td>0.89</td><td>：</td></tr><tr><td>Dimension importance:</td><td>：</td><td>[0.5, 0.5]</td><td>[0.8, 0.2] …</td><td>[0.6, 0.4]</td><td>…</td></tr></table>
+
+Where $^ +$ and − indicate the relative performance of the explored nodes, $t$ is the current search step. Interestingly, we see that the prediction on $n ^ { \prime }$ and the dimension importance evolve with the explored designs and their relations. For example, when weight decay changes from 0.99 to 0.9, there is a huge drop in the node performance, which affects the prediction of $n ^ { \prime }$ and increases the importance of Weight Decay as design performance seems to be sensitive to this dimension.
+
+Design representations. In Figure 4, we visualize the high-dimensional design representations via T-SNE (van der Maaten & Hinton, 2008) after training the meta-GNN on the Cora dataset.
+
+![](images/405009ffa4661b7d01289995029a33adb8280a96cab7a9117f73e2a94669bd2b.jpg)  
+Figure 4: T-SNE visualization for the design representations on Cora dataset.
+
+In the left figure, the better the design performance, the darker the color. Generally, the points with small distance have similar colors or performances, indicating that meta-GNN can distinguish “good” nodes from “bad” nodes. For the right figure, different colors represent different dropout ratios. The high discrimination indicates that the dropout ratio is an influential variable for learning the design representation, which further affects design performance. This evidence validates the meta-GNN’s expressiveness and capacity to learn the relational inductive bias between the design choices.
+
+# 5 CONCLUSION, LIMITATION, AND FUTURE WORK
+
+This work introduces FALCON, an efficient sample-based AutoML framework. We propose the concept of design graph that explicitly models and encodes relational information among model designs. On top of the design graph, we develop a sample-efficient strategy to navigate the search on the design graph with a novel meta-model. One future direction is to better tackle the high average node degree on the design graphwhich could cause over-smoothing, especially when the design variables include many categorical variables. And a simple solution is to use edge dropout to randomly remove a portion of edges at each training epoch. Another future direction is to better adapt FALCON on continuous design variables via developing a dynamic design graph that enable a more fine-grained search between the discretized values.
+
+# REPRODUCIBILITY STATEMENT
+
+All of the datasets used in this work are public. For experimental setup, we state the detailed settings in Appendix A and Appendix C, including the graph pre-processing, dataset splits, hyper-parameters. Moreover, we include our code in an anonymous link for public access. For the results, we report the best models found by our algorithm as well as their corresponding performances. Overall, we believe we have made great efforts to ensure reproducibility in this paper.
+
+# ETHICS STATEMENT
+
+In this work, we propose a novel algorithm to search for the best model designs where no human subject is related. This work could promote the discovery of more powerful and expressive models and provide insights into design relations. However, while best-performing models may be “experts” in fulfilling given tasks, they are not necessarily fair towards different user or entity groups. We believe this is a general issue in the AutoML area and should be well addressed to ensure the ethics of models in real-world applications.
+
+# REFERENCES
+
+Bowen Baker, Otkrist Gupta, Nikhil Naik, and Ramesh Raskar. Designing neural network architectures using reinforcement learning. In ICLR, 2017.
+
+Bowen Baker, Otkrist Gupta, Ramesh Raskar, and Nikhil Naik. Accelerating neural architecture search using performance prediction. In ICLR, 2018.
+
+Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc V. Le. Understand ing and simplifying one-shot architecture search. In ICML, 2018.
+
+James Bergstra, Remi Bardenet, Yoshua Bengio, and Bal ´ azs K ´ egl. Algorithms for hyper-parameter ´ optimization. In NeurIPS, 2011.
+
+Filippo Maria Bianchi, Daniele Grattarola, Lorenzo Livi, and Cesare Alippi. Graph neural networks with convolutional ARMA filters. arXiv, 2019.
+
+Christopher J. C. Burges, Tal Shaked, Erin Renshaw, Ari Lazier, Matt Deeds, Nicole Hamilton, and Gregory N. Hullender. Learning to rank using gradient descent. In ICML, 2005.
+
+Han Cai, Ligeng Zhu, and Song Han. Proxylessnas: Direct neural architecture search on target task and hardware. In ICLR, 2019.
+
+Shaofei Cai, Liang Li, Jincan Deng, Beichen Zhang, Zheng-Jun Zha, Li Su, and Qingming Huang. Rethinking graph neural architecture search from message-passing. In CVPR, 2021.
+
+Bo Chen, Xiangyu Zhao, Yejing Wang, Wenqi Fan, Huifeng Guo, and Ruiming Tang. Automated machine learning for deep recommender systems: A survey. 2022.
+
+Xiangning Chen, Ruochen Wang, Minhao Cheng, Xiaocheng Tang, and Cho-Jui Hsieh. Drnas: Dirichlet neural architecture search. In ICLR, 2021.
+
+Yukang Chen, Tong Yang, Xiangyu Zhang, Gaofeng Meng, Chunhong Pan, and Jian Sun. Detnas: Neural architecture search on object detection. 2019.
+
+Xiangxiang Chu, Bo Zhang, Hailong Ma, Ruijun Xu, and Qingyuan Li. Fast, accurate and lightweight super-resolution with neural architecture search. In ICPR. IEEE, 2020.
+
+Boyang Deng, Junjie Yan, and Dahua Lin. Peephole: Predicting network performance before training. Arxiv, 2017.
+
+Frederik Diehl. Edge contraction pooling for graph neural networks. CoRR, abs/1905.10990, 2019.
+
+Jian Du, Shanghang Zhang, Guanhang Wu, Jose M. F. Moura, and Soummya Kar. Topology adaptive ´ graph convolutional networks.
+
+Thomas Elsken, Jan Hendrik Metzen, and Frank Hutter. Neural architecture search: A survey. J. Mach. Learn. Res.
+
+Hongyang Gao and Shuiwang Ji. Graph u-nets. In ICML, volume 97, pp. 2083–2092, 2019.
+
+Yang Gao, Hong Yang, Peng Zhang, Chuan Zhou, and Yue Hu. Graphnas: Graph neural architecture search with reinforcement learning. arXiv, 1904.09981, 2019.
+
+Golnaz Ghiasi, Tsung-Yi Lin, and Quoc V. Le. NAS-FPN: learning scalable feature pyramid architecture for object detection. In CVPR, 2019.
+
+Chaoyu Guan, Xin Wang, and Wenwu Zhu. Autoattend: Automated attention representation search. In ICML, 2021.
+
+William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In NeurIPS, pp. 1024–1034, 2017.
+
+Chi Hu, Chenglong Wang, Xiangnan Ma, Xia Meng, Yinqiao Li, Tong Xiao, Jingbo Zhu, and Changliang Li. Ranknas: Efficient neural architecture search by pairwise ranking. In EMNLP, 2021.
+
+Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. arXiv preprint arXiv:2005.00687, 2020.
+
+Max Jaderberg, Valentin Dalibard, Simon Osindero, Wojciech M. Czarnecki, Jeff Donahue, Ali Razavi, Oriol Vinyals, Tim Green, Iain Dunning, Karen Simonyan, Chrisantha Fernando, and Koray Kavukcuoglu. Population based training of neural networks. CoRR, 2017.
+
+Zohar Shay Karnin, Tomer Koren, and Oren Somekh. Almost optimal exploration in multi-armed bandits. In ICML, 2013.
+
+Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In ICLR, 2017.
+
+Alex Krizhevsky. Learning multiple layers of features from tiny images. In Technical report, 2009.
+
+Hayeon Lee, Eunyoung Hyung, and Sung Ju Hwang. Rapid neural architecture search by learning to generate graphs from datasets. In ICLR, 2021a.
+
+Hayeon Lee, Sewoong Lee, Song Chong, and Sung Ju Hwang. Hardware-adaptive efficient latency prediction for NAS via meta-learning. In NeurIPS, 2021b.
+
+Junhyun Lee, Inyeop Lee, and Jaewoo Kang. Self-attention graph pooling. In ICML, 2019.
+
+Lisha Li, Kevin G. Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet Talwalkar. Hyperband: A novel bandit-based approach to hyperparameter optimization. J. Mach. Learn. Res., 2017.
+
+Chenxi Liu, Barret Zoph, Jonathon Shlens, Wei Hua, Li-Jia Li, Li Fei-Fei, Alan L. Yuille, Jonathan Huang, and Kevin Murphy. Progressive neural architecture search. 1712.00559, 2017.
+
+Hanxiao Liu, Karen Simonyan, Oriol Vinyals, Chrisantha Fernando, and Koray Kavukcuoglu. Hierarchical representations for efficient architecture search. In ICLR, 2018.
+
+Hanxiao Liu, Karen Simonyan, and Yiming Yang. DARTS: differentiable architecture search. In ICLR, 2019.
+
+Renqian Luo, Fei Tian, Tao Qin, Enhong Chen, and Tie-Yan Liu. Neural architecture optimization. In NeurIPS, 2018.
+
+Lizheng Ma, Jiaxu Cui, and Bo Yang. Deep neural architecture search with deep graph bayesian optimization. In WI. ACM, 2019.
+
+Zheng Ma, Junyu Xuan, Yu Guang Wang, Ming Li, and Pietro Lio. Path integral based convolution \` and pooling for graph neural networks. 2020.
+
+Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe. Weisfeiler and leman go neural: Higher-order graph neural networks. In AAAI, pp. 4602–4609, 2019.
+
+Christopher Morris, Nils M. Kriege, Franka Bause, Kristian Kersting, Petra Mutzel, and Marion Neumann. Tudataset: A collection of benchmark datasets for learning with graphs. 2020.
+
+Namyong Park, Ryan A. Rossi, Nesreen K. Ahmed, and Christos Faloutsos. Autogml: Fast automatic model selection for graph machine learning. CoRR, 2022.
+
+Hieu Pham, Melody Y. Guan, Barret Zoph, Quoc V. Le, and Jeff Dean. Efficient neural architecture search via parameter sharing. In ICML, 2018.
+
+Yijian Qin, Xin Wang, Zeyang Zhang, and Wenwu Zhu. Graph differentiable architecture search with structure learning. In NeurIPS, 2021.
+
+Esteban Real, Sherry Moore, Andrew Selle, Saurabh Saxena, Yutaka Leon Suematsu, Jie Tan, Quoc V. Le, and Alexey Kurakin. Large-scale evolution of image classifiers. In ICML, 2017.
+
+Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V. Le. Regularized evolution for image classifier architecture search. AAAI Press, 2019.
+
+Prithviraj Sen, Galileo Namata, Mustafa Bilgic, Lise Getoor, Brian Gallagher, and Tina Eliassi-Rad. Collective classification in network data. AI Mag., 2008.
+
+Oleksandr Shchur, Maximilian Mumme, Aleksandar Bojchevski, and Stephan Gunnemann. Pitfalls ¨ of graph neural network evaluation. 2018.
+
+Han Shi, Renjie Pi, Hang Xu, Zhenguo Li, James T. Kwok, and Tong Zhang. Multi-objective neural architecture search via predictive network performance optimization. 1911.09336, 2019.
+
+Han Shi, Renjie Pi, Hang Xu, Zhenguo Li, James T. Kwok, and Tong Zhang. Bridging the gap between sample-based and one-shot neural architecture search with BONAS. In NeurIPS, 2020.
+
+David R. So, Quoc V. Le, and Chen Liang. The evolved transformer. In ICML, 2019.
+
+Laurens van der Maaten and Geoffrey Hinton. Visualizing high-dimensional data using t-sne. Journal of Machine Learning Research, 2008.
+
+Colin White, Willie Neiswanger, and Yash Savani. BANANAS: bayesian optimization with neural architectures for neural architecture search. In AAAI, 2021.
+
+Lingxi Xie and Alan L. Yuille. Genetic CNN. In IEEE, 2017.
+
+Sirui Xie, Hehui Zheng, Chunxiao Liu, and Liang Lin. SNAS: stochastic neural architecture search. In ICLR, 2019.
+
+Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In ICLR, 2019.
+
+Yuhui Xu, Lingxi Xie, Xiaopeng Zhang, Xin Chen, Guo-Jun Qi, Qi Tian, and Hongkai Xiong. PC-DARTS: partial channel connections for memory-efficient architecture search. In ICLR, 2020.
+
+Zhitao Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec. Gnnexplainer: Generating explanations for graph neural networks. In NeurIPS, pp. 9240–9251, 2019.
+
+Jiaxuan You, Jure Leskovec, Kaiming He, and Saining Xie. Graph structure of neural networks. In ICML, 2020a.
+
+Jiaxuan You, Zhitao Ying, and Jure Leskovec. Design space for graph neural networks. In NeurIPS, 2020b.
+
+Kaicheng Yu, Christian Sciuto, Martin Jaggi, Claudiu Musat, and Mathieu Salzmann. Evaluating the search phase of neural architecture search. In ICLR, 2020.
+
+Hanqing Zeng, Hongkuan Zhou, Ajitesh Srivastava, Rajgopal Kannan, and Viktor K. Prasanna. Graphsaint: Graph sampling based inductive learning method. In ICLR, 2020.
+
+Chris Zhang, Mengye Ren, and Raquel Urtasun. Graph hypernetworks for neural architecture search. In ICLR, 2019a.
+
+Muhan Zhang, Shali Jiang, Zhicheng Cui, Roman Garnett, and Yixin Chen. D-VAE: A variational autoencoder for directed acyclic graphs. In NeurIPS, 2019b.
+
+Ziwei Zhang, Xin Wang, and Wenwu Zhu. Automated machine learning on graphs: A survey. In IJCAI, 2021.
+
+Yiren Zhao, Duo Wang, Xitong Gao, Robert D. Mullins, Pietro Lio, and Mateja Jamnik. Probabilistic \` dual network architecture search on graphs. 2020.
+
+Kaixiong Zhou, Qingquan Song, Xiao Huang, and Xia Hu. Auto-gnn: Neural architecture search of graph neural networks. 2019.
+
+Barret Zoph and Quoc V. Le. Neural architecture search with reinforcement learning. In ICLR, 2017.
+
+# A EXPERIMENT DETAILS
+
+A.1 SETTINGS
+
+Graph classification datasets. The graph classification datasets used in this work are summarized in Table 3. And the detailed dataset statics can be referred from https://chrsmrrs.github. io/datasets/docs/datasets/.
+
+Table 3: List of the graph classification datasets used in this work.   
+
+<table><tr><td>Small Scale</td><td>AIDS,BZR-MD,COX2-MD,DHFR-MD, Mutagenicity, NCI1, NCI109,PTC-MM, PTC-MR</td></tr><tr><td>Medium/Large Scale</td><td>Tox21-AhR,MCF-7, MOLT-4, UACC257, Yeast, NCI-H23, OVCAR-8, P388, PC-3, SF-295, SN12C, SW-620</td></tr></table>
+
+Specifically, all datasets are binary classification tasks that predict certain properties for small molecules. For example, the labels in Tox21-AhR represent toxicity/non-toxicity, while the graphs in Mutagenicity are classified into two classes based on their mutagenic effect on a bacterium (Morris et al., 2020). Consequently, we use atom types as the node features and bond types as edge features.
+
+Evaluation metrics. For Reddit, we use F1 score (micro) as the evaluation metric following the previous work (Zeng et al., 2020). For other node classification tasks and image dataset, we use classification accuracy as the evaluation metric. For the graph classification tasks, we use ROC-AUC as the evaluation metric.
+
+Dataset splits. For ogbn-arxiv and Reddit, we use the standardized dataset split. For other node classification datasets, we split the nodes in each graph into $70 \%$ , $10 \%$ , $20 \%$ in training, validation, and test sets, respectively. For graph classification tasks, we split the graphs into $80 \%$ , $10 \%$ , $10 \%$ for training, validation, and test sets, respectively.
+
+Hyper-Parameters. We tuned the hyper-parameters of the baselines based on the default setting in their public codes. For FALCON, we construct the candidate set as the 3-hop neighbors of the explored nodes and set the number of start nodes as $\operatorname* { m i n } ( \lceil 1 0 \% \cdot K \rceil , 1 0 )$ , where $K$ denotes the exploration size. The meta-GNN is constitute of 3 message-passing layers and 3 label propagation layers. All the experiments are repeated at least 3 times.
+
+# A.2 DESIGN SPACES
+
+# A.2.1 DESIGN SPACES FOR THE SAMPLE-BASED METHODS
+
+In this work, we use different design spaces for the datasets depending on the task types, i.e., node or graph level. We summarize the design variables and choices in Table 4 and Table 5. For the design space of Reddit, we replace ”Aggregation” in Table 4 with ”Convolutional layer type”, which takes values from {GCNConv (Kipf & Welling, 2017), SAGEConv (Hamilton et al., 2017), GraphConv (Morris et al., 2019), GINConv (Xu et al., 2019), ARMAConv (Bianchi et al., 2019), TAGConv (Du et al.)}.
+
+Table 4: Design Space for the node-level tasks (except for Reddit). 5,832 candidates in total.   
+
+<table><tr><td>Type</td><td>Variable</td><td>Candidate Values</td></tr><tr><td>Hyper-parameters</td><td>Dropout ratio</td><td>[0.0, 0.3, 0.6]</td></tr><tr><td rowspan="6">Architecture</td><td># Pre-process layers</td><td>[1,2, 3]</td></tr><tr><td># Message passing layers</td><td>[2,4,6, 8]</td></tr><tr><td>#Post-precess layers</td><td>[1,2,3]</td></tr><tr><td>Layer connectivity</td><td>STACK, SUM, CAT</td></tr><tr><td>Activation</td><td>ReLU, Swish,Prelu</td></tr><tr><td>Batch norm Aggregation</td><td>True,False Mean,Max, SUM</td></tr></table>
+
+Table 5: Design Space for the graph-level tasks. 58,320 candidates in total.   
+
+<table><tr><td>Type</td><td>Variable</td><td>Candidate Values</td></tr><tr><td>Hyper-parameters</td><td>Dropout ratio</td><td>[0.0, 0.3, 0.6]</td></tr><tr><td rowspan="10"></td><td># Pre-process layers</td><td>[1,2,3]</td></tr><tr><td># Message passing layers</td><td>[2,4,6,8]</td></tr><tr><td># Post-precess layers</td><td>[1,2,3]</td></tr><tr><td>Layer connectivity</td><td>STACK,SUM,CAT</td></tr><tr><td>Activation</td><td>ReLU, Swish,Prelu</td></tr><tr><td>Batch norm</td><td>True,False</td></tr><tr><td>Aggregation</td><td>Mean,Max,SUM</td></tr><tr><td>Node pooling flag (Use node pooling)</td><td>True,False</td></tr><tr><td>Node pooling type (if applicable)</td><td>TopkPool (Gao &amp; Ji,2019), SAGPool (Lee et al.,2019), PANPool (Ma et al.,202O),EdgePool (Diehl,2019)</td></tr><tr><td>Node pooling loop</td><td>[2,4,6]</td></tr></table>
+
+Specifically, The STACK design choice means directly stacking multiple GNN layers, i.e., without skip-connections. We also support node pooling operations for graph classification tasks, where the pooling loop stands for the number of message passing layers between each pooling operation. If the number of message passing layers is $m$ and the node pooling loop is $l$ , there will be a node pooling layer after the ith message passing layer in the design model (hierarchical pooling), where $i \in \{ 1 ^ { \cdot } + \dot { k } \cdot l \ | \ k = 0 , \ldots , \lceil ( m ^ { - } \bar { 1 } ) / l \rceil ^ { \cdot } - 1 \}$ . Moreover, to avoid duplicated and invalid designs, some design variables are required to satisfy specific dependency rules, and we take two examples to elaborate on this point.
+
+• If the node pooling flag of a design is False, then the design does not have any value on node pooling type and node pooling loop, and vice versa.
+
+For example, we denote node pooling flag as $f$ , node pooling type as $t$ , and $^ *$ as any design choice, then( $f { = } ]$ False, $\scriptstyle t = *$ ) or ( $f { = } ]$ False, $l { = } ^ { * }$ ) will both be invalid.
+
+• The node pooling loop should not exceed the number of message passing layers.
+
+For example, design $A ( m { = } 4 , l { = } 4 )$ and design $B$ $\because ( m { = } 4 , l { = } 6 )$ that take the same values on other design variables are duplicated.
+
+Thus, the design graph constructed under dependency rules is more complex. Without loss of generality, we define that the distance of $f { = } ]$ False) and $f =$ True, $l { = } \mathbf { M I N } ( \{ i \in \mathbb { L } \} ) )$ as 1, where $\mathbb { L }$ represents the design choice of node pooling loop. Thus, the design graph is a connected graph that enables the exploration of any node with random initialization. It is also worth mentioning that the search strategy of FALCON is modularized given the design graph. In contrast, the dependency rules constrain the action space of reinforcement learning methods, e.g., $( f { = } \mathrm { T u r e }  \mathrm { F a l s e } )$ is inapplicable, which requires special operation inside the controller.
+
+Table 7: Design space for the one-shot baselines on node and graph classification tasks.   
+
+<table><tr><td>Variable</td><td>Candidate Values</td></tr><tr><td>Dropout ratio</td><td>[0.0, 0.3, 0.6]</td></tr><tr><td>Layer connectivity</td><td>STACK, SUM</td></tr><tr><td># Pre-process layers</td><td>[1, 2, 3]</td></tr><tr><td>#Message passing layers</td><td>[2,4,6, 8]</td></tr><tr><td># Post-precess layers</td><td>[1,2,3]</td></tr><tr><td>Activation</td><td>ReLU,Swish,Prelu</td></tr><tr><td>Batch norm</td><td>True, False</td></tr><tr><td>Aggregation</td><td>Mean, Max, SUM</td></tr></table>
+
+Table 6: Statistics and the construction time of the design graphs.   
+
+<table><tr><td></td><td>#Nodes</td><td>#Edges (Undirected)</td><td> Ave. Degree</td><td>Diameter</td><td>construction time (s)</td></tr><tr><td>DG-1</td><td>5,832</td><td>78.732</td><td>13.5</td><td>13</td><td>13</td></tr><tr><td>DG-2</td><td>58,320</td><td>1,070,172</td><td>18.4</td><td>17</td><td>147</td></tr></table>
+
+We further summarize the statistics and construction time of the design graphs in Table 6, where DG-1 and DG-2 denote the design graphs for node-level and graph-level tasks, respectively. We use multi-processing programing on 50 CPUs (Intel Xeon Gold 5118 CPU $ @ ~ 2 . 3 0 \mathrm { G H z } \mathrm { \Omega }$ ) to conduct the graph construction. Note that we don’t have to construct the entire design graph in the pre-processing step, since we only extend the small portion of the design graph, i.e., , the design subgraph, during the search process. Thus, the total time cost of constructing the design subgraph will be $O ( E ^ { \prime } )$ where $E ^ { \prime }$ is the number of edges in the design subgraph, which largely lowers the time costs.
+
+# A.2.2 DESIGN SPACES FOR THE ONE-SHOT BASELINES
+
+The one-shot models (Liu et al., 2019; Pham et al., 2018) is built upon a super-model that is required to contain all of the architecture choices. We build the macro search space over entire models for both node classification and graph classification datasets with constraints. Firstly, we do not consider CAT (skip-concatenate) a layer connectivity choice, and we also remove design variables for node pooling. The reason is that CAT and node pooling operations change the input shape and make the output embeddings inapplicable for the subsequent weight-sharing modules in our settings. Secondly, the layer connectivity is customized for each layer following the previous works (Liu et al., 2019; Pham et al., 2018), instead of setting as a global value for every layer. Overall, we summarize the design space in Table 7.
+
+To enable a fair comparison, we fine-tune the hyper-parameters and report the best results of the architectures found by the one-shot methods according to their performance in the validation sets.
+
+# B MORE EXPERIMENTAL RESULTS ON GRAPH TASKS
+
+# B.1 GRAPH CLASSIFICATION TASKS
+
+Task performance. Here we provide more results of task performance on the graph classification dataset. We repeat each experiment at least 3 times and report the average performances and the standard errors. The results are summarized in Table 8. The results well demonstrate the preeminence of FALCON in searching for good designs under different data distributions.
+
+Search cost. As shown in Figure 5, we report the search cost of Random, DARTS, ENAS, GraphNAS, and FALCON on the selected datasets. The time measurements are conducted on a single NVIDIA GeForce 3070 GPU (24G). We see FALCON has a comparable time cost with Random and DARTS, which empirically proves the efficiency of FALCON.
+
+However, as FALCON still needs to sample designs and train them from scratch (i.e., the search cost of FALCON is bounded by the search cost of Random), the computational cost is relatively high in large datasets, e.g., OVCAR-8 and MCF-7. We can potentially alleviate this limitation via integrating dataset sampling to reduce time costs.
+
+Table 8: Test performance (ROC-AUC) on the graph classification datasets.   
+
+<table><tr><td></td><td>DHFR-MD</td><td>COX2-MD</td><td>Mutagenicity</td><td>MOLT-4</td><td>NCI-H23</td><td>PTC-MR</td><td>P388</td></tr><tr><td>Random</td><td>59.0±5.2</td><td>63.2±1.9</td><td>77.1±1.9</td><td>58.6±0.7</td><td>58.4±2.1</td><td>59.9±5.7</td><td>63.9±0.7</td></tr><tr><td>BO</td><td>55.1±0.0</td><td>71.6±5.5</td><td>78.3±0.7</td><td>58.1±2.0</td><td>63.6±0.0</td><td>58.8±7.7</td><td>68.9±0.0</td></tr><tr><td>SA</td><td>56.0±7.1</td><td>67.4±3.1</td><td>81.1±0.3</td><td>54.8±1.1</td><td>56.7±3.2</td><td>59.4±6.2</td><td>74.4±1.0</td></tr><tr><td>ENAS</td><td>53.5±3.7</td><td>57.9±1.7</td><td>75.0±1.6</td><td>61.5±0.1</td><td>61.2±1.1</td><td>59.8±1.6</td><td>68.3±1.2</td></tr><tr><td>DARTS</td><td>55.8±6.3</td><td>70.4±3.2</td><td>74.4±0.7</td><td>61.4±0.7</td><td>63.5±1.9</td><td>59.3±0.5</td><td>70.8±0.7</td></tr><tr><td>GraphNAS</td><td>61.6±4.3</td><td>63.9±2.5</td><td>80.2±1.5</td><td>62.1±1.0</td><td>62.4±3.9</td><td>58.6±6.7</td><td>68.2±2.5</td></tr><tr><td>AutoAttend</td><td>63.3±0.9</td><td>68.8±0.7</td><td>79.6±0.1</td><td>59.5±0.2</td><td>61.8±0.2</td><td>57.8±0.6</td><td>74.9±0.5</td></tr><tr><td>GASSO</td><td>60.9±2.3</td><td>68.5±2.0</td><td>75.1±0.5</td><td>57.4±0.9</td><td>64.7±1.5</td><td>51.9±5.2</td><td>71.3±1.4</td></tr><tr><td>FALCON-G</td><td>58.5±8.8</td><td>67.3±3.6</td><td>79.8±1.7</td><td>62.8±3.3</td><td>62.2±1.2</td><td>55.6±6.9</td><td>74.2±3.7</td></tr><tr><td>FALCON-LP</td><td>61.4±1.5</td><td>66.8 ±3.6</td><td>80.2±0.8</td><td>58.5 ±8.8</td><td>63.7±4.1</td><td>55.6±2.0</td><td>75.1±1.1</td></tr><tr><td>FALCON</td><td>63.6±7.9</td><td>67.3±3.2</td><td>81.1±0.5</td><td>64.4±4.0</td><td>66.6±3.3</td><td>60.0±1.4</td><td>77.0±1.4</td></tr><tr><td>(cont.) PTC-MM</td><td>PC-3</td><td>SF-295</td><td>NCI1</td><td>SW-620</td><td>UACC257</td><td>Yeast</td><td>Avg.</td></tr><tr><td>52.5±5.6</td><td>60.4±0.0</td><td>55.3±0.5</td><td>77.5±0.3</td><td>57.5±2.7</td><td>61.1±0.5</td><td>53.3±0.0</td><td>61.3</td></tr><tr><td>60.1±1.5</td><td>59.7±0.1</td><td>60.6±0.3</td><td>77.3±0.0</td><td>63.8±0.9</td><td>60.8±0.0</td><td>55.0±0.0</td><td>63.7</td></tr><tr><td>58.1±4.6</td><td>69.0±2.0</td><td>55.3±0.6</td><td>79.6±5.3</td><td>58.2±2.1</td><td>64.2±0.1</td><td>53.8±1.2</td><td>63.4</td></tr><tr><td>52.4±2.9</td><td>62.2±1.1</td><td>60.9±2.2</td><td>77.2±1.2</td><td>64.8±2.2</td><td>64.7±0.5</td><td>63.0±1.1</td><td>63.0</td></tr><tr><td>52.6±4.1</td><td>61.6±0.5</td><td>62.2±1.1</td><td>66.3±3.0</td><td>66.0±0.3</td><td>65.7±0.2</td><td>61.4±1.4</td><td>63.7</td></tr><tr><td>54.8±3.9</td><td>68.6±2.6</td><td>65.0±3.1</td><td>78.1±3.6</td><td>61.8±4.4</td><td>61.5±5.1</td><td>57.2±1.1</td><td>64.6</td></tr><tr><td>64.7±1.2</td><td>66.2±0.3</td><td>64.2±0.9</td><td>79.3±1.6</td><td>65.5±0.4</td><td>57.1±0.5</td><td>59.6±0.8</td><td>65.9</td></tr><tr><td>63.2±0.7</td><td>66.0±1.8</td><td>65.8±0.4</td><td>76.6±0.6</td><td>64.7±1.1</td><td>62.7±0.2</td><td>60.1±0.4</td><td>64.9</td></tr><tr><td>55.2±2.4</td><td>65.1±2.8</td><td>64.3±2.1</td><td>80.6±0.8</td><td>62.0±3.0</td><td>61.0±3.8</td><td>57.5±1.5</td><td>64.7</td></tr><tr><td>56.8±6.1</td><td>68.1±0.3</td><td>63.5±3.4</td><td>80.4±0.5</td><td>65.2±1.7</td><td>54.5±1.1</td><td>56.6±1.7</td><td>64.7</td></tr><tr><td>57.1±0.1</td><td>71.0±1.7</td><td>64.4±0.4</td><td>80.9±0.8</td><td>66.6±2.1</td><td>66.7±2.1</td><td>58.1±1.7</td><td>67.5*</td></tr></table>
+
+![](images/7a0b606254da566c19df066ac58aa4ea0e3d029a2a6ecee463de02fadb59227b.jpg)  
+Figure 5: Search cost on the selected datasets.
+
+ROC-AUC v.s. exploration size. Here we report the change in task performance on graph classification datasets with the number of explored nodes. In Figure 6, we visualize the results on two graph classification datasets. We see that FALCON can approach the best-performing designs quickly as the explored size grows.
+
+# B.2 BEST DESIGNS
+
+In Table 9 and Table 10, we summarize the best designs found by FALCON and BRUTEFORCE in each dataset, where the average number of parameters is $1 3 7 . 5 \mathrm { k }$ for all the graph classification datasets. Note that we select the best designs according to their performance on validation sets; thus, there are cases where FALCON surpasses BRUTEFORCE. We highlight the design variables that are different between FALCON and BRUTEFORCE for comparison.
+
+![](images/5c3ceca7328b352710dc2b8ff0170caf6dc14d8b860eb717ee5affe7c0b94069.jpg)  
+Figure 6: Accuracy v.s. the number of explored nodes on two graph classification datasets.
+
+Table 9: Average parameters & Best designs in the node classification datasets.   
+
+<table><tr><td>Dataset</td><td>Average Param (k)</td><td>Best design</td><td></td><td>Test perfor- mance (%)</td></tr><tr><td rowspan="2">ogbn-arxiv</td><td rowspan="2">44.5</td><td>FALCON</td><td>(0.0,1,4,2, STACK, Swish, True, Mean)</td><td>70.36</td></tr><tr><td>BRUTEFORCE</td><td>(0.3,1,4,2, SUM， Relu, True,Mean)</td><td>70.51</td></tr><tr><td>Cora</td><td>77.8</td><td>FALCON BRUTEFORCE</td><td>(0.0, 1, 6,1, SUM, Swish,False,Mean) (0.0,1,4,1, STACK, Swish,False,Mean)</td><td>87.18 86.99</td></tr><tr><td>Citeseer</td><td>289.0</td><td>FALCON BRUTEFORCE</td><td>(0.3,1,2,1,SUM, Prelu, True, Mean) (0.3,1,2,2, SUM, Prelu, False, Mean)</td><td>76.19 75.99</td></tr><tr><td>Pubmed</td><td>57.8</td><td>FALCON BRUTEFORCE</td><td>(0.3,1,8,1,SUM, Relu, True,Add) (0.3,1,8,1,SUM, Relu, True,Add)</td><td>90.04 90.04</td></tr><tr><td>AmazonComputers</td><td>46.2</td><td>FALCON BRUTEFORCE</td><td>(0.0,1,4,1,STACK,Swish,True,Mean) (0.0,3,4,2,STACK,Prelu,True,Mean)</td><td>91.64 91.35</td></tr><tr><td>Reddit</td><td>47.2</td><td>FALCON BRUTEFORCE</td><td>(0.0,3,4,2, STACK,Prelu, True,ARMAConv) (0.0,3,4,2, STACK,Prelu,True,ARMAConv)</td><td>95.46 95.46</td></tr></table>
+
+# B.3 BRUTEFORCE’S CONFIDENCE INTERVAL AND VARIANT
+
+To estimate the uncertainty of Bruteforce, we compute the $9 5 \%$ confidence interval of Bruteforce using bootstrapping. Moreover, we consider a variant of Bruteforce baseline to compare with Bruteforce. Specifically, we train all the designs in the design space for 30 epochs, select the top $10 \%$ design, and resume the training until 50 epochs. After that, we choose the top $50 \%$ designs to be fully trained and return the best fully trained design based on the validation performance. We run Bruteforce-bootstrap on four datasets as demonstrations. We summarize the results in Table 11.
+
+Table 11: Test performances of Bruteforce and its variant.   
+
+<table><tr><td></td><td>Cora</td><td>CiteSeer</td><td>ER-MD</td><td>AIDS</td></tr><tr><td>Bruteforce (max)</td><td>87.0</td><td>76.0</td><td>83.3</td><td>96.0</td></tr><tr><td>Confidence interval length</td><td>0.2</td><td>0.1</td><td>0.6</td><td>0.0</td></tr><tr><td>Bruteforce-bootstrap</td><td>87.0</td><td>76.4</td><td>83.8</td><td>95.7</td></tr></table>
+
+Surprisingly, we found that the performance of Bruteforce and Bruteforce-bootstrap are very close. This indicates that Bruteforce (fully trained $5 \%$ design) is a good surrogate of Bruteforcebootstrapping (fully trained $5 \%$ design, but using bootstrapping selection), and could also well approximate the ground truth performance of the best design.
+
+Table 10: Best designs in the graph classification datasets.   
+
+<table><tr><td>Dataset</td><td></td><td>Best design</td><td>Test perfor- mance (%)</td></tr><tr><td rowspan="2">AIDS</td><td>FALCON</td><td>(0.3,1,4,2， SUM，Prelu, True,Add, NoPool)</td><td>99.02</td></tr><tr><td>BRUTEFORCE</td><td>(0.0,3,8,2, STACK,Relu, True,Add, SAGPool, 2)</td><td>95.97</td></tr><tr><td rowspan="2">COX2-MD</td><td>FALCON</td><td>(0.0,2,6,1，SUM，Swish,True,Add,EdgePool,2)</td><td>69.87</td></tr><tr><td>BRUTEFORCE</td><td>(0.0,1, 4, 3, STACK,Prelu, True,Max, TopkPool, 2)</td><td>65.39</td></tr><tr><td>DHFR-MD</td><td>FALCON</td><td>(0.3,2,4,2,SUM,Swish,True,Mean,PANPool,2)</td><td>71.33</td></tr><tr><td rowspan="2">ER-MD</td><td>BRUTEFORCE</td><td>(0.0,1,4,3, CAT, Prelu, True, Mean, SAGPool,4)</td><td>56.22</td></tr><tr><td>FALCON</td><td>(0.3,3,4,2， CAT, Relu, True,Add,PANPool,2)</td><td>81.67</td></tr><tr><td rowspan="2">MCF-7</td><td>BRUTEFORCE</td><td>(0.0,3,5,3, CAT, Prelu, True,Max,PANPool,6)</td><td>83.33</td></tr><tr><td>FALCON BRUTEFORCE</td><td>(0.6,1,8, 2, CAT, Swish, True, Add, NoPool) (0.0,1,2, 6, SUM,Prelu, True,Add, NoPool)</td><td>67.85 70.61</td></tr><tr><td rowspan="2">MOLT-4</td><td></td><td></td><td></td></tr><tr><td>FALCON BRUTEFORCE</td><td>(0.0,3,6,2, SUM,Prelu,True,Max,NoPool) (0.0,1,6,1, SUM,Prelu,True,Add,NoPool)</td><td>69.03 70.30</td></tr><tr><td rowspan="2">Mutagenicity</td><td></td><td></td><td></td></tr><tr><td>FALCON BRUTEFORCE</td><td>(0.0,2, 6,1, CAT,Relu, True,Add, NoPool) (0.0,2,4,2, CAT, Relu, True,Add, PANPool, 2)</td><td>81.73</td></tr><tr><td rowspan="2">NCI1</td><td></td><td></td><td>81.17</td></tr><tr><td>FALCON BRUTEFORCE</td><td>(0.0,2,4,2, SUM, Swish, True, Max, EdgePool,2) (0.0,1,4,2,STACK,Prelu,True,Add,EdgePool,4)</td><td>80.13</td></tr><tr><td rowspan="2">NCI109</td><td></td><td></td><td>82.81</td></tr><tr><td>FALCON BRUTEFORCE</td><td>(0.0,2,8,2, STACK,Prelu, True,Max,NoPool) (0.0,3, 6,2, STACK,Prelu, True,Add,EdgePool, 6)</td><td>79.98 81.77</td></tr><tr><td rowspan="2">NCI-H23</td><td>FALCON</td><td></td><td></td></tr><tr><td>BRUTEFORCE</td><td>(0.0,2,6,1,CAT,Swish,True,Add,NoPool) (0.0,2,6,1,CAT,Swish,True,Add,NoPool)</td><td>71.14 71.14</td></tr><tr><td rowspan="2">OVCAR-8</td><td>FALCON</td><td></td><td></td></tr><tr><td>BRUTEFORCE</td><td>(0.6,2,6,2, CAT, Swish, True,Add, NoPool) (0.6,1,2,3,CAT,Swish,True,Add,NoPool)</td><td>68.21 67.40</td></tr><tr><td rowspan="2">P388</td><td>FALCON</td><td></td><td></td></tr><tr><td>BRUTEFORCE</td><td>(0.0,2,6,2,CAT,Prelu,True,Add,NoPool)</td><td>78.75</td></tr><tr><td rowspan="2">PC-3</td><td>FALCON</td><td>(0.0,2,6,2, CAT,Prelu,True,Add,NoPool)</td><td>78.75</td></tr><tr><td>BRUTEFORCE</td><td>(0.0,2,6,1, SUM,Relu,True,Max,NoPool)</td><td>73.28</td></tr><tr><td rowspan="2">PTC-MM</td><td></td><td>(0.0,2,6,1, SUM,Relu,True,Max,NoPool)</td><td>73.28</td></tr><tr><td>FALCON</td><td>(0.0,2,4,2,STACK,Swish,True，Max,EdgePool,2)</td><td>56.96</td></tr><tr><td rowspan="2">PTC-MR</td><td>BRUTEFORCE</td><td>(0.0,3,6,1， SUM，Swish, True,Mean,EdgePool,2)</td><td>52.93</td></tr><tr><td>FALCON</td><td>(0.0,2, 4, 2, SUM, Swish, True, Mean, TopkPool, 2)</td><td>60.56</td></tr><tr><td rowspan="2">SF-295</td><td>BRUTEFORCE</td><td>(0.3,1,6,2, SUM,Relu,True,Add,NoPool)</td><td>63.06</td></tr><tr><td>FALCON</td><td>(0.6,2, 6, 2, CAT, Swish, True,Add, NoPool)</td><td>64.75</td></tr><tr><td rowspan="2"></td><td>BRUTEFORCE</td><td>(0.0, 3, 8,3, SUM, Prelu, True, Max, PANPool, 4)</td><td>66.47</td></tr><tr><td>FALCON</td><td>(0.0,1, 8,1, CAT, Swish, True,Add, NoPool)</td><td>73.34</td></tr><tr><td rowspan="2">SN12C SW-620</td><td>BRUTEFORCE</td><td>(0.0,1,8,3, CAT,Prelu, True,Add,EdgePool, 6)</td><td>73.73</td></tr><tr><td>FALCON</td><td>(0.0,2,4,2,STACK,Prelu,True,Max,NoPool)</td><td>69.26</td></tr><tr><td rowspan="2"></td><td>BRUTEFORCE</td><td>(0.0,2,4,2, STACK,Prelu,True,Max,NoPool)</td><td>69.26</td></tr><tr><td>FALCON</td><td>(0.0,2,4,2, SUM,Prelu, True,Add,EdgePool,2)</td><td>79.10</td></tr><tr><td rowspan="2">Tox21-AhR</td><td>BRUTEFORCE</td><td>(0.0,3,6,2, SUM,Prelu, True,Add, NoPool)</td><td>82.02</td></tr><tr><td>FALCON</td><td>(0.3,2,6,2, CAT,Swish,True,Max,NoPool)</td><td>67.94</td></tr><tr><td rowspan="2">UACC257</td><td>BRUTEFORCE</td><td>(0.0,3,6,1,SUM,Prelu,True,Max,NoPool)</td><td>70.24</td></tr><tr><td>FALCON</td><td>(0.6,1,8,1, CAT, Prelu, True,Add, NoPool)</td><td>59.60</td></tr><tr><td rowspan="2">Yeast</td><td>BRUTEFORCE</td><td></td><td></td></tr><tr><td></td><td>(0.0,1,2,3, SUM, Swish, True,Add, EdgePool, 2)</td><td>60.41</td></tr></table>
+
+# C EXPERIMENTAL RESULTS ON THE IMAGE TASK
+
+# C.1 DATASET PRE-PROCESSING
+
+We use the CIFAR-10 (Krizhevsky, 2009) image dataset to show FALCON can work well on other machine learning domains. This dataset consists of 50,000 training images and 10,000 test images. We randomly crop them to size $3 2 \times 3 2$ , and conduct random flipping and normalization.
+
+# C.2 DESIGN SPACES
+
+Here we use two different design spaces to demonstrate FALCON’s ability in searching for both hyper-parameters and architectures on image dataset.
+
+Hyper-parameter Design Space. We consider a broad space of hyper-parameter search, including common hyper-parameters like Batch Size. We train each design using a SGD optimizer, which requires weight decay and momentum as hyper-parameters. We also use a learning rate (LR) scheduler, which reduces the learning rate when validation performance has stopped improving. Specifically, the scheduler will reduce the learning rate by a factor if no improvement is seen for a ‘patience’ number of epochs. It is also worth mentioning that FALCON is flexible for other sets of hyper-parameter choices determined by the user end.
+
+Table 12: Hyper-parameter design space for image tasks.   
+
+<table><tr><td>Variable</td><td>Candidate Values</td></tr><tr><td>Momentum (SGD)</td><td>[0.5, 0.9, 0.99]</td></tr><tr><td>Weight decay</td><td>[le-4, 5e-4,1e-3, 5e-3]</td></tr><tr><td>Batch size</td><td>[32, 64, 128,256]</td></tr><tr><td>LR decay factor</td><td>[0.1, 0.2, 0.5, 0.8]</td></tr><tr><td>LR decay patience</td><td>[3,5,10]</td></tr></table>
+
+Architecture Design Space. We construct micro design space for the computational cells. Each cell constitutes of two branches, where we enable five selections: separable convolution with kernel size 3 $\times 3$ and $5 \times 5$ , average pooling and max pooling with kernel size $3 { \times } 3$ , and identity. In each branch, we have one dropout layer, where the dropout ratio is one of $\{ 0 . 0 , 0 . 3 , 0 . 6 \}$ , and one batch normalization layer. We also use one of identity and skip-sum as skip-connection within each branch. After the input data is separately computed in each branch, the outputs are added as the final cell output, which is different with the original ENAS paper that searches the computational DAG on the defined nodes.
+
+# C.3 EXPERIMENTAL RESULTS
+
+Here we set the exploration size as 20 for all the sample-based methods. For hyper-parameter design space, we compare FALCON with the baselines that are available for hyper-parameter tuning. Moreover, to accelerate the search process, FALCON explores an unknown design by fine-tuning a pretrained model for several epochs based on the selected hyper-parameters, instead of training each candidate design from scratch. The results are summarized in Table 13.
+
+Table 13: Search results on the hyper-parameter design space for CIFAR-10 dataset.   
+
+<table><tr><td>Average Error (%)</td></tr><tr><td>Random 4.13</td></tr><tr><td>BO 4.95</td></tr><tr><td>SA 4.04</td></tr><tr><td>FALCON 3.80</td></tr></table>
+
+![](images/1fa7a05d86d07ca777cb741e0f0e55576b7a384e946274fcbd7f495e809a2ce8.jpg)  
+Figure 7: Sensitivity of FALCON’s hyper-parameters.
+
+For the architecture design space. For ENAS and DARTS, the learning rate is 0.01, and the maximum training epoch is 300. We repeat each experiment three times and summarize the results in Table 14.
+
+Table 14: Search results on the architecture design space for CIFAR-10 dataset.   
+
+<table><tr><td></td><td>Average Error (%)</td><td>Search Cost (GPU days)</td></tr><tr><td>Random</td><td>10.43</td><td>0.64</td></tr><tr><td>BO</td><td>9.83</td><td>0.67</td></tr><tr><td>SA</td><td>10.16</td><td>0.62</td></tr><tr><td>ENAS-micro</td><td>9.20</td><td>0.77</td></tr><tr><td>DARTS-micro</td><td>8.97</td><td>0.89</td></tr><tr><td>FALCON</td><td>8.87</td><td>0.81</td></tr></table>
+
+# D SENSITIVITY ANALYSIS
+
+We analyze the sensitivity of the hyper-parameters in the search strategy of FALCON, using a node classification task, CiteSeer, and a graph classification task, Tox21-AhR. Specifically, we study the influence of the number of random starting nodes and the candidate scale resulting from an explored node (i.e., how many hop neighbors of an explored node are to be included in the candidate set).
+
+As shown in Figure 7, we find that FALCON outperforms the best AutoML baselines with a large range of hyper-parameters. Specifically, $7 3 \%$ and $9 7 \%$ hyper-parameter combinations of FALCON rank best among the baselines in CiteSeer and Tox21-AhR, respectively.
+
+Moreover, we discover an interesting insight about the size of receptive field, i.e., the number of design candidates, during the search process of FALCON. According to the construction of design subgraph, the receptive field size is $\dot { O } ( r h ^ { d } )$ , where $r$ is the number of random start nodes, $h$ is the number of neighbor hops, and $d$ is the average node degree. We find that the performance of design searched by FALCON increases with the receptive field’s size until it reaches a certain scale.
+
+Such patterns have been widely observed in multiple datasets. While the receptive field on the design subgraph should contain sufficient candidates for sampling good ones, it should also prune inferior design space, which doesn’t provide insights on navigating the best-performing designs. Thus, the size of the receptive field may be a crucial factor influencing the search quality of FALCON.

parse/dev/OJ4mMfGKLN/OJ4mMfGKLN.md

@@ -0,0 +1,282 @@
+# Self-Supervised Contrastive Pre-Training for Time Series via Time-Frequency Consistency
+
+Xiang Zhang† ∗ Harvard University xiang_zhang@hms.harvard.edu
+
+Ziyuan Zhao∗ Harvard University ziyuanzhao@college.harvard.edu
+
+Theodoros Tsiligkaridis MIT Lincoln Laboratory ttsili@ll.mit.edu
+
+Marinka Zitnik Harvard University marinka@hms.harvard.edu
+
+# Abstract
+
+Pre-training on time series poses a unique challenge due to the potential mismatch between pre-training and target domains, such as shifts in temporal dynamics, fast-evolving trends, and long-range and short-cyclic effects, which can lead to poor downstream performance. While domain adaptation methods can mitigate these shifts, most methods need examples directly from the target domain, making them suboptimal for pre-training. To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequencybased representations of the same example are located close together in the timefrequency space. To this end, we posit that time-frequency consistency (TF-C) — embedding a time-based neighborhood of an example close to its frequency-based neighborhood — is desirable for pre-training. Motivated by TF-C, we define a decomposable pre-training model, where the self-supervised signal is provided by the distance between time and frequency components, each individually trained by contrastive estimation. We evaluate the new method on eight datasets, including electrodiagnostic testing, human activity recognition, mechanical fault detection, and physical status monitoring. Experiments against eight state-of-the-art methods show that TF-C outperforms baselines by $1 5 . 4 \%$ (F1 score) on average in one-toone settings (e.g., fine-tuning an EEG-pretrained model on EMG data) and by $8 . 4 \%$ (precision) in challenging one-to-many settings (e.g., fine-tuning an EEG-pretrained model for either hand-gesture recognition or mechanical fault prediction), reflecting the breadth of scenarios that arise in real-world applications. The source code and datasets are available at https://github.com/mims-harvard/TFC-pretraining.
+
+# 1 Introduction
+
+Time series plays important roles in many areas, including clinical diagnosis, traffic analysis, and climate science [1, 2, 3, 4, 5, 6]. While representation learning has considerably advanced analysis of time series [7, 8, 9] more broadly [10], learning generalizable representations for temporal data remains a fundamentally challenging problem [8, 11]. There are numerous immediate benefits from generating such representations, of which pre-training capability is particularly desirable and of great practical importance [12, 13]. Central to pre-training is a question of how to process time series in a diverse dataset to greatly improve generalization on new time series coming from different datasets [14, 15, 10]. By training a neural network model on a dataset and transferring it to a new target dataset for fine-tuning, i.e., without explicit retraining on that target data, we expect the resulting performance to be at least as good as that of state-of-the-art models tailored to the target dataset.
+
+![](images/d10b217529c8c9769db1cffb0fc4788ef4d9932c40aa683839b8bb19568af200.jpg)  
+Figure 1: a. Illustration of Time-Frequency Consistency (TF-C). Time-based embedding $\boldsymbol { z } _ { i } ^ { \mathrm { T } }$ and frequencybased embedding $\boldsymbol { z } _ { i } ^ { \mathrm { F } }$ of time series sample $\pmb { x } _ { i } ^ { \mathrm { T } }$ , along with $\widetilde { z } _ { i } ^ { \mathrm { T } }$ and $\widetilde { z } _ { i } ^ { \mathrm { F } }$ learned from augmentations of $\mathbf { \boldsymbol { x } } _ { i } ^ { \mathrm { { T } } }$ , should e ebe close to each other in the latent time-frequency space. b. Leveraging TF-C property in time series to optimize a pre-training model $\mathcal { F }$ with parameters $\Theta$ that get fine-tuned to $\Phi$ on a small scenario-specific dataset.
+
+However, unfortunately, the expected performance gains are often not realized for a variety of reasons (e.g., distribution shifts, properties of the target dataset unknown during pre-training) [16, 17] that get compounded by the complexity of time series: large variations of temporal dynamics across datasets, varying semantic meaning, irregular sampling, system factors (e.g., different devices or subjects), etc. [18, 17]. This complexity of time series limits the utility of knowledge transfer for pre-training [19, 20]. For example, pre-training a model on a diverse time series dataset with mostly low-frequency components (smooth trends) may not lead to positive transfer on downstream tasks with high-frequency components (transient events) [17]. Examining these challenges can provide clues to what kind of inductive biases could facilitate generalizable representations of time series – this paper offers a strategy for that through a novel time-frequency consistency principle.
+
+In addition, target datasets are not available during pre-training (different from domain adaption [21]; Appendix A), requiring that the pre-training model captures a latent property that holds true for previously unseen target datasets. At the center of this desideratum is the idea of a property that would be shared between pre-training and target datasets and would enable knowledge transfer from pre-training to fine-tuning. In computer vision (CV), pre-training is driven by findings that initial neural layers capture universal visual elements, such as edges and shapes, that are relevant regardless of image style and tasks [22]. In natural language processing (NLP), the foundation for pre-training is given by linguistic principles of semantics and grammar shared across different languages [23]. However, due to the aforementioned temporal complexity, such a principle for pre-training on time series has not yet been established. Moreover, supervised pre-training requires access to large annotated datasets, which limits its use in domains where richly labeled datasets are scarce [24, 25]. For example, in medical applications, labeling data at scale is often infeasible or can be expensive and noisy (experts can disagree on ground-truth labeling [26, 27], e.g., whether an ECG signal indicates a normal vs. abnormal rhythm) [28, 29]. To mitigate these issues, self-supervised learning emerged as a promising strategy to sidestep the lack of labeled datasets [30].
+
+Present work. We introduce a strategy for self-supervised pre-training in time series by modeling Time-Frequency Consistency (TF-C). TF-C specifies that time-based and frequency-based representations, learned from the same time series sample, should be closer to each other in the time-frequency space than representations of different time series samples. Specifically, we adopt contrastive learning in time-space to generate a time-based representation. In parallel, we propose a set of novel augmentations based on the characteristic of the frequency spectrum and produce a frequency-based embedding through contrastive instance discrimination. This is the first work to develop frequencybased contrastive augmentation to leverage rich spectral information and explore time-frequency consistency in time series. The pre-training objective is to minimize the distance between time-based and frequency-based embeddings using a novel consistency loss (Figure 1 (a)). The self-supervised loss is used to optimize the pre-training model and enforce consistency between time and frequency domains in the latent space. The learned relationship encoded in model parameters are transferred to initialize the fine-tuning model and improve performance in datasets of interest (Figure 1 (b)).
+
+We evaluate the TF-C model on eight time series datasets under two evaluation settings (i.e., oneto-one and one-to-many). The eight datasets cover a large set of variations: different numbers of channels (from univariate to 9-channel multivariate), varying time series lengths (from 128 to 5,120), different sampling rates (from $1 6 \ \mathrm { H z }$ to $4 { , } 0 0 0 ~ \mathrm { H z }$ ), different scenarios (neurological healthcare, human activity recognition, mechanical fault detection, physical status monitoring, etc.) and diverse types of signals (EEG, EMG, ECG, acceleration, and vibration). We compare TF-C approach to eight state-of-the-art baselines. Results show that TF-C achieves positive transfer, outperforming all baselines by a large margin of $1 5 . 4 \%$ (F1 score) on average. Further, the approach outperforms the strongest baselines with an improvement of up to $7 . 2 \%$ in the F1 score. Finally, the TF-C approach improves prior work by $8 . 4 \%$ in precision (when pre-training the model on sleep EEG signals and fine-tuning it on hand-gesture recognition) in challenging one-to-many setups that apply the same pre-trained model to multiple independent fine-tuning datasets.
+
+# 2 Related Work
+
+Pre-training for time series. Although there are studies on self-supervised representation learning for time series [7, 8, 31, 32] and self-supervised pre-training for images [33, 34, 35, 24], the intersection of these two areas, i.e., self-supervised pre-training for time series, remains underexplored. In time series, it’s not obvious what reasonable assumptions can bridge pre-training and target datasets. Hence, pre-training models in CV [36, 37, 14] and NLP [10, 15, 38] are not directly applicable due to data modality mismatch, and the existing results leave room for improvement [31, 39, 40]. Shi et al. [12] developed the only model to date that is explicitly designed for self-supervised time series pre-training. The model captures the local and global temporal pattern, but it is not convincing why the designed pretext task can capture generalizable representations. Although several studies applied transfer learning in the context of time series [7, 8, 18, 41], there is no foundation yet of which conceptual properties are most suitable for pre-training on time series and why. Addressing this gap, we show that TF-C, designed to be invariant to different time-series datasets, can produce generalizable pre-training models.
+
+Unlike domain adaptation [21, 42] that requires access to target datasets during training, pre-training models do not have access to fine-tuning datasets. As a result, one needs to identify a generalizable time-series property to benefit from pre-training. Further, self-supervised domain adaptation does not need labels in the target dataset but still requires labels for model training [43, 44]. In contrast, TF-C does not need any labels during pre-training.
+
+Contrastive learning with time series. Contrastive learning, a popular type of self-supervised learning, aims to learn an encoder that maps inputs into an embedding space such that positive sample pairs (original augmentation and another alternative augmentation/view of the same input sample) are pulled closer and negative sample pairs (original augmentation and an alternative input sample augmentation) are pushed apart [30, 45]. Contrastive learning in time series is less investigated in comparison, partly due to the challenge of identifying augmentations that capture key invariance properties in time series data. For example, CLOCS defines adjacent time segments as positive pairs [41], and TNC assumes overlapping temporal neighborhoods have similar representations [46]. These methods leverage temporal invariance to define positive pairs which are used to calculate contrastive loss, but other invariances, such as transformation invariance (e.g., SimCLR [40]), contextual invariance (e.g., TS2vec [47] and TS-TCC [48]) and augmentations are possible. In this work, we propose an augmentation bank that exploits multiple invariances to generate diverse augmentations (Sec. 4.1), which adds richness to the pre-training model [48]. Importantly, we propose frequencybased augmentations by perturbing the frequency spectrum of time series (e.g., adding or removing the frequency components and manipulating their amplitude; more details in Sec. 4.2) to learn better representations by exposing the model to a local range of frequency variations. In previous work, CoST processes sequential signals through the frequency domain, but the augmentations are still implemented in time space [49]. Similarly, although BTSF [50] involves frequency domain, its data transformation is solely implemented in the time domain using instance-level dropout. Additional commentary on differences between CoST and BTSF is in Appendix B. To the best of our knowledge, this is the first work that directly perturbs the frequency spectrum to leverage frequency-invariance for contrastive learning. Further, we develop a pre-training model that subjects to TF-C upon two individual contrastive encoders.
+
+# 3 Problem Formulation
+
+We are given a pre-training dataset $\mathcal { D } ^ { \mathrm { p r e t } } = \{ { \pmb x } _ { i } ^ { \mathrm { p r e t } } \ | \ i = 1 , \ldots , N \}$ of unlabeled time series samples where sample $\pmb { x } _ { i } ^ { \mathrm { p r e t } }$ has $K ^ { \mathrm { p r e t } }$ channels and $L ^ { \mathrm { p r e t } }$ timestamps. Let ${ \mathcal { D } } ^ { \mathrm { u n e } } = \{ ( { \pmb x } _ { i } ^ { \mathrm { t u n e } } , y _ { i } ) \ | \ i = 1 , \ldots , M \}$ be a fine-tuning (i.e., target; target and fine-tuning are used interchangeably) dataset of labeled time series samples, each having $K ^ { \mathrm { t u n e } }$ channels and $L ^ { \mathrm { t u n e } }$ timestamps. Furthermore, every sample ${ \pmb x } _ { i } ^ { \mathrm { t u n e } }$ is associated with a label $y _ { i } \in \{ 1 , \ldots , C \}$ , where $C$ is the number of classes. Without loss of generality, in the following descriptions, we focus on univariate (single-channel) time series, while noting that our approach can accommodate multivariate time series of varying lengths across datasets (shown in experiments in Sec. 5.2). We use superscript symbol  to denote contrastive augmentations. We note that ${ \pmb x } _ { i } ^ { \mathrm { T } } \equiv { \pmb x } _ { i }$ edenotes an input time series sample, and $\pmb { x } _ { i } ^ { \mathrm { F } }$ denotes discrete frequency spectrum of $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$
+
+Problem (Self-Supervised Contrastive Pre-Training For Time Series). Given are an unlabeled pre-training dataset $\mathcal { D } ^ { p r e t }$ with $N$ samples and a target dataset $\mathcal { D } ^ { t u n e }$ with $M$ samples $( M \ll N ,$ ). The goal is to use $\mathcal { D } ^ { p r e t }$ to pre-train a model $\mathcal { F }$ so that by fine-tuning model parameters on $\mathcal { D } ^ { t u n e }$ , the fine-tuned model produces generalizable representations $z _ { i } ^ { t u n e } = \mathcal { F } ( \mathbf { x } _ { i } ^ { t u n e } )$ for every $\pmb { x } _ { i } ^ { t u n e }$ .
+
+We follow an established setup, e.g., [41]: for pre-training, only the unlabeled dataset $\mathcal { D } ^ { \mathrm { p r e t } }$ is available while, for fine-tuning, a small labeled dataset $\mathcal { D } ^ { \mathrm { t u n e } }$ can be used. In short, a model $\mathcal { F }$ is pre-trained on the unlabeled time series dataset $\mathcal { D } ^ { \mathrm { p r e t } }$ and its optimized model parameters $\Theta$ are fine-tuned to go from $\mathcal { F } ( \cdot , \Theta )$ to $\mathcal { F } ( \cdot , \Phi )$ using the dataset $\mathcal { D } ^ { \mathrm { t u n e } }$ . The $\Phi$ denotes fine-tuned model parameters. Note that this problem (i.e., $\mathcal { D } ^ { \mathrm { p r e t } }$ is independent of the target dataset) is distinct from domain adaptation as fine-tuning dataset $\mathcal { D } ^ { \mathrm { t u n e } }$ is not accessed during pre-training. As a result, the pre-trained model can be used with many different fine-tuning datasets without re-training.
+
+Rationale for Time-Frequency Consistency (TF-C). The central idea is to identify a general property that is preserved across time series datasets and use it to induce transfer learning for effective pre-training. The time domain shows how sensor readouts change with time, whereas the frequency domain shows how much of the signal lies within each frequency component over the entire spectrum [51]. Explicitly considering the frequency domain can provide an understanding of time series behavior that cannot be directly captured solely in the time domain [52]. However, existing contrastive methods (e.g., [47, 48]) focus exclusively on modeling the time domain and ignore the frequency domain altogether. One can argue that approach is sufficient in the case of high-capacity methods as time and frequency domains are different views of the same data [53], which can be cross-translated using transformation, such as Fourier and inverse Fourier [54, 52]. The relationship between the two domains, grounded in signal processing theory, provides an invariance that is valid regardless of the time series distribution [55, 56] and thus can serve as an inductive bias for pretraining. Appendix C provides a commentary with analogies for images. Approaching this invariance through the lens of representation learning, we next formulate Time-Frequency Consistency (TF-C). The TF-C property postulates there exists a latent time-frequency space such that for every sample $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ , time-based representation $z _ { i } ^ { \mathrm { T } }$ and frequency-based representation $z _ { i } ^ { \mathrm { F } }$ of the same sample, together with their local augmentations (defined later), are close to each other in the latent space.
+
+Representational Time-Frequency Consistency (TF-C). Let $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ be a time series and $\mathcal { F }$ be a model satisfying TF-C. Then, time-based representation $z _ { i } ^ { \mathrm { T } }$ and frequency-based representation $z _ { i } ^ { \mathrm { F } }$ as well as representations of $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ ’s local augmentations are proximal in the latent time-frequency space.
+
+Our strategy is to use dataset $\mathcal { D } ^ { \mathrm { p r e t } }$ to induce TF-C in $\mathcal { F }$ ’s model parameters $\Theta$ , which, in turn, are used to initialize the target model on $\mathcal { D } ^ { \mathrm { t u n e } }$ and produce generalizable representations for downstream prediction. The invariant nature of TF-C means that the approach can bridge $\mathcal { D } ^ { \mathrm { p r e t } }$ and $\mathcal { D } ^ { \mathrm { t u n e } }$ even when large discrepancies exist between them (in terms of temporal dynamics, semantic meaning, etc.), providing a vehicle for a general pre-training on time series.
+
+To realize TF-C, our model $\mathcal { F }$ has four components (Figure 2): a time encoder $G _ { \mathrm { T } }$ , a frequency encoder $G _ { \mathrm { F } }$ , and two cross-space projectors $R _ { \mathrm { T } }$ and $R _ { \mathrm { F } }$ that map time-based and frequency-based representations, respectively, to the same time-frequency space. Together, the four components provide a way to embed $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ to the latent time-frequency space such that the time-based embedding $\mathsf { \bar { z } } _ { i } ^ { \mathrm { T } } = R _ { \mathrm { T } } ( G _ { \mathrm { T } } ( \pmb { x } _ { i } ^ { \mathrm { T } } ) )$ and the frequency-based embedding $\pmb { z } _ { i } ^ { \tilde { \mathrm { F } } } = R _ { \mathrm { F } } ( G _ { \mathrm { F } } ( \pmb { x } _ { i } ^ { \mathrm { F } } ) )$ are close together.
+
+![](images/4fff8ef6cb147c6684ddfe8763075015b75664914b9d5d216868779968c9610a.jpg)  
+Figure 2: Overview of TF-C approach. Our TF-C pre-training model $\mathcal { F }$ has four components: a time encoder $G _ { \mathrm { T } }$ , a frequency encoder $G _ { \mathrm { { F } } }$ , and two cross-space projectors $R _ { \mathrm { T } }$ and $R _ { \mathrm { F } }$ . For an input time series ${ \bf { x } } _ { i }$ , the model produces time-based representations (i.e., $\boldsymbol { z } _ { i } ^ { \intercal }$ and $\widetilde { z } _ { i } ^ { \mathrm { T } }$ of input $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ and its augmented version, respectively) and frequency-based representations (i.e., $\boldsymbol { z } _ { i } ^ { \mathrm { F } }$ and $\widetilde { z } _ { i } ^ { \mathrm { F } }$ eof input $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ and its augmented version, respectively). The TF-C eproperty is realized by promoting the alignment of time- and frequency-based representations in the latent time-frequency space, providing a vehicle for transferring $\mathcal { F }$ to a target dataset not seen before.
+
+# 4 Our Approach
+
+Next, we present the architecture of the developed self-supervised contrastive pre-training model $\mathcal { F }$ . Unless specified otherwise, the data mentioned in this section are from pre-training dataset and the superscript $\mathrm { p r e t }$ is omitted for simplification. Here we describe the model using univariate time series as an example, but our model can be straightforwardly applied to multivariate time series (Sec 5).
+
+# 4.1 Time-based Contrastive Encoder
+
+For a given input time series sample $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ , we generate an augmentation set $\mathcal { X } _ { i } ^ { \mathrm { { T } } }$ through a time-based augmentation bank $B ^ { \mathrm { { r } } } : { \pmb x } _ { i } ^ { \mathrm { { r } } }  \mathcal { X } _ { i } ^ { \mathrm { { r } } }$ . Each element $\widetilde { \pmb x } _ { i } ^ { \mathrm { T } } \ \in \ \mathcal { X } _ { i } ^ { \mathrm { T } }$ is augmented from $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ based on ethe temporal characteristics. Here, the time-based augmentation bank includes jittering, scaling, time-shifts, and neighborhood segments, all well-established in contrastive learning [40, 48, 41]. We develop an augmentation bank to produce diverse augmentations (rather than a single type of augmentation) and expose the model to complex temporal dynamics, which produces more robust time-based embeddings [48].
+
+For the input $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ , we randomly select an augmented sample $\widetilde { \pmb x } _ { i } ^ { \mathrm { T } } \in \mathcal { X } _ { i } ^ { \mathrm { T } }$ and feed into a contrastive time encoder $G _ { \mathrm { T } }$ that maps samples to embeddings. We have ${ h } _ { i } ^ { \mathrm { T } } = { G } _ { \mathrm { T } } ( { \pmb x } _ { i } ^ { \mathrm { T } } )$ and $\widetilde { \pmb { h } } _ { i } ^ { \mathrm { T } } = \pmb { G } _ { \mathrm { T } } ( \widetilde { \pmb { x } } _ { i } ^ { \mathrm { T } } )$ . As $\widetilde { \pmb { x } } _ { i } ^ { \mathrm { T } }$ is generated based on $\pmb { x } _ { i } ^ { \mathrm { T } }$ , after passing through $G _ { \mathrm { r } }$ , we assume the embedding of $\pmb { x } _ { i } ^ { \mathrm { T } }$ eis close to ethe embedding of $\widetilde { \pmb { x } } _ { i } ^ { \mathrm { T } }$ but far away from the embedding of $\pmb { x } _ { j } ^ { \mathrm { T } }$ and $\widetilde { \pmb { x } } _ { j } ^ { \mathrm { T } }$ that are derived from another sample $\pmb { x } _ { j } ^ { \mathrm { { T } } } \in \mathcal { D } ^ { \mathrm { p r e t } }$ e e[34, 47, 41]. In specific, we select the positive pair as $( \pmb { x } _ { i } ^ { \mathrm { T } } , \widetilde { \pmb { x } } _ { i } ^ { \mathrm { T } } )$ and negative pairs as $( \pmb { x } _ { i } ^ { \mathrm { scriptscriptstyle T } } , \pmb { x } _ { j } ^ { \mathrm { \scriptscriptstyle T } } )$ and $( \pmb { x } _ { i } ^ { \mathrm { scriptscriptstyle T } } , \widetilde { \pmb { x } } _ { j } ^ { \mathrm { \scriptscriptstyle T } } )$ [34].
+
+Contrastive time loss. To maximize the similarity within a positive pair and minimize the similarity within a negative pair, we adopt the NT-Xent (the normalized temperature-scaled cross entropy loss) as distance function $d$ which is widely used in contrastive learning [34, 40]. In specific, we define the loss function of the time-based contrastive encoder in terms of sample $\pmb { x } _ { i } ^ { \mathrm { T } }$ as:
+
+$$
+\mathcal { L } _ { \mathrm { T } , i } = d ( h _ { i } ^ { \mathrm { T } } , \widetilde { h } _ { i } ^ { \mathrm { r } } , \mathcal { D } ^ { \mathrm { p r e t } } ) = - \log \frac { \exp ( \sin ( h _ { i } ^ { \mathrm { T } } , \widetilde { h } _ { i } ^ { \mathrm { T } } ) / \tau ) } { \sum _ { x _ { j } \in \mathcal { D } ^ { \mathrm { p r e t } } } \mathbb { 1 } _ { i \neq j } \exp ( \sin ( h _ { i } ^ { \mathrm { T } } , G _ { \mathrm { T } } ( x _ { j } ) ) / \tau ) } ,
+$$
+
+where $\sin ( \pmb { u } , \pmb { v } ) = \pmb { u } ^ { T } \pmb { v } / \left\| \pmb { u } \right\| \left\| \pmb { v } \right\|$ denotes the cosine similarity, the $\mathbb { 1 } _ { i \neq j }$ is an indicator function that equals to 0 when $i = j$ and 1 otherwise, and $\tau$ is a temporal parameter to adjust scale. The $\pmb { x } _ { j } \in \mathcal { D } ^ { \mathrm { p r e t } }$ refers to a different time series sample or its augmented sample. This loss function
+
+urges the time encoder $G _ { \mathrm { T } }$ to generate closer time-based embeddings for positive pairs and push the embeddings for negative pairs apart from each other.
+
+# 4.2 Frequency-based Contrastive Encoder
+
+We generate the frequency spectrum $\pmb { x } _ { i } ^ { \mathrm { F } }$ from a time series sample $\mathbf { \boldsymbol { x } } _ { i } ^ { \mathrm { { T } } }$ through a transform operator (e.g., Fourier Transformation [54]). The frequency information in time series is universal and plays a key role in classic signal processing [57, 53, 55], but it is rarely investigated in self-supervised contrastive representation learning for time series [58]. In this section, we develop augmentation method to perturb $\pmb { x } _ { i } ^ { \mathrm { F } }$ based on characteristics of frequency spectra and show how to generate frequency-based representations.
+
+As every frequency component in the frequency spectrum denotes a basis function (e.g., sinusoidal function for Fourier transformation) with the corresponding frequency and amplitude, we perturb the frequency spectrum by adding or removing frequency components. A small perturbation in the frequency domain may cause large changes to the temporal patterns in the time domain [55]. To make sure the perturbed time series is still similar to the original sample (not only in frequency domain but also in time domain; Figure 6), we use a small budget $E$ in the perturbations where $E$ denotes the number of frequency components we manipulate. While removing frequency components, we randomly select $E$ frequency components and set their amplitudes to 0. While adding frequency components, we randomly choose $E$ frequency components from the ones have smaller amplitude than $\alpha \cdot A _ { m }$ , and increase their amplitude to $\alpha \cdot A _ { m }$ . The $A _ { m }$ is the maximum amplitude in the frequency spectrum and $\alpha$ is a pre-defined coefficient to adjust the scale of the perturbed frequency component $\mathrm { \Delta } ( \alpha = 0 . 5$ in this work). We produce an augmentation set $\mathcal { X } _ { i } ^ { \mathrm { F } }$ for $\pmb { x } _ { i } ^ { \mathrm { F } }$ through frequencyaugmentation bank $B ^ { \mathrm { F } } : { \pmb x } _ { i } ^ { \mathrm { F } }  \mathcal { X } _ { i } ^ { \mathrm { F } }$ . As described above, we have two augmentation methods (i.e., removing or adding frequency components) in $B ^ { \mathrm { F } }$ , $| \mathcal { X } _ { i } ^ { \mathrm { F } } | = 2$ . Details on the exploration of frequency augmentation strategies are covered in Appendix J.
+
+We utilize a frequency encoder $G _ { \mathrm { F } }$ to map the frequency spectrum $( e . g . , \pmb { x } _ { i } ^ { \mathrm { F } } ,$ to a frequency-based embedding (e.g., $\pmb { h } _ { i } ^ { \mathrm { F } } \overset { \cdot } { = } G _ { \mathrm { F } } ( \pmb { x } _ { i } ^ { \mathrm { F } } ) )$ . We assume the frequency encoder $G _ { \mathrm { F } }$ can learn similar embedding for the original frequency spectrum $\pmb { x } _ { i } ^ { \mathrm { F } }$ and a slightly perturbed frequency spectrum $ { \widetilde { \mathbf { x } } } _ { i } ^ { \mathrm { F } } \in  { \mathcal { X } } _ { i } ^ { \mathrm { F } }$ . Thus, we set the positive pair as $( \pmb { x } _ { i } ^ { \mathrm { F } } , \widetilde { \pmb { x } } _ { i } ^ { \mathrm { F } } )$ and the negative pairs as $( \pmb { x } _ { i } ^ { \mathrm { F } } , \pmb { x } _ { j } ^ { \mathrm { F } } )$ and $( \pmb { x } _ { i } ^ { \mathrm { F } } , \widetilde { \pmb { x } } _ { j } ^ { \mathrm { F } } )$ .
+
+Contrastive frequency loss. We calculate frequency-based contrastive loss for sample $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ as:
+
+$$
+\mathcal { L } _ { \mathrm { F } , i } = d ( h _ { i } ^ { \mathrm { F } } , \widetilde { h } _ { i } ^ { \mathrm { F } } , \mathcal { D } ^ { \mathrm { p r e t } } ) = - \log \frac { \exp ( \sin ( h _ { i } ^ { \mathrm { F } } , \widetilde { h } _ { i } ^ { \mathrm { F } } ) / \tau ) } { \sum _ { x _ { j } \in \mathcal { D } ^ { \mathrm { p r e t } } } \mathbb { 1 } _ { i \neq j } \exp ( \sin ( h _ { i } ^ { \mathrm { F } } , G _ { \mathrm { F } } ( x _ { j } ) ) / \tau ) } .
+$$
+
+In preliminary experiments, we find that the value of $\tau$ has little effect on performance and use the same $\tau$ throughout all experiments. The $\mathcal { L } _ { \mathrm { F } , i }$ yield a frequency encoder $G _ { \mathrm { F } }$ producing embeddings invariant to frequency spectrum perturbations.
+
+# 4.3 Time-Frequency Consistency
+
+We develop a consistency loss item $\mathcal { L } _ { \mathrm { C } , i }$ to urge the learned embeddings to satisfy TF-C: for a given sample, its time-based and frequency-based embeddings (and their local neighborhoods) are supposed to be close to each other (see Sec. 3 for justification). To make sure the distance between embeddings is measurable, we map ${ \mathbf { } } h _ { i } ^ { \mathrm { { T } } }$ from time space and $\boldsymbol { h } _ { i } ^ { \mathrm { F } }$ from frequency space to a joint time-frequency space through projectors $R _ { \mathrm { T } }$ and $R _ { \mathrm { F } }$ , respectively. In specific, for every input sample $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ , we have four embeddings, which are $z _ { i } ^ { \mathrm { T } } = R _ { \mathrm { T } } ( h _ { i } ^ { \mathrm { T } } )$ , $\widetilde z _ { i } ^ { \mathrm { T } } = \dot { R } _ { \mathrm { T } } ( \widetilde h _ { i } ^ { \mathrm { T } } )$ , $z _ { i } ^ { \mathrm { F } } = R _ { \mathrm { F } } ( h _ { i } ^ { \mathrm { F } } )$ , and $\widetilde { z } _ { i } ^ { \mathrm { F } } = R _ { \mathrm { F } } ( \widetilde { h } _ { i } ^ { \mathrm { F } } )$ . The first e etwo embeddings are generated based on temporal characteristics and the latter two embeddings are produced based on the properties of frequency spectrum.
+
+To enforce the embeddings in the time-frequency space subject to TF-C, we design a consistency loss $\mathcal { L } _ { \mathrm { C } , i }$ that measures the distance between a time-based embedding and a frequency-based embedding. We use $S _ { i } ^ { \mathrm { T F } } = d ( z _ { i } ^ { \mathrm { T } } , z _ { i } ^ { \mathrm { F } } , \mathcal { D } ^ { \mathrm { p r e t } } )$ to denote the distance between $z _ { i } ^ { \mathrm { T } }$ and $z _ { i } ^ { \mathrm { F } }$ ). Similarly, we define $S _ { i } ^ { \mathrm { T F } }$ $S _ { i } ^ { \mathrm { { \widetilde T F } } }$ , and $\widetilde { S _ { i } ^ { \mathrm { T F } } }$ . Note, in this time-frequency space, we don’t consider the distance between $z _ { i } ^ { \mathrm { T } }$ and $\widetilde { z } _ { i } ^ { \mathrm { T } }$ ewhere the two embeddings are from the same domain (i.e., time domain). The same applies to pair the distance between $z _ { i } ^ { \mathrm { F } }$ and $\widetilde { z } _ { i } ^ { \mathrm { F } }$ . We have already considered information of above two pairs in the calculation of $\mathcal { L } _ { \mathrm { T } , i }$ and $\mathcal { L } _ { \mathrm { F } , i }$ .
+
+Next, let’s closely observe $S _ { i } ^ { \mathrm { T F } }$ and $S _ { i } ^ { \mathrm { T F } }$ that involve three embeddings: $z _ { i } ^ { \mathrm { T } }$ , $z _ { i } ^ { \mathrm { F } }$ , and $\widetilde { z } _ { i } ^ { \mathrm { F } }$ . Here, $z _ { i } ^ { \mathrm { T } }$ and $z _ { i } ^ { \mathrm { F } }$ are learned from the original sample $( \pmb { x } _ { i } ^ { \mathrm { T } }$ and $\pmb { x } _ { i } ^ { \mathrm { F } }$ ) while $\widetilde { z } _ { i } ^ { \mathrm { F } }$ eis learned from the augmented $\widetilde { \pmb { x } } _ { i } ^ { \mathrm { F } }$ . Thus, intuitively, $z _ { i } ^ { \mathrm { T } }$ should be closer to $z _ { i } ^ { \mathrm { F } }$ in comparison to $\widetilde { z } _ { i } ^ { \mathrm { F } }$ e e. Motivated by the relative relationship, we encourage the proposed model to learn a $S _ { i } ^ { \mathrm { T F } }$ ethat is smaller than $S _ { i } ^ { \mathrm { T F } }$ . Inspired by the triplet loss [59], we design $( S _ { i } ^ { \mathrm { T F } } - S _ { i } ^ { \mathrm { T F } } + \delta )$ as a term of consistency loss $\mathcal { L } _ { \mathrm { c } , i }$ where $\delta$ is a given constant margin to keep negative samples far apart [60]. This term optimizes the model towards a smaller $S _ { i } ^ { \mathrm { T F } }$ and relatively larger $S _ { i } ^ { \mathrm { T F } }$ . Similarly, $S _ { i } ^ { \mathrm { T F } }$ is supposed to be smaller than $S _ { i } ^ { \mathrm { { \widetilde T F } } }$ and $\widetilde { S _ { i } ^ { \mathrm { T F } } }$ . In summary, we calculate the consistency loss $\mathcal { L } _ { \mathrm { c } , i }$ for sample $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ by:
+
+$$
+\mathcal { L } _ { \mathrm { c } , i } = \sum _ { S ^ { \mathrm { p a i r } } } ( S _ { i } ^ { \mathrm { T F } } - S _ { i } ^ { \mathrm { p a i r } } + \delta ) , \quad S ^ { \mathrm { p a i r } } \in \{ S _ { i } ^ { \mathrm { T F } } , S _ { i } ^ { \mathrm { T F } } , S _ { i } ^ { \mathrm { \widetilde { T F } } } \} ,
+$$
+
+where $S _ { i } ^ { \mathrm { p a i r } }$ denotes the distance between a time-based embedding (e.g., $z _ { i } ^ { \mathrm { T } }$ or $\widetilde { z } _ { i } ^ { \mathrm { T } }$ ) and a frequencybased embedding (e.g., $z _ { i } ^ { \mathrm { F } }$ or $\widetilde { z } _ { i } ^ { \mathrm { F } }$ e). In each pair, there is at least one embedding that is derived from eaugmented sample instead of the original sample. The $\delta$ is a pre-defined constant. By combining all the triplet loss items, ${ \mathcal { L } } _ { \mathrm { c } }$ encourages the pre-training model to capture the consistency between time-based and frequency-based embeddings in model optimization. Note, although the Eq. 3 does not explicitly measure the loss across different time series samples (e.g., $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { i } }$ and $\mathbf { \Delta } _ { \mathbf { \mathcal { X } } _ { j } }$ ), the cross-sample relationships are implicitly covered in the calculation of $S _ { i } ^ { \mathrm { T F } }$ and $S _ { i } ^ { \mathrm { p a i r } }$ .
+
+# 4.4 Implementation and Technical Details
+
+The overall loss function in pre-training has three terms. First, the time-based contrastive loss ${ \mathcal { L } } _ { \mathrm { T } }$ urges the model to learn embeddings invariant to temporal augmentations. Second, the frequencybased contrastive loss $\mathcal { L } _ { \mathrm { F } }$ promotes learning of embeddings invariant to frequency spectrum-based augmentations. Third, the consistency loss ${ \mathcal { L } } _ { \mathrm { c } }$ guides the model to retain the consistency between time-based and frequency-based embeddings. In summary, the pre-training loss is defined as:
+
+$$
+{ \mathcal { L } } _ { \mathrm { T F } - \mathbb { C } , i } = \lambda ( { \mathcal { L } } _ { \mathrm { T } , i } + { \mathcal { L } } _ { \mathrm { F } , i } ) + ( 1 - \lambda ) { \mathcal { L } } _ { \mathrm { c } , i }
+$$
+
+where $\lambda$ controls the relative importance of the contrastive and consistency losses. We calculate the total loss by summing $\mathcal { L } _ { \mathrm { T F - C } , i }$ across all pre-training samples. In implementation, the contrastive losses are calculated within the batch. From our problem definition, the model $\mathcal { F }$ we want to learn is the combination of neural networks $G _ { \mathrm { T } } , R _ { \mathrm { T } } , G _ { \mathrm { F } }$ , and $R _ { \mathrm { F } }$ . When pre-training is completed, we store parameters of entire model, and denote it as $\mathcal { F } ( \cdot , \Theta )$ where $\Theta$ represents all trainable parameters. When a sample ${ \pmb x } _ { i } ^ { \mathrm { t u n e } }$ is presented, fine-tuned model $\mathcal { F }$ generates an embedding $z _ { i } ^ { \mathrm { t u n e } }$ via concatenation as: $z _ { i } ^ { \mathrm { t u n e } } = \mathcal { F } ( \pmb { x } _ { i } ^ { \mathrm { t u n e } } , \Phi ) = [ z _ { i } ^ { \mathrm { t u n e , T } } ; z _ { i } ^ { \mathrm { t u n e , F } } ]$ where $\Phi$ are fine-tuned model’s parameters.
+
+# 5 Experiments
+
+We compare the developed TF-C model with 10 baselines on 8 diverse datasets. We investigate the time series classification tasks in the context of one-to-one and one-to-many transfer learning setups (the many-to-one setting is fundamentally different as discussed in Appendix K). We also assess TF-C in extensive downstream tasks including clustering and anomaly detection.
+
+Datasets. (1) SLEEPEEG [61] has 371,055 univariate brainwaves (EEG; $1 0 0 \mathrm { H z } ,$ ) collected from 197 individuals. Each sample is associated with one of five sleeping stages. (2) EPILEPSY [62] monitors the brain activities of 500 subjects with single-channel EEG sensor $\boldsymbol { 1 7 4 } \ : \mathrm { H z } )$ . A sample is labeled in binary based on whether the subject has epilepsy or not. (3) FD-A [63] gathers the vibration signals from rolling bearing from a mechanical system aiming at fault detection. Every sample has 5,120 timestamps and an indicator for one out of three mechanical device states. (4) FD-B [63] has the same setting as the FD-A but the rolling bearings are performed in different working conditions (e.g., varying rotational speed). (5) HAR [64] has 10,299 9-dimension samples from 6 daily activities. (6) GESTURE [65] includes 440 samples that are collected from 8 hand gestures recorded by an accelerometer. (7) ECG [26] contains 8,528 single-sensor ECG recordings with sorted into four classes based on human physiology. (8) EMG [66] consists of 163 EMG samples with 3-class labels implying muscular diseases. Dataset labels are not used in pre-training. Further dataset statistics are in Appendix $\mathrm { D }$ and Table 3.
+
+Baselines. We consider 10 baseline methods. This includes 8 state-of-the-art methods: TS-SD [12], TS2vec [47], CLOCS [41], Mixing-up [18], TS-TCC [48], SimCLR [40], TNC [46], and CPC [30].
+
+Table 1: One-to-one pre-training evaluation (Scenario 3). Pre-training is performed on HAR, followed by fine-tuning on GESTURE. Results for other three scenarios are shown in Tables 4-6.   
+
+<table><tr><td>Models</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1 score</td><td>AUROC</td><td>AUPRC</td></tr><tr><td>Non-DL (KNN)</td><td>0.6766±0.0000</td><td>0.6500±0.0000</td><td>0.6821±0.0000</td><td>0.6442±0.0000</td><td>0.8190±0.0000</td><td>0.5231±0.0000</td></tr><tr><td>Random Init.</td><td>0.4219±0.0865</td><td>0.4751±0.0925</td><td>0.4963±0.1026</td><td>0.4886±0.0967</td><td>0.7129±0.1206</td><td>0.3358±0.1194</td></tr><tr><td>TS-SD</td><td>0.6937±0.0533</td><td>0.6806±0.0496</td><td>0.6883±0.0525</td><td>0.6785±0.0495</td><td>0.8708±0.0305</td><td>0.6261±0.0790</td></tr><tr><td>TS2vec</td><td>0.6453±0.0260</td><td>0.6287±0.0339</td><td>0.6451±0.0218</td><td>0.6261±0.0294</td><td>0.8890±0.0054</td><td>0.6670±0.0118</td></tr><tr><td>CLOCS</td><td>0.4731±0.0229</td><td>0.4639±0.0432</td><td>0.4766±0.0266</td><td>0.4392±0.0198</td><td>0.8161±0.0068</td><td>0.4916±0.0103</td></tr><tr><td>Mixing-up</td><td>0.7183±0.0123</td><td>0.7001±0.0166</td><td>0.7183±0.0123</td><td>0.6991±0.0145</td><td>0.9127±0.0018</td><td>0.7654±0.0071</td></tr><tr><td>TS-TCC</td><td>0.7593±0.0242</td><td>0.7668±0.0257</td><td>0.7566±0.0231</td><td>0.7457±0.0210</td><td>0.8866±0.0040</td><td>0.7217±0.0121</td></tr><tr><td>SimCLR</td><td>0.4383±0.0652</td><td>0.4255±0.1072</td><td>0.4383±0.0652</td><td>0.3713±0.0919</td><td>0.7721±0.0559</td><td>0.4116±0.0971</td></tr><tr><td>TF-C (Ours)</td><td>0.7824±0.0237</td><td>0.7982±0.0496</td><td>0.8011±0.0322</td><td>0.7991±0.0296</td><td>0.9052±0.0136</td><td>0.7861±0.0149</td></tr></table>
+
+The TS2Vec, TS-TCC, SimCLR, TNC, and CPC are designed for representation learning on a single dataset rather than for transfer learning, so we apply them to fit our settings and make the results comparable. As the training of TNC and CPC are very time-consuming and relatively less competitive (Table 4), we only compare them in the one-to-one setting (scenario 1) while not in other experiments. To examine the utility of pre-training, we consider two additional approaches that are applied directly to fine-tuning datasets without any pre-training: Non-DL (a non-deep learning KNN model) and Random Init. (randomly initializes the fine-tuning model). The evaluation metrics are accuracy, precision (macro-averaged), recall, F1 score, AUROC, and AUPRC.
+
+Implementation. We use two 3-layer 1-D ResNets [67] as backbones for encoders $G _ { \mathrm { T } }$ and $G _ { \mathrm { F } }$ Our datasets contain long time series (samples in FD-A and FD-B have 5,120 observations), and preliminary experiments identified ResNet as a better option than a Transformer variant [68]. We use 2 fully-connected layers for $R _ { \mathrm { T } }$ and $R _ { \mathrm { F } }$ , with no sharing of parameters. We set $E = 1$ and $\alpha = 0 . 5$ in frequency augmentations and $\tau = 0 . 2$ , $\delta = 1$ , $\lambda = 0 . 5$ in loss functions. Reported are mean and standard deviation values across 5 independent runs (both pre-training and fine-tuning) on the same data split. Results for KNN $( \mathrm { K } { = } 2 )$ do not change so the standard deviation is zero. Method details and hyper-parameter selection are in Appendix E.
+
+# 5.1 Results: One-to-One Pre-Training Evaluation
+
+Setup. In one-to-one evaluation, we pre-train a model on one pre-training dataset and use it for fine-tuning on one target dataset only. Scenario 1 (SLEEPEEG EPILEPSY): Pre-training is done on SLEEPEEG and fine-tuning on EPILEPSY. While both datasets describe a single-channel EEG, the signals are from different channels/positions on scalps, track different physiology (sleep vs. epilepsy), and are collected from different patients. Scenario 2 $\mathrm { F D - A } \longrightarrow \mathrm { F D - B }$ ): Datasets describe mechanical devices that operate in different working conditions, including rotational speed, load torque, and radial force. Scenario 3 (HAR GESTURE): Datasets record different activities (6 types of human daily activities vs. 8 hand gestures). While both datasets contain acceleration signals, HAR has 9 channels while GESTURE has 1 channel. Scenario 4 ( $\operatorname { E C G } \to \operatorname { E M G }$ ): While both are physiological datasets, the ECG records the electrical signal from the heart whereas EMG measures muscle response in response to a nerve’s stimulation of the muscle. We note that the discrepancies between pre-training and fine-tuning datasets in the above four scenarios are substantial, and they cover a diverse range of variation in time series datasets: varying semantic meaning, sampling frequency, time series length, number of classes, and system factors (e.g., number of devices or subjects). The setup is further challenged by the relatively small number of samples available for fine-tuning (EPILEPSY: 60; FD-B: 60; GESTURE: 480; EMG: 122). Further details are in Appendix F.
+
+Results. The results for the four scenarios are shown in Table 1 and Tables 4-6. Overall, our TF-C model has won 16 out of 24 tests (6 metrics in 4 scenarios) and is the second-best performer in only 8 other tests. We report all metrics but discuss the F1 score in the following. On average, our TF-C model claims a large margin of $1 5 . 4 \%$ over all baselines. Although the strongest baseline is varying (such as TS-TCC in Scenario 2; Mixing-up in Scenario 3), our model outperforms the strongest baselines by $1 . 5 \%$ across all scenarios. Specifically, as shown in Table 1 $\mathrm { \Delta \mathrm { \cdot } G A R  G E S T U R E }$ ; Scenario 3), TF-C achieves the highest performance of $7 9 . 9 1 \%$ in F1 score, which yields a margin of $7 . 2 \%$ over the best baseline TS-TCC $( 7 4 . 5 7 \% )$ . One potential explanation is that Scenario 3 involves a complex dataset (HAR has 6 classes while GESTURE has 8 classes) that can be difficult to model. The complexity of Scenario 3 is further verified by poor performance of all models $( \pm 8 0 \% )$ relative to performance on other Scenarios $( \pm 9 0 \% )$ : TF-C shows strong robustness by learning more generalizable representations. Additionally, we visualize the learned representations in time-frequency space (Appendix I), and the analyses provide further support for the TF-C property.
+
+Table 2: One-to-many pre-training evaluation. Pre-training is performed on SLEEPEEG, followed by an independent fine-tuning on EPILEPSY, FD-B, GESTURE, and EMG.   
+
+<table><tr><td>Scenarios</td><td>Models</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1 score</td><td>AUROC</td><td>AUPRC</td></tr><tr><td rowspan="10">SLEEPEEG √ EPILEPSY</td><td>Non-DL (KNN)</td><td>0.8525±0.0000</td><td>0.8639±0.0000</td><td>0.6431±0.0000</td><td>0.6791±0.0000</td><td>0.6434±0.0000</td><td>0.6279±0.0000</td></tr><tr><td>Random Init.</td><td>0.8983±0.0656</td><td>0.9213±0.1369</td><td>0.7447±0.1135</td><td>0.7959±0.1208</td><td>0.8578±0.2153</td><td>0.6489±0.1926</td></tr><tr><td>TS-SD</td><td>0.8952±0.0522</td><td>0.8018±0.2244</td><td>0.7647±0.1485</td><td>0.7767±0.1855</td><td>0.7677±0.2452</td><td>0.7940±0.1825</td></tr><tr><td>TS2vec</td><td>0.9395±0.0044</td><td>0.9059±0.0116</td><td>0.9039±0.0118</td><td>0.9045±0.0067</td><td>0.9587±0.0086</td><td>0.9430±0.0103</td></tr><tr><td>CLOCS</td><td>0.9507±0.0027</td><td>0.9301±0.0067</td><td>0.9127±0.0165</td><td>0.9206±0.0066</td><td>0.9803±0.0023</td><td>0.9609±0.0116</td></tr><tr><td>Mixing-up</td><td>0.8021±0.0000</td><td>0.4011±0.0000</td><td>0.5000±0.0000</td><td>0.4451±0.0000</td><td>0.9743±0.0081</td><td>0.9618±0.0104</td></tr><tr><td>TS-TCC</td><td>0.9253±0.0098</td><td>0.9451±0.0049</td><td>0.8181±0.0257</td><td>0.8633±0.0215</td><td>0.9842±0.0034</td><td>0.9744±0.0043</td></tr><tr><td>SimCLR</td><td>0.9071±0.0344</td><td>0.9221±0.0166</td><td>0.7864±0.1071</td><td>0.8178±0.0998</td><td>0.9045±0.0539</td><td>0.9128±0.0205</td></tr><tr><td>TF-C (Ours)</td><td>0.9495±0.0249</td><td>0.9456±0.0108</td><td>0.8908±0.0216</td><td>0.9149±0.0534</td><td>0.9811±0.0237</td><td>0.9703±0.0199</td></tr><tr><td>Non-DL (KNN)</td><td>0.4473±0.0000</td><td>0.2847±0.0000</td><td>0.3275±0.0000</td><td>0.2284±0.0000</td><td>0.4946±0.0000</td><td>0.3308±0.0000</td></tr><tr><td rowspan="8">SLEEPEEG √ FD-B</td><td>Random Init.</td><td>0.4736±0.0623</td><td>0.4829±0.0529</td><td>0.5235±0.1023</td><td>0.4911±0.0590</td><td>0.7864±0.0349</td><td>0.7528±0.0254</td></tr><tr><td>TS-SD</td><td>0.5566±0.0210</td><td>0.5710±0.0535</td><td>0.6054±0.0272</td><td>0.5703±0.0328</td><td>0.7196±0.0113</td><td>0.5693±0.0532</td></tr><tr><td>TS2vec</td><td>0.4790±0.0113</td><td>0.4339±0.0092</td><td>0.4842±0.0197</td><td>0.4389±0.0107</td><td>0.6463±0.0130</td><td>0.4442±0.0162</td></tr><tr><td>CLOCS</td><td>0.4927±0.0310</td><td>0.4824±0.0316</td><td>0.5873±0.0387</td><td>0.4746±0.0485</td><td>0.6992±0.0099</td><td>0.5501±0.0365</td></tr><tr><td>Mixing-up</td><td>0.6789±0.0246</td><td>0.7146±0.0343</td><td>0.7613±0.0198</td><td>0.7273±0.0228</td><td>0.8209±0.0035</td><td>0.7707±0.0042</td></tr><tr><td>TS-TCC</td><td>0.5499±0.0220</td><td>0.5279±0.0293</td><td>0.6396±0.0178</td><td>0.5418±0.0338</td><td>0.7329±0.0203</td><td>0.5824±0.0468</td></tr><tr><td>SimCLR</td><td>0.4917±0.0437</td><td>0.5446±0.1024</td><td>0.4760±0.0885</td><td>0.4224±0.1138</td><td>0.6619±0.0219</td><td>0.5009±0.0477</td></tr><tr><td>TF-C (Ours)</td><td>0.6938±0.0231</td><td>0.7559±0.0349</td><td>0.7202±0.0257</td><td>0.7487±0.0268</td><td>0.8965±0.0135</td><td>0.7871±0.0267</td></tr><tr><td rowspan="10">SLEEPEEG √ GESTURE</td><td>Non-DL (KNN)</td><td>0.6833±0.0000</td><td>0.6501±0.0000</td><td>0.6833±0.0000</td><td>0.6443±0.0000</td><td>0.8190±0.0000</td><td>0.5232±0.0000</td></tr><tr><td>Random Init.</td><td>0.4219±0.0629</td><td>0.4751±0.0175</td><td>0.4963±0.0679</td><td>0.4886±0.0459</td><td>0.7129±0.0166</td><td>0.3358±0.1439</td></tr><tr><td>TS-SD</td><td>0.6922±0.0444</td><td>0.6698±0.0472</td><td>0.6867±0.0488</td><td>0.6656±0.0443</td><td>0.8725±0.0324</td><td>0.6185±0.0966</td></tr><tr><td>TS2vec</td><td>0.6917±0.0333</td><td>0.6545±0.0358</td><td>0.6854±0.0349</td><td>0.6570±0.0392</td><td>0.8968±0.0123</td><td>0.6989±0.0346</td></tr><tr><td>CLOCS</td><td>0.4433±0.0518</td><td>0.4237±0.0794</td><td>0.4433±0.0518</td><td>0.4014±0.0602</td><td>0.8073±0.0109</td><td>0.4460±0.0384</td></tr><tr><td>Mixing-up</td><td>0.6933±0.0231</td><td>0.6719±0.0232</td><td>0.6933±0.0231</td><td>0.6497±0.0306</td><td>0.8915±0.0261</td><td>0.7279±0.0558</td></tr><tr><td>TS-TCC</td><td>0.7188±0.0349</td><td>0.7135±0.0352</td><td>0.7167±0.0373</td><td>0.6984±0.0360</td><td>0.9099±0.0085</td><td>0.7675±0.0201</td></tr><tr><td>SimCLR</td><td>0.4804±0.0594</td><td>0.5946±0.1623</td><td>0.5411±0.1946</td><td>0.4955±0.1870</td><td>0.8131±0.0521</td><td>0.5076±0.1588</td></tr><tr><td>TF-C (Ours)</td><td>0.7642±0.0196</td><td>0.7731±0.0355</td><td>0.7429±0.0268</td><td>0.7572±0.0311</td><td>0.9238±0.0159</td><td>0.7961±0.0109</td></tr><tr><td>Non-DL (KNN)</td><td>0.4390±0.0000</td><td>0.3772±0.0000</td><td>0.5143±0.0000</td><td>0.3979±0.0000</td><td>0.6025±0.0000</td><td>0.4084±0.0000</td></tr><tr><td rowspan="8">SLEEPEEG √ EMG</td><td>Random Init.</td><td>0.7780±0.0729</td><td>0.5909±0.0625</td><td>0.6667±0.0135</td><td>0.6238±0.0267</td><td>0.9109±0.1239</td><td>0.7771±0.1427</td></tr><tr><td>TS-SD</td><td>0.4606±0.0000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>TS2vec</td><td>0.7854±0.0318</td><td>0.1545±0.0000 0.8040±0.0750</td><td>0.3333±0.0000 0.6785±0.0396</td><td>0.2111±0.0000 0.6766±0.0501</td><td>0.5005±0.0126 0.9331±0.0164</td><td>0.3775±0.0110</td></tr><tr><td>CLOCS</td><td>0.6985±0.0323</td><td>0.5306±0.0750</td><td>0.5354±0.0291</td><td>0.5139±0.0409</td><td>0.7923±0.0573</td><td>0.8436±0.0372 0.6484±0.0680</td></tr><tr><td>Mixing-up</td><td>0.3024±0.0534</td><td>0.1099±0.0126</td><td>0.2583±0.0456</td><td>0.1541±0.0204</td><td>0.4506±0.1718</td><td>0.3660±0.1635</td></tr><tr><td>TS-TCC</td><td>0.7889±0.0192</td><td>0.5851±0.0974</td><td>0.6310±0.0991</td><td>0.5904±0.0952</td><td>0.8851±0.0113</td><td>0.7939±0.0386</td></tr><tr><td>SimCLR</td><td>0.6146±0.0582</td><td>0.5361±0.1724</td><td>0.4990±0.1214</td><td>0.4708±0.1486</td><td>0.7799±0.1344</td><td>0.6392±0.1596</td></tr><tr><td>TF-C (Ours)</td><td>0.8171±0.0287</td><td>0.7265±0.0353</td><td>0.8159±0.0289</td><td>0.7683±0.0311</td><td>0.9152±0.0211</td><td>0.8329±0.0137</td></tr></table>
+
+# 5.2 Results: One-to-Many Pre-Training Evaluation
+
+Setup. In one-to-many evaluation, pre-training is done using one dataset followed by fine-tuning on multiple target datasets independently without starting pre-training from scratch. Out of eight datasets, SLEEPEEG has most complex temporal dynamics [69] and is the largest (371,055 samples). For that reason, we pre-train a model on SLEEPEEG and separately fine-tune a well-pre-trained model on EPILEPSY, FD-B, GESTURE, and EMG.
+
+Results. Results are shown in Table 2. As there are fewer commonalities between EEG signals vs. vibration, and acceleration vs. EMG, we expect that transfer learning will be less effective for them than one-to-one evaluations. The pre-training and fine-tuning datasets are largely different in the bottom three blocks (SLEEPEEG $ \{ \mathrm { F D - B }$ , GESTURE, EMG}). The large gap reasonably leads to a deterioration in baseline performances, however, our model has a noticeably higher tolerance to knowledge transfer across datasets with large gaps. Notably, We find that the proposed model with TF-C earned the best performance in 14 out of 18 settings in the three challenging settings: indicating our TF-C assumption is universal in time series. For example, our approach outperforms the strongest baseline by $8 . 4 \%$ (in precision) when fine-tuning on GESTURE. Our model has great potential to serve as a universal model when there is no large pre-training dataset that is similar to the small fine-tuning dataset. Furthermore, the TF-C consistently outperforms KNN and Random Init. (which are not pre-trained) by a large margin of $4 2 . 8 \%$ and $2 5 . 1 \%$ (both in F1 score) on average.
+
+Ablation study. We evaluate how relevant the model components are for effective pre-training. As shown in Table 9 (SLEEPEEG GESTURE; Appendix H), removing $\mathcal { L } _ { \mathrm { C } } , \mathcal { L } _ { \mathrm { T } }$ , and $\mathcal { L } _ { \mathrm { F } }$ result in performance degradation (precision) of $6 . 1 \%$ , $7 . 2 \%$ , and $6 . 7 \%$ , respectively. To validate that the performance increment is not solely brought by a third loss term no matter what consistency it measures, we replaced consistency loss $\mathcal { L } _ { \mathrm { C } }$ with a loss term measuring the consistency within time space (named $\mathcal { L } _ { \mathrm { T T - C } } )$ or within frequency space (named $\mathcal { L } _ { \mathrm { F F - C , } }$ ). Results show our consistency loss outperforms $\mathcal { L } _ { \mathrm { T T - C } }$ and $\mathcal { L } _ { \mathrm { F F - C } }$ by $5 . 3 \%$ and $7 . 2 \%$ (accuracy), respectively.
+
+# 5.3 Additional Downstream Tasks: Clustering and Anomaly Detection
+
+Clustering Task. We evaluate the clustering performance of TF-C taking SLEEPEEG EPILEPSY as an example. Specifically, we added a K-means $( \mathrm { K } { = } 2 )$ , as Epilepsy has 2 classes, on top of $z _ { i } ^ { \mathrm { t u n e } }$ in fine-tuning. We adopt commonly used evaluation metrics: Silhouette score, Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI). Table 7 shows our TF-C obtains the best clustering surpassing the strongest baseline (TS-TCC) by a large margin ( $5 . 4 \%$ in Silhouette score). It conveys that TF-C can capture more distinctive representations with the knowledge transferred from pre-training, which is consistent with the superiority of TF-C in the above classification tasks.
+
+Anomaly Detection Task. We assess how TF-C performs on a sample-level anomaly detection task. Note we work on the sample-level rather than the observation-level anomaly detection. Based on global patterns, the former aims to detect abnormal time series samples instead of outlier observations in a sample (as in BTSF [50] and USAD [70]) which emphasizes local context. Specifically, In the scenario of $\mathrm { F D - A }  \mathrm { F D - B }$ , we built a small subset of FD-B with 1,000 samples, of which 900 are from undamaged bearings, and the remaining 100 are from bearings with inner or outer damage. Undamaged samples are considered “normal,” and inner/outer damaged samples are “outliers.” In fine-tuning, we used one-class SVM on top of learned representations $z _ { i } ^ { \mathrm { t u n e } }$ . The experimental results (Table 8) show that our TF-C outperforms five competitive baselines with $4 . 5 \%$ in F-1 Score. Results show that the proposed TF-C is more sensitive to anomalous samples and can effectively detect the abnormal status in mechanical devices.
+
+# 6 Conclusion
+
+We develop a pre-training approach that introduces time-frequency consistency (TF-C) as a mechanism to support knowledge transfer between time-series datasets. The approach uses self-supervised contrastive estimation and injects TF-C into pre-training, bringing time-based and frequency-based representations and their local neighborhoods close together in the latent space.
+
+Limitations and future directions. TF-C property can serve as a universal property for pre-training on diverse time series datasets. Additional generalizable properties, such as temporal autoregressive processes, could also be helpful for pre-training on time series. Further, while our method expects as input a regularly sampled time series, it can handle irregularly sampled time series by using an encoder (such as Raindrop [71] and SeFT [72]) that can embed irregular time series. For frequency encoder inputs $\pmb { x } _ { i } ^ { \mathrm { F } }$ , alternatives include resampling or interpolation to obtain regularly sampled signals and using regular or non-uniform FFT operations. Furthermore, TF-C’s current embedding strategy and loss functions are favorable for classification, leveraging global information over tasks that use local context (e.g., forecasting). Results show that the TF-C approach performs well across broad downstream tasks, including classification, clustering, and anomaly detection (Sec. 5.3).
+
+# Acknowledgments and Disclosure of Funding
+
+We gratefully acknowledge support by US Air Force Contract No. FA8702-15-D-0001, Harvard Data Science Initiative, and awards from Amazon Research, Bayer Early Excellence in Science, AstraZeneca Research, and Roche Alliance with Distinguished Scientists. T.T. is supported by the Under Secretary of Defense for Research and Engineering under US Air Force Contract No. FA8702- 15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funders.
+
+# References
+
+[1] Hrayr Harutyunyan, Hrant Khachatrian, David C Kale, Greg Ver Steeg, and Aram Galstyan. Multitask learning and benchmarking with clinical time series data. Scientific data, 6(1):1–18, 2019.   
+[2] Shahbaz Rezaei and Xin Liu. Deep learning for encrypted traffic classification: An overview. IEEE communications magazine, 57(5):76–81, 2019.   
+[3] Suman Ravuri, Karel Lenc, Matthew Willson, Dmitry Kangin, Remi Lam, Piotr Mirowski, Megan Fitzsimons, Maria Athanassiadou, Sheleem Kashem, Sam Madge, et al. Skilful precipitation nowcasting using deep generative models of radar. Nature, 597(7878):672–677, 2021.   
+[4] Omer Berat Sezer, Mehmet Ugur Gudelek, and Ahmet Murat Ozbayoglu. Financial time series forecasting with deep learning: A systematic literature review: 2005–2019. Applied soft computing, 90:106181, 2020.   
+[5] Bing Su and Ji-Rong Wen. Temporal alignment prediction for supervised representation learning and few-shot sequence classification. In ICLR, 2022.   
+[6] Yixiang Deng, Lu Lu, Laura Aponte, Angeliki M Angelidi, Vera Novak, George Em Karniadakis, and Christos S Mantzoros. Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. NPJ Digital Medicine, 4(1):1–13, 2021.   
+[7] Quentin Rebjock, Baris Kurt, Tim Januschowski, and Laurent Callot. Online false discovery rate control for anomaly detection in time series. NeurIPS, 34:26487–26498, 2021.   
+[8] Fan-Keng Sun, Chris Lang, and Duane Boning. Adjusting for autocorrelated errors in neural networks for time series. NeurIPS, 34:29806–29819, 2021.   
+[9] Angus Dempster, François Petitjean, and Geoffrey I Webb. Rocket: exceptionally fast and accurate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery, 34(5):1454–1495, 2020.   
+[10] Wenyong Huang, Zhenhe Zhang, Yu Ting Yeung, Xin Jiang, and Qun Liu. Spiral: Selfsupervised perturbation-invariant representation learning for speech pre-training. ICLR, 2022.   
+[11] Hassan Ismail Fawaz, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and PierreAlain Muller. Deep learning for time series classification: a review. Data mining and knowledge discovery, 33(4):917–963, 2019.   
+[12] Pengxiang Shi, Wenwen Ye, and Zheng Qin. Self-supervised pre-training for time series classification. In IJCNN, pages 1–8, 2021.   
+[13] Weixia Dang, Biyu Zhou, Lingwei Wei, Weigang Zhang, Ziang Yang, and Songlin Hu. Tsbert: Time series anomaly detection via pre-training model bert. In International Conference on Computational Science, pages 209–223. Springer, 2021.   
+[14] Soravit Changpinyo, Piyush Sharma, Nan Ding, and Radu Soricut. Conceptual $1 2 \mathrm { m }$ : Pushing web-scale image-text pre-training to recognize long-tail visual concepts. In CVPR, pages 3558– 3568, 2021.   
+[15] Kailai Sun, Zuchao Li, and Hai Zhao. Multilingual pre-training with universal dependency learning. NeurIPS, 34:8444–8456, 2021.   
+[16] Rui Ye and Qun Dai. Implementing transfer learning across different datasets for time series forecasting. Pattern Recognition, 109:107617, 2021.   
+[17] Hassan Ismail Fawaz, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and PierreAlain Muller. Transfer learning for time series classification. In 2018 IEEE international conference on big data (Big Data), pages 1367–1376. IEEE, 2018.   
+[18] Kristoffer Wickstrøm, Michael Kampffmeyer, Karl Øyvind Mikalsen, and Robert Jenssen. Mixing up contrastive learning: Self-supervised representation learning for time series. PRL, 155:54–61, 2022.   
+[19] Priyanka Gupta, Pankaj Malhotra, Jyoti Narwariya, Lovekesh Vig, and Gautam Shroff. Transfer learning for clinical time series analysis using deep neural networks. Journal of Healthcare Informatics Research, 4(2):112–137, 2020.   
+[20] Amiel Meiseles and Lior Rokach. Source model selection for deep learning in the time series domain. IEEE Access, 8:6190–6200, 2020.   
+[21] Ankit Singh. Clda: Contrastive learning for semi-supervised domain adaptation. NeurIPS, 34:5089–5101, 2021.   
+[22] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. Imagenet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In ICLR, 2019.   
+[23] Alec Radford and Karthik Narasimhan. Improving language understanding by generative pre-training. OpenAI, 2018.   
+[24] Ting Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi, and Geoffrey Hinton. Big self-supervised models are strong semi-supervised learners. In NeurIPS, volume 33, pages 22243–22255, 2020.   
+[25] Alexei Baevski, Henry Zhou, Abdelrahman Mohamed, and Michael Auli. wav2vec 2.0: A framework for self-supervised learning of speech representations. In NeurIPS, volume 33, pages 12449–12460, 2020.   
+[26] Gari D Clifford, Chengyu Liu, Benjamin Moody, H Lehman Li-wei, Ikaro Silva, Qiao Li, AE Johnson, and Roger G Mark. Af classification from a short single lead ecg recording: The physionet/computing in cardiology challenge 2017. In 2017 Computing in Cardiology (CinC), pages 1–4. IEEE, 2017.   
+[27] Mitchell L Gordon, Kaitlyn Zhou, Kayur Patel, Tatsunori Hashimoto, and Michael S Bernstein. The disagreement deconvolution: Bringing machine learning performance metrics in line with reality. In CHI, pages 1–14, 2021.   
+[28] Simon Rogers, Derek Sleeman, and John Kinsella. Investigating the disagreement between clinicians’ ratings of patients in icus. IEEE Journal of Biomedical and Health Informatics, 17(4):843–852, 2013.   
+[29] Leonard M Horowitz, Rita de Sales French, Kirk D Wallis, David L Post, and Ellen Y Siegelman. The prototype as a construct in abnormal psychology: Ii. clarifying disagreement in psychiatric judgments. Journal of Abnormal Psychology, 90(6):575, 1981.   
+[30] Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. In arXiv:1807.03748, 2019.   
+[31] Pritam Sarkar and Ali Etemad. Self-supervised learning for ecg-based emotion recognition. In ICASSP, pages 3217–3221, 2020.   
+[32] Joseph Y Cheng, Hanlin Goh, Kaan Dogrusoz, Oncel Tuzel, and Erdrin Azemi. Subject-aware contrastive learning for biosignals. arXiv preprint arXiv:2007.04871, 2020.   
+[33] Sriram Ravula, Georgios Smyrnis, Matt Jordan, and Alexandros G Dimakis. Inverse problems leveraging pre-trained contrastive representations. NeurIPS, 34:8753–8765, 2021.   
+[34] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, pages 1597–1607, 2020.   
+[35] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen. Up-detr: Unsupervised pre-training for object detection with transformers. In CVPR, pages 1601–1610, 2021.   
+[36] Hsin-Ying Lee, Jia-Bin Huang, Maneesh Singh, and Ming-Hsuan Yang. Unsupervised representation learning by sorting sequences. In Proceedings of the IEEE international conference on computer vision, pages 667–676, 2017.   
+[37] Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Unsupervised pre-training of image features on non-curated data. In ICCV, pages 2959–2968, 2019.   
+[38] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.   
+[39] Neo Wu, Bradley Green, Xue Ben, and Shawn O’Banion. Deep transformer models for time series forecasting: The influenza prevalence case. In arXiv:2001.08317, 2020.   
+[40] Chi Ian Tang, Ignacio Perez-Pozuelo, Dimitris Spathis, and Cecilia Mascolo. Exploring contrastive learning in human activity recognition for healthcare. arXiv preprint arXiv:2011.11542, 2020.   
+[41] Dani Kiyasseh, Tingting Zhu, and David A Clifton. Clocs: Contrastive learning of cardiac signals across space, time, and patients. In ICML, pages 5606–5615, 2021.   
+[42] David Berthelot, Rebecca Roelofs, Kihyuk Sohn, Nicholas Carlini, and Alex Kurakin. Adamatch: A unified approach to semi-supervised learning and domain adaptation. ICLR, 2022.   
+[43] Guoqiang Wei, Cuiling Lan, Wenjun Zeng, Zhizheng Zhang, and Zhibo Chen. Toalign: Taskoriented alignment for unsupervised domain adaptation. NeurIPS, 34:13834–13846, 2021.   
+[44] Tongkun Xu, Weihua Chen, Pichao Wang, Fan Wang, Hao Li, and Rong Jin. Cdtrans: Crossdomain transformer for unsupervised domain adaptation. ICLR, 2022.   
+[45] Bernd Illing, Jean Ventura, Guillaume Bellec, and Wulfram Gerstner. Local plasticity rules can learn deep representations using self-supervised contrastive predictions. NeurIPS, 34:30365– 30379, 2021.   
+[46] Sana Tonekaboni, Danny Eytan, and Anna Goldenberg. Unsupervised representation learning for time series with temporal neighborhood coding. In ICLR, 2021.   
+[47] Zhihan Yue, Yujing Wang, Juanyong Duan, Tianmeng Yang, Congrui Huang, Yunhai Tong, and Bixiong Xu. Ts2vec: Towards universal representation of time series. In AAAI, volume 36, pages 8980–8987, 2022.   
+[48] Emadeldeen Eldele, Mohamed Ragab, Zhenghua Chen, Min Wu, Chee Keong Kwoh, Xiaoli Li, and Cuntai Guan. Time-series representation learning via temporal and contextual contrasting. In IJCAI, pages 2352–2359, 2021.   
+[49] Gerald Woo, Chenghao Liu, Doyen Sahoo, Akshat Kumar, and Steven Hoi. CoST: Contrastive learning of disentangled seasonal-trend representations for time series forecasting. In ICLR, 2022.   
+[50] Ling Yang and Shenda Hong. Unsupervised time-series representation learning with iterative bilinear temporal-spectral fusion. In ICML, pages 25038–25054. PMLR, 2022.   
+[51] Rob J Hyndman and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2018.   
+[52] Ronald Newbold Bracewell and Ronald N Bracewell. The Fourier transform and its applications, volume 31999. McGraw-hill New York, 1986.   
+[53] Leon Cohen. Time-frequency analysis, volume 778. Prentice hall New Jersey, 1995.   
+[54] Henri J Nussbaumer. The fast fourier transform. In Fast Fourier Transform and Convolution Algorithms, pages 80–111. Springer, 1981.   
+[55] Patrick Flandrin. Time-frequency/time-scale analysis. Academic press, 1998.   
+[56] Antonia Papandreou-Suppappola. Applications in time-frequency signal processing. CRC press, 2018.   
+[57] Ryan Soklaski, Michael Yee, and Theodoros Tsiligkaridis. Fourier-based augmentations for improved robustness and uncertainty calibration. NeurIPS’W, 2021.   
+[58] Ashish Jaiswal, Ashwin Ramesh Babu, Mohammad Zaki Zadeh, Debapriya Banerjee, and Fillia Makedon. A survey on contrastive self-supervised learning. Technologies, 9(1):2, 2020.   
+[59] Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International workshop on similarity-based pattern recognition, pages 84–92. Springer, 2015.   
+[60] Vassileios Balntas, Edgar Riba, Daniel Ponsa, and Krystian Mikolajczyk. Learning local feature descriptors with triplets and shallow convolutional neural networks. In Bmvc, volume 1, page 3, 2016.   
+[61] Bob Kemp, Aeilko H Zwinderman, Bert Tuk, Hilbert AC Kamphuisen, and Josefien JL Oberye. Analysis of a sleep-dependent neuronal feedback loop: the slow-wave microcontinuity of the eeg. IEEE Transactions on Biomedical Engineering, 47(9):1185–1194, 2000.   
+[62] Ralph G Andrzejak, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Peter David, and Christian E Elger. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Physical Review E, 64(6):061907, 2001.   
+[63] Christian Lessmeier, James Kuria Kimotho, Detmar Zimmer, and Walter Sextro. Condition monitoring of bearing damage in electromechanical drive systems by using motor current signals of electric motors: A benchmark data set for data-driven classification. In PHM Society European Conference, volume 3, 2016.   
+[64] Davide Anguita, Alessandro Ghio, Luca Oneto, Xavier Parra Perez, and Jorge Luis Reyes Ortiz. A public domain dataset for human activity recognition using smartphones. In ESANN, pages 437–442, 2013.   
+[65] Jiayang Liu, Lin Zhong, Jehan Wickramasuriya, and Venu Vasudevan. uwave: Accelerometerbased personalized gesture recognition and its applications. Pervasive and Mobile Computing, 5(6):657–675, 2009.   
+[66] Ary L Goldberger, Luis AN Amaral, Leon Glass, Jeffrey M Hausdorff, Plamen Ch Ivanov, Roger G Mark, Joseph E Mietus, George B Moody, Chung-Kang Peng, and H Eugene Stanley. Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. circulation, 101(23):e215–e220, 2000.   
+[67] Amrutha Ramanathan and James McDermott. Fall detection with accelerometer data using residual networks adapted to multi-variate time series classification. In IJCNN, pages 1–8, 2021.   
+[68] George Zerveas, Srideepika Jayaraman, Dhaval Patel, Anuradha Bhamidipaty, and Carsten Eickhoff. A transformer-based framework for multivariate time series representation learning. In KDD, pages 2114–2124, 2021.   
+[69] Xiang Zhang and Lina Yao. Deep Learning for EEG-Based Brain–Computer Interfaces: Representations, Algorithms and Applications. World Scientific, 2021.   
+[70] Julien Audibert, Pietro Michiardi, Frédéric Guyard, Sébastien Marti, and Maria A Zuluaga. Usad: Unsupervised anomaly detection on multivariate time series. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 3395–3404, 2020.   
+[71] Xiang Zhang, Marko Zeman, Theodoros Tsiligkaridis, and Marinka Zitnik. Graph-guided network for irregularly sampled multivariate time series. In ICLR, 2022.   
+[72] Max Horn, Michael Moor, Christian Bock, Bastian Rieck, and Karsten Borgwardt. Set functions for time series. In ICML, pages 4353–4363, 2020.
+
+# Broader Impacts
+
+Our approach for self-supervised pre-training improves classification performance on target datasets in different application scenarios. The recognition of time-frequency consistency as a universal property specific to time series data is a weak assumption that enables effective, task- and domainagnostic transfer learning. We believe our work will inspire the research community to uncover other universal properties for transfer learning. We also hope our work will also attract more researchers to the more general problem of time series representation learning which is still underappreciated relative to problems from CV and NLP fields.
+
+On the society level, our work, along the line of transfer learning, can facilitate more efficient use of time series data in various settings. For example, in medical settings, some diseases of clinical interest may have very small labelled dataset. In this case, unlabelled data from patients of different diseases but with similar underlying physiological conditions can be used to pre-train the model. However, practitioners need to be aware of the limitations of the model, including that it may make biased predictions. Specifically, bias may exist in the source dataset used for pre-training due to an imbalance of samples from subjects of different demographic attributes. Also, the standardized medical protocols for collecting these datasets might be unsuitable for subjects with certain physiological attributes, creating unforeseen bias that may be transferred to fine-tuning.
+
+All datasets in this paper are publicly available and are not associated with any privacy or security concern. Furthermore, we have followed guidelines on responsible use specified by primary authors of the datasets used in the current work.
+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] In abstract and introduction, we claim that TF-C is a generalizable property of time series that can support pre-training, which is welljustified in Sec. 3 and experimentally demonstrated in Sec. 5 (our model consistently performs comparatively to or above baseline methods).   
+(b) Did you describe the limitations of your work? [Yes] See Section 6.   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Broader Impact on Page 10.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] Yes, we include an anonymous link (see Abstract) that provides the source codes with all implementation details, implementation of baselines, and eight datasets. The link will be updated to an non-anonymous link after acceptance.   
+(b) Did you specify all the training details (e.g., data splits, hyper-parameters, how they were chosen)? [Yes] See implementation details in Sec. 5. See Appendix $\mathrm { E }$ for baseline architectures and hyper-parameter settings. More details can be found in the included URL.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We run experiments for 5 times and report the average value with standard deviation. See Table 1, Tables 4-6, and Table 2.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Appendix E.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] We used eight existing datasets and 6 state-of-the-art baselines in contrastive learning and pre-training for time series. We cited the creators for every exist asset we used. See Sec. 5.   
+(b) Did you mention the license of the assets? [Yes] All dataset licenses are mentioned in the Appendix D.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] See the anonymous link in Abstract.   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No] All data we use is freely available for download, without any requirement to re-contact the data curator.   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No] Our datasets are public, well-established, and do not contain PII or offensive content
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/dev/OJ4mMfGKLN/OJ4mMfGKLN_content_list.json

@@ -0,0 +1,1136 @@
+[
+    {
+        "type": "text",
+        "text": "Self-Supervised Contrastive Pre-Training for Time Series via Time-Frequency Consistency ",
+        "text_level": 1,
+        "bbox": [
+            192,
+            122,
+            805,
+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xiang Zhang† ∗ Harvard University xiang_zhang@hms.harvard.edu ",
+        "bbox": [
+            200,
+            224,
+            465,
+            268
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ziyuan Zhao∗ Harvard University ziyuanzhao@college.harvard.edu ",
+        "bbox": [
+            501,
+            226,
+            797,
+            268
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Theodoros Tsiligkaridis MIT Lincoln Laboratory ttsili@ll.mit.edu ",
+        "bbox": [
+            264,
+            289,
+            433,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Marinka Zitnik Harvard University marinka@hms.harvard.edu ",
+        "bbox": [
+            535,
+            289,
+            764,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            367,
+            535,
+            382
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Pre-training on time series poses a unique challenge due to the potential mismatch between pre-training and target domains, such as shifts in temporal dynamics, fast-evolving trends, and long-range and short-cyclic effects, which can lead to poor downstream performance. While domain adaptation methods can mitigate these shifts, most methods need examples directly from the target domain, making them suboptimal for pre-training. To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequencybased representations of the same example are located close together in the timefrequency space. To this end, we posit that time-frequency consistency (TF-C) — embedding a time-based neighborhood of an example close to its frequency-based neighborhood — is desirable for pre-training. Motivated by TF-C, we define a decomposable pre-training model, where the self-supervised signal is provided by the distance between time and frequency components, each individually trained by contrastive estimation. We evaluate the new method on eight datasets, including electrodiagnostic testing, human activity recognition, mechanical fault detection, and physical status monitoring. Experiments against eight state-of-the-art methods show that TF-C outperforms baselines by $1 5 . 4 \\%$ (F1 score) on average in one-toone settings (e.g., fine-tuning an EEG-pretrained model on EMG data) and by $8 . 4 \\%$ (precision) in challenging one-to-many settings (e.g., fine-tuning an EEG-pretrained model for either hand-gesture recognition or mechanical fault prediction), reflecting the breadth of scenarios that arise in real-world applications. The source code and datasets are available at https://github.com/mims-harvard/TFC-pretraining. ",
+        "bbox": [
+            233,
+            400,
+            766,
+            729
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            757,
+            310,
+            775
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Time series plays important roles in many areas, including clinical diagnosis, traffic analysis, and climate science [1, 2, 3, 4, 5, 6]. While representation learning has considerably advanced analysis of time series [7, 8, 9] more broadly [10], learning generalizable representations for temporal data remains a fundamentally challenging problem [8, 11]. There are numerous immediate benefits from generating such representations, of which pre-training capability is particularly desirable and of great practical importance [12, 13]. Central to pre-training is a question of how to process time series in a diverse dataset to greatly improve generalization on new time series coming from different datasets [14, 15, 10]. By training a neural network model on a dataset and transferring it to a new target dataset for fine-tuning, i.e., without explicit retraining on that target data, we expect the resulting performance to be at least as good as that of state-of-the-art models tailored to the target dataset. ",
+        "bbox": [
+            174,
+            790,
+            823,
+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/d10b217529c8c9769db1cffb0fc4788ef4d9932c40aa683839b8bb19568af200.jpg",
+        "image_caption": [
+            "Figure 1: a. Illustration of Time-Frequency Consistency (TF-C). Time-based embedding $\\boldsymbol { z } _ { i } ^ { \\mathrm { T } }$ and frequencybased embedding $\\boldsymbol { z } _ { i } ^ { \\mathrm { F } }$ of time series sample $\\pmb { x } _ { i } ^ { \\mathrm { T } }$ , along with $\\widetilde { z } _ { i } ^ { \\mathrm { T } }$ and $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ learned from augmentations of $\\mathbf { \\boldsymbol { x } } _ { i } ^ { \\mathrm { { T } } }$ , should e ebe close to each other in the latent time-frequency space. b. Leveraging TF-C property in time series to optimize a pre-training model $\\mathcal { F }$ with parameters $\\Theta$ that get fine-tuned to $\\Phi$ on a small scenario-specific dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            194,
+            90,
+            820,
+            218
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            300,
+            825,
+            371
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "However, unfortunately, the expected performance gains are often not realized for a variety of reasons (e.g., distribution shifts, properties of the target dataset unknown during pre-training) [16, 17] that get compounded by the complexity of time series: large variations of temporal dynamics across datasets, varying semantic meaning, irregular sampling, system factors (e.g., different devices or subjects), etc. [18, 17]. This complexity of time series limits the utility of knowledge transfer for pre-training [19, 20]. For example, pre-training a model on a diverse time series dataset with mostly low-frequency components (smooth trends) may not lead to positive transfer on downstream tasks with high-frequency components (transient events) [17]. Examining these challenges can provide clues to what kind of inductive biases could facilitate generalizable representations of time series – this paper offers a strategy for that through a novel time-frequency consistency principle. ",
+        "bbox": [
+            174,
+            377,
+            825,
+            515
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In addition, target datasets are not available during pre-training (different from domain adaption [21]; Appendix A), requiring that the pre-training model captures a latent property that holds true for previously unseen target datasets. At the center of this desideratum is the idea of a property that would be shared between pre-training and target datasets and would enable knowledge transfer from pre-training to fine-tuning. In computer vision (CV), pre-training is driven by findings that initial neural layers capture universal visual elements, such as edges and shapes, that are relevant regardless of image style and tasks [22]. In natural language processing (NLP), the foundation for pre-training is given by linguistic principles of semantics and grammar shared across different languages [23]. However, due to the aforementioned temporal complexity, such a principle for pre-training on time series has not yet been established. Moreover, supervised pre-training requires access to large annotated datasets, which limits its use in domains where richly labeled datasets are scarce [24, 25]. For example, in medical applications, labeling data at scale is often infeasible or can be expensive and noisy (experts can disagree on ground-truth labeling [26, 27], e.g., whether an ECG signal indicates a normal vs. abnormal rhythm) [28, 29]. To mitigate these issues, self-supervised learning emerged as a promising strategy to sidestep the lack of labeled datasets [30]. ",
+        "bbox": [
+            174,
+            521,
+            825,
+            728
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Present work. We introduce a strategy for self-supervised pre-training in time series by modeling Time-Frequency Consistency (TF-C). TF-C specifies that time-based and frequency-based representations, learned from the same time series sample, should be closer to each other in the time-frequency space than representations of different time series samples. Specifically, we adopt contrastive learning in time-space to generate a time-based representation. In parallel, we propose a set of novel augmentations based on the characteristic of the frequency spectrum and produce a frequency-based embedding through contrastive instance discrimination. This is the first work to develop frequencybased contrastive augmentation to leverage rich spectral information and explore time-frequency consistency in time series. The pre-training objective is to minimize the distance between time-based and frequency-based embeddings using a novel consistency loss (Figure 1 (a)). The self-supervised loss is used to optimize the pre-training model and enforce consistency between time and frequency domains in the latent space. The learned relationship encoded in model parameters are transferred to initialize the fine-tuning model and improve performance in datasets of interest (Figure 1 (b)). ",
+        "bbox": [
+            174,
+            732,
+            826,
+            911
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the TF-C model on eight time series datasets under two evaluation settings (i.e., oneto-one and one-to-many). The eight datasets cover a large set of variations: different numbers of channels (from univariate to 9-channel multivariate), varying time series lengths (from 128 to 5,120), different sampling rates (from $1 6 \\ \\mathrm { H z }$ to $4 { , } 0 0 0 ~ \\mathrm { H z }$ ), different scenarios (neurological healthcare, human activity recognition, mechanical fault detection, physical status monitoring, etc.) and diverse types of signals (EEG, EMG, ECG, acceleration, and vibration). We compare TF-C approach to eight state-of-the-art baselines. Results show that TF-C achieves positive transfer, outperforming all baselines by a large margin of $1 5 . 4 \\%$ (F1 score) on average. Further, the approach outperforms the strongest baselines with an improvement of up to $7 . 2 \\%$ in the F1 score. Finally, the TF-C approach improves prior work by $8 . 4 \\%$ in precision (when pre-training the model on sleep EEG signals and fine-tuning it on hand-gesture recognition) in challenging one-to-many setups that apply the same pre-trained model to multiple independent fine-tuning datasets. ",
+        "bbox": [
+            173,
+            90,
+            826,
+            257
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            289,
+            321,
+            306
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Pre-training for time series. Although there are studies on self-supervised representation learning for time series [7, 8, 31, 32] and self-supervised pre-training for images [33, 34, 35, 24], the intersection of these two areas, i.e., self-supervised pre-training for time series, remains underexplored. In time series, it’s not obvious what reasonable assumptions can bridge pre-training and target datasets. Hence, pre-training models in CV [36, 37, 14] and NLP [10, 15, 38] are not directly applicable due to data modality mismatch, and the existing results leave room for improvement [31, 39, 40]. Shi et al. [12] developed the only model to date that is explicitly designed for self-supervised time series pre-training. The model captures the local and global temporal pattern, but it is not convincing why the designed pretext task can capture generalizable representations. Although several studies applied transfer learning in the context of time series [7, 8, 18, 41], there is no foundation yet of which conceptual properties are most suitable for pre-training on time series and why. Addressing this gap, we show that TF-C, designed to be invariant to different time-series datasets, can produce generalizable pre-training models. ",
+        "bbox": [
+            174,
+            332,
+            825,
+            512
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Unlike domain adaptation [21, 42] that requires access to target datasets during training, pre-training models do not have access to fine-tuning datasets. As a result, one needs to identify a generalizable time-series property to benefit from pre-training. Further, self-supervised domain adaptation does not need labels in the target dataset but still requires labels for model training [43, 44]. In contrast, TF-C does not need any labels during pre-training. ",
+        "bbox": [
+            174,
+            518,
+            825,
+            588
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Contrastive learning with time series. Contrastive learning, a popular type of self-supervised learning, aims to learn an encoder that maps inputs into an embedding space such that positive sample pairs (original augmentation and another alternative augmentation/view of the same input sample) are pulled closer and negative sample pairs (original augmentation and an alternative input sample augmentation) are pushed apart [30, 45]. Contrastive learning in time series is less investigated in comparison, partly due to the challenge of identifying augmentations that capture key invariance properties in time series data. For example, CLOCS defines adjacent time segments as positive pairs [41], and TNC assumes overlapping temporal neighborhoods have similar representations [46]. These methods leverage temporal invariance to define positive pairs which are used to calculate contrastive loss, but other invariances, such as transformation invariance (e.g., SimCLR [40]), contextual invariance (e.g., TS2vec [47] and TS-TCC [48]) and augmentations are possible. In this work, we propose an augmentation bank that exploits multiple invariances to generate diverse augmentations (Sec. 4.1), which adds richness to the pre-training model [48]. Importantly, we propose frequencybased augmentations by perturbing the frequency spectrum of time series (e.g., adding or removing the frequency components and manipulating their amplitude; more details in Sec. 4.2) to learn better representations by exposing the model to a local range of frequency variations. In previous work, CoST processes sequential signals through the frequency domain, but the augmentations are still implemented in time space [49]. Similarly, although BTSF [50] involves frequency domain, its data transformation is solely implemented in the time domain using instance-level dropout. Additional commentary on differences between CoST and BTSF is in Appendix B. To the best of our knowledge, this is the first work that directly perturbs the frequency spectrum to leverage frequency-invariance for contrastive learning. Further, we develop a pre-training model that subjects to TF-C upon two individual contrastive encoders. ",
+        "bbox": [
+            174,
+            593,
+            826,
+            910
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Problem Formulation ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            89,
+            387,
+            106
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We are given a pre-training dataset $\\mathcal { D } ^ { \\mathrm { p r e t } } = \\{ { \\pmb x } _ { i } ^ { \\mathrm { p r e t } } \\ | \\ i = 1 , \\ldots , N \\}$ of unlabeled time series samples where sample $\\pmb { x } _ { i } ^ { \\mathrm { p r e t } }$ has $K ^ { \\mathrm { p r e t } }$ channels and $L ^ { \\mathrm { p r e t } }$ timestamps. Let ${ \\mathcal { D } } ^ { \\mathrm { u n e } } = \\{ ( { \\pmb x } _ { i } ^ { \\mathrm { t u n e } } , y _ { i } ) \\ | \\ i = 1 , \\ldots , M \\}$ be a fine-tuning (i.e., target; target and fine-tuning are used interchangeably) dataset of labeled time series samples, each having $K ^ { \\mathrm { t u n e } }$ channels and $L ^ { \\mathrm { t u n e } }$ timestamps. Furthermore, every sample ${ \\pmb x } _ { i } ^ { \\mathrm { t u n e } }$ is associated with a label $y _ { i } \\in \\{ 1 , \\ldots , C \\}$ , where $C$ is the number of classes. Without loss of generality, in the following descriptions, we focus on univariate (single-channel) time series, while noting that our approach can accommodate multivariate time series of varying lengths across datasets (shown in experiments in Sec. 5.2). We use superscript symbol  to denote contrastive augmentations. We note that ${ \\pmb x } _ { i } ^ { \\mathrm { T } } \\equiv { \\pmb x } _ { i }$ edenotes an input time series sample, and $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ denotes discrete frequency spectrum of $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ ",
+        "bbox": [
+            174,
+            132,
+            825,
+            262
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Problem (Self-Supervised Contrastive Pre-Training For Time Series). Given are an unlabeled pre-training dataset $\\mathcal { D } ^ { p r e t }$ with $N$ samples and a target dataset $\\mathcal { D } ^ { t u n e }$ with $M$ samples $( M \\ll N ,$ ). The goal is to use $\\mathcal { D } ^ { p r e t }$ to pre-train a model $\\mathcal { F }$ so that by fine-tuning model parameters on $\\mathcal { D } ^ { t u n e }$ , the fine-tuned model produces generalizable representations $z _ { i } ^ { t u n e } = \\mathcal { F } ( \\mathbf { x } _ { i } ^ { t u n e } )$ for every $\\pmb { x } _ { i } ^ { t u n e }$ . ",
+        "bbox": [
+            173,
+            275,
+            825,
+            332
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We follow an established setup, e.g., [41]: for pre-training, only the unlabeled dataset $\\mathcal { D } ^ { \\mathrm { p r e t } }$ is available while, for fine-tuning, a small labeled dataset $\\mathcal { D } ^ { \\mathrm { t u n e } }$ can be used. In short, a model $\\mathcal { F }$ is pre-trained on the unlabeled time series dataset $\\mathcal { D } ^ { \\mathrm { p r e t } }$ and its optimized model parameters $\\Theta$ are fine-tuned to go from $\\mathcal { F } ( \\cdot , \\Theta )$ to $\\mathcal { F } ( \\cdot , \\Phi )$ using the dataset $\\mathcal { D } ^ { \\mathrm { t u n e } }$ . The $\\Phi$ denotes fine-tuned model parameters. Note that this problem (i.e., $\\mathcal { D } ^ { \\mathrm { p r e t } }$ is independent of the target dataset) is distinct from domain adaptation as fine-tuning dataset $\\mathcal { D } ^ { \\mathrm { t u n e } }$ is not accessed during pre-training. As a result, the pre-trained model can be used with many different fine-tuning datasets without re-training. ",
+        "bbox": [
+            173,
+            353,
+            825,
+            450
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Rationale for Time-Frequency Consistency (TF-C). The central idea is to identify a general property that is preserved across time series datasets and use it to induce transfer learning for effective pre-training. The time domain shows how sensor readouts change with time, whereas the frequency domain shows how much of the signal lies within each frequency component over the entire spectrum [51]. Explicitly considering the frequency domain can provide an understanding of time series behavior that cannot be directly captured solely in the time domain [52]. However, existing contrastive methods (e.g., [47, 48]) focus exclusively on modeling the time domain and ignore the frequency domain altogether. One can argue that approach is sufficient in the case of high-capacity methods as time and frequency domains are different views of the same data [53], which can be cross-translated using transformation, such as Fourier and inverse Fourier [54, 52]. The relationship between the two domains, grounded in signal processing theory, provides an invariance that is valid regardless of the time series distribution [55, 56] and thus can serve as an inductive bias for pretraining. Appendix C provides a commentary with analogies for images. Approaching this invariance through the lens of representation learning, we next formulate Time-Frequency Consistency (TF-C). The TF-C property postulates there exists a latent time-frequency space such that for every sample $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ , time-based representation $z _ { i } ^ { \\mathrm { T } }$ and frequency-based representation $z _ { i } ^ { \\mathrm { F } }$ of the same sample, together with their local augmentations (defined later), are close to each other in the latent space. ",
+        "bbox": [
+            174,
+            453,
+            825,
+            688
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Representational Time-Frequency Consistency (TF-C). Let $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ be a time series and $\\mathcal { F }$ be a model satisfying TF-C. Then, time-based representation $z _ { i } ^ { \\mathrm { T } }$ and frequency-based representation $z _ { i } ^ { \\mathrm { F } }$ as well as representations of $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ ’s local augmentations are proximal in the latent time-frequency space. ",
+        "bbox": [
+            174,
+            702,
+            821,
+            744
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our strategy is to use dataset $\\mathcal { D } ^ { \\mathrm { p r e t } }$ to induce TF-C in $\\mathcal { F }$ ’s model parameters $\\Theta$ , which, in turn, are used to initialize the target model on $\\mathcal { D } ^ { \\mathrm { t u n e } }$ and produce generalizable representations for downstream prediction. The invariant nature of TF-C means that the approach can bridge $\\mathcal { D } ^ { \\mathrm { p r e t } }$ and $\\mathcal { D } ^ { \\mathrm { t u n e } }$ even when large discrepancies exist between them (in terms of temporal dynamics, semantic meaning, etc.), providing a vehicle for a general pre-training on time series. ",
+        "bbox": [
+            174,
+            765,
+            825,
+            835
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To realize TF-C, our model $\\mathcal { F }$ has four components (Figure 2): a time encoder $G _ { \\mathrm { T } }$ , a frequency encoder $G _ { \\mathrm { F } }$ , and two cross-space projectors $R _ { \\mathrm { T } }$ and $R _ { \\mathrm { F } }$ that map time-based and frequency-based representations, respectively, to the same time-frequency space. Together, the four components provide a way to embed $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ to the latent time-frequency space such that the time-based embedding $\\mathsf { \\bar { z } } _ { i } ^ { \\mathrm { T } } = R _ { \\mathrm { T } } ( G _ { \\mathrm { T } } ( \\pmb { x } _ { i } ^ { \\mathrm { T } } ) )$ and the frequency-based embedding $\\pmb { z } _ { i } ^ { \\tilde { \\mathrm { F } } } = R _ { \\mathrm { F } } ( G _ { \\mathrm { F } } ( \\pmb { x } _ { i } ^ { \\mathrm { F } } ) )$ are close together. ",
+        "bbox": [
+            174,
+            842,
+            825,
+            911
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4fff8ef6cb147c6684ddfe8763075015b75664914b9d5d216868779968c9610a.jpg",
+        "image_caption": [
+            "Figure 2: Overview of TF-C approach. Our TF-C pre-training model $\\mathcal { F }$ has four components: a time encoder $G _ { \\mathrm { T } }$ , a frequency encoder $G _ { \\mathrm { { F } } }$ , and two cross-space projectors $R _ { \\mathrm { T } }$ and $R _ { \\mathrm { F } }$ . For an input time series ${ \\bf { x } } _ { i }$ , the model produces time-based representations (i.e., $\\boldsymbol { z } _ { i } ^ { \\intercal }$ and $\\widetilde { z } _ { i } ^ { \\mathrm { T } }$ of input $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ and its augmented version, respectively) and frequency-based representations (i.e., $\\boldsymbol { z } _ { i } ^ { \\mathrm { F } }$ and $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ eof input $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ and its augmented version, respectively). The TF-C eproperty is realized by promoting the alignment of time- and frequency-based representations in the latent time-frequency space, providing a vehicle for transferring $\\mathcal { F }$ to a target dataset not seen before. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            184,
+            85,
+            787,
+            334
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Our Approach ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            429,
+            328,
+            446
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next, we present the architecture of the developed self-supervised contrastive pre-training model $\\mathcal { F }$ . Unless specified otherwise, the data mentioned in this section are from pre-training dataset and the superscript $\\mathrm { p r e t }$ is omitted for simplification. Here we describe the model using univariate time series as an example, but our model can be straightforwardly applied to multivariate time series (Sec 5). ",
+        "bbox": [
+            174,
+            460,
+            826,
+            517
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 Time-based Contrastive Encoder ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            534,
+            442,
+            549
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For a given input time series sample $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ , we generate an augmentation set $\\mathcal { X } _ { i } ^ { \\mathrm { { T } } }$ through a time-based augmentation bank $B ^ { \\mathrm { { r } } } : { \\pmb x } _ { i } ^ { \\mathrm { { r } } }  \\mathcal { X } _ { i } ^ { \\mathrm { { r } } }$ . Each element $\\widetilde { \\pmb x } _ { i } ^ { \\mathrm { T } } \\ \\in \\ \\mathcal { X } _ { i } ^ { \\mathrm { T } }$ is augmented from $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ based on ethe temporal characteristics. Here, the time-based augmentation bank includes jittering, scaling, time-shifts, and neighborhood segments, all well-established in contrastive learning [40, 48, 41]. We develop an augmentation bank to produce diverse augmentations (rather than a single type of augmentation) and expose the model to complex temporal dynamics, which produces more robust time-based embeddings [48]. ",
+        "bbox": [
+            173,
+            559,
+            826,
+            657
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For the input $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ , we randomly select an augmented sample $\\widetilde { \\pmb x } _ { i } ^ { \\mathrm { T } } \\in \\mathcal { X } _ { i } ^ { \\mathrm { T } }$ and feed into a contrastive time encoder $G _ { \\mathrm { T } }$ that maps samples to embeddings. We have ${ h } _ { i } ^ { \\mathrm { T } } = { G } _ { \\mathrm { T } } ( { \\pmb x } _ { i } ^ { \\mathrm { T } } )$ and $\\widetilde { \\pmb { h } } _ { i } ^ { \\mathrm { T } } = \\pmb { G } _ { \\mathrm { T } } ( \\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { T } } )$ . As $\\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { T } }$ is generated based on $\\pmb { x } _ { i } ^ { \\mathrm { T } }$ , after passing through $G _ { \\mathrm { r } }$ , we assume the embedding of $\\pmb { x } _ { i } ^ { \\mathrm { T } }$ eis close to ethe embedding of $\\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { T } }$ but far away from the embedding of $\\pmb { x } _ { j } ^ { \\mathrm { T } }$ and $\\widetilde { \\pmb { x } } _ { j } ^ { \\mathrm { T } }$ that are derived from another sample $\\pmb { x } _ { j } ^ { \\mathrm { { T } } } \\in \\mathcal { D } ^ { \\mathrm { p r e t } }$ e e[34, 47, 41]. In specific, we select the positive pair as $( \\pmb { x } _ { i } ^ { \\mathrm { T } } , \\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { T } } )$ and negative pairs as $( \\pmb { x } _ { i } ^ { \\mathrm { scriptscriptstyle T } } , \\pmb { x } _ { j } ^ { \\mathrm { \\scriptscriptstyle T } } )$ and $( \\pmb { x } _ { i } ^ { \\mathrm { scriptscriptstyle T } } , \\widetilde { \\pmb { x } } _ { j } ^ { \\mathrm { \\scriptscriptstyle T } } )$ [34]. ",
+        "bbox": [
+            173,
+            662,
+            825,
+            755
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Contrastive time loss. To maximize the similarity within a positive pair and minimize the similarity within a negative pair, we adopt the NT-Xent (the normalized temperature-scaled cross entropy loss) as distance function $d$ which is widely used in contrastive learning [34, 40]. In specific, we define the loss function of the time-based contrastive encoder in terms of sample $\\pmb { x } _ { i } ^ { \\mathrm { T } }$ as: ",
+        "bbox": [
+            174,
+            757,
+            825,
+            813
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/19b444150b3cb5fc9f311f44de9226190f4260dfa38922530e221efd92c7068b.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { T } , i } = d ( h _ { i } ^ { \\mathrm { T } } , \\widetilde { h } _ { i } ^ { \\mathrm { r } } , \\mathcal { D } ^ { \\mathrm { p r e t } } ) = - \\log \\frac { \\exp ( \\sin ( h _ { i } ^ { \\mathrm { T } } , \\widetilde { h } _ { i } ^ { \\mathrm { T } } ) / \\tau ) } { \\sum _ { x _ { j } \\in \\mathcal { D } ^ { \\mathrm { p r e t } } } \\mathbb { 1 } _ { i \\neq j } \\exp ( \\sin ( h _ { i } ^ { \\mathrm { T } } , G _ { \\mathrm { T } } ( x _ { j } ) ) / \\tau ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            258,
+            820,
+            738,
+            861
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\sin ( \\pmb { u } , \\pmb { v } ) = \\pmb { u } ^ { T } \\pmb { v } / \\left\\| \\pmb { u } \\right\\| \\left\\| \\pmb { v } \\right\\|$ denotes the cosine similarity, the $\\mathbb { 1 } _ { i \\neq j }$ is an indicator function that equals to 0 when $i = j$ and 1 otherwise, and $\\tau$ is a temporal parameter to adjust scale. The $\\pmb { x } _ { j } \\in \\mathcal { D } ^ { \\mathrm { p r e t } }$ refers to a different time series sample or its augmented sample. This loss function ",
+        "bbox": [
+            174,
+            868,
+            825,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "urges the time encoder $G _ { \\mathrm { T } }$ to generate closer time-based embeddings for positive pairs and push the embeddings for negative pairs apart from each other. ",
+        "bbox": [
+            173,
+            90,
+            823,
+            119
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 Frequency-based Contrastive Encoder ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            138,
+            478,
+            155
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We generate the frequency spectrum $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ from a time series sample $\\mathbf { \\boldsymbol { x } } _ { i } ^ { \\mathrm { { T } } }$ through a transform operator (e.g., Fourier Transformation [54]). The frequency information in time series is universal and plays a key role in classic signal processing [57, 53, 55], but it is rarely investigated in self-supervised contrastive representation learning for time series [58]. In this section, we develop augmentation method to perturb $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ based on characteristics of frequency spectra and show how to generate frequency-based representations. ",
+        "bbox": [
+            173,
+            165,
+            825,
+            250
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As every frequency component in the frequency spectrum denotes a basis function (e.g., sinusoidal function for Fourier transformation) with the corresponding frequency and amplitude, we perturb the frequency spectrum by adding or removing frequency components. A small perturbation in the frequency domain may cause large changes to the temporal patterns in the time domain [55]. To make sure the perturbed time series is still similar to the original sample (not only in frequency domain but also in time domain; Figure 6), we use a small budget $E$ in the perturbations where $E$ denotes the number of frequency components we manipulate. While removing frequency components, we randomly select $E$ frequency components and set their amplitudes to 0. While adding frequency components, we randomly choose $E$ frequency components from the ones have smaller amplitude than $\\alpha \\cdot A _ { m }$ , and increase their amplitude to $\\alpha \\cdot A _ { m }$ . The $A _ { m }$ is the maximum amplitude in the frequency spectrum and $\\alpha$ is a pre-defined coefficient to adjust the scale of the perturbed frequency component $\\mathrm { \\Delta } ( \\alpha = 0 . 5$ in this work). We produce an augmentation set $\\mathcal { X } _ { i } ^ { \\mathrm { F } }$ for $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ through frequencyaugmentation bank $B ^ { \\mathrm { F } } : { \\pmb x } _ { i } ^ { \\mathrm { F } }  \\mathcal { X } _ { i } ^ { \\mathrm { F } }$ . As described above, we have two augmentation methods (i.e., removing or adding frequency components) in $B ^ { \\mathrm { F } }$ , $| \\mathcal { X } _ { i } ^ { \\mathrm { F } } | = 2$ . Details on the exploration of frequency augmentation strategies are covered in Appendix J. ",
+        "bbox": [
+            173,
+            256,
+            825,
+            463
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We utilize a frequency encoder $G _ { \\mathrm { F } }$ to map the frequency spectrum $( e . g . , \\pmb { x } _ { i } ^ { \\mathrm { F } } ,$ to a frequency-based embedding (e.g., $\\pmb { h } _ { i } ^ { \\mathrm { F } } \\overset { \\cdot } { = } G _ { \\mathrm { F } } ( \\pmb { x } _ { i } ^ { \\mathrm { F } } ) )$ . We assume the frequency encoder $G _ { \\mathrm { F } }$ can learn similar embedding for the original frequency spectrum $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ and a slightly perturbed frequency spectrum $ { \\widetilde { \\mathbf { x } } } _ { i } ^ { \\mathrm { F } } \\in  { \\mathcal { X } } _ { i } ^ { \\mathrm { F } }$ . Thus, we set the positive pair as $( \\pmb { x } _ { i } ^ { \\mathrm { F } } , \\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { F } } )$ and the negative pairs as $( \\pmb { x } _ { i } ^ { \\mathrm { F } } , \\pmb { x } _ { j } ^ { \\mathrm { F } } )$ and $( \\pmb { x } _ { i } ^ { \\mathrm { F } } , \\widetilde { \\pmb { x } } _ { j } ^ { \\mathrm { F } } )$ . ",
+        "bbox": [
+            174,
+            469,
+            826,
+            526
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Contrastive frequency loss. We calculate frequency-based contrastive loss for sample $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ as: ",
+        "bbox": [
+            176,
+            527,
+            785,
+            542
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4243d1978340597237709d620bb6d1e47f3f7617166666536f50f3124c1ca91a.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { F } , i } = d ( h _ { i } ^ { \\mathrm { F } } , \\widetilde { h } _ { i } ^ { \\mathrm { F } } , \\mathcal { D } ^ { \\mathrm { p r e t } } ) = - \\log \\frac { \\exp ( \\sin ( h _ { i } ^ { \\mathrm { F } } , \\widetilde { h } _ { i } ^ { \\mathrm { F } } ) / \\tau ) } { \\sum _ { x _ { j } \\in \\mathcal { D } ^ { \\mathrm { p r e t } } } \\mathbb { 1 } _ { i \\neq j } \\exp ( \\sin ( h _ { i } ^ { \\mathrm { F } } , G _ { \\mathrm { F } } ( x _ { j } ) ) / \\tau ) } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            258,
+            551,
+            738,
+            592
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In preliminary experiments, we find that the value of $\\tau$ has little effect on performance and use the same $\\tau$ throughout all experiments. The $\\mathcal { L } _ { \\mathrm { F } , i }$ yield a frequency encoder $G _ { \\mathrm { F } }$ producing embeddings invariant to frequency spectrum perturbations. ",
+        "bbox": [
+            173,
+            601,
+            825,
+            642
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 Time-Frequency Consistency ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            662,
+            415,
+            678
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We develop a consistency loss item $\\mathcal { L } _ { \\mathrm { C } , i }$ to urge the learned embeddings to satisfy TF-C: for a given sample, its time-based and frequency-based embeddings (and their local neighborhoods) are supposed to be close to each other (see Sec. 3 for justification). To make sure the distance between embeddings is measurable, we map ${ \\mathbf { } } h _ { i } ^ { \\mathrm { { T } } }$ from time space and $\\boldsymbol { h } _ { i } ^ { \\mathrm { F } }$ from frequency space to a joint time-frequency space through projectors $R _ { \\mathrm { T } }$ and $R _ { \\mathrm { F } }$ , respectively. In specific, for every input sample $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ , we have four embeddings, which are $z _ { i } ^ { \\mathrm { T } } = R _ { \\mathrm { T } } ( h _ { i } ^ { \\mathrm { T } } )$ , $\\widetilde z _ { i } ^ { \\mathrm { T } } = \\dot { R } _ { \\mathrm { T } } ( \\widetilde h _ { i } ^ { \\mathrm { T } } )$ , $z _ { i } ^ { \\mathrm { F } } = R _ { \\mathrm { F } } ( h _ { i } ^ { \\mathrm { F } } )$ , and $\\widetilde { z } _ { i } ^ { \\mathrm { F } } = R _ { \\mathrm { F } } ( \\widetilde { h } _ { i } ^ { \\mathrm { F } } )$ . The first e etwo embeddings are generated based on temporal characteristics and the latter two embeddings are produced based on the properties of frequency spectrum. ",
+        "bbox": [
+            173,
+            688,
+            825,
+            803
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To enforce the embeddings in the time-frequency space subject to TF-C, we design a consistency loss $\\mathcal { L } _ { \\mathrm { C } , i }$ that measures the distance between a time-based embedding and a frequency-based embedding. We use $S _ { i } ^ { \\mathrm { T F } } = d ( z _ { i } ^ { \\mathrm { T } } , z _ { i } ^ { \\mathrm { F } } , \\mathcal { D } ^ { \\mathrm { p r e t } } )$ to denote the distance between $z _ { i } ^ { \\mathrm { T } }$ and $z _ { i } ^ { \\mathrm { F } }$ ). Similarly, we define $S _ { i } ^ { \\mathrm { T F } }$ $S _ { i } ^ { \\mathrm { { \\widetilde T F } } }$ , and $\\widetilde { S _ { i } ^ { \\mathrm { T F } } }$ . Note, in this time-frequency space, we don’t consider the distance between $z _ { i } ^ { \\mathrm { T } }$ and $\\widetilde { z } _ { i } ^ { \\mathrm { T } }$ ewhere the two embeddings are from the same domain (i.e., time domain). The same applies to pair the distance between $z _ { i } ^ { \\mathrm { F } }$ and $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ . We have already considered information of above two pairs in the calculation of $\\mathcal { L } _ { \\mathrm { T } , i }$ and $\\mathcal { L } _ { \\mathrm { F } , i }$ . ",
+        "bbox": [
+            174,
+            809,
+            825,
+            912
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Next, let’s closely observe $S _ { i } ^ { \\mathrm { T F } }$ and $S _ { i } ^ { \\mathrm { T F } }$ that involve three embeddings: $z _ { i } ^ { \\mathrm { T } }$ , $z _ { i } ^ { \\mathrm { F } }$ , and $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ . Here, $z _ { i } ^ { \\mathrm { T } }$ and $z _ { i } ^ { \\mathrm { F } }$ are learned from the original sample $( \\pmb { x } _ { i } ^ { \\mathrm { T } }$ and $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ ) while $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ eis learned from the augmented $\\widetilde { \\pmb { x } } _ { i } ^ { \\mathrm { F } }$ . Thus, intuitively, $z _ { i } ^ { \\mathrm { T } }$ should be closer to $z _ { i } ^ { \\mathrm { F } }$ in comparison to $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ e e. Motivated by the relative relationship, we encourage the proposed model to learn a $S _ { i } ^ { \\mathrm { T F } }$ ethat is smaller than $S _ { i } ^ { \\mathrm { T F } }$ . Inspired by the triplet loss [59], we design $( S _ { i } ^ { \\mathrm { T F } } - S _ { i } ^ { \\mathrm { T F } } + \\delta )$ as a term of consistency loss $\\mathcal { L } _ { \\mathrm { c } , i }$ where $\\delta$ is a given constant margin to keep negative samples far apart [60]. This term optimizes the model towards a smaller $S _ { i } ^ { \\mathrm { T F } }$ and relatively larger $S _ { i } ^ { \\mathrm { T F } }$ . Similarly, $S _ { i } ^ { \\mathrm { T F } }$ is supposed to be smaller than $S _ { i } ^ { \\mathrm { { \\widetilde T F } } }$ and $\\widetilde { S _ { i } ^ { \\mathrm { T F } } }$ . In summary, we calculate the consistency loss $\\mathcal { L } _ { \\mathrm { c } , i }$ for sample $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ by: ",
+        "bbox": [
+            173,
+            89,
+            826,
+            212
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9130369416ff1ed0bd9618890c257e02fa21baa497bfb086fae067ef8ddf4f2a.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { c } , i } = \\sum _ { S ^ { \\mathrm { p a i r } } } ( S _ { i } ^ { \\mathrm { T F } } - S _ { i } ^ { \\mathrm { p a i r } } + \\delta ) , \\quad S ^ { \\mathrm { p a i r } } \\in \\{ S _ { i } ^ { \\mathrm { T F } } , S _ { i } ^ { \\mathrm { T F } } , S _ { i } ^ { \\mathrm { \\widetilde { T F } } } \\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            313,
+            215,
+            681,
+            250
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $S _ { i } ^ { \\mathrm { p a i r } }$ denotes the distance between a time-based embedding (e.g., $z _ { i } ^ { \\mathrm { T } }$ or $\\widetilde { z } _ { i } ^ { \\mathrm { T } }$ ) and a frequencybased embedding (e.g., $z _ { i } ^ { \\mathrm { F } }$ or $\\widetilde { z } _ { i } ^ { \\mathrm { F } }$ e). In each pair, there is at least one embedding that is derived from eaugmented sample instead of the original sample. The $\\delta$ is a pre-defined constant. By combining all the triplet loss items, ${ \\mathcal { L } } _ { \\mathrm { c } }$ encourages the pre-training model to capture the consistency between time-based and frequency-based embeddings in model optimization. Note, although the Eq. 3 does not explicitly measure the loss across different time series samples (e.g., $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ and $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { j } }$ ), the cross-sample relationships are implicitly covered in the calculation of $S _ { i } ^ { \\mathrm { T F } }$ and $S _ { i } ^ { \\mathrm { p a i r } }$ . ",
+        "bbox": [
+            173,
+            252,
+            825,
+            356
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 Implementation and Technical Details ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            369,
+            478,
+            385
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The overall loss function in pre-training has three terms. First, the time-based contrastive loss ${ \\mathcal { L } } _ { \\mathrm { T } }$ urges the model to learn embeddings invariant to temporal augmentations. Second, the frequencybased contrastive loss $\\mathcal { L } _ { \\mathrm { F } }$ promotes learning of embeddings invariant to frequency spectrum-based augmentations. Third, the consistency loss ${ \\mathcal { L } } _ { \\mathrm { c } }$ guides the model to retain the consistency between time-based and frequency-based embeddings. In summary, the pre-training loss is defined as: ",
+        "bbox": [
+            174,
+            395,
+            825,
+            465
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9950f00409a2963af05d7980b3d9a0e125321610b081df725f062e0f8152ef58.jpg",
+        "text": "$$\n{ \\mathcal { L } } _ { \\mathrm { T F } - \\mathbb { C } , i } = \\lambda ( { \\mathcal { L } } _ { \\mathrm { T } , i } + { \\mathcal { L } } _ { \\mathrm { F } , i } ) + ( 1 - \\lambda ) { \\mathcal { L } } _ { \\mathrm { c } , i }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            366,
+            468,
+            629,
+            484
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda$ controls the relative importance of the contrastive and consistency losses. We calculate the total loss by summing $\\mathcal { L } _ { \\mathrm { T F - C } , i }$ across all pre-training samples. In implementation, the contrastive losses are calculated within the batch. From our problem definition, the model $\\mathcal { F }$ we want to learn is the combination of neural networks $G _ { \\mathrm { T } } , R _ { \\mathrm { T } } , G _ { \\mathrm { F } }$ , and $R _ { \\mathrm { F } }$ . When pre-training is completed, we store parameters of entire model, and denote it as $\\mathcal { F } ( \\cdot , \\Theta )$ where $\\Theta$ represents all trainable parameters. When a sample ${ \\pmb x } _ { i } ^ { \\mathrm { t u n e } }$ is presented, fine-tuned model $\\mathcal { F }$ generates an embedding $z _ { i } ^ { \\mathrm { t u n e } }$ via concatenation as: $z _ { i } ^ { \\mathrm { t u n e } } = \\mathcal { F } ( \\pmb { x } _ { i } ^ { \\mathrm { t u n e } } , \\Phi ) = [ z _ { i } ^ { \\mathrm { t u n e , T } } ; z _ { i } ^ { \\mathrm { t u n e , F } } ]$ where $\\Phi$ are fine-tuned model’s parameters. ",
+        "bbox": [
+            174,
+            487,
+            825,
+            588
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            604,
+            312,
+            622
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare the developed TF-C model with 10 baselines on 8 diverse datasets. We investigate the time series classification tasks in the context of one-to-one and one-to-many transfer learning setups (the many-to-one setting is fundamentally different as discussed in Appendix K). We also assess TF-C in extensive downstream tasks including clustering and anomaly detection. ",
+        "bbox": [
+            174,
+            635,
+            825,
+            690
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets. (1) SLEEPEEG [61] has 371,055 univariate brainwaves (EEG; $1 0 0 \\mathrm { H z } ,$ ) collected from 197 individuals. Each sample is associated with one of five sleeping stages. (2) EPILEPSY [62] monitors the brain activities of 500 subjects with single-channel EEG sensor $\\boldsymbol { 1 7 4 } \\ : \\mathrm { H z } )$ . A sample is labeled in binary based on whether the subject has epilepsy or not. (3) FD-A [63] gathers the vibration signals from rolling bearing from a mechanical system aiming at fault detection. Every sample has 5,120 timestamps and an indicator for one out of three mechanical device states. (4) FD-B [63] has the same setting as the FD-A but the rolling bearings are performed in different working conditions (e.g., varying rotational speed). (5) HAR [64] has 10,299 9-dimension samples from 6 daily activities. (6) GESTURE [65] includes 440 samples that are collected from 8 hand gestures recorded by an accelerometer. (7) ECG [26] contains 8,528 single-sensor ECG recordings with sorted into four classes based on human physiology. (8) EMG [66] consists of 163 EMG samples with 3-class labels implying muscular diseases. Dataset labels are not used in pre-training. Further dataset statistics are in Appendix $\\mathrm { D }$ and Table 3. ",
+        "bbox": [
+            173,
+            696,
+            826,
+            876
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Baselines. We consider 10 baseline methods. This includes 8 state-of-the-art methods: TS-SD [12], TS2vec [47], CLOCS [41], Mixing-up [18], TS-TCC [48], SimCLR [40], TNC [46], and CPC [30]. ",
+        "bbox": [
+            173,
+            882,
+            823,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/e73c66f6249e16f1e14b76f3da0ccdeda5b3b7f739ae180a0258e82d5db241b8.jpg",
+        "table_caption": [
+            "Table 1: One-to-one pre-training evaluation (Scenario 3). Pre-training is performed on HAR, followed by fine-tuning on GESTURE. Results for other three scenarios are shown in Tables 4-6. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Models</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1 score</td><td>AUROC</td><td>AUPRC</td></tr><tr><td>Non-DL (KNN)</td><td>0.6766±0.0000</td><td>0.6500±0.0000</td><td>0.6821±0.0000</td><td>0.6442±0.0000</td><td>0.8190±0.0000</td><td>0.5231±0.0000</td></tr><tr><td>Random Init.</td><td>0.4219±0.0865</td><td>0.4751±0.0925</td><td>0.4963±0.1026</td><td>0.4886±0.0967</td><td>0.7129±0.1206</td><td>0.3358±0.1194</td></tr><tr><td>TS-SD</td><td>0.6937±0.0533</td><td>0.6806±0.0496</td><td>0.6883±0.0525</td><td>0.6785±0.0495</td><td>0.8708±0.0305</td><td>0.6261±0.0790</td></tr><tr><td>TS2vec</td><td>0.6453±0.0260</td><td>0.6287±0.0339</td><td>0.6451±0.0218</td><td>0.6261±0.0294</td><td>0.8890±0.0054</td><td>0.6670±0.0118</td></tr><tr><td>CLOCS</td><td>0.4731±0.0229</td><td>0.4639±0.0432</td><td>0.4766±0.0266</td><td>0.4392±0.0198</td><td>0.8161±0.0068</td><td>0.4916±0.0103</td></tr><tr><td>Mixing-up</td><td>0.7183±0.0123</td><td>0.7001±0.0166</td><td>0.7183±0.0123</td><td>0.6991±0.0145</td><td>0.9127±0.0018</td><td>0.7654±0.0071</td></tr><tr><td>TS-TCC</td><td>0.7593±0.0242</td><td>0.7668±0.0257</td><td>0.7566±0.0231</td><td>0.7457±0.0210</td><td>0.8866±0.0040</td><td>0.7217±0.0121</td></tr><tr><td>SimCLR</td><td>0.4383±0.0652</td><td>0.4255±0.1072</td><td>0.4383±0.0652</td><td>0.3713±0.0919</td><td>0.7721±0.0559</td><td>0.4116±0.0971</td></tr><tr><td>TF-C (Ours)</td><td>0.7824±0.0237</td><td>0.7982±0.0496</td><td>0.8011±0.0322</td><td>0.7991±0.0296</td><td>0.9052±0.0136</td><td>0.7861±0.0149</td></tr></table>",
+        "bbox": [
+            173,
+            122,
+            821,
+            258
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The TS2Vec, TS-TCC, SimCLR, TNC, and CPC are designed for representation learning on a single dataset rather than for transfer learning, so we apply them to fit our settings and make the results comparable. As the training of TNC and CPC are very time-consuming and relatively less competitive (Table 4), we only compare them in the one-to-one setting (scenario 1) while not in other experiments. To examine the utility of pre-training, we consider two additional approaches that are applied directly to fine-tuning datasets without any pre-training: Non-DL (a non-deep learning KNN model) and Random Init. (randomly initializes the fine-tuning model). The evaluation metrics are accuracy, precision (macro-averaged), recall, F1 score, AUROC, and AUPRC. ",
+        "bbox": [
+            173,
+            268,
+            825,
+            381
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Implementation. We use two 3-layer 1-D ResNets [67] as backbones for encoders $G _ { \\mathrm { T } }$ and $G _ { \\mathrm { F } }$ Our datasets contain long time series (samples in FD-A and FD-B have 5,120 observations), and preliminary experiments identified ResNet as a better option than a Transformer variant [68]. We use 2 fully-connected layers for $R _ { \\mathrm { T } }$ and $R _ { \\mathrm { F } }$ , with no sharing of parameters. We set $E = 1$ and $\\alpha = 0 . 5$ in frequency augmentations and $\\tau = 0 . 2$ , $\\delta = 1$ , $\\lambda = 0 . 5$ in loss functions. Reported are mean and standard deviation values across 5 independent runs (both pre-training and fine-tuning) on the same data split. Results for KNN $( \\mathrm { K } { = } 2 )$ do not change so the standard deviation is zero. Method details and hyper-parameter selection are in Appendix E. ",
+        "bbox": [
+            174,
+            382,
+            825,
+            494
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.1 Results: One-to-One Pre-Training Evaluation ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            512,
+            531,
+            527
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Setup. In one-to-one evaluation, we pre-train a model on one pre-training dataset and use it for fine-tuning on one target dataset only. Scenario 1 (SLEEPEEG EPILEPSY): Pre-training is done on SLEEPEEG and fine-tuning on EPILEPSY. While both datasets describe a single-channel EEG, the signals are from different channels/positions on scalps, track different physiology (sleep vs. epilepsy), and are collected from different patients. Scenario 2 $\\mathrm { F D - A } \\longrightarrow \\mathrm { F D - B }$ ): Datasets describe mechanical devices that operate in different working conditions, including rotational speed, load torque, and radial force. Scenario 3 (HAR GESTURE): Datasets record different activities (6 types of human daily activities vs. 8 hand gestures). While both datasets contain acceleration signals, HAR has 9 channels while GESTURE has 1 channel. Scenario 4 ( $\\operatorname { E C G } \\to \\operatorname { E M G }$ ): While both are physiological datasets, the ECG records the electrical signal from the heart whereas EMG measures muscle response in response to a nerve’s stimulation of the muscle. We note that the discrepancies between pre-training and fine-tuning datasets in the above four scenarios are substantial, and they cover a diverse range of variation in time series datasets: varying semantic meaning, sampling frequency, time series length, number of classes, and system factors (e.g., number of devices or subjects). The setup is further challenged by the relatively small number of samples available for fine-tuning (EPILEPSY: 60; FD-B: 60; GESTURE: 480; EMG: 122). Further details are in Appendix F. ",
+        "bbox": [
+            173,
+            535,
+            825,
+            756
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results. The results for the four scenarios are shown in Table 1 and Tables 4-6. Overall, our TF-C model has won 16 out of 24 tests (6 metrics in 4 scenarios) and is the second-best performer in only 8 other tests. We report all metrics but discuss the F1 score in the following. On average, our TF-C model claims a large margin of $1 5 . 4 \\%$ over all baselines. Although the strongest baseline is varying (such as TS-TCC in Scenario 2; Mixing-up in Scenario 3), our model outperforms the strongest baselines by $1 . 5 \\%$ across all scenarios. Specifically, as shown in Table 1 $\\mathrm { \\Delta \\mathrm { \\cdot } G A R  G E S T U R E }$ ; Scenario 3), TF-C achieves the highest performance of $7 9 . 9 1 \\%$ in F1 score, which yields a margin of $7 . 2 \\%$ over the best baseline TS-TCC $( 7 4 . 5 7 \\% )$ . One potential explanation is that Scenario 3 involves a complex dataset (HAR has 6 classes while GESTURE has 8 classes) that can be difficult to model. The complexity of Scenario 3 is further verified by poor performance of all models $( \\pm 8 0 \\% )$ relative to performance on other Scenarios $( \\pm 9 0 \\% )$ : TF-C shows strong robustness by learning more generalizable representations. Additionally, we visualize the learned representations in time-frequency space (Appendix I), and the analyses provide further support for the TF-C property. ",
+        "bbox": [
+            173,
+            758,
+            825,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2dcfb753b5ad6d74dc0fc3dde5f815b0856f1a73c11d5b91d6a6523b873f10fe.jpg",
+        "table_caption": [
+            "Table 2: One-to-many pre-training evaluation. Pre-training is performed on SLEEPEEG, followed by an independent fine-tuning on EPILEPSY, FD-B, GESTURE, and EMG. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Scenarios</td><td>Models</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1 score</td><td>AUROC</td><td>AUPRC</td></tr><tr><td rowspan=\"10\">SLEEPEEG √ EPILEPSY</td><td>Non-DL (KNN)</td><td>0.8525±0.0000</td><td>0.8639±0.0000</td><td>0.6431±0.0000</td><td>0.6791±0.0000</td><td>0.6434±0.0000</td><td>0.6279±0.0000</td></tr><tr><td>Random Init.</td><td>0.8983±0.0656</td><td>0.9213±0.1369</td><td>0.7447±0.1135</td><td>0.7959±0.1208</td><td>0.8578±0.2153</td><td>0.6489±0.1926</td></tr><tr><td>TS-SD</td><td>0.8952±0.0522</td><td>0.8018±0.2244</td><td>0.7647±0.1485</td><td>0.7767±0.1855</td><td>0.7677±0.2452</td><td>0.7940±0.1825</td></tr><tr><td>TS2vec</td><td>0.9395±0.0044</td><td>0.9059±0.0116</td><td>0.9039±0.0118</td><td>0.9045±0.0067</td><td>0.9587±0.0086</td><td>0.9430±0.0103</td></tr><tr><td>CLOCS</td><td>0.9507±0.0027</td><td>0.9301±0.0067</td><td>0.9127±0.0165</td><td>0.9206±0.0066</td><td>0.9803±0.0023</td><td>0.9609±0.0116</td></tr><tr><td>Mixing-up</td><td>0.8021±0.0000</td><td>0.4011±0.0000</td><td>0.5000±0.0000</td><td>0.4451±0.0000</td><td>0.9743±0.0081</td><td>0.9618±0.0104</td></tr><tr><td>TS-TCC</td><td>0.9253±0.0098</td><td>0.9451±0.0049</td><td>0.8181±0.0257</td><td>0.8633±0.0215</td><td>0.9842±0.0034</td><td>0.9744±0.0043</td></tr><tr><td>SimCLR</td><td>0.9071±0.0344</td><td>0.9221±0.0166</td><td>0.7864±0.1071</td><td>0.8178±0.0998</td><td>0.9045±0.0539</td><td>0.9128±0.0205</td></tr><tr><td>TF-C (Ours)</td><td>0.9495±0.0249</td><td>0.9456±0.0108</td><td>0.8908±0.0216</td><td>0.9149±0.0534</td><td>0.9811±0.0237</td><td>0.9703±0.0199</td></tr><tr><td>Non-DL (KNN)</td><td>0.4473±0.0000</td><td>0.2847±0.0000</td><td>0.3275±0.0000</td><td>0.2284±0.0000</td><td>0.4946±0.0000</td><td>0.3308±0.0000</td></tr><tr><td rowspan=\"8\">SLEEPEEG √ FD-B</td><td>Random Init.</td><td>0.4736±0.0623</td><td>0.4829±0.0529</td><td>0.5235±0.1023</td><td>0.4911±0.0590</td><td>0.7864±0.0349</td><td>0.7528±0.0254</td></tr><tr><td>TS-SD</td><td>0.5566±0.0210</td><td>0.5710±0.0535</td><td>0.6054±0.0272</td><td>0.5703±0.0328</td><td>0.7196±0.0113</td><td>0.5693±0.0532</td></tr><tr><td>TS2vec</td><td>0.4790±0.0113</td><td>0.4339±0.0092</td><td>0.4842±0.0197</td><td>0.4389±0.0107</td><td>0.6463±0.0130</td><td>0.4442±0.0162</td></tr><tr><td>CLOCS</td><td>0.4927±0.0310</td><td>0.4824±0.0316</td><td>0.5873±0.0387</td><td>0.4746±0.0485</td><td>0.6992±0.0099</td><td>0.5501±0.0365</td></tr><tr><td>Mixing-up</td><td>0.6789±0.0246</td><td>0.7146±0.0343</td><td>0.7613±0.0198</td><td>0.7273±0.0228</td><td>0.8209±0.0035</td><td>0.7707±0.0042</td></tr><tr><td>TS-TCC</td><td>0.5499±0.0220</td><td>0.5279±0.0293</td><td>0.6396±0.0178</td><td>0.5418±0.0338</td><td>0.7329±0.0203</td><td>0.5824±0.0468</td></tr><tr><td>SimCLR</td><td>0.4917±0.0437</td><td>0.5446±0.1024</td><td>0.4760±0.0885</td><td>0.4224±0.1138</td><td>0.6619±0.0219</td><td>0.5009±0.0477</td></tr><tr><td>TF-C (Ours)</td><td>0.6938±0.0231</td><td>0.7559±0.0349</td><td>0.7202±0.0257</td><td>0.7487±0.0268</td><td>0.8965±0.0135</td><td>0.7871±0.0267</td></tr><tr><td rowspan=\"10\">SLEEPEEG √ GESTURE</td><td>Non-DL (KNN)</td><td>0.6833±0.0000</td><td>0.6501±0.0000</td><td>0.6833±0.0000</td><td>0.6443±0.0000</td><td>0.8190±0.0000</td><td>0.5232±0.0000</td></tr><tr><td>Random Init.</td><td>0.4219±0.0629</td><td>0.4751±0.0175</td><td>0.4963±0.0679</td><td>0.4886±0.0459</td><td>0.7129±0.0166</td><td>0.3358±0.1439</td></tr><tr><td>TS-SD</td><td>0.6922±0.0444</td><td>0.6698±0.0472</td><td>0.6867±0.0488</td><td>0.6656±0.0443</td><td>0.8725±0.0324</td><td>0.6185±0.0966</td></tr><tr><td>TS2vec</td><td>0.6917±0.0333</td><td>0.6545±0.0358</td><td>0.6854±0.0349</td><td>0.6570±0.0392</td><td>0.8968±0.0123</td><td>0.6989±0.0346</td></tr><tr><td>CLOCS</td><td>0.4433±0.0518</td><td>0.4237±0.0794</td><td>0.4433±0.0518</td><td>0.4014±0.0602</td><td>0.8073±0.0109</td><td>0.4460±0.0384</td></tr><tr><td>Mixing-up</td><td>0.6933±0.0231</td><td>0.6719±0.0232</td><td>0.6933±0.0231</td><td>0.6497±0.0306</td><td>0.8915±0.0261</td><td>0.7279±0.0558</td></tr><tr><td>TS-TCC</td><td>0.7188±0.0349</td><td>0.7135±0.0352</td><td>0.7167±0.0373</td><td>0.6984±0.0360</td><td>0.9099±0.0085</td><td>0.7675±0.0201</td></tr><tr><td>SimCLR</td><td>0.4804±0.0594</td><td>0.5946±0.1623</td><td>0.5411±0.1946</td><td>0.4955±0.1870</td><td>0.8131±0.0521</td><td>0.5076±0.1588</td></tr><tr><td>TF-C (Ours)</td><td>0.7642±0.0196</td><td>0.7731±0.0355</td><td>0.7429±0.0268</td><td>0.7572±0.0311</td><td>0.9238±0.0159</td><td>0.7961±0.0109</td></tr><tr><td>Non-DL (KNN)</td><td>0.4390±0.0000</td><td>0.3772±0.0000</td><td>0.5143±0.0000</td><td>0.3979±0.0000</td><td>0.6025±0.0000</td><td>0.4084±0.0000</td></tr><tr><td rowspan=\"8\">SLEEPEEG √ EMG</td><td>Random Init.</td><td>0.7780±0.0729</td><td>0.5909±0.0625</td><td>0.6667±0.0135</td><td>0.6238±0.0267</td><td>0.9109±0.1239</td><td>0.7771±0.1427</td></tr><tr><td>TS-SD</td><td>0.4606±0.0000</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>TS2vec</td><td>0.7854±0.0318</td><td>0.1545±0.0000 0.8040±0.0750</td><td>0.3333±0.0000 0.6785±0.0396</td><td>0.2111±0.0000 0.6766±0.0501</td><td>0.5005±0.0126 0.9331±0.0164</td><td>0.3775±0.0110</td></tr><tr><td>CLOCS</td><td>0.6985±0.0323</td><td>0.5306±0.0750</td><td>0.5354±0.0291</td><td>0.5139±0.0409</td><td>0.7923±0.0573</td><td>0.8436±0.0372 0.6484±0.0680</td></tr><tr><td>Mixing-up</td><td>0.3024±0.0534</td><td>0.1099±0.0126</td><td>0.2583±0.0456</td><td>0.1541±0.0204</td><td>0.4506±0.1718</td><td>0.3660±0.1635</td></tr><tr><td>TS-TCC</td><td>0.7889±0.0192</td><td>0.5851±0.0974</td><td>0.6310±0.0991</td><td>0.5904±0.0952</td><td>0.8851±0.0113</td><td>0.7939±0.0386</td></tr><tr><td>SimCLR</td><td>0.6146±0.0582</td><td>0.5361±0.1724</td><td>0.4990±0.1214</td><td>0.4708±0.1486</td><td>0.7799±0.1344</td><td>0.6392±0.1596</td></tr><tr><td>TF-C (Ours)</td><td>0.8171±0.0287</td><td>0.7265±0.0353</td><td>0.8159±0.0289</td><td>0.7683±0.0311</td><td>0.9152±0.0211</td><td>0.8329±0.0137</td></tr></table>",
+        "bbox": [
+            171,
+            122,
+            823,
+            551
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            559,
+            820,
+            587
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.2 Results: One-to-Many Pre-Training Evaluation ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            604,
+            542,
+            621
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Setup. In one-to-many evaluation, pre-training is done using one dataset followed by fine-tuning on multiple target datasets independently without starting pre-training from scratch. Out of eight datasets, SLEEPEEG has most complex temporal dynamics [69] and is the largest (371,055 samples). For that reason, we pre-train a model on SLEEPEEG and separately fine-tune a well-pre-trained model on EPILEPSY, FD-B, GESTURE, and EMG. ",
+        "bbox": [
+            173,
+            628,
+            825,
+            698
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Results. Results are shown in Table 2. As there are fewer commonalities between EEG signals vs. vibration, and acceleration vs. EMG, we expect that transfer learning will be less effective for them than one-to-one evaluations. The pre-training and fine-tuning datasets are largely different in the bottom three blocks (SLEEPEEG $ \\{ \\mathrm { F D - B }$ , GESTURE, EMG}). The large gap reasonably leads to a deterioration in baseline performances, however, our model has a noticeably higher tolerance to knowledge transfer across datasets with large gaps. Notably, We find that the proposed model with TF-C earned the best performance in 14 out of 18 settings in the three challenging settings: indicating our TF-C assumption is universal in time series. For example, our approach outperforms the strongest baseline by $8 . 4 \\%$ (in precision) when fine-tuning on GESTURE. Our model has great potential to serve as a universal model when there is no large pre-training dataset that is similar to the small fine-tuning dataset. Furthermore, the TF-C consistently outperforms KNN and Random Init. (which are not pre-trained) by a large margin of $4 2 . 8 \\%$ and $2 5 . 1 \\%$ (both in F1 score) on average. ",
+        "bbox": [
+            173,
+            700,
+            825,
+            866
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ablation study. We evaluate how relevant the model components are for effective pre-training. As shown in Table 9 (SLEEPEEG GESTURE; Appendix H), removing $\\mathcal { L } _ { \\mathrm { C } } , \\mathcal { L } _ { \\mathrm { T } }$ , and $\\mathcal { L } _ { \\mathrm { F } }$ result in performance degradation (precision) of $6 . 1 \\%$ , $7 . 2 \\%$ , and $6 . 7 \\%$ , respectively. To validate that the performance increment is not solely brought by a third loss term no matter what consistency it measures, we replaced consistency loss $\\mathcal { L } _ { \\mathrm { C } }$ with a loss term measuring the consistency within time space (named $\\mathcal { L } _ { \\mathrm { T T - C } } )$ or within frequency space (named $\\mathcal { L } _ { \\mathrm { F F - C , } }$ ). Results show our consistency loss outperforms $\\mathcal { L } _ { \\mathrm { T T - C } }$ and $\\mathcal { L } _ { \\mathrm { F F - C } }$ by $5 . 3 \\%$ and $7 . 2 \\%$ (accuracy), respectively. ",
+        "bbox": [
+            174,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            92,
+            825,
+            147
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5.3 Additional Downstream Tasks: Clustering and Anomaly Detection ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            162,
+            673,
+            178
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Clustering Task. We evaluate the clustering performance of TF-C taking SLEEPEEG EPILEPSY as an example. Specifically, we added a K-means $( \\mathrm { K } { = } 2 )$ , as Epilepsy has 2 classes, on top of $z _ { i } ^ { \\mathrm { t u n e } }$ in fine-tuning. We adopt commonly used evaluation metrics: Silhouette score, Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI). Table 7 shows our TF-C obtains the best clustering surpassing the strongest baseline (TS-TCC) by a large margin ( $5 . 4 \\%$ in Silhouette score). It conveys that TF-C can capture more distinctive representations with the knowledge transferred from pre-training, which is consistent with the superiority of TF-C in the above classification tasks. ",
+        "bbox": [
+            174,
+            185,
+            825,
+            282
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Anomaly Detection Task. We assess how TF-C performs on a sample-level anomaly detection task. Note we work on the sample-level rather than the observation-level anomaly detection. Based on global patterns, the former aims to detect abnormal time series samples instead of outlier observations in a sample (as in BTSF [50] and USAD [70]) which emphasizes local context. Specifically, In the scenario of $\\mathrm { F D - A }  \\mathrm { F D - B }$ , we built a small subset of FD-B with 1,000 samples, of which 900 are from undamaged bearings, and the remaining 100 are from bearings with inner or outer damage. Undamaged samples are considered “normal,” and inner/outer damaged samples are “outliers.” In fine-tuning, we used one-class SVM on top of learned representations $z _ { i } ^ { \\mathrm { t u n e } }$ . The experimental results (Table 8) show that our TF-C outperforms five competitive baselines with $4 . 5 \\%$ in F-1 Score. Results show that the proposed TF-C is more sensitive to anomalous samples and can effectively detect the abnormal status in mechanical devices. ",
+        "bbox": [
+            174,
+            285,
+            825,
+            436
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            455,
+            299,
+            473
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We develop a pre-training approach that introduces time-frequency consistency (TF-C) as a mechanism to support knowledge transfer between time-series datasets. The approach uses self-supervised contrastive estimation and injects TF-C into pre-training, bringing time-based and frequency-based representations and their local neighborhoods close together in the latent space. ",
+        "bbox": [
+            174,
+            488,
+            825,
+            542
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Limitations and future directions. TF-C property can serve as a universal property for pre-training on diverse time series datasets. Additional generalizable properties, such as temporal autoregressive processes, could also be helpful for pre-training on time series. Further, while our method expects as input a regularly sampled time series, it can handle irregularly sampled time series by using an encoder (such as Raindrop [71] and SeFT [72]) that can embed irregular time series. For frequency encoder inputs $\\pmb { x } _ { i } ^ { \\mathrm { F } }$ , alternatives include resampling or interpolation to obtain regularly sampled signals and using regular or non-uniform FFT operations. Furthermore, TF-C’s current embedding strategy and loss functions are favorable for classification, leveraging global information over tasks that use local context (e.g., forecasting). Results show that the TF-C approach performs well across broad downstream tasks, including classification, clustering, and anomaly detection (Sec. 5.3). ",
+        "bbox": [
+            173,
+            546,
+            825,
+            684
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            704,
+            553,
+            720
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We gratefully acknowledge support by US Air Force Contract No. FA8702-15-D-0001, Harvard Data Science Initiative, and awards from Amazon Research, Bayer Early Excellence in Science, AstraZeneca Research, and Roche Alliance with Distinguished Scientists. T.T. is supported by the Under Secretary of Defense for Research and Engineering under US Air Force Contract No. FA8702- 15-D-0001. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funders. ",
+        "bbox": [
+            174,
+            734,
+            826,
+            819
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            90,
+            267,
+            106
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "[1] Hrayr Harutyunyan, Hrant Khachatrian, David C Kale, Greg Ver Steeg, and Aram Galstyan. Multitask learning and benchmarking with clinical time series data. Scientific data, 6(1):1–18, 2019.   \n[2] Shahbaz Rezaei and Xin Liu. Deep learning for encrypted traffic classification: An overview. IEEE communications magazine, 57(5):76–81, 2019.   \n[3] Suman Ravuri, Karel Lenc, Matthew Willson, Dmitry Kangin, Remi Lam, Piotr Mirowski, Megan Fitzsimons, Maria Athanassiadou, Sheleem Kashem, Sam Madge, et al. Skilful precipitation nowcasting using deep generative models of radar. Nature, 597(7878):672–677, 2021.   \n[4] Omer Berat Sezer, Mehmet Ugur Gudelek, and Ahmet Murat Ozbayoglu. Financial time series forecasting with deep learning: A systematic literature review: 2005–2019. Applied soft computing, 90:106181, 2020.   \n[5] Bing Su and Ji-Rong Wen. Temporal alignment prediction for supervised representation learning and few-shot sequence classification. In ICLR, 2022.   \n[6] Yixiang Deng, Lu Lu, Laura Aponte, Angeliki M Angelidi, Vera Novak, George Em Karniadakis, and Christos S Mantzoros. Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. NPJ Digital Medicine, 4(1):1–13, 2021.   \n[7] Quentin Rebjock, Baris Kurt, Tim Januschowski, and Laurent Callot. Online false discovery rate control for anomaly detection in time series. NeurIPS, 34:26487–26498, 2021.   \n[8] Fan-Keng Sun, Chris Lang, and Duane Boning. Adjusting for autocorrelated errors in neural networks for time series. NeurIPS, 34:29806–29819, 2021.   \n[9] Angus Dempster, François Petitjean, and Geoffrey I Webb. Rocket: exceptionally fast and accurate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery, 34(5):1454–1495, 2020.   \n[10] Wenyong Huang, Zhenhe Zhang, Yu Ting Yeung, Xin Jiang, and Qun Liu. Spiral: Selfsupervised perturbation-invariant representation learning for speech pre-training. ICLR, 2022.   \n[11] Hassan Ismail Fawaz, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and PierreAlain Muller. Deep learning for time series classification: a review. Data mining and knowledge discovery, 33(4):917–963, 2019.   \n[12] Pengxiang Shi, Wenwen Ye, and Zheng Qin. Self-supervised pre-training for time series classification. In IJCNN, pages 1–8, 2021.   \n[13] Weixia Dang, Biyu Zhou, Lingwei Wei, Weigang Zhang, Ziang Yang, and Songlin Hu. Tsbert: Time series anomaly detection via pre-training model bert. In International Conference on Computational Science, pages 209–223. Springer, 2021.   \n[14] Soravit Changpinyo, Piyush Sharma, Nan Ding, and Radu Soricut. Conceptual $1 2 \\mathrm { m }$ : Pushing web-scale image-text pre-training to recognize long-tail visual concepts. In CVPR, pages 3558– 3568, 2021.   \n[15] Kailai Sun, Zuchao Li, and Hai Zhao. Multilingual pre-training with universal dependency learning. NeurIPS, 34:8444–8456, 2021.   \n[16] Rui Ye and Qun Dai. Implementing transfer learning across different datasets for time series forecasting. Pattern Recognition, 109:107617, 2021.   \n[17] Hassan Ismail Fawaz, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and PierreAlain Muller. Transfer learning for time series classification. In 2018 IEEE international conference on big data (Big Data), pages 1367–1376. IEEE, 2018.   \n[18] Kristoffer Wickstrøm, Michael Kampffmeyer, Karl Øyvind Mikalsen, and Robert Jenssen. Mixing up contrastive learning: Self-supervised representation learning for time series. PRL, 155:54–61, 2022.   \n[19] Priyanka Gupta, Pankaj Malhotra, Jyoti Narwariya, Lovekesh Vig, and Gautam Shroff. Transfer learning for clinical time series analysis using deep neural networks. Journal of Healthcare Informatics Research, 4(2):112–137, 2020.   \n[20] Amiel Meiseles and Lior Rokach. Source model selection for deep learning in the time series domain. IEEE Access, 8:6190–6200, 2020.   \n[21] Ankit Singh. Clda: Contrastive learning for semi-supervised domain adaptation. NeurIPS, 34:5089–5101, 2021.   \n[22] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. Imagenet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In ICLR, 2019.   \n[23] Alec Radford and Karthik Narasimhan. Improving language understanding by generative pre-training. OpenAI, 2018.   \n[24] Ting Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi, and Geoffrey Hinton. Big self-supervised models are strong semi-supervised learners. In NeurIPS, volume 33, pages 22243–22255, 2020.   \n[25] Alexei Baevski, Henry Zhou, Abdelrahman Mohamed, and Michael Auli. wav2vec 2.0: A framework for self-supervised learning of speech representations. In NeurIPS, volume 33, pages 12449–12460, 2020.   \n[26] Gari D Clifford, Chengyu Liu, Benjamin Moody, H Lehman Li-wei, Ikaro Silva, Qiao Li, AE Johnson, and Roger G Mark. Af classification from a short single lead ecg recording: The physionet/computing in cardiology challenge 2017. In 2017 Computing in Cardiology (CinC), pages 1–4. IEEE, 2017.   \n[27] Mitchell L Gordon, Kaitlyn Zhou, Kayur Patel, Tatsunori Hashimoto, and Michael S Bernstein. The disagreement deconvolution: Bringing machine learning performance metrics in line with reality. In CHI, pages 1–14, 2021.   \n[28] Simon Rogers, Derek Sleeman, and John Kinsella. Investigating the disagreement between clinicians’ ratings of patients in icus. IEEE Journal of Biomedical and Health Informatics, 17(4):843–852, 2013.   \n[29] Leonard M Horowitz, Rita de Sales French, Kirk D Wallis, David L Post, and Ellen Y Siegelman. The prototype as a construct in abnormal psychology: Ii. clarifying disagreement in psychiatric judgments. Journal of Abnormal Psychology, 90(6):575, 1981.   \n[30] Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. In arXiv:1807.03748, 2019.   \n[31] Pritam Sarkar and Ali Etemad. Self-supervised learning for ecg-based emotion recognition. In ICASSP, pages 3217–3221, 2020.   \n[32] Joseph Y Cheng, Hanlin Goh, Kaan Dogrusoz, Oncel Tuzel, and Erdrin Azemi. Subject-aware contrastive learning for biosignals. arXiv preprint arXiv:2007.04871, 2020.   \n[33] Sriram Ravula, Georgios Smyrnis, Matt Jordan, and Alexandros G Dimakis. Inverse problems leveraging pre-trained contrastive representations. NeurIPS, 34:8753–8765, 2021.   \n[34] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, pages 1597–1607, 2020.   \n[35] Zhigang Dai, Bolun Cai, Yugeng Lin, and Junying Chen. Up-detr: Unsupervised pre-training for object detection with transformers. In CVPR, pages 1601–1610, 2021.   \n[36] Hsin-Ying Lee, Jia-Bin Huang, Maneesh Singh, and Ming-Hsuan Yang. Unsupervised representation learning by sorting sequences. In Proceedings of the IEEE international conference on computer vision, pages 667–676, 2017.   \n[37] Mathilde Caron, Piotr Bojanowski, Julien Mairal, and Armand Joulin. Unsupervised pre-training of image features on non-curated data. In ICCV, pages 2959–2968, 2019.   \n[38] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.   \n[39] Neo Wu, Bradley Green, Xue Ben, and Shawn O’Banion. Deep transformer models for time series forecasting: The influenza prevalence case. In arXiv:2001.08317, 2020.   \n[40] Chi Ian Tang, Ignacio Perez-Pozuelo, Dimitris Spathis, and Cecilia Mascolo. Exploring contrastive learning in human activity recognition for healthcare. arXiv preprint arXiv:2011.11542, 2020.   \n[41] Dani Kiyasseh, Tingting Zhu, and David A Clifton. Clocs: Contrastive learning of cardiac signals across space, time, and patients. In ICML, pages 5606–5615, 2021.   \n[42] David Berthelot, Rebecca Roelofs, Kihyuk Sohn, Nicholas Carlini, and Alex Kurakin. Adamatch: A unified approach to semi-supervised learning and domain adaptation. ICLR, 2022.   \n[43] Guoqiang Wei, Cuiling Lan, Wenjun Zeng, Zhizheng Zhang, and Zhibo Chen. Toalign: Taskoriented alignment for unsupervised domain adaptation. NeurIPS, 34:13834–13846, 2021.   \n[44] Tongkun Xu, Weihua Chen, Pichao Wang, Fan Wang, Hao Li, and Rong Jin. Cdtrans: Crossdomain transformer for unsupervised domain adaptation. ICLR, 2022.   \n[45] Bernd Illing, Jean Ventura, Guillaume Bellec, and Wulfram Gerstner. Local plasticity rules can learn deep representations using self-supervised contrastive predictions. NeurIPS, 34:30365– 30379, 2021.   \n[46] Sana Tonekaboni, Danny Eytan, and Anna Goldenberg. Unsupervised representation learning for time series with temporal neighborhood coding. In ICLR, 2021.   \n[47] Zhihan Yue, Yujing Wang, Juanyong Duan, Tianmeng Yang, Congrui Huang, Yunhai Tong, and Bixiong Xu. Ts2vec: Towards universal representation of time series. In AAAI, volume 36, pages 8980–8987, 2022.   \n[48] Emadeldeen Eldele, Mohamed Ragab, Zhenghua Chen, Min Wu, Chee Keong Kwoh, Xiaoli Li, and Cuntai Guan. Time-series representation learning via temporal and contextual contrasting. In IJCAI, pages 2352–2359, 2021.   \n[49] Gerald Woo, Chenghao Liu, Doyen Sahoo, Akshat Kumar, and Steven Hoi. CoST: Contrastive learning of disentangled seasonal-trend representations for time series forecasting. In ICLR, 2022.   \n[50] Ling Yang and Shenda Hong. Unsupervised time-series representation learning with iterative bilinear temporal-spectral fusion. In ICML, pages 25038–25054. PMLR, 2022.   \n[51] Rob J Hyndman and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2018.   \n[52] Ronald Newbold Bracewell and Ronald N Bracewell. The Fourier transform and its applications, volume 31999. McGraw-hill New York, 1986.   \n[53] Leon Cohen. Time-frequency analysis, volume 778. Prentice hall New Jersey, 1995.   \n[54] Henri J Nussbaumer. The fast fourier transform. In Fast Fourier Transform and Convolution Algorithms, pages 80–111. Springer, 1981.   \n[55] Patrick Flandrin. Time-frequency/time-scale analysis. Academic press, 1998.   \n[56] Antonia Papandreou-Suppappola. Applications in time-frequency signal processing. CRC press, 2018.   \n[57] Ryan Soklaski, Michael Yee, and Theodoros Tsiligkaridis. Fourier-based augmentations for improved robustness and uncertainty calibration. NeurIPS’W, 2021.   \n[58] Ashish Jaiswal, Ashwin Ramesh Babu, Mohammad Zaki Zadeh, Debapriya Banerjee, and Fillia Makedon. A survey on contrastive self-supervised learning. Technologies, 9(1):2, 2020.   \n[59] Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International workshop on similarity-based pattern recognition, pages 84–92. Springer, 2015.   \n[60] Vassileios Balntas, Edgar Riba, Daniel Ponsa, and Krystian Mikolajczyk. Learning local feature descriptors with triplets and shallow convolutional neural networks. In Bmvc, volume 1, page 3, 2016.   \n[61] Bob Kemp, Aeilko H Zwinderman, Bert Tuk, Hilbert AC Kamphuisen, and Josefien JL Oberye. Analysis of a sleep-dependent neuronal feedback loop: the slow-wave microcontinuity of the eeg. IEEE Transactions on Biomedical Engineering, 47(9):1185–1194, 2000.   \n[62] Ralph G Andrzejak, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Peter David, and Christian E Elger. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Physical Review E, 64(6):061907, 2001.   \n[63] Christian Lessmeier, James Kuria Kimotho, Detmar Zimmer, and Walter Sextro. Condition monitoring of bearing damage in electromechanical drive systems by using motor current signals of electric motors: A benchmark data set for data-driven classification. In PHM Society European Conference, volume 3, 2016.   \n[64] Davide Anguita, Alessandro Ghio, Luca Oneto, Xavier Parra Perez, and Jorge Luis Reyes Ortiz. A public domain dataset for human activity recognition using smartphones. In ESANN, pages 437–442, 2013.   \n[65] Jiayang Liu, Lin Zhong, Jehan Wickramasuriya, and Venu Vasudevan. uwave: Accelerometerbased personalized gesture recognition and its applications. Pervasive and Mobile Computing, 5(6):657–675, 2009.   \n[66] Ary L Goldberger, Luis AN Amaral, Leon Glass, Jeffrey M Hausdorff, Plamen Ch Ivanov, Roger G Mark, Joseph E Mietus, George B Moody, Chung-Kang Peng, and H Eugene Stanley. Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. circulation, 101(23):e215–e220, 2000.   \n[67] Amrutha Ramanathan and James McDermott. Fall detection with accelerometer data using residual networks adapted to multi-variate time series classification. In IJCNN, pages 1–8, 2021.   \n[68] George Zerveas, Srideepika Jayaraman, Dhaval Patel, Anuradha Bhamidipaty, and Carsten Eickhoff. A transformer-based framework for multivariate time series representation learning. In KDD, pages 2114–2124, 2021.   \n[69] Xiang Zhang and Lina Yao. Deep Learning for EEG-Based Brain–Computer Interfaces: Representations, Algorithms and Applications. World Scientific, 2021.   \n[70] Julien Audibert, Pietro Michiardi, Frédéric Guyard, Sébastien Marti, and Maria A Zuluaga. Usad: Unsupervised anomaly detection on multivariate time series. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 3395–3404, 2020.   \n[71] Xiang Zhang, Marko Zeman, Theodoros Tsiligkaridis, and Marinka Zitnik. Graph-guided network for irregularly sampled multivariate time series. In ICLR, 2022.   \n[72] Max Horn, Michael Moor, Christian Bock, Bastian Rieck, and Karsten Borgwardt. Set functions for time series. In ICML, pages 4353–4363, 2020. ",
+        "bbox": [
+            171,
+            109,
+            828,
+            916
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            60,
+            828,
+            915
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            63,
+            828,
+            921
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            90,
+            828,
+            478
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Broader Impacts ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            89,
+            316,
+            107
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Our approach for self-supervised pre-training improves classification performance on target datasets in different application scenarios. The recognition of time-frequency consistency as a universal property specific to time series data is a weak assumption that enables effective, task- and domainagnostic transfer learning. We believe our work will inspire the research community to uncover other universal properties for transfer learning. We also hope our work will also attract more researchers to the more general problem of time series representation learning which is still underappreciated relative to problems from CV and NLP fields. ",
+        "bbox": [
+            174,
+            121,
+            825,
+            218
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "On the society level, our work, along the line of transfer learning, can facilitate more efficient use of time series data in various settings. For example, in medical settings, some diseases of clinical interest may have very small labelled dataset. In this case, unlabelled data from patients of different diseases but with similar underlying physiological conditions can be used to pre-train the model. However, practitioners need to be aware of the limitations of the model, including that it may make biased predictions. Specifically, bias may exist in the source dataset used for pre-training due to an imbalance of samples from subjects of different demographic attributes. Also, the standardized medical protocols for collecting these datasets might be unsuitable for subjects with certain physiological attributes, creating unforeseen bias that may be transferred to fine-tuning. ",
+        "bbox": [
+            173,
+            224,
+            825,
+            348
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "All datasets in this paper are publicly available and are not associated with any privacy or security concern. Furthermore, we have followed guidelines on responsible use specified by primary authors of the datasets used in the current work. ",
+        "bbox": [
+            176,
+            354,
+            821,
+            397
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Checklist ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            417,
+            254,
+            433
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "1. For all authors... ",
+        "bbox": [
+            214,
+            445,
+            339,
+            459
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] In abstract and introduction, we claim that TF-C is a generalizable property of time series that can support pre-training, which is welljustified in Sec. 3 and experimentally demonstrated in Sec. 5 (our model consistently performs comparatively to or above baseline methods).   \n(b) Did you describe the limitations of your work? [Yes] See Section 6.   \n(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Broader Impact on Page 10.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
+        "bbox": [
+            236,
+            463,
+            826,
+            611
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "2. If you are including theoretical results... ",
+        "bbox": [
+            214,
+            616,
+            493,
+            631
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
+        "bbox": [
+            238,
+            635,
+            738,
+            666
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "3. If you ran experiments... ",
+        "bbox": [
+            214,
+            671,
+            393,
+            685
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] Yes, we include an anonymous link (see Abstract) that provides the source codes with all implementation details, implementation of baselines, and eight datasets. The link will be updated to an non-anonymous link after acceptance.   \n(b) Did you specify all the training details (e.g., data splits, hyper-parameters, how they were chosen)? [Yes] See implementation details in Sec. 5. See Appendix $\\mathrm { E }$ for baseline architectures and hyper-parameter settings. More details can be found in the included URL.   \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We run experiments for 5 times and report the average value with standard deviation. See Table 1, Tables 4-6, and Table 2.   \n(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Appendix E. ",
+        "bbox": [
+            238,
+            690,
+            825,
+            892
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... ",
+        "bbox": [
+            210,
+            897,
+            823,
+            911
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(a) If your work uses existing assets, did you cite the creators? [Yes] We used eight existing datasets and 6 state-of-the-art baselines in contrastive learning and pre-training for time series. We cited the creators for every exist asset we used. See Sec. 5.   \n(b) Did you mention the license of the assets? [Yes] All dataset licenses are mentioned in the Appendix D.   \n(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] See the anonymous link in Abstract.   \n(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No] All data we use is freely available for download, without any requirement to re-contact the data curator.   \n(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No] Our datasets are public, well-established, and do not contain PII or offensive content ",
+        "bbox": [
+            238,
+            90,
+            825,
+            281
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "5. If you used crowdsourcing or conducted research with human subjects... ",
+        "bbox": [
+            215,
+            285,
+            705,
+            300
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   \n(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   \n(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] ",
+        "bbox": [
+            238,
+            304,
+            826,
+            393
+        ],
+        "page_idx": 15
+    }
+]

parse/dev/UROBiQEOLP/UROBiQEOLP.md

@@ -0,0 +1,457 @@
+# E-FORCING: IMPROVING AUTOREGRESSIVE MODELS BY TREATING IT AS AN ENERGY-BASED ONE
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Autoregressive generative models are commonly used to solve tasks involving sequential data. They have, however, been plagued by a slew of inherent flaws due to the intrinsic characteristics of chain-style conditional modeling (e.g., exposure bias or lack of long-range coherence), severely limiting their ability to model distributions properly. In this paper, we propose a unique method termed EForcing for training autoregressive generative models that takes advantage of a well-designed energy-based learning objective. By leveraging the extra degree of freedom of the softmax operation, we are allowed to make the autoregressive model itself an energy-based model for measuring the likelihood of input without introducing any extra parameters. Furthermore, we show that with the help of E-Forcing, we can alleviate the above flaws for autoregressive models. Extensive empirical results, covering numerous benchmarks demonstrate the effectiveness of the proposed approach.
+
+# 1 INTRODUCTION
+
+By factorizing the joint distribution into the product of a series of conditional distributions, autoregressive generative models (abbr. ARGMs) (Vaswani et al., 2017; Dai et al., 2019; van den Oord et al., 2016a;b; Salimans et al., 2017; Chen et al., 2018) simplify the difficult challenge of modeling high-dimensional joint distributions. They can be trained efficiently via maximum likelihood and generate samples of exceptional quality, making this technique popular for modeling distributions, especially for sequential data. Nonetheless, despite their potency and flexibility, and huge success, ARGMs still have inherent weaknesses due to the intrinsic characteristics of chain-style conditional modeling, especially when the training data is less diverse 1. For example, ARGMs usually suffer from a discrepancy in distributions of input contexts between the training and inference stages, which causes a consequent performance drop, i.e., Exposure Bias (Ranzato et al., 2016; Bengio et al., 2015). Besides, due to the nature of the greedy selection of beam search approximations, the decoded results from ARGMs may also lack long-range coherence (Deng et al., 2020).
+
+Earlier work, both heuristic and theoretical, has been proposed to address these concerns. For instance, the exposure bias problem of ARGMs can be alleviated to some extent with scheduled sampling (Bengio et al., 2015; Mihaylova & Martins, 2019), by mixing input contexts from both real data and autoregressive generation, during the training stage. However, this scheme introduces some new problems like the over-correcting (Zhang et al., 2019) issue. In addition, at the inference stage, sampling methods such as beam search is employed to generate diverse candidates with high likelihoods, improving the quality of generated sequences. Nevertheless, these approaches result in only marginal improvements in temporal coherence.
+
+In this paper, we propose an elegant solution, i.e., E-Forcing, for the above problems of ARGMs by leveraging a deep connection between ARGMs and Energy-based models (EBMs). EBMs are a popular class of generative models that have demonstrated their effectiveness in modeling high-dimensional distributions in a variety of machine learning applications, without requiring the transformation of the target distribution into a product of conditional distributions (Zhao et al., 2017;
+
+Arbel et al., 2021; Gao et al., 2021). As a result, several studies (Deng et al., 2020; Bakhtin et al., 2021; Durkan & Nash, 2019) have made their attempts to benefit ARGMs from the advantages of EBMs. However, though some positive results were obtained, the existing works preferred a two-stage optimization, which first obtained a well-trained ARGM and then trained an additional EBM based on it. Such an optimization strategy not only introduced a heavy training process for EBM but also did not enable ARGMs themselves to benefit from the properties of EBM in modeling the joint distribution in a temporally more coherent way, and required more training parameters to estimate energy scores, burdening the intricacy of the learning task.
+
+Our method of combing ARGMs and EBMs takes a different approach, which seamlessly integrates energy-based models into autoregressive models by utilizing the extra degree of freedom within the final softmax layer of the model. We show that in this way the ARGM can be trained using an energy-based learning objective, which allows the ARGM to avoid those intrinsic concerns, such as exposure bias, with the help of energy-based models as former work did (Deng et al., 2020; Bakhtin et al., 2021) whilst being free of increasing the learning model’s complexity. This property makes our E-Forcing rather easy to be applied in the training process of any ARGM for any specific task, as no structural changes are required.
+
+Besides, we follow the predominant approach for training explicit density generative models to minimize the KL divergence between the (empirical) data distribution and model distribution, which gives rise to the gradient-based contrastive divergence (CD) methods (Hinton, 2002; Kim & Bengio, 2016) for energy-based models. Typically, these methods require a Markov Chain Monte Carlo (MCMC) process to sample data from the EBM for the “negative phase” gradient estimation, which is extremely time-consuming and, meanwhile, inapplicable for discrete data, such as text. To solve this, we present a way to estimate those “negative phase” gradients through those samples generated with the network’s autoregressive view instead of the EBM view, making the training feasible. Since our method combines the EBM and ARGM seamlessly as a whole, i.e., the ARGM is also an EBM itself, the exposure bias problem can be mitigated due to the fact that autoregressively sampled data is involved in the “negative phase” of CD methods. On top of it, unlike ARGMs, which factor the joint distribution into a product of conditional distributions, EBMs are able to model the joint distribution directly and score each input at the sequence level instead of at the token level, which makes them capable of modeling long-range coherence.
+
+In summary, the following contributions are made to this paper: i) We introduce a novel scheme by integrating the EBM view into autoregressive generative models seamlessly; ii) We proposed a novel method, named E-Forcing, for efficiently optimizing the energy-based autoregressive model via contrastive divergence based on importance sampling but not MCMC; iii) We successfully decrease the inherent flaws of autoregressive models — exposure bias and weak temporal coherence — by leveraging E-Forcing’s two-phase optimization, which makes use of both real and generated data; iv) We demonstrate clear improvements of the proposed methods on various tasks such as language modeling, machine translation, and image generation.
+
+# 2 BACKGROUND AND RELATED WORKS
+
+# 2.1 ENERGY-BASED MODELS
+
+Let $p _ { d }$ denote the data distribution. Energy-based models (LeCun et al., 2006) are interested in learning an unnormalized energy function $\mathbf { E } _ { \theta } ( \mathbf { x } )$ that defines the density(mass) function $\pi _ { \boldsymbol { \theta } } ( \mathbf { x } )$ as
+
+$$
+\pi _ { \boldsymbol { \theta } } ( \mathbf { x } ) = \frac { \exp ( - \mathbf { E } _ { \boldsymbol { \theta } } ( \mathbf { x } ) ) } { \mathbf { Z } _ { \boldsymbol { \theta } } } ,
+$$
+
+where $E _ { \theta } : \mathcal { X }  \mathbb { R }$ denotes an energy function which aims to map a data sample from data space $\mathcal { X }$ to an energy scalar, and $\begin{array} { r } { \mathbf { Z } ( \theta ) = \sum _ { \mathbf { x } } \exp ( - \mathbf { E } _ { \theta } ( \mathbf { x } ) ) } \end{array}$ denotes the normalizing constant, also known as the partition function, which can be barely estimated. Any function can be used as an energy function to represent an EBM as long as it can generate a single scalar given some input $\mathbf { x }$ and the normalizing constant is finite2. Contrastive divergence algorithms are commonly used to optimize EBMs via maximum log-likelihood (Hinton, 2002; Kim & Bengio, 2016; Grathwohl et al., 2020).
+
+Correspondingly, the gradient of the log-likelihood, which needs to be maximized, with respect to $\theta$ can be expressed as
+
+$$
+\nabla _ { \boldsymbol { \theta } } \mathbb { E } _ { p _ { d } ( \mathbf { x } ) } \Big [ \log \pi _ { \boldsymbol { \theta } } ( \mathbf { x } ) \Big ] = \mathbb { E } _ { \pi _ { \boldsymbol { \theta } } ( \mathbf { x } ) } \Big [ \nabla _ { \boldsymbol { \theta } } \mathbf { E } _ { \boldsymbol { \theta } } ( \mathbf { x } ) \Big ] - \mathbb { E } _ { p _ { d } ( \mathbf { x } ) } \Big [ \nabla _ { \boldsymbol { \theta } } \mathbf { E } _ { \boldsymbol { \theta } } ( \mathbf { x } ) \Big ] .
+$$
+
+The first term on the right-hand side of Eq.2 is usually called the “negative phase” term while the second term is called the “positive phase” term.
+
+In general, due to the challenge of sampling from EBMs, training EBMs by contrastive divergence methods (Hinton, 2002; Kim & Bengio, 2016; Grathwohl et al., 2021) is difficult, especially on high-dimensional data. MCMC methods (Nijkamp et al., 2019; Du & Mordatch, 2019; Grathwohl et al., 2020) are usually adopted for data sampling. However, these methods require enormous extra computing overheads and are not applicable when the input is discrete such as text sequences (Deng et al., 2020). As a result, a variety of recent works attempt to explore the strategy of training an EBM without MCMC. In particular, Bakhtin et al. (2021); Xu et al. (2021); Gao et al. (2020) optimize the EBMs by using noise contrastive estimation (NCE) (Gutmann & Hyvarinen, 2010; Ma & Collins, ¨ 2018). Durkan & Nash (2019) estimate the intractable normalization component by utilizing ARGMs and importance sampling. Bengio et al.; Che et al. (2020); Wang et al. (2021) skirt the challenge of collecting data in the high-dimensional data space by performing sampling using a carefully crafted latent space, which improves sampling efficiency.
+
+# 2.2 MODELING DISTRIBUTIONS AUTOREGRESSIVELY
+
+Modeling high-dimensional data distributions directly is usually a rather challenging task due to “the curse of dimensionality” (Bellman, 1954). One alternative method is to sequential the random variables and then factorize the joint probability distribution into the product of conditionals based on the sequence structure, which is the core idea of autoregressive generative models (ARGMs). ARGMs have been very successful, in particular for sequential data. For example, ARGMs have been widely used in language modeling (Vaswani et al., 2017; Dai et al., 2019; Radford et al., 2019), audio synthesis (van den Oord et al., 2016a), and even image generation (van den Oord et al., 2016c;b; Salimans et al., 2017).
+
+However, the advantages of ARGMs are balanced to some extent by issues of (1) exposure bias (Ranzato et al., 2016; Bengio et al., 2015; Song et al., 2020), due to the discrepancy in input context distributions between the training and inference stages, and (2) weak long-range coherence (Deng et al., 2020), due to the inherent greedy selection of one token at a time without look-ahead.
+
+# 2.3 THE MIXTURE OF EBMS AND GENERATIVE MODELS
+
+The seminal idea of combing a generative model and an energy-based model has been explored by a plethora of great works (Pang et al., 2020; Durkan & Nash, 2019; Xie et al., 2019; 2020; Xiao et al., 2021; Bakhtin et al., 2021; Che et al., 2020; Arbel et al., 2021; Deng et al., 2020; Bakhtin et al., 2021; Durkan & Nash, 2019). In particular, Pang et al. (2020) aimed to learn an energy-based model (EBM) in the latent space of a generator model, so that the EBM can act as a prior model on the generator model’s top-down network. VAEBM, a symbiotic composition of a variational auto-encoder and an EBM, was proposed by (Xiao et al., 2021). Arbel et al. (2021) proposed a novel training method for a GAN/EBM combined model by leveraging the Donsker-Varadham representation of KL-divergence.
+
+Among these works, Residual EBM (Deng et al., 2020; Bakhtin et al., 2021; Durkan & Nash, 2019) and EBR (Naskar et al., 2020) may be the most related works to our paper. Authors of these works have made their attempt to benefit ARGMs from the advantages of EBMs. However, different from our work, these works utilize a two-stage optimization scheme, which first obtained a well-trained generative model and then trained an additional EBM on top of it. Such an optimization strategy does not enable ARGMs themselves to benefit from the properties of EBM in modeling the joint distribution. Besides, in order to benefit from the EBM, complicated re-sampling or re-ranking schemes are needed during inference time. It also increases parameters since it uses independent networks to represent the ARGM and the EBM, burdening the intricacy of the learning task. In contrast, we introduce the EBM inside the ARGM, treating the ARGM directly as an EBM itself.
+
+# 3 TREATING THE ARGM AS AN EBM
+
+In this section, we present the overall framework of our E-Forcing method for training better autoregressive models. Let $\left( \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { K } \right)$ be a random sequence of length $K$ drawn from the real data distribution $p _ { d } , \mathbf { x } _ { k }$ denote the random variable at time step $k$ , and $\mathbf { x } _ { < k }$ represent the random subsequence before time step $k$ , i.e. $\mathbf { x } _ { < k } = ( \mathbf { x } _ { 1 } , \mathbf { x } _ { 2 } , \ldots , \mathbf { x } _ { k - 1 } )$ . The general spirit of our design is to model the joint distribution $p _ { d } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ by integrating an EBM inside the autoregressive model $q _ { \theta }$ .
+
+Formally, given an autoregressive model $\begin{array} { r } { q _ { \theta } ( \mathbf { x } _ { 1 } , . . . , \mathbf { x } _ { K } ) = \prod _ { k = 1 } ^ { K } q _ { \theta } ( \mathbf { x } _ { k } | \mathbf { x } _ { < k } ) } \end{array}$ parameterized by $\theta$ we introduce $K$ independent energy-based models $p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ for each time step $k \leq K$ , with the formulation following
+
+$$
+p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) = q _ { \theta } ( \mathbf { x } _ { < k } ) \cdot \frac { e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbf { Z } _ { \theta } } ,
+$$
+
+where $\mathbf { Z } _ { \theta }$ is equal to $\begin{array} { r } { \mathbb { E } _ { q _ { \theta } } [ \sum _ { { \bf x } _ { k } } e ^ { - \phi _ { \theta } ( { \bf x } _ { k } , { \bf x } _ { < k } ) } ] } \end{array}$ , indicating the normalization constant, $\phi _ { \theta } ( \cdot )$ represents the energy function. Essentially, $p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ is a product EBM, defined as the product of $q _ { \theta }$ and another EBM $\phi _ { \theta }$ .
+
+# 3.1 DEFINITION OF THE ENERGY FUNCTION
+
+We define the energy function $\phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ using $\mathbf { x } _ { k }$ ’s corresponding component of network’s output logits given the input context $\mathbf { x } _ { < k }$ (e.g., given a sequence “This is Friday.” and assuming the corresponding index of the token “Friday” in the vocabulary is $i$ , then the value of $- \phi _ { \theta }$ (“Friday”, “This is”) is the $i$ -th component of the output logit, namely, the input tensor of the final softmax layer).
+
+The rationale behind such a design of energy function is out of the extra degree of freedom concealed inside the softmax transformation $\boldsymbol { \mathcal { S } } : \mathbb { R } ^ { \boldsymbol { \breve { M } ^ { \bullet } } } \to ( 0 , 1 ) ^ { M }$ , which can convert an unnormalized vector with size $M$ into a probability distribution consisting of $M$ probabilities
+
+$$
+S ( [ z _ { 1 } , \ldots , z _ { M } ] ) = [ \frac { e ^ { z _ { 1 } } } { \sum _ { i = 1 } ^ { M } e ^ { z _ { i } } } , \ldots , \frac { e ^ { z _ { M } } } { \sum _ { i = 1 } ^ { M } e ^ { z _ { i } } } ] .
+$$
+
+It’s easy to observe that the softmax operation is unaffected by the input vector’s overall magnitude, that is, $S ( [ z _ { 1 } , \dots , z _ { M } ] ) = S ( [ z _ { 1 } , \dots , z _ { M } ] + C ) , \forall C \in \mathbb { R }$ . Such a property allows us to model the energy function by using the ARGM itself instead of introducing a new network.
+
+# 3.2 ENERGY-BASED LEARNING OBJECTIVE
+
+Other than making the $q _ { \theta }$ to match $p _ { d }$ , E-forcing has an additional training objective to make the $K$ parametric distributions $p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ to match the real data distribution $p _ { d } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ at any time step $k \leq K$ . This can be achieved by minimizing the Kullback-Leibler (KL) divergence between the distributions for each time step of a sequence,
+
+$$
+\begin{array} { r } { \mathbf { D } _ { K L } \Big ( p _ { d } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) | | p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) \Big ) , \forall k \in [ 1 , K ] , } \end{array}
+$$
+
+We attempt to use contrastive divergence methods (Hinton et al., 1995; Kim & Bengio, 2016) to minimize the objective 5 by descending the gradient w.r.t. $\theta$ according to Eq. 2 for each time step. Specifically, given an arbitrary time step $k$ , we have the corresponding gradient of objective 5 with respect to $\theta$
+
+$$
+\nabla _ { \theta } \mathcal { L } _ { E B M - C D } = \mathbb { E } _ { p _ { d } } \Big [ \nabla _ { \theta } \mathbf { E } _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } \big ) \Big ] - \underbrace { \mathbb { E } _ { p _ { \theta } } \Big [ \nabla _ { \theta } \mathbf { E } _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } \big ) \Big ] } _ { \displaystyle } .
+$$
+
+where $\begin{array} { r } { \mathbf { E } _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) = \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) - \log q _ { \theta } ( \mathbf { x } _ { < k } ) . } \end{array}$
+
+Optimization via Eq. 6 involves sampling data from the model distribution $p _ { \theta }$ and can thus lead to the discovery of non-data-like samples, whose likelihood is then explicitly reduced as the corresponding energy increases during the training. E-Forcing is therefore not plagued by the exposure bias problem naturally. Besides, because we model the joint distribution at each time step, E-Forcing can assess the sequence up to the current time step as a whole and generate more coherent data using energy sampling (Deng et al., 2020). However, the negative phase gradient is frustrating to compute, especially for discrete data (e.g. text) where common MCMC methods (Welling & Teh, 2011) can not even be applied. Therefore, we propose a novel variant of contrastive divergence methods for E-Forcing’s optimization in Section 4.
+
+# 4 OPTIMIZATION
+
+The key obstacle of optimizing the objective 5 via contrastive divergence methods (Hinton, 2002)(i.e. descends the gradient of Eq. 6) is sampling data from the model distribution $p _ { \theta }$ for estimating the negative phase gradient. The common MCMC algorithms are not desirable for generating “negative” samples because they are rather time-consuming, and not applicable to discrete data. In order to make the optimization process both efficient and feasible, we modified the original CD methods by means of the importance sampling technique (Horvitz & Thompson, 1952), which holds two parts of gradient estimation.
+
+# 4.1 POSITIVE PHASE GRADIENTS
+
+Since the training set consists of i.i.d. samples sampled from the real distribution $p _ { d }$ , the computing of positive phase gradients is not difficult. To be specific, by replacing ${ \bf E } _ { \theta } ( { \bf x } _ { k } , { \bf x } _ { < k } )$ with the form $\phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) - \log q _ { \theta } ( \mathbf { x } _ { < k } )$ in Eq.6, the positive phase gradient ${ \mathcal G } _ { + } ^ { ( k ) } ( \theta )$ with respect to parameter $\theta$ can be written into
+
+$$
+\mathcal { G } _ { + } ^ { ( k ) } ( \theta ) = \mathbb { E } _ { p _ { d } } \Big [ \nabla _ { \theta } \phi _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } \big ) - \nabla _ { \theta } \log q _ { \theta } \big ( \mathbf { x } _ { < k } \big ) \Big ] .
+$$
+
+Since carrying out sample estimation of the expectation over the data distribution $p _ { d }$ is viable, and the score $\phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ can be acquired by simply accessing the output logit of ARGM (according to the definition of $\phi _ { \theta }$ in Sec. 3), the first term of the positive phase gradient $\mathcal { G } _ { + } ^ { ( k ) }$ can likewise be readily computed. Besides, we can observe that the second term $\mathbb { E } _ { p _ { d } } [ - \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) ]$ of ${ \mathcal { G } } _ { + } ^ { ( k ) } ( \theta )$ is the negative gradient of likelihood ’s logarithm, which is exactly the objective of maximizing the autoregressive generative model $q _ { \theta }$ ’s log-likelihood.
+
+# 4.2 NEGATIVE PHASE GRADIENTS
+
+The estimation of negative phase gradients $\mathcal { G } _ { - } ^ { ( k ) } ( \theta ) = \mathbb { E } _ { p _ { \theta } } [ \nabla _ { \theta } \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) - \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) ]$ , on the other hand, is more involved. Sampling data from $p _ { \theta }$ θ  is required for estimating the expectation $\mathbb { E } _ { p _ { \theta } }$ , whereas $p _ { \theta }$ is the introduced energy-based autoregressive model, which is an explicit autoregressive generative model and we can only access its modeled density(mass) function $p _ { \theta }$ .
+
+Inspired by the idea of importance sampling, we substitute the troublesome estimation of the expectation over distribution $p _ { \theta }$ with the expectation over distribution $q _ { \theta }$ , which is the underlying autoregressive model that can generate samples considerably easier. Accordingly, the negative phase gradient $\mathbb { E } _ { \mathbf { x } _ { k } , \mathbf { x } _ { < k } \sim p _ { \theta } } \left[ \nabla _ { \theta } \mathbf { E } _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) \right]$ has the following form (See the detailed derivation in Appendix B),
+
+$$
+\begin{array} { r l r } {  { \mathcal { G } _ { - } ^ { ( k ) } ( \theta ) = \mathbb { E } _ { q _ { \theta } } \Big [ { \mathbf { w } } \big ( \mathbf { x } _ { < k } \big ) \big [ \nabla _ { \theta } \phi _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } \big ) - \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) \big ] \Big ] , } } \\ & { } & { \quad \mathrm { w h e r e ~ } { \mathbf { w } } \big ( \mathbf { x } _ { < k } \big ) = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } \big ) } } { \mathbb { E } _ { q _ { \theta } ( \mathbf { x } _ { < k } ^ { \prime } ) } \big [ \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } \big ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ^ { \prime } \big ) } \big ] } . } \end{array}
+$$
+
+According to Eq.8, all the estimated expectations only need sampling from the autoregressive model $q _ { \theta }$ rather than the distribution $p _ { \theta }$ , and the reweighing weight $\mathbf { w }$ in Eq. 9 does not involve expectation computation over distribution $p _ { \theta }$ either. Generally speaking, producing data from an autoregressive model is a simple ancestral sampling process and naturally suitable for discrete data, as compared with sampling straight from an explicit generative density estimator, which needs MCMC approaches (Durkan & Nash, 2019). Besides, the term $\mathbb { E } _ { { \mathbf { x } } < k \sim q _ { \theta } ( { \mathbf { x } } < k ) } [ { \mathbf { w } } ( { \mathbf { x } } < k ) \nabla _ { \theta } \log q _ { \theta } ( { \mathbf { x } } _ { < k } ) ]$ in Eq. 8 can be regarded as a re-weighted gradient of $q _ { \theta }$ ’s information entropy with respect to $\theta$ . This term can be optimized similarly to the teacher-forcing training of the autoregressive model with the “teacher” sequence generated autoregressively by the model itself. The scheduled sampling methods (Bengio et al., 2015; Ranzato et al., 2016; Mihaylova & Martins, 2019) are similar to this term but without the re-weighting factor.
+
+Moreover, the reweighing weight w of Eq. 9 can be further refined (see the derivation in Appendix B.3) and we can observe that $\mathbf { w } ( \mathbf { \bar { x } } _ { < k } ) = \mu ( \mathbf { x } _ { < k } ) / \mathbb { E } _ { \mathbf { x } _ { < k } ^ { \prime } } \mu ( \mathbf { x } _ { < k } )$ , where $\mu ( \mathbf { x } _ { < k } ) = p _ { \theta } ( \mathbf { x } _ { < k } ) / q _ { \theta } ( \mathbf { x } _ { < k } )$ , indicating the possibility of which distribution $\scriptstyle \mathbf { \hat { \phi } } _ { p _ { \theta } }$ or $q _ { \theta . }$ ) the input context $\mathbf { x } _ { < k }$ is most likely to come from. Correspondingly, $\mathbf { w } ( \mathbf { x } _ { < k } )$ reflects the context $\mathbf { x } _ { < k }$ ’s relative magnitude of $\mu ( \mathbf { x } _ { < k } )$ compared with the average among all potential contexts—the larger the value of $\mathbf { w } ( \mathbf { x } _ { < k } )$ , the more likely the context $\mathbf { x } _ { < k }$ in the data space coming from $p _ { \theta }$ , which is modeled by the product of autoregressive models and EBMs. During training, those input sequences with contexts more likely from $p _ { \theta }$ than $q _ { \theta }$ will be assigned larger weights w while others will be assigned smaller weights $\mathbf { w }$ .
+
+# 4.3 FINAL OPTIMIZATION OF E-FORCING
+
+# Algorithm 1 Optimizing ARGMs with E-Forcing
+
+<table><tr><td>generation length</td><td>Given: a training dataset ε ~ Pd ，random-initialized autoregressive model qo,K ∈ N is the</td></tr><tr><td>for iteration i= 1;i ≤max iterations;i+1 do Sample minibatch B = {(Ci, Si)}²=1 ~ ε</td><td>√ si is of length K,ci is the context of Si</td></tr><tr><td>if i≤Nthen</td><td>After N iterations,we start applying E-Forcing</td></tr><tr><td>VLtotal ←∑1 VθCAR(B)</td><td></td></tr><tr><td>else</td><td></td></tr><tr><td></td><td>Autoregressively generate |B| samples from qe conditioned on Ci, denoted as B</td></tr><tr><td>K</td><td></td></tr><tr><td>end if</td><td></td></tr><tr><td>Updateθ←θ-nVθLtotal</td><td></td></tr><tr><td></td><td>η denotes learning rate</td></tr><tr><td></td><td></td></tr><tr><td>end for</td><td></td></tr><tr><td></td><td></td></tr></table>
+
+Finally, with the help of the above estimation of gradients regarding two phases of Eq. 6, we are able to optimize the product EBM $p _ { \theta }$ via descending the estimated gradient of contrastive divergence loss $\nabla _ { \boldsymbol { \theta } } \mathcal { L } _ { E B M - C D }$ for any time step $k$
+
+$$
+\nabla _ { \boldsymbol { \theta } } \mathcal { L } _ { E B M - C D } ^ { ( k ) } ( \boldsymbol { \theta } ) = \mathcal { G } _ { + } ^ { ( k ) } ( \boldsymbol { \theta } ) - \mathcal { G } _ { - } ^ { ( k ) } ( \boldsymbol { \theta } ) .
+$$
+
+Eq. 10 can be easily estimated by using “positive” samples from the given training dataset and autoregressively generated “negative” samples from $q _ { \theta }$ .
+
+Nevertheless, training the model from scratch with the energy-based learning objective alone can not work well in practice. The reason is simple: at the initial stage of the training process, what we have is just a randomly initialized network that can barely generate anything meaningful. This fact indicates disjoint supports between the real distribution $p _ { d }$ and modeled distribution $p _ { \theta }$ . Importance sampling fails in this case. Hence, to make the optimization more feasible, we pre-train the entire model with an autoregressive loss $\mathcal { L } _ { A R }$ by teacher-forcing for a few epochs before introducing the energy-based learning objective. In sum, the final gradient concerning parameter $\theta$ at each update iteration is
+
+$$
+\nabla _ { \theta } \mathcal { L } _ { t o t a l } ( \theta ) = \sum _ { k = 1 } ^ { K } \nabla _ { \theta } \mathcal { L } _ { A R } ^ { ( k ) } ( \theta ) + \lambda _ { k } \nabla _ { \theta } \mathcal { L } _ { E B M - C D } ^ { ( k ) } ( \theta ) ,
+$$
+
+where $\lambda _ { k }$ adjusts the ratio between the two objectives for the time step $k$ . The intact optimization procedure is shown in Algorithm $1 ^ { 3 }$ . We found that an exponentially descending configuration of coefficients $\lambda _ { k }$ according to the order of time steps works well. One possible reason is that such a set of coefficients can remedy the imbalanced training signal by negative phase gradients in Eq. 8 among time steps.
+
+# 5 EXPERIMENTS
+
+To empirically corroborate the effectiveness of E-Forcing and show its broad applicability, we have conducted extensive experiments on applications, such as language modeling and machine translation. In this section, we will first introduce these experimental setups and analyze the obtained results. Besides, we also carried out a series of experiments to further show our E-Forcing method’s ability to resolve ARGMs’ inherent flaws(i.e. exposure bias and incoherence generation). More experimental settings as well as analytical experiments are shown in Appendix A and C.
+
+# 5.1 APPLICATION TO LANGUAGE MODELING
+
+For the language modeling task, three different datasets, WikiText-103 (Merity et al., 2017), Toronto Book Corpus (Zhu et al., 2015; Kiros et al., 2015), and CC-news (Mackenzie et al., 2020), are chosen as testbeds; two autoregressive network structures are used to evaluate the effectiveness: vanilla Transformer (Vaswani et al., 2017) (“Tr-Base” for short) and Transformer-XL (Dai et al., 2019) (“Tr-XL” for short). We regard the vanilla training with the teacher forcing technique as the baseline method. Besides, we also compared our E-Forcing with the residual EBM Deng et al. (2020) method, which is a typical method to improve the performance of language models by utilizing EBMs. In order to benefit from the EBM, the residual EBM method requires a new network to estimate the energy scores and imposes a Top-K energy resampling scheme during inference4.
+
+The final results are reported in Table 1. We can see from the results that E-Forcing outperforms two pure autoregressive models with clear margins over all three benchmarks. Specifically, on the Wikitext-103 benchmark, our E-Forcing improves the performance of the Transformer-Base model and Transformer-XL model by $0 . 6 2 \ : \mathrm { P P L }$ points (from 30.56 to 29.94) and $0 . 3 0 \mathrm { P P L }$ points (from 24.20 to 23.90) respectively; on CC-news and Toronto Book Corpus benchmarks, our method obtains $0 . 5 1 \ \mathrm { p p l }$ and $0 . 4 7 ~ \mathrm { p p l }$ performance gain respectively and gets further improvement once energy resampling technique was applied. Besides, though residual EBM’s learning parameters are twice as ours and their method is unable to directly benefit autoregressive models without Top-K energy resampling, our E-Forcing achieves comparable results to them, even slightly better on Toronto Book Corpus and Wikitext-103 benchmarks.
+
+Table 1: Language modeling performance of different models on three benchmarks. Evaluation is conducted using perplexity (PPL). E.R. is the abbreviation of Energy Resampling technique (Bakhtin et al., 2021), which serves as a necessary module of Residual EBM.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">PPL↓</td></tr><tr><td>CC-News</td><td>Toronto Book Corpus</td><td>WikiText103</td></tr><tr><td>Baseline (Tr-Base)</td><td>18.29</td><td>17.57</td><td>30.56</td></tr><tr><td>Baseline (Tr-XL)</td><td>-</td><td>1</td><td>24.20</td></tr><tr><td>Residual EBM(Tr-Base)</td><td>15.57-15.58</td><td>16.98-17.00</td><td>29.88-29.93</td></tr><tr><td>Residual EBM(Tr-XL)</td><td>-</td><td>1</td><td>23.85-23.87</td></tr><tr><td>E-Forcing (Tr-Base)</td><td>15.78</td><td>17.10</td><td>29.94</td></tr><tr><td>E-Forcing(Tr-XL)</td><td>1</td><td>-</td><td>23.90</td></tr><tr><td>E-Forcing+E.R.(Tr-Base)</td><td>15.63-15.67</td><td>16.89-16.93</td><td>29.81-29.84</td></tr><tr><td>E-Forcing + E.R.(Tr-XL)</td><td>=</td><td>=</td><td>23.79-23.82</td></tr></table>
+
+# 5.2 APPLICATION TO NEURAL MACHINE TRANSLATION
+
+We further evaluate E-Forcing’s effectiveness on neural machine translation (NMT), which can be regarded as a conditional generation task. We mainly analyze E-Forcing on the IWSLT14 dataset, which includes six different language pairs ({German, Spanish, Italian} English and English {German, Spanish, Italian}) (Hereafter we abbreviate English, German, Spanish, Italian as “EN”, “DE”, “ES”, “IT”). In addition, we also reported the result of E-Forcing over the WMT16 (English German) benchmark, which is a relatively larger dataset, in Table 3.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Label Smoothing</td><td rowspan="2">Scheduled Sampling</td><td rowspan="2">Beam Searching</td><td colspan="6">BLEU个</td><td rowspan="2">Avg.</td></tr><tr><td>DE→EN</td><td>EN→DE</td><td>EN→IT</td><td>IT→EN</td><td>ES→EN</td><td>EN→ES</td></tr><tr><td rowspan="6">Base</td><td>=</td><td>·</td><td>-</td><td>32.44±0.06</td><td>26.64±0.10</td><td>27.92±0.03</td><td>30.48±0.08</td><td>38.61±0.11</td><td>35.42±0.09</td><td>31.92</td></tr><tr><td></td><td></td><td>5B</td><td>33.62±0.07</td><td>27.41±0.08</td><td>28.72±0.04</td><td>31.39±0.05</td><td>39.55±0.12</td><td>36.38±0.07</td><td>32.85</td></tr><tr><td>v</td><td>·</td><td>-</td><td>33.68±0.03</td><td>27.62±0.04</td><td>28.81±0.07</td><td>31.42±0.07</td><td>39.85±0.13</td><td>36.71±0.09</td><td>33.02</td></tr><tr><td></td><td></td><td>5B</td><td>34.61±0.08</td><td>28.46±0.06</td><td>29.72±0.10</td><td>32.29±0.03</td><td>40.64±0.07</td><td>37.48±0.05</td><td>33.87</td></tr><tr><td>√</td><td>&lt;</td><td>-</td><td>34.23±0.06</td><td>27.96±0.03</td><td>29.26±0.11</td><td>31.93±0.08</td><td>40.16±0.03</td><td>37.21±0.04</td><td>33.46</td></tr><tr><td></td><td></td><td>5B</td><td>35.10±0.04</td><td>28.73±0.04</td><td>29.97±0.07</td><td>32.64±0.12</td><td>40.91±0.06</td><td>37.93±0.10</td><td>34.21</td></tr><tr><td rowspan="6">E-Forcing</td><td>-</td><td>·</td><td>-</td><td>32.99±0.10</td><td>27.15±0.03</td><td>28.33±0.12</td><td>31.13±0.04</td><td>39.56±0.01</td><td>36.07±0.02</td><td>32.54</td></tr><tr><td></td><td></td><td>5B</td><td>34.06±0.06</td><td>27.97±0.08</td><td>29.26±0.09</td><td>31.90 ±0.13</td><td>40.30 ±0.03</td><td>36.92 ±0.09</td><td>33.40</td></tr><tr><td>√</td><td>·</td><td>-</td><td>33.97 ±0.08</td><td>28.03 ±0.04</td><td>29.13 ±0.02</td><td>31.84 ±0.11</td><td>40.32 ±0.03</td><td>36.96 ±0.07</td><td>33.38</td></tr><tr><td></td><td></td><td>5B</td><td>34.93 ±0.05</td><td>28.91 ±0.12</td><td>30.04 ±0.11</td><td>32.56 ±0.04</td><td>41.01 ±0.06</td><td>37.73 ±0.12</td><td>34.20</td></tr><tr><td>√</td><td>√</td><td>-</td><td>34.58 ±0.09</td><td>28.38 ±0.12</td><td>29.56 ±0.10</td><td>32.11 ±0.03</td><td>40.93 ±0.03</td><td>37.56 ±0.07</td><td>33.85</td></tr><tr><td></td><td></td><td>5B</td><td>35.36±0.05</td><td>29.11 ±0.04</td><td>30.25 ±0.09</td><td>32.82 ±0.11</td><td>41.58 ±0.07</td><td>38.19 ±0.03</td><td>34.55</td></tr></table>
+
+Table 2: Comparison of BLEU scores between our approach E-Forcing and the base ARGM trained just with cross-entropy loss on six translation pairs of IWSLT14 datasets. We use “-” to denote that the training trick is not used while $" \big .$ indicates we use it. “5 B” represents we use beam searching with 5 beams.
+
+Results concerning IWSLT14 are shown in Table 2, where we use a six-layer vanilla transformer as the base autoregressive model. We test not only the pure performance of E-Forcing but also the compatibility with other techniques. In detail, we can observe that (1) without any particular engineering, E-Forcing outperforms the vanilla training with cross-entropy singly(teacherforcing) by 0.62 ( $3 1 . 9 2  3 2 . 5 4 _ { . }$ ) BLEU points on average, especially on three translation pairs— $3 8 . 6 1  3 9 . 5 6 $ on Spanish-to-English, $3 0 . 4 8  3 1 . 1 3$ on Italian-to-English, $3 5 . 4 2  3 6 . 0 7$ on English-to-Spanish. (2) E-Forcing is compatible with other techniques like scheduled sampling, which can help alleviate the exposure bias problem to some extent. They are not mutually exclusive and can work together to further improve the performance of the base ARGM. (3) However, since scheduled sampling can reduce exposure bias and beam search can somewhat alleviate the flaws caused by greedy selection at each time step, the performance gain of E-Forcing when all these tactics are combined is only 0.34 $3 4 . 2 1  3 4 . 5 5 )$ ), which is lower than the 0.62 $3 1 . 9 2  3 2 . 5 4 )$ obtained when the model is purely trained without these other techniques.
+
+Additionally, Table 3 shows the performance of E-Forcing on the WMT16 English German task. For two different model sizes, enabling label smoothing (L.S.) improves model performance by 0.52 and 0.35, respectively. The performance of the base transformer model further increases to 28.36 BLEU points when scheduled sampling (S.S.) is used, while the larger model improves to 29.23 points. E-Forcing paired with label smoothing and scheduled sampling yields the highest scores of 28.62 and 29.44, respectively. Overall, our training strategy outperforms ARGM’s vanilla teacher-forcing training and can have uniformly favorable impacts across different models and dataset sizes.
+
+Table 3: Translation performance of proposed EForcing on WMT16 English German, evaluated with BLEU. We uniformly use 5 beams when applying beam search. “L.S.” denotes Label Smoothing and “S.S.” denotes Scheduled Sampling.   
+
+<table><tr><td>Model</td><td>L.S.</td><td>S.S.</td><td>E-Forcing</td><td>BLEU↑</td></tr><tr><td rowspan="4">Tr-Base</td><td>1</td><td>-</td><td></td><td>27.56</td></tr><tr><td>v</td><td>1</td><td></td><td>28.04</td></tr><tr><td></td><td>v</td><td></td><td>28.36</td></tr><tr><td>：</td><td>v</td><td>√</td><td>28.62</td></tr><tr><td rowspan="4">Tr-Large</td><td>1</td><td>-</td><td></td><td>28.70</td></tr><tr><td>v</td><td>-</td><td></td><td>29.05</td></tr><tr><td>&lt;</td><td>&lt;</td><td></td><td>29.23</td></tr><tr><td>1</td><td>&lt;</td><td></td><td>29.44</td></tr></table>
+
+# 5.3 EFFECT ON THE EXPOSURE BIAS
+
+We follow the analytic experiments in the work (Zhang et al., 2019) to show that our E-Forcing is capable of alleviating the exposure bias problem. To be concrete, we randomly select 1K pairs from the training data for each translation pair and use the trained autoregressive model which applied E-Forcing to decode the source sentences, and then count the ground truth words whose probabilities in the predicted distributions produced by our E-Forcing are greater than those produced by the baseline and denote the number as $\mathcal { N }$ . The ratio of $\mathcal { N }$ to the total number of words tested is calculated. The detailed results are shown in Table 4. We find that the results on all different tasks are greater
+
+than $50 \%$ , which demonstrates the ability of our E-Forcing in alleviating the exposure bias problem to some extent.   
+
+<table><tr><td>Trans. Pairs</td><td>DE→EN</td><td>EN→DE</td><td>EN→IT</td><td>IT→EN</td><td>ES→EN</td><td>EN→ES</td></tr><tr><td>N</td><td>14203</td><td>14554</td><td>14976</td><td>13952</td><td>16021</td><td>15359</td></tr><tr><td>Total</td><td>22148</td><td>23057</td><td>23654</td><td>23744</td><td>23860</td><td>22775</td></tr><tr><td>Ratio</td><td>64.12%</td><td>63.12%</td><td>63.31%</td><td>59.76%</td><td>68.33%</td><td>67.43%</td></tr></table>
+
+Table 4: The effect of E-Forcing on the exposure bias problem. Each test set of translation tasks contains 1K sentences selected randomly. $\mathcal { N }$ denotes the ground truth words whose probabilities in the predicted distributions produced by E-Forcing are greater than those produced by the baseline.
+
+5.4 EFFECT ON THE INCOHERENCE OF GENERATION   
+Table 5: Performance comparison on the IWSLT14 test set for the different lengths of sentences on three translation tasks (German to English, Italian to English, and Spanish to English). Performance is evaluated by the BLEU score.   
+
+<table><tr><td rowspan="2">Translation Task</td><td rowspan="2">Scheduled Sampling</td><td rowspan="2">E-Forcing Training</td><td colspan="3">Target Sentence Length</td><td rowspan="2">All Test</td></tr><tr><td>[0, 25)</td><td>[25, 49)</td><td>[50,00）</td></tr><tr><td rowspan="3">De→En</td><td>-</td><td>1</td><td>37.72 ±0.04</td><td>33.24 ±0.06</td><td>30.86 ±0.07</td><td>34.61 ±0.08</td></tr><tr><td>v</td><td>1</td><td>38.20 ±0.07</td><td>33.76 ±0.03</td><td>31.08 ±0.06</td><td>35.10 ±0.04</td></tr><tr><td>V</td><td>v</td><td>38.37 ±0.06</td><td>33.92 ±0.09</td><td>31.43 ±0.04</td><td>35.36 ±0.05</td></tr><tr><td rowspan="3">It-→En</td><td>1</td><td>-</td><td>35.20 ±0.03</td><td>32.73 ±0.02</td><td>26.86 ±0.05</td><td>32.29 ±0.03</td></tr><tr><td>v</td><td></td><td>35.52 ±0.09</td><td>33.25 ±0.08</td><td>26.95 ±0.14</td><td>32.64 ±0.12</td></tr><tr><td>v</td><td>&lt;</td><td>35.56 ±0.10</td><td>33.33 ±0.13</td><td>27.21 ±0.07</td><td>32.82 ±0.11</td></tr><tr><td rowspan="3">Es→En</td><td>1</td><td>1</td><td>43.37 ±0.05</td><td>39.67 ±0.08</td><td>37.14 ±0.06</td><td>40.64 ±0.07</td></tr><tr><td>v</td><td>=</td><td>43.61 ±0.09</td><td>40.00 ±0.04</td><td>37.38 ±0.06</td><td>40.91 ±0.06</td></tr><tr><td>v</td><td>&lt;</td><td>43.84 ±0.10</td><td>40.35 ±0.05</td><td>38.07 ±0.04</td><td>41.58 ±0.07</td></tr></table>
+
+We also attempted to quantitatively validate that our E-Forcing can benefit ARGMs by improving the coherence of generation. Table 5 shows the BLEU scores of generated translations on the IWSLT14 test set with respect to different lengths of the source sentences. Intuitively, due to the cumulative effect of greedy selection at each time step, the collection of samples with longer sentences ought to be more plagued by the incoherence of generations problem. Our approach can outperform the vanilla training in all three length intervals, especially in the lengthy sentence interval $[ 5 0 , \infty ]$ , indicating that our E-Forcing can resolve the incoherence problem to a degree.
+
+# 6 CONCLUSIONS AND FUTURE WORK
+
+In this paper, we propose a novel training method dubbed E-Forcing for ARGMs by treating them as EBMs. This is achieved by defining the energy function using the softmax operation’s extra degree of freedom within an autoregressive network. We further design a unique way to improve the training of E-Forcing using importance sampling. Experimental results demonstrate the effectiveness of E-Forcing to alleviate exposure bias and incoherence problems of ARGMs. In the future, we expect to extend E-Forcing on other sequential generation tasks (e.g. text summarization, audio generation) and incorporate the proposed methodology into other advanced autoregressive architectures.
+
+# REFERENCES
+
+Michael Arbel, Liang Zhou, and Arthur Gretton. Generalized energy based models. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021, 2021.
+
+Shaojie Bai, J. Zico Kolter, and Vladlen Koltun. Deep equilibrium models. In Advances in Neural Information Processing Systems (NeurIPS), 2019a.
+
+Shaojie Bai, J. Zico Kolter, and Vladlen Koltun. Trellis networks for sequence modeling. In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019, 2019b.
+
+Anton Bakhtin, Yuntian Deng, Sam Gross, Myle Ott, Marc’Aurelio Ranzato, and Arthur Szlam. Residual energy-based models for text. J. Mach. Learn. Res., 22:40:1–40:41, 2021.
+
+Satanjeev Banerjee and Alon Lavie. METEOR: An automatic metric for MT evaluation with improved correlation with human judgments. In Proceedings of the ACL Workshop on Intrinsic and Extrinsic Evaluation Measures for Machine Translation and/or Summarization, pp. 65–72, Ann Arbor, Michigan, jun 2005.
+
+Richard Ernest Bellman. The Theory of Dynamic Programming. Santa Monica, CA, 1954.
+
+Samy Bengio, Oriol Vinyals, Navdeep Jaitly, and Noam Shazeer. Scheduled sampling for sequence prediction with recurrent neural networks. In Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, December 7-12, 2015, Montreal, Quebec, Canada, pp. 1171–1179, 2015.
+
+Yoshua Bengio, Gregoire Mesnil, Yann N. Dauphin, and Salah Rifai. Better mixing via deep ´ representations. In Proceedings of the 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, USA, 16-21 June 2013, volume 28, pp. 552–560.
+
+Tong Che, Ruixiang Zhang, Jascha Sohl-Dickstein, Hugo Larochelle, Liam Paull, Yuan Cao, and Yoshua Bengio. Your GAN is secretly an energy-based model and you should use discriminator driven latent sampling. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020.
+
+Xi Chen, Nikhil Mishra, Mostafa Rohaninejad, and Pieter Abbeel. Pixelsnail: An improved autoregressive generative model. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmassan, Stockholm, Sweden, July 10-15, 2018 ¨ , volume 80 of Proceedings of Machine Learning Research, pp. 863–871, 2018.
+
+Junyoung Chung, C¸ aglar Gul¨ c¸ehre, KyungHyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks on sequence modeling. CoRR, abs/1412.3555, 2014.
+
+Zihang Dai, Zhilin Yang, Yiming Yang, Jaime G. Carbonell, Quoc Viet Le, and Ruslan Salakhutdinov. Transformer-xl: Attentive language models beyond a fixed-length context. In Proceedings of the 57th Conference of the Association for Computational Linguistics, ACL 2019, Florence, Italy, July 28- August 2, 2019, Volume 1: Long Papers, pp. 2978–2988, 2019.
+
+Yuntian Deng, Anton Bakhtin, Myle Ott, Arthur Szlam, and Marc’Aurelio Ranzato. Residual energybased models for text generation. In 8th International Conference on Learning Representations, ICLR 2020, 2020.
+
+Yilun Du and Igor Mordatch. Implicit generation and modeling with energy based models. In Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pp. 3603–3613, 2019.
+
+Conor Durkan and Charlie Nash. Autoregressive energy machines. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on Machine Learning, ICML 2019, volume 97, pp. 1735–1744, 2019.
+
+Ruiqi Gao, Erik Nijkamp, Diederik P. Kingma, Zhen Xu, Andrew M. Dai, and Ying Nian Wu. Flow contrastive estimation of energy-based models. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pp. 7515–7525, 2020.
+
+Ruiqi Gao, Yang Song, Ben Poole, Ying Nian Wu, and Diederik P. Kingma. Learning energybased models by diffusion recovery likelihood. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021, 2021.
+
+Will Grathwohl, Kuan-Chieh Wang, Jorn-Henrik Jacobsen, David Duvenaud, Mohammad Norouzi, ¨ and Kevin Swersky. Your classifier is secretly an energy based model and you should treat it like one. In 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020, 2020.
+
+Will Sussman Grathwohl, Jacob Jin Kelly, Milad Hashemi, Mohammad Norouzi, Kevin Swersky, and David Duvenaud. No MCMC for me: Amortized sampling for fast and stable training of energy-based models. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021, 2021.
+
+Michael Gutmann and Aapo Hyvarinen. Noise-contrastive estimation: A new estimation principle ¨ for unnormalized statistical models. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, AISTATS 2010, Chia Laguna Resort, Sardinia, Italy, May 13-15, 2010, volume 9 of JMLR Proceedings, pp. 297–304, 2010.
+
+G. Hinton, P. Dayan, B. Frey, and R. Neal. The “wake-sleep” algorithm for unsupervised neural networks. Science, 268 5214:1158–61, 1995.
+
+Geoffrey E. Hinton. Training products of experts by minimizing contrastive divergence. Neural Comput., 14(8):1771–1800, 2002.
+
+Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.
+
+Daniel G Horvitz and Donovan J Thompson. A generalization of sampling without replacement from a finite universe. Journal of the American statistical Association, 47(260):663–685, 1952.
+
+Taesup Kim and Yoshua Bengio. Deep directed generative models with energy-based probability estimation. CoRR, abs/1606.03439, 2016.
+
+Ryan Kiros, Yukun Zhu, Ruslan Salakhutdinov, Richard S. Zemel, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Skip-thought vectors. In Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, December 7-12, 2015, Montreal, Quebec, Canada, pp. 3294–3302, 2015.
+
+Yann LeCun, Sumit Chopra, Raia Hadsell, M Ranzato, and F Huang. A tutorial on energy-based learning. Predicting structured data, 1(0), 2006.
+
+Chin-Yew Lin. ROUGE: A package for automatic evaluation of summaries. In Text Summarization Branches Out, pp. 74–81, Barcelona, Spain, jul 2004.
+
+Zhuang Ma and Michael Collins. Noise contrastive estimation and negative sampling for conditional models: Consistency and statistical efficiency. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, Brussels, Belgium, October 31 - November 4, 2018, pp. 3698–3707, 2018.
+
+Joel M. Mackenzie, Rodger Benham, Matthias Petri, Johanne R. Trippas, J. Shane Culpepper, and Alistair Moffat. Cc-news-en: A large english news corpus. In CIKM ’20: The 29th ACM International Conference on Information and Knowledge Management, Virtual Event, Ireland, October 19-23, 2020, pp. 3077–3084, 2020.
+
+Mitchell P. Marcus, Beatrice Santorini, and Mary Ann Marcinkiewicz. Building a large annotated corpus of English: The Penn treebank. Computational Linguistics, 19(2):313–330, June 1993.
+
+Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture models. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings, 2017.
+
+Tsvetomila Mihaylova and Andre F. T. Martins. Scheduled sampling for transformers. In Fer- ´ nando Emilio Alva-Manchego, Eunsol Choi, and Daniel Khashabi (eds.), Proceedings of the 57th Conference of the Association for Computational Linguistics, ACL 2019, Florence, Italy, July 28 - August 2, 2019, Volume 2, pp. 351–356, 2019.
+
+Subhajit Naskar, Amirmohammad Rooshenas, Simeng Sun, Mohit Iyyer, and Andrew McCallum. Energy-based reranking: Improving neural machine translation using energy-based models. CoRR, abs/2009.13267, 2020.
+
+Erik Nijkamp, Mitch Hill, Song-Chun Zhu, and Ying Nian Wu. Learning non-convergent nonpersistent short-run MCMC toward energy-based model. In Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pp. 5233–5243, 2019.
+
+Aaron van den Oord, Nal Kalchbrenner, Oriol Vinyals, Lasse Espeholt, Alex Graves, and Koray Kavukcuoglu. Conditional image generation with pixelcnn decoders. arXiv preprint arXiv:1606.05328, 2016.
+
+Myle Ott, Sergey Edunov, Alexei Baevski, Angela Fan, Sam Gross, Nathan Ng, David Grangier, and Michael Auli. fairseq: A fast, extensible toolkit for sequence modeling. In Proceedings of NAACL-HLT 2019: Demonstrations, 2019.
+
+Bo Pang, Tian Han, Erik Nijkamp, Song-Chun Zhu, and Ying Nian Wu. Learning latent space energy-based prior model. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020.
+
+Hieu Pham, Melody Guan, Barret Zoph, Quoc Le, and Jeff Dean. Efficient neural architecture search via parameters sharing. In Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pp. 4095–4104, 10–15 Jul 2018.
+
+Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.
+
+Marc’Aurelio Ranzato, Sumit Chopra, Michael Auli, and Wojciech Zaremba. Sequence level training with recurrent neural networks. In 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings, 2016.
+
+Tim Salimans, Andrej Karpathy, Xi Chen, and Diederik P. Kingma. Pixelcnn $^ { + + }$ : Improving the pixelcnn with discretized logistic mixture likelihood and other modifications. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings, 2017.
+
+Kaitao Song, Xu Tan, and Jianfeng Lu. Neural machine translation with error correction. In Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020, pp. 3891–3897, 2020.
+
+Aaron van den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, ¨ Nal Kalchbrenner, Andrew W. Senior, and Koray Kavukcuoglu. Wavenet: A generative model for raw audio. In The 9th ISCA Speech Synthesis Workshop, Sunnyvale, CA, USA, 13-15 September 2016, pp. 125, 2016a.
+
+Aaron van den Oord, Nal Kalchbrenner, Lasse Espeholt, Koray Kavukcuoglu, Oriol Vinyals, and Alex ¨ Graves. Conditional image generation with pixelcnn decoders. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain, pp. 4790–4798, 2016b.
+
+Aaron van den Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. ¨ In Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19-24, 2016, volume 48 of JMLR Workshop and Conference Proceedings, pp. 1747–1756, 2016c.
+
+Aaron Van Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. In International Conference on Machine Learning, pp. 1747–1756. PMLR, 2016.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pp. 5998–6008, 2017.
+
+Yezhen Wang, Bo Li, Tong Che, Kaiyang Zhou, Ziwei Liu, and Dongsheng Li. Energy-based open-world uncertainty modeling for confidence calibration. CoRR, abs/2107.12628, 2021.
+
+Max Welling and Yee Whye Teh. Bayesian learning via stochastic gradient langevin dynamics. In Proceedings of the 28th International Conference on Machine Learning, ICML 2011, Bellevue, Washington, USA, June 28 - July 2, 2011, pp. 681–688, 2011.
+
+Zhisheng Xiao, Karsten Kreis, Jan Kautz, and Arash Vahdat. VAEBM: A symbiosis between variational autoencoders and energy-based models. In 9th International Conference on Learning Representations, ICLR 2021, 2021.
+
+J. Xie, Z. Zheng, X. Fang, S. Zhu, and Y. Wu. Cooperative training of fast thinking initializer and slow thinking solver for conditional learning. IEEE Transactions on Pattern Analysis & Machine Intelligence, (01):1–1, mar 2019. ISSN 1939-3539.
+
+Jianwen Xie, Yang Lu, Ruiqi Gao, Song-Chun Zhu, and Ying Nian Wu. Cooperative training of descriptor and generator networks. IEEE Trans. Pattern Anal. Mach. Intell., 42(1):27–45, 2020.
+
+Minkai Xu, Shitong Luo, Yoshua Bengio, Jian Peng, and Jian Tang. Learning neural generative dynamics for molecular conformation generation. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021, 2021.
+
+Wen Zhang, Yang Feng, Fandong Meng, Di You, and Qun Liu. Bridging the gap between training and inference for neural machine translation. In Anna Korhonen, David R. Traum, and Llu´ıs Marquez \` (eds.), Proceedings of the 57th Conference of the Association for Computational Linguistics, ACL 2019, Florence, Italy, July 28- August 2, 2019, Volume 1, pp. 4334–4343, 2019.
+
+Junbo Jake Zhao, Michael Mathieu, and Yann LeCun. Energy-based generative adversarial networks. ¨ In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings, 2017.
+
+Yukun Zhu, Ryan Kiros, Richard S. Zemel, Ruslan Salakhutdinov, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, December 7-13, 2015, pp. 19–27, 2015.
+
+# A EXPERIMENTAL SETTINGS
+
+In this section, we introduce detailed setups of different benchmarks as well as the information of corresponding datasets.
+
+# A.1 DATASETS
+
+We conducted our experiments based on 7 datasets over different learning tasks:
+
+1. WikiText-103 comprises 103 million training tokens from 28 thousand articles, with an average length of 3.6 thousand tokens per article.   
+2. Toronto Book Corpus consists of fiction books in 16 different genres, totaling about half a billion words.   
+3. CC-news is a de-duplicated subset of the English portion of the CommonCrawl news dataset, which totals around 16 Billion words.   
+4. IWSLT14 contains about $1 7 0 \mathrm { k }$ training sentence pairs, 7k valid pairs, and $\mathrm { 7 k }$ test pairs. It has six different domains of language, and each two of them can consist of a translation pair.   
+5. WMT16 contains 103M training tokens from 28K articles, with an average length of 3.6K tokens per article, which allows testing the ability of long-term dependency modeling.   
+6. MNIST is a large collection of handwritten digits. It has a training set of 60,000 examples and a test set of 10,000 examples.   
+7. CIFAR-10 is a subset of the Tiny Images dataset and consists of $6 0 0 0 0 \ 3 2 { \mathrm { x } } 3 2$ color images. The images are labeled with one of 10 mutually exclusive classes.
+
+# A.2 IMPLEMENTING SETUPS
+
+Table 6: Hyperparameters of different model structures and datasets. “Tr-Base”, “Tr-Large”, and “Tr-XL” indicate Transformer-Base, Transformer-Large, and Transformer-XL respectively   
+
+<table><tr><td rowspan="2">Hyper-Parameters</td><td>Translation-IWSLT14</td><td colspan="2">Translation-WMT16</td><td colspan="2">Language Modeling</td></tr><tr><td>Tr-Base</td><td>Tr-Base</td><td>Tr-Large</td><td>Tr-Base</td><td>Tr-XL</td></tr><tr><td>Number of Layers</td><td>12</td><td>12</td><td>12</td><td>6</td><td>16</td></tr><tr><td>Hidden Embed Size</td><td>512</td><td>512</td><td>1024</td><td>512</td><td>410</td></tr><tr><td>FC-Layer Embed Size</td><td>1024</td><td>2048</td><td>4096</td><td>2048</td><td>2100</td></tr><tr><td>Attention Heads</td><td>4</td><td>8</td><td>16</td><td>8</td><td>10</td></tr><tr><td>Dropout</td><td>0.3</td><td>0.3</td><td>0.3</td><td>0.1</td><td>0.1</td></tr><tr><td>Learning Rate</td><td>5e-4</td><td>1e-3</td><td>1e-3</td><td>5e-4</td><td>2.5e-4</td></tr><tr><td>lr scheduler</td><td>inverse_sqrt</td><td>inverse_sqrt</td><td>inverse_sqrt</td><td>inverse_sqrt</td><td>cosine</td></tr><tr><td>Warm up Updates</td><td>4000</td><td>4000</td><td>4000</td><td>4000</td><td>10000</td></tr><tr><td>Weigth Decay</td><td>1e-4</td><td>0.0</td><td>0.0</td><td>1e-2</td><td>0.0</td></tr><tr><td>E-Forcing Start Epoch</td><td>15</td><td>15</td><td>10</td><td>15</td><td>10</td></tr></table>
+
+We uniformly use the Adam optimizer. The training will be stopped once the model has not obtained better performance for 20 epochs on the validation set. For translation tasks, the length of generated fake sentences, which is used for the computing of the negative phase in Eq. 10, is dependent on the source sequence whilst for language modeling tasks, we fix the length of generated fake sentences as 50 during training. The model structures for language modeling and machine translation tasks are shown in Table 6. As for the model structures of the image generation task, we use the official structure reported by PixelCNN (van den Oord et al., 2016c) and Gated PixelCNN (van den Oord et al., 2016b) without modification. The source code will be released once upon acceptance. We use the same batch of samples generated autoregressively to approximate both the expectations in Eq.10 and weight w (i.e., shared), which does not need to sample twice. The number of samples in a batch is dynamic while the maximum number of the total tokens in a batch is fixed (4096 in our experiments). If the length of sequences in a batch is 32, then it includes $4 0 9 6 / 3 2 = 1 2 8$ samples in total. It is a common strategy in language generation tasks and has been used in many frameworks(e.g.
+
+Fairseq (Ott et al., 2019)). We generate samples autoregressively as many as the number of sequences in the current batch at each update iteration.
+
+# B DERIVATION OF THE NEGATIVE PHASE GRADIENT
+
+In this section, we show the detailed derivation of Eq. 8. Formally, as shown in Sec. 3, given an autoregressive model $\begin{array} { r } { q _ { \theta } \big ( \mathbf { x } _ { < k } \big ) = \prod _ { l = 1 } ^ { k - 1 } q _ { \theta } \big ( \mathbf { x } _ { l } | \mathbf { x } _ { < l } \big ) } \end{array}$ ( $k$ denotes the time step) with parameters $\theta$ , we define a product of the autoregressive model and an EBM as follows
+
+$$
+p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) = q _ { \theta } ( \mathbf { x } _ { < k } ) \cdot \frac { e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbf { Z } _ { \theta } } ,
+$$
+
+where $\begin{array} { r l r } { q _ { \theta } ( \mathbf { x } _ { < k } ) } & { { } = } & { \prod _ { l = 1 } ^ { k - 1 } q _ { \theta } ( \mathbf { x } _ { l } \vert \mathbf { x } _ { < l } ) } \end{array}$ , $\mathbf { Z } _ { \theta }$ is the normalization term and equal to $\begin{array} { r } { \mathbb { E } _ { \mathbf { x } _ { < k } ^ { \prime } \sim q _ { \theta } } [ \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ^ { \prime } ) } ] } \end{array}$ . The optimization of $p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } )$ includes two phases, and the gradient w.r.t $\theta$ of “negative phase” is
+
+$$
+- \mathbb { E } _ { \mathbf { x } _ { < k } \sim p _ { \theta } } [ \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) ] + \mathbb { E } _ { \mathbf { x } _ { k } , \mathbf { x } _ { < k } \sim p _ { \theta } } [ \nabla _ { \theta } \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) ] .
+$$
+
+Next, we will show the specific derivation about how to transform Eq. 13 into Eq. 8.
+
+# B.1 DERIVATION OF THE FIRST TERM
+
+The first term $\mathbb { E } _ { \mathbf { x } _ { < k } \sim p _ { \theta } } [ \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) ]$ can be processed as follows
+
+$$
+\begin{array} { r l } { \mathbb { E } _ { \mathbf { x } _ { < k } \sim p _ { \theta } } \big [ \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) \big ] = \displaystyle \sum _ { \mathbf { x } _ { < k } } p _ { \theta } ( \mathbf { x } _ { < k } ) \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) } & { } \\ & { = \displaystyle \sum _ { \mathbf { x } _ { < k } } \displaystyle \sum _ { \mathbf { x } _ { k } } p _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) } \\ & { = \displaystyle \sum _ { \mathbf { x } _ { < k } } q _ { \theta } ( \mathbf { x } _ { < k } ) \frac { \displaystyle \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \displaystyle \mathbf { Z } _ { \theta } } \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) } \\ & { = \mathbb { E } _ { \mathbf { x } _ { < k } \sim q _ { \theta } ( \mathbf { x } _ { < k } ) } \big [ \mathbf { w } ( \mathbf { x } _ { < k } ) \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) \big ] , } \end{array}
+$$
+
+where we have $\begin{array} { r } { \mathbf { w } \big ( \mathbf { x } _ { < k } \big ) = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbb { E } _ { \mathbf { x } _ { < k } ^ { \prime } \sim q _ { \theta } ( \mathbf { x } _ { < k } ) } [ \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ^ { \prime } ) } ] } } \end{array}$ because
+
+$$
+\begin{array} { r l }   { \mathbf { w } ( \mathbf { x } _ { < k } ) = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbf { Z } _ { \theta } } = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \sum _ { \mathbf { x } _ { < k } } \sum _ { \mathbf { x } _ { k } } q _ { \theta } ( \mathbf { x } _ { < k } ) e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } } \\ & { = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \sum _ { \mathbf { x } _ { < k } } q _ { \theta } ( \mathbf { x } _ { < k } ) \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } } \\ & { = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbb { E } _ { \mathbf { x } _ { < k } \sim q _ { \theta } ( \mathbf { x } _ { < k } ) } [ \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } ] } . } \end{array}
+$$
+
+# B.2 DERIVATION OF THE SECOND TERM
+
+Then, we tackle the second term $\mathbb { E } _ { \mathbf { x } _ { k } , \mathbf { x } _ { < k } \sim p _ { \theta } } \left[ \nabla _ { \theta } \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) \right]$ as follows
+
+$$
+\begin{array} { r l } { \left| \nabla _ { x } \sqrt { \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \right| } \\ { = } & { \sum _ { q \in \mathcal { X } _ { \neq } } \sqrt { \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \sqrt { \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \sqrt { \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \sum _ { q \in \mathcal { X } _ { \neq } } \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \operatorname* { m a x } \log } \\ & { = \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \log \operatorname* { m a x } \log \log \operatorname* { m a x } \log \log } \\ &  = \log \log \log \log \log \log \log \end{array}
+$$
+
+where $\mathbf { w } ( \mathbf { x } _ { < k } )$ is also equal to Pxk e−ϕ(xk,x<k) . Combining Eq. 14 and Eq. 16, we can obtain an Zθ equivalent form of the gradient of the negative phase without any expectation over $p _ { \theta }$ as
+
+$$
+\begin{array} { r l } { - \mathbb { E } _ { \mathbf { x } _ { < k } \sim q _ { \theta } ( \mathbf { x } _ { < k } ) } \big [ \mathbf { w } ( \mathbf { x } _ { < k } ) \nabla _ { \theta } \log q _ { \theta } ( \mathbf { x } _ { < k } ) \big ] + \mathbb { E } _ { \mathbf { x } _ { k } , \mathbf { x } _ { < k } \sim q _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } \big [ \mathbf { w } ( \mathbf { x } _ { < k } ) \nabla _ { \theta } \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) \big ] , } & { } \\ { \mathbf { w h e r e } \quad \mathbf { w } ( \mathbf { x } _ { < k } ) = \frac { \sum _ { \mathbf { x } _ { k } } e ^ { - \phi ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ) } } { \mathbb { E } _ { \mathbf { x } _ { < k } ^ { \prime } \sim q _ { \theta } ( \mathbf { x } _ { < k } ) } \big [ \sum _ { \mathbf { x } _ { k } } e ^ { - \phi _ { \theta } ( \mathbf { x } _ { k } , \mathbf { x } _ { < k } ^ { \prime } ) } \big ] } . } & { } \end{array}
+$$
+
+# B.3 FURTHER REFINEMENT OF w
+
+The reweighing weight w can be further deduced as
+
+$$
+\begin{array} { r l } & { \mathbf w ( \mathbf x _ { < k } ) = \frac { \sum _ { \mathbf x _ { k } } e ^ { - \phi ( \mathbf x _ { k } , \mathbf x _ { < k } ) } } { \mathbb E _ { \mathbf x _ { < k } ^ { \prime } \sim q \theta ( \mathbf x _ { < k } ) } [ \sum _ { \mathbf x _ { k } } e ^ { - \phi _ { \theta } ( \mathbf x _ { k } , \mathbf x _ { < k } ^ { \prime } ) } ] } = \frac { \sum _ { \mathbf x _ { k } } \frac { p _ { \theta } ( \mathbf x _ { k } , \mathbf x _ { < k } ) } { q _ { \theta } ( \mathbf x _ { < k } ) } } { \mathbb E _ { \mathbf x _ { < k } ^ { \prime } \sim q \theta ( \mathbf x _ { < k } ) } [ \sum _ { \mathbf x _ { k } } \frac { p _ { \theta } ( \mathbf x _ { k } , \mathbf x _ { < k } ) } { q _ { \theta } ( \mathbf x _ { < k } ) } ] } } \\ & { \quad \quad \quad = \frac { \frac { p _ { \theta } ( \mathbf x _ { < k } ) } { q _ { \theta } ( \mathbf x _ { < k } ) } } { \mathbb E _ { \mathbf x _ { < k } ^ { \prime } \sim q _ { \theta } ( \mathbf x _ { < k } ) } [ \frac { p _ { \theta } ( \mathbf x _ { < k } ) } { q _ { \theta } ( \mathbf x _ { < k } ) } ] } = \frac { \mu ( \mathbf x _ { < k } ) } { \mathbb E _ { \mathbf x _ { < k } ^ { \prime } } \mu ( \mathbf x _ { < k } ) } , } \end{array}
+$$
+
+where $\mu ( \mathbf { x } _ { < k } )$ is defined as $\frac { p _ { \theta } \left( \mathbf { x } _ { < k } \right) } { \tilde { q } _ { \theta } \left( \mathbf { x } _ { < k } \right) }$ .
+
+# C MORE EXPERIMENTAL ANALYSIS
+
+# C.1 ANALYSIS TO TOP-K ENERGY RE-SAMPLING
+
+Top-K energy re-sampling in the inference stage is introduced by Bakhtin et al. (2021), which collects many candidate sequences generated autoregressively in the inference stage and then re-samples from them depending on their energy scores estimated by the network. To measure the effectiveness of the Top-K energy re-sampling towards our method, we conduct an ablation study on neural machine translation task by selecting different $\mathsf { K } = \{ 0 , 5 , 1 0 \}$ . The results are shown in Table 7 and performances are evaluated by using the BLEU score. From Table 7, we observe that the benefits brought by Top-K sampling is minor $( \mathsf { K } { = } \{  5 , 1 0 \} )$ ), when compared with the model without Top-K sampling $\scriptstyle ( \mathrm { K = 0 } )$ . This together with the results shown in Table 1 shows that our E-Forcing can considerably benefit the base autoregressive model even without the energy resampling technique.
+
+<table><tr><td colspan="2">Trans. Pairs</td><td>DE→EN</td><td>EN→DE</td><td>EN→IT</td><td>IT→EN</td><td>ES→EN</td><td>EN→ES</td></tr><tr><td rowspan="3">k</td><td>0</td><td>34.93</td><td>28.91</td><td>30.04</td><td>32.56</td><td>41.01</td><td>37.73</td></tr><tr><td>5</td><td>34.97</td><td>28.92</td><td>30.08</td><td>32.60</td><td>41.07</td><td>37.71</td></tr><tr><td>10</td><td>34.95</td><td>28.95</td><td>30.07</td><td>32.59</td><td>41.03</td><td>37.75</td></tr></table>
+
+Table 7: The effect of Top-K correction in the inference stage. We tested BLEU scores of using different $k$ on different translation pairs of IWSLT14 dataset.
+
+# C.2 APPLICATION TO IMAGE GENERATION
+
+In order to illustrate the effectiveness and generality of our method in processing different modality tasks, we further show the results of applying E-Forcing to image generation in this section. We apply E-Forcing to Pixel-CNN (Van Oord et al., 2016) and its variant Gated Pixel-CNN (Oord et al., 2016). Experiments are carried out on the MNIST and CIFAR-10 datasets.
+
+Table 8 summarizes the quantitative results measured by per-pixel negative log-likelihood (NLL). We can see that with the help of our E-Forcing, both the Pixel-CNN and the Gated Pixel-CNN can obtain improvements in all datasets $( 0 . 1 7  0 . 1 5 $ and 3.14 $ 3 . 0 7$ for Pixel-CNN on MNIST and CIFAR10 respectively and 0.14 $ 0 . 1 2$ and $3 . 0 3  2 . 9 7$ for Gated Pixel-CNN on MNIST and CIFAR10 respectively). This is further evidence in favor of the energy-based learning
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">Test (Train) NLL↓</td></tr><tr><td>MNIST</td><td>CIFAR-10</td></tr><tr><td>Pixel-CNN</td><td>0.17 (0.13)</td><td>3.14 (3.08)</td></tr><tr><td>Pixel-CNN (w/E-Forcing)</td><td>0.15 (0.12)</td><td>3.07 (2.98)</td></tr><tr><td>Gated Pixel-CNN</td><td>0.14 (0.11)</td><td>3.03 (2.90)</td></tr><tr><td>Gated Pixel-CNN (w/E-Forcing)</td><td>0.12 (0.10)</td><td>2.97 (2.87)</td></tr></table>
+
+Table 8: Performance of E-Forcing with different base networks on MNIST and CIFAR-10 in bits/dim (lower is better), training performance in brackets.
+
+objective for improving autoregressive models.
+
+# C.3 THE EFFECT OF DIFFERENT START EPOCHS OF E-FORCING
+
+In addition, we have studied the effect of different start epochs of E-Forcing on the performance of language modeling, which can be seen in Table 9. From this, we may deduce that starting E-Forcing training at the 15th and 10th epoch yields the best results for Transformer-Base and TransformerXL respectively, whereas starting earlier or later yields a performance decline. It is reasonable because, if E
+
+Table 9: Exploring the effect of different start epochs of E-Forcing on Wikitext103 benchmark. Performances are evaluated by perplexity (PPL).   
+
+<table><tr><td rowspan="2">Model Structure</td><td colspan="5">Start Epoch of E-Forcing</td></tr><tr><td>5</td><td>10</td><td>15</td><td>20</td><td>25</td></tr><tr><td>Tr-Base</td><td>30.38</td><td>30.12</td><td>29.94</td><td>30.05</td><td>30.29</td></tr><tr><td>Tr-XL</td><td>24.12</td><td>23.90</td><td>23.96</td><td>24.05</td><td>24.16</td></tr></table>
+
+Forcing was introduced too early, the autoregressive model may not have been optimized well at that moment. As a result, the quality of generation for the “negative phase” would be terrible, making energy-based training unstable. On the other hand, the underlying autoregressive model can be modified only marginally if E-Forcing was introduced when the ARGM training is virtually complete.
+
+![](images/a85466e37ce0d243de641c70b05f0e749bcb79043328b6617691e7ddaf0e2f36.jpg)  
+Figure 1: (a) Cross entropy loss curves on IWSLT14 Spanish to English translation task on training set. The blue and orange colors represent base model and E-Forcing respectively; (b) Cross entropy loss curves on IWSLT14 Spanish English translation task on test set.
+
+# C.4 ANALYSIS TO MODEL’S CONVERGENCE
+
+In this section, we will investigate the convergence of our E-Forcing. To begin, we first train a base Transformer model (“Tr-Base” architecture shown in Table 6) on the IWSLT14 Spanish to English training set for baseline and E-Forcing method respectively, and then record the training loss and test loss (in cross-entropy) at the end of each epoch. The loss curves are plotted in Figure 1. From Figure 1, we can see that (1) at the start of the training, our E-Forcing converges slightly faster than the baseline. (2) As the training process progresses, the cross entropy of the baseline on the training set will gradually decrease, at a faster rate than E-Forcing. On the other hand, the test loss curve of the baseline will fall initially and then slowly rise after 50 epochs while E-Forcing always remains stable convergence. This phenomenon also shows that our E-Forcing method can effectively prevent over-fitting so that obtaining better generalization.
+
+C.5 ABLATION STUDY WITH DIFFERENT ARCHITECTURE CHOICES   
+Table 10: The ablation study of E-forcing over different choices of the architecture of AR models with the comparison of vanilla teacher-forcing training. We tested PPL scores using different AR models on the Penn Treebank dataset   
+
+<table><tr><td>Training Methods</td><td>GRU</td><td>LSTM</td><td>ENAS</td><td>DEQ</td><td>Tr-XL</td><td>TNet</td></tr><tr><td>Teacher-Forcing</td><td>92.48</td><td>78.93</td><td>58.60</td><td>57.10</td><td>54.55</td><td>54.19</td></tr><tr><td>E-Forcing</td><td>90.12</td><td>76.97</td><td>56.89</td><td>55.55</td><td>53.49</td><td>53.24</td></tr></table>
+
+In this section, we conducted an ablation study to investigate our E-Forcing model’s generalization ability over different sequential models. We tested over 6 different sequential models, which are GRU (Chung et al., 2014), LSTM (Hochreiter & Schmidhuber, 1997), ENAS (Pham et al., 2018), TrelisNet(TNET for short) (Bai et al., 2019b), DEQ (Bai et al., 2019a) and Transformer-XL (Dai et al., 2019) on Penn Treebank (Marcus et al., 1993) dataset, which is a relatively small dataset and widely used in machine learning for NLP (Natural Language Processing) research. In general, we can observe that our E-Forcing can achieve improvement over all base AR models applied, which indicates it is a universally applicable training method for AR models.
+
+# C.6 CASES STUDIES
+
+To better understand the advantages of our method in correcting error tokens, we also prepare some translation cases in IWSLT14 German English, as shown in Table 11.
+
+Table 11: Translation cases on IWSLT14 $_ \mathrm { D e \to E n }$ test set, generated by the baseline method, baseline with scheduled sampling and our E-Forcing. The italic font means the mismatch translation   
+
+<table><tr><td>Source Sentence(German)</td><td>Predicted Target Sentence(English)</td></tr><tr><td>ihnen 400 zeitschriften zeige,und diese in 2O kategorien aufteile,dann glauben sie,dass ich ihnen mehr auswahl und eine bessere auswahlerfahrung gegeben habe,als ich ihnen die 4OO gegeben hätte gegenuber dem, wenn ich ihnen die 600 gegeben hätte.</td><td>GroundTruth:if i show you 6Oo magazines and i divide them up into 10 categories,versus i show you 4Oo magazines and divide them up into 20 categories,you believe thati have given you more choice and a better choosing experience if i gave you the 4Oo than if i gave you the 600. Baseline: if i show you 6OO magazines and i split them in 1O categories,or i’m showing them 4OO magazines,and i&#x27;m going to split them up into 2O categories, you think i&#x27;ve given them more choices and better choice than i would have</td></tr><tr><td></td><td>given them the 4OO over the time that i gave them the 600. Baseline + S.S.: if i show you 6OO magazines andi give you 4OO magazines in 10 categories,and i give you 4Oo magazines,and ican split them up in 20 categories,then you think i&#x27;ve given you more choice and a better selection than i would have given you the 4OO of which if i gave you the 600. Ours: if i show you 6Oo magazines and i divide them into 10 categories,or i show you 4O0 magazines,and i divide them into 20 categories,you think i&#x27;ve given you more choices and beter selection experience than i gave you the 400 of whom if i gave you the 600.</td></tr><tr><td>und ich weiB definitiv, dass es flir mich-in meiner situation-sehr gefahrlich wäre,anzufangen, diesen dunklen pfad der vermutung sozusagen herunterzu- sickern-besonders in dem umstand, in dem ich mich in meiner karriere gerade befinde.</td><td>GroundTruth:andi definitely know that, in my case-in my situation-it would be very dangerous for me to start sort of leaking down that dark path of assumption, particularly given the circumstance that i&#x27;m in right now in my career. Baseline: and i know definitely,for me,it would be very dangerous to begin to do this dark path of suspect-especially in the circumstance that i&#x27;m in my</td></tr><tr><td></td><td>career right now. Baseline + S.S.: and i know definitely it would be-in my situation- very dangerous to start, to kind of settle down this dark path of presumption -</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>especially in the circumstance in which i&#x27;m in my career right now.</td></tr><tr><td></td><td>Ours:and i definitely know that it&#x27;s for me-in my situation-very danger-</td></tr><tr><td></td><td>ous to start to sickle down this dark path of suspection,in particular, in the</td></tr><tr><td>wirhaben das licht ausgeschaltet, legten es in ein vakuumund saugten die</td><td>circumstance of where i&#x27;m in my career right now.</td></tr><tr><td>ganze luft aus und kihlten es bis fast zum jetzt,ganz alleine im aufzug, war das stiick metall frei, sich zu verhalten wie immer es wollte.</td><td>GroundTruth:we turned off the lights,and thenwe put it ina vacuumand sucked out all the air, and then we cooled it down now,all alone in the elevator,</td></tr><tr><td></td><td>the little chunk of metal is free to act however it wanted.</td></tr><tr><td></td><td>Baseline: we turned the light off, put it in a vacuum and sucked it out all the air and cooled it up until almost now,all the way alone,the piece of metal was</td></tr><tr><td></td><td>open to behave as it was. Baseline + S.S.: we turned the lights off, we put it into a vacuum,and we</td></tr><tr><td></td><td>sucked allte air,and we cooled it all the wayup to now,all over the place,the</td></tr><tr><td></td><td>piece of metal was free to behave whatever it wanted. Ours: we turned off the lights,we put it into a vacuum and we sucked all the</td></tr><tr><td>und im grunde konnen sie das betrachten,wissen sie,als eine tyrannei des erin-</td><td>air out,and we cooled it up until almost now,all alone in the elevator,the piece of metal was free to behave whatever it wanted.</td></tr><tr><td>nernden selbst,und sie konnen sich das erinnernde selbst denken als eins, das sozusagen das erlebende selbst schleppt durch erfahrungen,die das erlebende</td><td>GroundTruth: and basically you can look at this,you know,asa tyranny of the remembering self,and you can think of the remembering self sort of dragging</td></tr><tr><td>selbst nicht braucht.</td><td>the experiencing self through experiences that the experiencing self doesn&#x27;t need.</td></tr><tr><td></td><td>Baseline: and basically,you can think of this,you know,as a tyranny of self,</td></tr><tr><td></td><td>and you can think of the memorable self as one that kind of weaves the living self through experiences that don&#x27;t need the life itself.</td></tr><tr><td></td><td>Baseline +S.S.: and basically,you can look at this,you know,as a tyrannei of memorial self,and you can think of the memorial self as one that kind of sucks</td></tr><tr><td></td><td>the living self through experiences that don&#x27;t need the living self.</td></tr><tr><td></td><td>Ours:and basically,you can look at that,you know,as a tyranny of the</td></tr><tr><td>wir sind an der schwelle zu erstaunlichen, erstaunlichen ereignissen auf vielen</td><td>remembering self,and you can think of the memory itself as one,which is sort of dragging the living self through experiences that the living self doesn&#x27;t need.</td></tr><tr><td>gebieten.und doch denke ich wirklich,dass wir hunderte,3OO jahre vor die</td><td>GroundTruth:we&#x27;re on the verge of amazing,amazing eventsin many fields,</td></tr><tr><td>aufklärung zuruck gehen müssten,um eine zeit zu finden,in der wir fortschritt bekämpft haben,in der wir über diese dinge heftiger getritten haben,an mehr</td><td>and yeti actually think we&#x27;d have to go back hundreds,3OO years, before the</td></tr><tr><td>fronten als jetzt.</td><td>enlightenment,to find a time when we battled progress, when we fought about these things more vigorously, on more fronts,than we do now.</td></tr><tr><td></td><td></td></tr><tr><td></td><td>Baseline:we are at the threshold of amazing,amazing events in many areas, and yetireally think that we have to go back hundreds and 3OO years before</td></tr><tr><td></td><td>the enlightenment to find a time when we have fought progress in which we</td></tr><tr><td></td><td>have driven more of these things than now.</td></tr><tr><td></td><td>Baseline + S.S.: we&#x27;re at the threshold of amazing,amazing events in many areas.and yet,i really think that we have to go back hundreds and hundreds</td></tr><tr><td></td><td></td></tr><tr><td></td><td>of years before the enlightenment to find a time when we have struggled with</td></tr><tr><td></td><td>progress in which we have driven on these things more powerful, more fronts</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>than now.</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td>Ours: we&#x27;re at the threshold to amazing,amazing events in many areas,and</td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td></td><td></td></tr><tr><td>yet i really think that we have to go back hundreds and 3OO years before the enlightenment to find a time when we fought progress,where we&#x27;ve been</td><td></td></tr></table>
+
+C.7 EVALUATION WITH OTHER METRICS   
+Table 12: Comparison of ROUGE-1, ROUGE-2, ROUGE-L, METEOR, and BLEU scores between our approach E-Forcing and the base ARGM trained just with cross-entropy loss on three translation pairs of IWSLT14 datasets. The value is expressed in percentage. We use “Tr-Base” as the network architecture.   
+
+<table><tr><td rowspan="2">Trans.Pairs</td><td rowspan="2">Scheduled Sampling</td><td rowspan="2">E-Forcing Training</td><td colspan="5">Metrics</td></tr><tr><td>ROUGE-1↑</td><td>ROUGE-2个</td><td>ROUGE-L↑</td><td>METEOR↑</td><td>BLEU个</td></tr><tr><td rowspan="3">De→En</td><td>-</td><td>-</td><td>66.51</td><td>43.69</td><td>63.69</td><td>64.35</td><td>34.61</td></tr><tr><td>√</td><td>-</td><td>66.83</td><td>44.08</td><td>64.02</td><td>64.61</td><td>35.10</td></tr><tr><td>V</td><td>√</td><td>67.46</td><td>44.77</td><td>64.78</td><td>65.13</td><td>35.36</td></tr><tr><td rowspan="3">It→En</td><td>1</td><td>-</td><td>64.50</td><td>40.65</td><td>61.69</td><td>62.18</td><td>32.29</td></tr><tr><td>v</td><td>-</td><td>64.73</td><td>40.97</td><td>61.94</td><td>62.51</td><td>32.64</td></tr><tr><td>&lt;</td><td>√</td><td>65.27</td><td>41.51</td><td>62.49</td><td>62.80</td><td>32.82</td></tr><tr><td rowspan="3">Es→En</td><td>-</td><td>-</td><td>71.10</td><td>49.47</td><td>68.78</td><td>68.94</td><td>40.64</td></tr><tr><td>&lt;</td><td>-</td><td>71.36</td><td>49.53</td><td>68.96</td><td>69.28</td><td>40.91</td></tr><tr><td>&lt;</td><td>√</td><td>71.91</td><td>50.17</td><td>69.65</td><td>69.63</td><td>41.58</td></tr></table>
+
+To further evaluate the effectiveness of our proposed E-Forcing, we also evaluate our method by using other metrics, such as ROUGE Lin (2004) and METEOR Banerjee & Lavie (2005) for neural machine translation. The results are shown in Table 12. In Table 12, the improvements of E-Forcing in different metrics is consistent with the conclusion of Table 2, which further prove the effectiveness of our E-Forcing method.

parse/dev/Zk1SbbdZwS/Zk1SbbdZwS.md

@@ -0,0 +1,310 @@
+# Model-Based Imitation Learning for Urban Driving
+
+Anthony $\mathbf { H } \mathbf { u } ^ { 1 , 2 }$ Gianluca Corrado1 Nicolas Griffiths1 Zak Murez1 Corina Gurau1
+
+Hudson Yeo1 Alex Kendall1 Roberto Cipolla2 Jamie Shotton1
+
+1Wayve, UK. 2University of Cambridge, UK. research@wayve.ai
+
+# Abstract
+
+An accurate model of the environment and the dynamic agents acting in it offers great potential for improving motion planning. We present MILE: a Model-based Imitation LEarning approach to jointly learn a model of the world and a policy for autonomous driving. Our method leverages 3D geometry as an inductive bias and learns a highly compact latent space directly from high-resolution videos of expert demonstrations. Our model is trained on an offline corpus of urban driving data, without any online interaction with the environment. MILE improves upon prior state-of-the-art by $31 \%$ in driving score on the CARLA simulator when deployed in a completely new town and new weather conditions. Our model can predict diverse and plausible states and actions, that can be interpretably decoded to bird’s-eye view semantic segmentation. Further, we demonstrate that it can execute complex driving manoeuvres from plans entirely predicted in imagination. Our approach is the first camera-only method that models static scene, dynamic scene, and ego-behaviour in an urban driving environment. The code and model weights are available at https://github.com/wayveai/mile.
+
+# 1 Introduction
+
+From an early age we start building internal representations of the world through observation and interaction [1]. Our ability to estimate scene geometry and dynamics is paramount to generating complex and adaptable movements. This accumulated knowledge of the world, part of what we often refer to as common sense, allows us to navigate effectively in unfamiliar situations [2].
+
+In this work, we present MILE, a Model-based Imitation LEarning approach to jointly learn a model of the world and a driving policy. We demonstrate the effectiveness of our approach in the autonomous driving domain, operating on complex visual inputs labelled only with expert action and semantic segmentation. Unlike prior work on world models [3, 4, 5], our method does not assume access to a ground truth reward, nor does it need any online interaction with the environment. Further, previous environments in OpenAI Gym [3], MuJoCo [4], and Atari [5] were characterised by simplified visual inputs as small as $6 4 \times 6 4$ images. In contrast, MILE operates on high-resolution camera observations of urban driving scenes.
+
+Driving inherently requires a geometric understanding of the environment, and MILE exploits 3D geometry as an important inductive bias by first lifting image features to 3D and pooling them into a bird’s-eye view $\mathrm { ( B e V ) }$ representation. The evolution of the world is modelled by a latent dynamics model that infers compact latent states from observations and expert actions. The learned latent state is the input to a driving policy that outputs vehicle control, and can additionally be decoded to BeV segmentation for visualisation and as a supervision signal.
+
+Our method also relaxes the assumption made in some recent work [6, 7] that neither the agent nor its actions influence the environment. This assumption rarely holds in urban driving, and therefore MILE is action-conditioned, allowing us to model how other agents respond to ego-actions. We show that our model can predict plausible and diverse futures from latent states and actions over long time horizons. It can even predict entire driving plans in imagination to successfully execute complex driving manoeuvres, such as negotiating a roundabout, or swerving to avoid a motorcyclist (see videos in the supplementary material).
+
+We showcase the performance of our model on the driving simulator CARLA [8], and demonstrate a new state-of-the-art. MILE achieves a $31 \%$ improvement in driving score with respect to previous methods [9, 10] when tested in a new town and new weather conditions. Finally, during inference, because we model time with a recurrent neural network, we can maintain a single state that summarises all the past observations and then efficiently update the state when a new observation is available. We demonstrate that this design decision has important benefits for deployment in terms of latency, with negligible impact on the driving performance.
+
+To summarise the main contributions of this paper:
+
+• We introduce a novel model-based imitation learning architecture that scales to the visual complexity of autonomous driving in urban environments by leveraging 3D geometry as an inductive bias. Our method is trained solely using an offline corpus of expert driving data, and does not require any interaction with an online environment or access to a reward, offering strong potential for real-world application.   
+• Our camera-only model sets a new state-of-the-art on the CARLA simulator, surpassing other approaches, including those requiring LiDAR inputs.   
+• Our model predicts a distribution of diverse and plausible futures states and actions. We demonstrate that it can execute complex driving manoeuvres from plans entirely predicted in imagination.
+
+# 2 Related Work
+
+Our work is at the intersection of imitation learning, 3D scene representation, and world modelling.
+
+Imitation learning. Despite that the first end-to-end method for autonomous driving was envisioned more than 30 years ago [11], early autonomous driving approaches were dominated by modular frameworks, where each module solves a specific task [12, 13, 14]. Recent years have seen the development of several end-to-end self-driving systems that show strong potential to improve driving performance by predicting driving commands from high-dimensional observations alone. Conditional imitation learning has proven to be one successful method to learn end-to-end driving policies that can be deployed in simulation [15] and real-world urban driving scenarios [16]. Nevertheless, difficulties of learning end-to-end policies from high-dimensional visual observations and expert trajectories alone have been highlighted [17].
+
+Several works have attempted to overcome such difficulties by moving past pure imitation learning. DAgger [18] proposes iterative dataset aggregation to collect data from trajectories that are likely to be experienced by the policy during deployment. NEAT [19] additionally supervises the model with BeV semantic segmentation. ChauffeurNet [20] exposes the learner to synthesised perturbations of the expert data in order to produce more robust driving policies. Learning from All Vehicles (LAV) [10] boosts sample efficiency by learning behaviours from not only the ego vehicle, but from all the vehicles in the scene. Roach [9] presents an agent trained with supervision from a reinforcement learning coach that was trained on-policy and with access to privileged information.
+
+3D scene representation. Successful planning for autonomous driving requires being able to understand and reason about the 3D scene, and this can be challenging from monocular cameras. One common solution is to condense the information from multiple cameras to a single bird’s-eye representation of the scene. This can be achieved by lifting each image in 3D (by learning a depth distribution of features) and then splatting all frustums into a common rasterised BeV grid [21, 22, 23]. An alternative approach is to rely on transformers to learn the direct mapping from image to bird’s-eye view [24, 25, 26], without explicitly modelling depth.
+
+World models. Model-based methods have mostly been explored in a reinforcement learning setting and have been shown to be extremely successful [3, 27, 5]. These methods assume access to a reward, and online interaction with the environment, although progress has been made on fully offline reinforcement learning [28, 29]. Model-based imitation learning has emerged as an alternative to reinforcement learning in robotic manipulation [30] and OpenAI Gym [31]. Even though these methods do not require access to a reward, they still require online interaction with the environment to achieve good performance.
+
+Learning the latent dynamics of a world model from image observations was first introduced in video prediction [32, 33, 34]. Most similar to our approach, [4, 5] additionally modelled the reward function and optimised a policy inside their world model. Contrarily to prior work, our method does not assume access to a reward function, and directly learns a policy from an offline dataset. Additionally, previous methods operate on simple visual inputs, mostly of size $6 4 \times 6 4$ . In contrast, MILE is able to learn the latent dynamics of complex urban driving scenes from high resolution $6 0 0 \times 9 6 0$ input observations, which is important to ensure small details such as traffic lights can be perceived reliably.
+
+Trajectory forecasting. The goal of trajectory forecasting is to estimate the future trajectories of dynamic agents using past physical states (e.g. position, velocity), and scene context (e.g. as an offline HD map) [35, 36, 37, 38]. World models build a latent representation of the environment that explains the observations from the sensory inputs of the ego-agent (e.g. camera images) conditioned on their actions. While trajectory forecasting methods only model the dynamic scene, world models jointly reason on static and dynamic scenes. The future trajectories of moving agents is implicitly encoded in the learned latent representation of the world model, and could be explicitly decoded given we have access to future trajectory labels.
+
+[35, 37, 38] forecast the future trajectory of moving agents, but did not control the ego-agent. They focused on the prediction problem and not on learning expert behaviour from demonstrations. [39] inferred future trajectories of the ego-agent from expert demonstrations, and conditioned on some specified goal to perform new tasks. [36] extended their work to jointly model the future trajectories of moving agents as well as of the ego-agent.
+
+Our proposed model jointly models the motion of other dynamics agents, the behaviour of the ego-agent, as well as the static scene. Contrary to prior work, we do not assume access to ground truth physical states (position, velocity) or to an offline HD map for scene context. Our approach is the first camera-only method that models static scene, dynamic scene, and ego-behaviour in an urban driving environment.
+
+# 3 MILE: Model-based Imitation LEarning
+
+In this section, we present MILE: our method that learns to jointly control an autonomous vehicle and model the world and its dynamics. An overview of the architecture is presented in Figure 1 and the full description of the network can be found in Appendix C. We begin by defining the generative model (Section 3.1), and then derive the inference model (Section 3.2). Section 3.3 and Section 3.4 describe the neural networks that parametrise the inference and generative models respectively. Finally, in Section 3.5 we show how our model can predict future states and actions to drive in imagination.
+
+# 3.1 Probabilistic Generative Model
+
+Let $\mathbf { o } _ { 1 : T }$ be a sequence of $T$ video frames with associated expert actions $\mathbf { a } _ { 1 : T }$ and ground truth $\mathbf { B e V }$ semantic segmentation labels $\mathbf { y } _ { 1 : T }$ . We model their evolution by introducing latent variables $\mathbf { s } _ { 1 : T }$ that govern the temporal dynamics. The initial distribution is parameterised as $\mathbf { s } _ { 1 } \sim \mathcal { N } ( \mathbf { 0 } , I )$ , and we additionally introduce a variable ${ \bf h } _ { 1 } \sim \delta ( { \bf 0 } )$ that serves as a deterministic history. The transition consists of (i) a deterministic update $\mathbf { h } _ { t + 1 } = f _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } )$ that depends on the past history $\mathbf { h } _ { t }$ and past state $\mathbf { s } _ { t }$ , followed by (ii) a stochastic update $\mathbf { \dot { s } } _ { t + 1 } \sim \mathcal { N } ( \mu _ { \theta } ( \mathbf { \bar { h } } _ { t + 1 } , \mathbf { a } _ { t } ) , \sigma _ { \theta } ( \mathbf { \bar { h } } _ { t + 1 } , \mathbf { a } _ { t } ) \bar { \mathbf { I } } )$ , where we parameterised $\mathbf { s } _ { t }$ as a normal distribution with diagonal covariance. We model these transitions with neural networks: $f _ { \theta }$ is a gated recurrent cell, and $\left( \mu _ { \boldsymbol { \theta } } , \sigma _ { \boldsymbol { \theta } } \right)$ are multi-layer perceptrons. The full probabilistic model is given by Equation (1).
+
+![](images/07c5c0627aa498a160e9e555c211525e8cedbd640c19afee53a2015c017c24c2.jpg)  
+Figure 1: Architecture of MILE.
+
+(i) The goal is to infer the latent dynamics $\left( \mathbf { h } _ { 1 : T } , \mathbf { s } _ { 1 : T } \right)$ that generated the observations $\mathbf { o } _ { 1 : T }$ , the expert actions $\mathbf { a } _ { 1 : T }$ and the bird’s-eye view labels $\mathbf { y } _ { 1 : T }$ . The latent dynamics contains a deterministic history $\mathbf { h } _ { t }$ and a stochastic state $\mathbf { s } _ { t }$ .   
+(ii) The inference model, with parameters $\phi$ , estimates the posterior distribution of the stochastic state $\begin{array} { r } { q ( \mathbf { s } _ { t } | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } ) \sim \mathcal { N } ( \mu _ { \phi } ( \mathbf { h } _ { t } , \mathbf { a } _ { t - 1 } , \mathbf { x } _ { t } ) , \sigma _ { \phi } ( \mathbf { h } _ { t } , \mathbf { \bar { a } } _ { t - 1 } , \mathbf { x } _ { t } ) I ) } \end{array}$ with $\mathbf { x } _ { t } = e _ { \phi } ( \mathbf { o } _ { t } )$ . $e _ { \phi }$ is the observation encoder that lifts image features to 3D, pools them to bird’s-eye view, and compresses to a 1D vector.   
+(iii) The generative model, with parameters $\theta$ , estimates the prior distribution of the stochastic state $p ( \mathbf { s } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) \sim \mathcal { N } ( \mu _ { \theta } ( \mathbf { h } _ { t } , \hat { \mathbf { a } } _ { t - 1 } ) , \sigma _ { \theta } ( \mathbf { h } _ { t } , \hat { \mathbf { a } } _ { t - 1 } ) \bar { \mathbf { I } } )$ , with $\mathbf h _ { t } = f _ { \theta } ( \mathbf h _ { t - 1 } , \mathbf s _ { t - 1 } )$ the deterministic transition, and $\hat { \mathbf { a } } _ { t - 1 } = \pi _ { \theta } ( \mathbf h _ { t - 1 } , \mathbf s _ { t - 1 } )$ the predicted action. It additionally estimates the distributions of the observation $p ( \mathbf { o } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) \sim \mathcal { N } ( g _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) , I )$ , the bird’s-eye view segmentation $p ( \mathbf { y } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) \sim \mathrm { C a t e g o r i c a l } ( l _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) )$ , and the action $p ( \mathbf { a } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) \dot { } \sim$ Laplace $( \pi _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) , \mathbf { 1 } )$ .   
+(iv) In the diagram, we represented our model observing inputs for $T = 2$ timesteps, and then imagining future latent states and actions for one step.
+
+$$
+\left\{ \begin{array} { l l } { \mathbf { h } _ { 1 } } & { \sim \delta ( \mathbf { 0 } ) } \\ { \mathbf { s } _ { 1 } } & { \sim \mathcal { N } ( \mathbf { 0 } , I ) } \\ { \mathbf { h } _ { t + 1 } } & { = f _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) } \\ { \mathbf { s } _ { t + 1 } } & { \sim \mathcal { N } ( \mu _ { \theta } ( \mathbf { h } _ { t + 1 } , \mathbf { a } _ { t } ) , \sigma _ { \theta } ( \mathbf { h } _ { t + 1 } , \mathbf { a } _ { t } ) I ) } \\ { \mathbf { o } _ { t } } & { \sim \mathcal { N } ( g _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) , I ) } \\ { \mathbf { y } _ { t } } & { \sim \mathrm { C a t e g o r i c a l } ( l _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) ) } \\ { \mathbf { a } _ { t } } & { \sim \mathrm { L a p l a c e } ( \pi _ { \theta } ( \mathbf { h } _ { t } , \mathbf { s } _ { t } ) , \mathbf { 1 } ) } \end{array} \right.
+$$
+
+with $\delta$ the Dirac delta function, $g _ { \theta }$ the image decoder, $l _ { \theta }$ the $\mathbf { B e V }$ decoder, and $\pi _ { \theta }$ the policy, which will be described in Section 3.4.
+
+# 3.2 Variational Inference
+
+Following the generative model described in Equation (1), we can factorise the joint probability as:
+
+$$
+p ( \mathbf { o } _ { 1 : T } , \mathbf { y } _ { 1 : T } , \mathbf { a } _ { 1 : T } , \mathbf { h } _ { 1 : T } , \mathbf { s } _ { 1 : T } ) = \prod _ { t = 1 } ^ { T } p ( \mathbf { h } _ { t } , \mathbf { s } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } , \mathbf { a } _ { t - 1 } ) p ( \mathbf { o } _ { t } , \mathbf { y } _ { t } , \mathbf { a } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } )
+$$
+
+with
+
+$$
+\begin{array} { r l } & { p ( \mathbf { h } _ { t } , \mathbf { s } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } , \mathbf { a } _ { t - 1 } ) = p ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) p ( \mathbf { s } _ { t } | \mathbf { h } _ { t } , \mathbf { a } _ { t - 1 } ) } \\ & { \qquad p ( \mathbf { o } _ { t } , \mathbf { y } _ { t } , \mathbf { a } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) = p ( \mathbf { o } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) p ( \mathbf { y } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) p ( \mathbf { a } _ { t } | \mathbf { h } _ { t } , \mathbf { s } _ { t } ) } \end{array}
+$$
+
+Given that $\mathbf { h } _ { t }$ is deterministic according to Equation (1), we have $p ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) = \delta ( \mathbf { h } _ { t } - \mathbf { \tilde { k } }$ $f _ { \theta } ( \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) )$ . Therefore, in order to maximise the marginal likelihood of the observed data $p ( \mathbf { o } _ { 1 : T } , \mathbf { y } _ { 1 : T } , \mathbf { a } _ { 1 : T } )$ , we need to infer the latent variables $\mathbf { s } _ { 1 : T }$ . We do this through deep variational inference by introducing a variational distribution $q _ { H , S }$ defined and factorised as follows:
+
+$$
+q _ { H , S } \triangleq q ( \mathbf { h } _ { 1 : T } , \mathbf { s } _ { 1 : T } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T - 1 } ) = \prod _ { t = 1 } ^ { T } q ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) q ( \mathbf { s } _ { t } | \mathbf { o } _ { \le t } , \mathbf { a } _ { < t } )
+$$
+
+with $q ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) = p ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } )$ , the Delta dirac function defined above, and $q ( { \bf h } _ { 1 } ) = \delta ( { \bf 0 } )$ We parameterise this variational distribution with a neural network with weights $\phi$ . By applying Jensen’s inequality, we can obtain a variational lower bound on the log evidence:
+
+$$
+\begin{array} { r l } { \log p \big ( \mathbf { o } _ { 1 : T } , \mathbf { y } _ { 1 : T } , \mathbf { a } _ { 1 : T } \big ) \geq } & { \mathcal { L } \big ( \mathbf { o } _ { 1 : T } , \mathbf { y } _ { 1 : T } , \mathbf { a } _ { 1 : T } ; \theta , \phi \big ) } \\ { \triangleq } & { \displaystyle \sum _ { t = 1 } ^ { T } \mathbb { E } _ { q ( \mathbf { h } _ { 1 : t } , \mathbf { s } _ { 1 : t } | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } ) } \left[ \underbrace { \log p \big ( \mathbf { o } _ { t } \big | \mathbf { h } _ { t } , \mathbf { s } _ { t } \big ) } _ { \mathrm { i m a g e r e c o n s t u r a t i o n } } + \underbrace { \log p \big ( \mathbf { y } _ { t } \big | \mathbf { h } _ { t } , \mathbf { s } _ { t } \big ) } _ { \mathrm { b i f i ^ { * } \times \mathrm { e y r e s e p u r a t i o n } } } + \underbrace { \log p \big ( \mathbf { a } _ { t } \big | \mathbf { h } _ { t } , \mathbf { s } _ { t } \big ) } _ { \mathrm { a c t i o n } } \right] } \\ & { \displaystyle - \sum _ { t = 1 } ^ { T } \mathbb { E } _ { q ( \mathbf { h } _ { 1 : t - 1 } , \mathbf { s } _ { 1 : t - 1 } | \mathbf { o } _ { \leq t - 1 } , \mathbf { a } _ { < t - 1 } ) } \left[ \underbrace { D _ { \mathrm { K L } } \Big ( q \big ( \mathbf { s } _ { t } \big | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } \big ) \big | | \ p \big ( \mathbf { s } _ { t } \big | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } \big ) \Big ) } _ { \mathrm { o r } \mathrm { e x t } \big ( \mathbf { y } + \mathbf { s } _ { t } , \mathbf { a } _ { < t } \big ) } \right] \enspace ( \mathbf { s } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) } \end{array}
+$$
+
+{zposterior and prior matching
+
+Please refer to Appendix B for the full derivation. We model $q ( \mathbf { s } _ { t } | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } )$ as a Gaussian distribution so that the Kullback-Leibler (KL) divergence can be computed in closed-form. Given that the image observations $\mathbf { o } _ { t }$ are modelled as Gaussian distributions with unit variance, the resulting loss is the mean-squared error. Similarly, the action being modelled as a Laplace distribution and the $\mathbf { B e V }$ labels as a categorical distribution, the resulting losses are, respectively, $L _ { 1 }$ and cross-entropy. The expectations over the variational distribution can be efficiently approximated with a single sequence sample from $q _ { H , S }$ , and backpropagating gradients with the reparametrisation trick [40].
+
+# 3.3 Inference Network $\phi$
+
+The inference network, parameterised by $\phi$ , models $q ( \mathbf { s } _ { t } | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } )$ , which approximates the true posterior $p ( \mathbf { s } _ { t } | \mathbf { o } _ { \leq t } , \mathbf { a } _ { < t } )$ . It is constituted of two elements: the observation encoder $e _ { \phi }$ , that embeds input images, route map and vehicle control sensor data to a low-dimensional vector, and the posterior network $\left( \mu _ { \phi } , \sigma _ { \phi } \right)$ , that estimates the probability distribution of the Gaussian posterior.
+
+# 3.3.1 Observation Encoder
+
+The state of our model should be compact and low-dimensional in order to effectively learn dynamics. Therefore, we need to embed the high resolution input images to a low-dimensional vector. Naively encoding this image to a 1D vector similarly to an image classification task results in poor performance as shown in Section 5.2. Instead, we explicitly encode 3D geometric inductive biases in the model.
+
+Lifting image features to 3D. Since autonomous driving is a geometric problem where it is necessary to reason on the static scene and dynamic agents in 3D, we first lift the image features to 3D. More precisely, we encode the image inputs $\mathbf { \sigma } _ { \mathbf { o } _ { t } } ~ \in ~ \mathbb { R } ^ { 3 \times H \times W }$ with an image encoder to extract features $\mathbf { u } _ { t } \in \dot { \mathbb { R } } ^ { C _ { e } \times H _ { e } \times W _ { e } }$ . Then similarly to Philion and Fidler [21], we predict a depth probability distribution for each image feature along a predefined grid of depth bins $\mathbf { \dot { d } } _ { t } \in \mathbb { R } ^ { D \times \dot { H } _ { e } , \times \mathbf { \dot { W } } _ { e } }$ . Using the depth probability distribution, the camera intrinsics $K$ and extrinsics $M$ , we can lift the image features to 3D: L $\mathrm { i f t } ( \mathbf { \bar { u } } _ { t } , \mathbf { d } _ { t } , K ^ { - 1 } , M ) ) \in \mathbb { R } ^ { C _ { e } \times D \times H _ { e } \times D _ { e } \times 3 }$ .
+
+Pooling to BeV. The 3D feature voxels are then sum-pooled to $\mathbf { B e V }$ space using a predefined grid with spatial extent $H _ { b } \times W _ { b }$ and spatial resolution $b _ { \mathrm { r e s } }$ . The resulting feature is $\mathbf { \breve { b } } _ { t } \in \mathbb { R } ^ { C _ { e } \times H _ { b } \times \mathbf { \breve { W } } _ { b } }$ .
+
+Mapping to a 1D vector. In traditional computer vision tasks (e.g. semantic segmentation [41], depth prediction [42]), the bottleneck feature is usually a spatial tensor, in the order of $1 0 ^ { 5 } - 1 0 ^ { \bar { 6 } }$ features. Such high dimensionality is prohibitive for a world model that has to match the distribution of the priors (what it thinks will happen given the executed action) to the posteriors (what actually happened by observing the image input). Therefore, using a convolutional backbone, we compress the $\mathbf { B e V }$ feature $\mathbf { b } _ { t }$ to a single vector $\mathbf { x } _ { t } ^ { \prime } \in \mathbb { R } ^ { C ^ { \prime } }$ . As shown in Section 5.2, we found it critical to compress in $\mathbf { B e V }$ space rather than directly in image space.
+
+Route map and speed. We provide the agent with a goal in the form of a route map [9], which is a small grayscale image indicating to the agent where to navigate at intersections. The route map is encoded using a convolutional module resulting in a 1D feature $\mathbf { r } _ { t }$ . The current speed is encoded with fully connected layers as $\mathbf { m } _ { t }$ . At each timestep $t$ , the observation embedding $\mathbf { x } _ { t }$ is the concatenation of the image feature, route map feature and speed feature: $\mathbf { x } _ { t } = [ \mathbf { x } _ { t } ^ { \prime } , \mathbf { r } _ { t } , \mathbf { m } _ { t } ] \in \mathbb { R } ^ { C }$ , with $C = 5 1 2$
+
+# 3.3.2 Posterior Network
+
+The posterior network $\left( \mu _ { \phi } , \sigma _ { \phi } \right)$ estimates the parameters of the variational distribution ${ q ( \mathbf { s } _ { t } | \bar { \mathbf { o } } _ { \le t } , \mathbf { a } _ { < t } ) \ \sim \ \mathcal { N } \left( \mu _ { \phi } ( \mathbf { \bar { h } } _ { t } , \mathbf { a } _ { t - 1 } , e _ { \phi } ( \mathbf { o } _ { t } ) ) , \sigma _ { \phi } ( \mathbf { \bar { h } } _ { t } , \mathbf { \bar { a } } _ { t - 1 } , e _ { \phi } ( \mathbf { o } _ { t } ) ) I \right) }$ with $\mathbf h _ { t } \ = \ f _ { \theta } ( \mathbf h _ { t - 1 } , \mathbf s _ { t - 1 } )$ . Note that $\mathbf { h } _ { t }$ was inferred using $f _ { \theta }$ because we have assumed that $\mathbf { h } _ { t }$ is deterministic, meaning that $q ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) = p ( \mathbf { h } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) = \delta { \bigl ( } \mathbf { h } _ { t } - f _ { \theta } { \bigl ( } \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } { \bigr ) } { \bigr ) }$ . The dimension of the Gaussian distribution is equal to 512.
+
+# 3.4 Generative Network $\theta$
+
+The generative network, parameterised by $\theta$ , models the latent dynamics $\left( \mathbf { h } _ { 1 : T } , \mathbf { s } _ { 1 : T } \right)$ as well as the generative process of $\left( \mathbf { o } _ { 1 : T } , \mathbf { y } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)$ . It comprises a gated recurrent cell $f _ { \theta }$ , a prior network $\left( \mu _ { \boldsymbol { \theta } } , \sigma _ { \boldsymbol { \theta } } \right)$ , an image decoder $g _ { \theta }$ , a BeV decoder $l _ { \theta }$ , and a policy $\pi _ { \theta }$ .
+
+The prior network estimates the parameters of the Gaussian distribution   
+$p ( \mathbf { s } _ { t } | \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } ) \ \sim \ { \mathcal { N } } \left( \mu _ { \theta } ( \mathbf { h } _ { t } , { \hat { \mathbf { a } } } _ { t - 1 } ) , \sigma _ { \theta } ( \mathbf { h } _ { t } , { \hat { \mathbf { a } } } _ { t - 1 } ) I \right)$ with $\mathbf h _ { t } \ = \ f _ { \theta } ( \mathbf h _ { t - 1 } , \mathbf s _ { t - 1 } )$ and $\hat { { \bf a } } _ { t - 1 } =$ $\pi _ { \theta } ( \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } )$ . Since the prior does not have access to the ground truth action $\mathbf { a } _ { t - 1 }$ , the latter is estimated with the learned policy $\hat { \mathbf { a } } _ { t - 1 } = \pi _ { \theta } ( \mathbf h _ { t - 1 } , \mathbf s _ { t - 1 } )$ .
+
+The Kullback-Leibler divergence loss between the prior and posterior distributions can be interpreted as follows. Given the past state $\left( \mathbf { h } _ { t - 1 } , \mathbf { s } _ { t - 1 } \right)$ , the objective is to predict the distribution of the next state $\mathbf { s } _ { t }$ . As we model an active agent, this transition is decomposed into (i) action prediction and (ii) next state prediction. This transition estimation is compared to the posterior distribution that has access to the ground truth action $\mathbf { a } _ { t - 1 }$ , and the image observation $\mathbf { o } _ { t }$ . The prior distribution tries to match the posterior distribution. This divergence matching framework ensures the model predicts actions and future states that explain the observed data. The divergence of the posterior from the prior measures how many nats of information were missing from the prior when observing the posterior. At training convergence, the prior distribution should be able to model all action-state transitions from the expert dataset.
+
+The image and $\mathbf { B e V }$ decoders have an architecture similar to StyleGAN [43]. The prediction starts as a learned constant tensor, and is progressively upsampled to the final resolution. At each resolution, the latent state is injected in the network with adaptive instance normalisation. This allows the latent states to modulate the predictions at different resolutions. The policy is a multi-layer perceptron. Please refer to Appendix C for a full description of the neural networks.
+
+# 3.5 Imagining Future States and Actions
+
+Our model can imagine future latent states by using the learned policy to infer actions $\hat { \mathbf { a } } _ { T + i } =$ $\pi _ { \boldsymbol { \theta } } ( \mathbf { h } _ { T + i } , \mathbf { s } _ { T + i } )$ , predicting the next deterministic state $\mathbf { h } _ { T + i + 1 } = f _ { \theta } ( \mathbf { h } _ { T + i } , \mathbf { s } _ { T + i } )$ and sampling from the prior distribution $\mathbf { s } _ { T + i + 1 } \sim \mathcal { N } ( \mu _ { \theta } ( \mathbf { h } _ { T + i + 1 } , \hat { \mathbf { a } } _ { T + i } ) , \sigma _ { \theta } ( \mathbf { h } _ { T + i + 1 } , \hat { \mathbf { a } } _ { T + i } ) I ) ,$ for $i \geq 0$ . This process can be iteratively applied to generate sequences of longer futures in latent space, and the predicted futures can be visualised through the decoders.
+
+Table 1: Driving performance on a new town and new weather conditions in CARLA. Metrics are averaged across three runs. We include reward signals from past work where available.   
+
+<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm. Reward</td></tr><tr><td>CILRS [17]</td><td>7.8± 0.3</td><td>10.3 ± 0.0</td><td>76.2 ± 0.5</td><td></td><td></td></tr><tr><td>LBC [47]</td><td>12.3 ± 2.0</td><td>31.9 ± 2.2</td><td>66.0 ± 1.7</td><td></td><td></td></tr><tr><td>TransFuser [48]</td><td>31.0 ± 3.6</td><td>47.5 ± 5.3</td><td>76.8 ± 3.9</td><td></td><td></td></tr><tr><td>Roach [9]</td><td>41.6 ± 1.8</td><td>96.4 ± 2.1</td><td>43.3 ± 2.8</td><td>4236 ± 468</td><td>0.34 ± 0.05</td></tr><tr><td>LAV[10]</td><td>46.5 ± 3.0</td><td>69.8 ± 2.3</td><td>73.4±2.2</td><td></td><td></td></tr><tr><td>MILE</td><td>61.1 ± 3.2</td><td>97.4 ± 0.8</td><td>63.0± 3.0</td><td>7621 ± 460</td><td>0.67 ± 0.02</td></tr><tr><td>Expert</td><td>88.4 ± 0.9</td><td>97.6 ± 1.2</td><td>90.5 ± 1.2</td><td>8694 ±88</td><td>0.70 ± 0.01</td></tr></table>
+
+# 4 Experimental Setting
+
+Dataset. The training data was collected in the CARLA simulator with an expert reinforcement learning (RL) agent [9] that was trained using privileged information as input $\mathrm { B e V }$ semantic segmentations and vehicle measurements). This RL agent generates more diverse runs and has greater driving performance than CARLA’s in-built autopilot [9].
+
+We collect data at $2 5 \mathrm { H z }$ in four different training towns (Town01, Town03, Town04, Town06) and four weather conditions (ClearNoon, WetNoon, HardRainNoon, ClearSunset) for a total of 2.9M frames, or 32 hours of driving data. At each timestep, we save a tuple $\left( \mathbf { o } _ { t } , \mathbf { r o u t e } _ { t } , \mathbf { s p e e d } _ { t } , \mathbf { a } _ { t } , \mathbf { y } _ { t } \right)$ , with $\mathbf { o } _ { t } \in \mathbb { R } ^ { 3 \times 6 0 0 \times 9 6 0 }$ the forward camera RGB image, route $\mathbf { \Phi } _ { t } \in \mathbb { R } ^ { 1 \times 6 4 \times 6 4 }$ the route map (visualized as an inset on the top right of the RGB images in Figure 2), $\mathbf { s p e e d } _ { t } \in \mathbb { R }$ the current velocity of the vehicle, $\mathbf { a } _ { t } \in \mathbb { R } ^ { 2 }$ the action executed by the expert (acceleration and steering), and $\mathbf { y } _ { t } \in \mathbb { R } ^ { C _ { b } \times \mathbf { \bar { 1 } 9 2 } \times 1 9 2 }$ the $\mathbf { B e V }$ semantic segmentation. There are $C _ { b } = 8$ semantic classes: background, road, lane marking, vehicles, pedestrians, and traffic light states (red, yellow, green). In urban driving environments, the dynamics of the scene do not contain high frequency components, which allows us to subsample frames at $\mathrm { 5 H z }$ in our sequence model.
+
+Training. Our model was trained for 50, 000 iterations on a batch size of 64 on 8 V100 GPUs, with training sequence length $T = 1 2$ . We used the AdamW optimiser [44] with learning rate $1 0 ^ { - 4 }$ and weight decay 0.01.
+
+Metrics. We report metrics from the CARLA challenge [45] to measure on-road performance: route completion, infraction penalty, and driving score. These metrics are however very coarse, as they only give a sense of how well the agent performs with hard penalties (such as hitting virtual pedestrians). Core driving competencies such as lane keeping and driving at an appropriate speed are obscured. Therefore we also report the cumulative reward of the agent. At each timestep the reward [46] penalises the agent for deviating from the lane center, for driving too slowly/fast, or for causing infractions. It measures how well the agent drives at the timestep level. In order to account for the length of the simulation (due to various stochastic events, it can be longer or shorter), we also report the normalised cumulative reward. More details on the experimental setting is given in Appendix D.
+
+# 5 Results
+
+# 5.1 Driving Performance
+
+We evaluate our model inside the CARLA simulator on a town and weather conditions never seen during training. We picked Town05 as it is the most complex testing town, and use the 10 routes of Town05 as specified in the CARLA challenge [45], in four different weather conditions. Table 1 shows the comparison against prior state-of-the-art methods: CILRS [17], LBC [47], TransFuser [48], Roach [9], and LAV [10]. We evaluate these methods using their publicly available pre-trained weights.
+
+MILE outperforms previous works on all metrics, with a $31 \%$ relative improvement in driving score with respect to LAV. Even though some methods have access to additional sensor information such as LiDAR (TransFuser [48], LAV [10]), our approach demonstates superior performance while only using RGB images from the front camera. Moreover, we observe that our method almost doubles the cumulative reward of Roach (which was trained on the same dataset) and approaches the performance of the privileged expert.
+
+Table 2: Ablation studies. We report driving performance on a new town and new weather conditions in CARLA. Results are averaged across three runs.   
+
+<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm.Reward</td></tr><tr><td>Single frame, no 3D</td><td>51.8 ± 3.0</td><td>78.3 ± 3.0</td><td>68.3 ± 2.8</td><td>1878± 296</td><td>0.20 ± 0.04</td></tr><tr><td>Single frame</td><td>59.6 ± 3.6</td><td>94.5 ± 0.6</td><td>64.7 ± 3.3</td><td>6630 ± 168</td><td>0.60 ± 0.01</td></tr><tr><td>No 3D</td><td>63.0 ±1.5</td><td>91.5± 5.5</td><td>69.1 ± 2.8</td><td>4564 ± 1791</td><td>0.40 ± 0.15</td></tr><tr><td>No prior/post. matching</td><td>63.3 ± 2.2</td><td>91.5 ± 5.0</td><td>68.7 ± 1.8</td><td>6084 ± 1429</td><td>0.55 ± 0.07</td></tr><tr><td>No segmentation</td><td>55.0 ± 3.3</td><td>92.5 ± 2.4</td><td>60.9 ± 3.9</td><td>7183 ±107</td><td>0.64 ± 0.02</td></tr><tr><td>MILE</td><td>61.1 ± 3.2</td><td>97.4 ± 0.8</td><td>63.0±3.0</td><td>7621 ± 460</td><td>0.67 ± 0.02</td></tr><tr><td>Expert</td><td>88.4± 0.9</td><td>97.6 ± 1.2</td><td>90.5 ± 1.2</td><td>8694 ±88</td><td>0.70 ± 0.01</td></tr></table>
+
+# 5.2 Ablation Studies
+
+We next examine the effect of various design decisions in our approach.
+
+3D geometry. We compare our model to the following baselines. Single frame that predicts the action and BeV segmentation from a single image observation. Single frame, no 3D which is the same model but without the 3D lifting step. And finally, No $3 D$ which is MILE without 3D lifting. As shown in Table 2, in both cases, there is a significant drop in performance when not modelling 3D geometry. For the single frame model, the cumulative reward drops from 6084 to 1878. For MILE, the reward goes from 7621 to 4564. These results highlights the importance of the 3D geometry inductive bias.
+
+Probabilistic modelling. At any given time while driving, there exist multiple possible valid behaviours. For example, the driver can slightly adjust its speed, decide to change lane, or decide what is a safe distance to follow behind a vehicle. A deterministic driving policy cannot model these subtleties. In ambiguous situations where multiple choices are possible, it will often learn the mean behaviour, which is valid in certain situations (e.g. the mean safety distance and mean cruising speed are reasonable choices), but unsafe in others (e.g. in lane changing: the expert can change lane early, or late; the mean behaviour is to drive on the lane marking). We compare MILE with a No prior/post. matching baseline that does not have a Kullback-Leibler divergence loss between the prior and posterior distributions, and observe this results in a drop in cumulative reward from 7621 to 6084.
+
+# 5.3 Fully Recurrent Inference in Closed-Loop Driving
+
+We compare the closed-loop performance of our model with two different strategies:
+
+(i) Reset state: for every new observation, we re-initialise the latent state and recompute the new state $\left[ h _ { T } , s _ { T } \right]$ , with $T$ matching the training sequence length.
+
+(ii) Fully recurrent: the latent state is initialised at the beginning of the evaluation, and is recursively updated with new observations. It is never reset, and instead, the model must have learned a representation that generalises to integrating information for orders of magnitude more steps than the $T$ used during training.
+
+Table 3 shows that our model can be deployed with recurrent updates, matching the performance of the Reset state approach, while being much more computationally efficient $7 \times$ faster from $6 . 2 \mathrm { H z }$ with $T = 1 2$ of fixed context to $4 3 . 0 \mathrm { H z }$ with a fully recurrent approach). A hypothesis that could explain why the Fully recurrent deployment method works well is because the world model has learned to always discard all past information and rely solely on the present input. To test this hypothesis, we add Gaussian noise to the past latent state during deployment. If the recurrent network is simply discarding all past information, its performance should not be affected. However in Table 3, we see that the cumulative reward significantly decreases, showing our model does not simply discard all past context, but actively makes use of it.
+
+Table 3: Comparison of two deployment methods. (i) Reset state: for each new observation a fresh state is computed from a zero-initialised latent state using the last $T$ observations, and (ii) Fully recurrent: the latent state is recurrently updated with new observations. We report driving performance on an unseen town and unseen weather conditions in CARLA. Frequency is in Hertz.   
+
+<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm. Reward</td><td>Freq.</td></tr><tr><td>Reset state</td><td>61.1 ± 3.2</td><td>97.4± 0.8</td><td>63.0±3.0</td><td>7621± 460</td><td>0.67 ± 0.02</td><td>6.2</td></tr><tr><td>Fully recurrent</td><td>62.1 ± 0.5</td><td>93.5± 4.8</td><td>66.6 ± 3.4</td><td>7532±1122</td><td>0.67 ± 0.04</td><td>43.0</td></tr><tr><td>Recurrent+noise</td><td>48.8± 1.8</td><td>81.1 ± 7.0</td><td>61.5± 6.4</td><td>3603± 780</td><td>0.35 ± 0.07</td><td>43.0</td></tr></table>
+
+# 5.4 Long Horizon, Diverse Future Predictions
+
+Our model can imagine diverse futures in the latent space, which can be decoded to $\mathbf { B e V }$ semantic segmentation for interpretability. Figure 2 shows examples of multi-modal futures predicted by MILE.
+
+![](images/677bd3a03b6da96fa3ba6da7de23bced3e4d3e99f2c17bccb368ab61eef57a21.jpg)  
+Figure 2: Qualitative example of multi-modal predictions, for 8 seconds in the future. BeV segmentation legend: black $=$ ego-vehicle, white $=$ background, gray $=$ road, dark gray=lane marking, blue $=$ vehicles, cyan $=$ pedestrians, green/yellow/red $=$ traffic lights. Ground truth labels (GT) outside the field-of-view of the front camera are masked out. In this example, we visualise two distinct futures predicted by the model: 1) (top row) driving through the green light, 2) (bottom row) stopping because the model imagines the traffic light turning red. Note the light transition from green, to yellow, to red, and also at the last frame $t + 8 . 0 8$ how the traffic light in the left lane turns green.
+
+# 6 Insights from the World Model
+
+# 6.1 Latent State Dimension
+
+In our model, we have set the latent state to be a low-dimensional 1D vector of size 512. In dense image reconstruction however, the bottleneck feature is often a 3D spatial tensor of dimension (channel, height, width). We test whether it is possible to have a 3D tensor as a latent probabilistic state instead of a 1D vector. We change the latent state to have dimension $2 5 6 \times 1 2 \times 1 2$ (40k distributions), $1 2 8 \times 2 4 \times 2 4$ (80k distributions), and $6 4 \times 4 8 \times 4 8$ $1 6 0 \mathrm { k }$ distributions, which is the typical bottleneck size in dense image prediction). Since the latent state is now a spatial tensor, we adapt the recurrent network to be convolutional by switching the fully-connected operations with convolutions. We evaluate the model in the reset state and fully recurrent setting and report the results in Figure 3.
+
+![](images/16fd01ca573e3503e5c25413c1cd039bc7dd449aa748b36ec6b74a51c5a92d1b.jpg)  
+Figure 3: Analysis on the latent state dimension. We report closed-loop driving performance in a new town and new weather in CARLA.
+
+In the reset state setting, performance decreases as the dimensionality of the latent state increases. Surprisingly, even though the latent space is larger and has more capacity, driving performance is negatively impacted. This seems to indicate that optimising the prior and posterior distributions in the latent space is difficult, and especially more so as dimensionality increases. The prior, which is a multivariate Gaussian distribution needs to match the posterior, another multivariate Gaussian distribution. What makes this optimisation tricky is that the two distributions are non-stationary and change over time during the course of training. The posterior needs to extract the relevant information from the high-resolution images and incorporate it in the latent state in order to reconstruct BeV segmentation and regress the expert action. The prior has to predict the transition that matches the distribution of the posterior.
+
+Even more intriguing is when we look at the results in the fully recurrent deployment setting. When deployed in a fully recurrent manner in the simulator, without resetting the latent state, the model needs to discard information that is no longer relevant and continuously update its internal state with new knowledge coming from image observations. In our original latent state dimension of 512, there is almost no different in driving performance between the two deployment modes. The picture is dramatically different when using a higher dimensional spatial latent state. For all the tested dimensions, there is a large gap between the two deployment settings. This result seems to indicate that the world model operating on high-dimensional spatial states has not optimally learned this behaviour, contrarily to the one operating on low-dimensional vector states.
+
+# 6.2 Driving in Imagination
+
+Humans are believed to build an internal model of the world in order to navigate in it [49, 50, 51]. Since the stream of information they perceive is often incomplete and noisy, their brains fill missing information through imagination. This explains why it is possible for them to continue driving when blinded by sunlight for example. Even if no visual observations are available for a brief moment, they can still reliably predict their next states and actions to exhibit a safe driving behaviour. We demonstrate that similarly, MILE can execute accurate driving plans entirely predicted from imagination, without having access to image observations. We qualitatively show that it can perform complex driving maneuvers such as navigating a roundabout, marking a pause a stop sign, or swerving to avoid a motorcyclist, using an imagined plan from the model (see supplementary material).
+
+Quantitatively, we measure how accurate the predicted plans are by operating in the fully recurrent setting. We alternate between the observing mode where the model can see image observations, and the imagining mode where the model has to imagine the next states and actions, similarly to a driver that temporarily loses sight due to sun glare. In Appendix A.1 we show that our model can retain the same driving performance with up to $30 \%$ of the drive in imagining mode. This demonstrates that the model can imagine driving plans that are accurate enough for closed loop driving. Further, it shows that the latent state of the world model can seamlessly switch between the observing and imagining modes. The evolution of the latent state is predicted from imagination when observations are not available, and updated with image observations when they become accessible.
+
+# 7 Conclusion
+
+We presented MILE: a Model-based Imitation LEarning approach for urban driving, that jointly learns a driving policy and a world model from offline expert demonstrations alone. Our approach exploits geometric inductive biases, operates on high-dimensional visual inputs, and sets a new state-of-the-art on the CARLA simulator. MILE can predict diverse and plausible future states and actions, allowing the model to drive from a plan entirely predicted from imagination.
+
+An open problem is how to infer the driving reward function from expert data, as this would enable explicit planning in the world model. Another exciting avenue is self-supervision in order to relax the dependency on the bird’s-eye view segmentation labels. Self-supervision could fully unlock the potential of world models for real-world driving and other robotics tasks.
+
+Acknowledgements. We would like to thank Vijay Badrinarayanan, Przemyslaw Mazur, and Oleg Sinavski for insightful research discussions. We are also grateful to Lorenzo Bertoni, Lloyd Russell, Juba Nait Saada, Thomas Uriot, and the anonymous reviewers for their helpful feedback and comments on the paper.
+
+References   
+[1] H. B. Barlow. Unsupervised learning. Neural computation, 1(3):295–311, 1989.   
+[2] D. M. Wolpert and M. Kawato. Multiple paired forward and inverse models for motor control. Neural networks, 11(7-8):1317–1329, 1998.   
+[3] D. Ha and J. Schmidhuber. Recurrent world models facilitate policy evolution. In Advances in Neural Information Processing Systems (NeurIPS), 2018.   
+[4] D. Hafner, T. Lillicrap, I. Fischer, R. Villegas, D. Ha, H. Lee, and J. Davidson. Learning Latent Dynamics for Planning from Pixels. In Proceedings of the International Conference on Machine Learning (ICML), 2019.   
+[5] D. Hafner, T. Lillicrap, M. Norouzi, and J. Ba. Mastering atari with discrete world models. Proceedings of the International Conference on Learning Representations (ICLR), 2021.   
+[6] D. Chen, V. Koltun, and P. Krähenbühl. Learning to drive from a world on rails. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 15590– 15599, 2021.   
+[7] V. Sobal, A. Canziani, N. Carion, K. Cho, and Y. LeCun. Separating the world and ego models for self-driving. arXiv preprint arXiv:2204.07184, 2022.   
+[8] A. Dosovitskiy, G. Ros, F. Codevilla, A. Lopez, and V. Koltun. CARLA: An Open Urban Driving Simulator. In Proceedings of the Conference on Robot Learning (CoRL), pages 1–16, 2017.   
+[9] Z. Zhang, A. Liniger, D. Dai, F. Yu, and L. Van Gool. End-to-end urban driving by imitating a reinforcement learning coach. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 15222–15232, 2021.   
+[10] D. Chen and P. Krähenbühl. Learning from all vehicles. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022.   
+[11] D. A. Pomerleau. ALVINN: An autonomous land vehicle in a neural network. Advances in Neural Information Processing Systems (NeurIPS), 1, 1988.   
+[12] A. Bacha, C. Bauman, R. Faruque, M. Fleming, C. Terwelp, C. Reinholtz, D. Hong, A. Wicks, T. Alberi, D. Anderson, et al. Odin: Team VictorTango’s Entry in the DARPA Urban Challenge. Journal of Field Robotics, 25(8):467–492, 2008.   
+[13] D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel. Practical search techniques in path planning for autonomous driving. Ann Arbor, 1001(48105):18–80, 2008.   
+[14] J. Leonard, J. How, S. Teller, M. Berger, S. Campbell, G. Fiore, L. Fletcher, E. Frazzoli, A. Huang, S. Karaman, et al. A perception-driven autonomous urban vehicle. Journal of Field Robotics, 25(10):727–774, 2008.   
+[15] F. Codevilla, M. Müller, A. López, V. Koltun, and A. Dosovitskiy. End-to-end driving via conditional imitation learning. In Proceedings of the International Conference on Robotics and Automation (ICRA), 2018.   
+[16] J. Hawke, R. Shen, C. Gurau, S. Sharma, D. Reda, N. Nikolov, P. Mazur, S. Micklethwaite, N. Griffiths, A. Shah, et al. Urban Driving with Conditional Imitation Learning. In Proceedings of the International Conference on Robotics and Automation (ICRA), pages 251–257, 2020.   
+[17] F. Codevilla, E. Santana, A. M. López, and A. Gaidon. Exploring the Limitations of Behavior Cloning for Autonomous Driving. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 9329–9338, 2019.   
+[18] S. Ross, G. Gordon, and D. Bagnell. A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning. In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), pages 627–635, 2011.   
+[19] K. Chitta, A. Prakash, and A. Geiger. NEAT: Neural Attention Fields for End-to-End Autonomous Driving. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2021.   
+[20] M. Bansal, A. Krizhevsky, and A. Ogale. ChauffeurNet: Learning to drive by imitating the best and synthesizing the worst. In Proceedings of Robotics: Science and Systems (RSS), 2019.   
+[21] J. Philion and S. Fidler. Lift, splat, shoot: Encoding images from arbitrary camera rigs by implicitly unprojecting to 3d. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   
+[22] A. Saha, O. Mendez, C. Russell, and R. Bowden. Enabling Spatio-temporal aggregation in Birds-Eye-View Vehicle Estimation. In Proceedings of the International Conference on Robotics and Automation (ICRA), 2021.   
+[23] A. Hu, Z. Murez, N. Mohan, S. Dudas, J. Hawke, V. Badrinarayanan, R. Cipolla, and A. Kendall. FIERY: Future Instance Prediction in Bird’s-Eye View From Surround Monocular Cameras. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 15273–15282, 2021.   
+[24] L. Peng, Z. Chen, Z. Fu, P. Liang, and E. Cheng. Bevsegformer: Bird’s eye view semantic segmentation from arbitrary camera rigs. arXiv preprint arXiv:2203.04050, 2022.   
+[25] N. Gosala and A. Valada. Bird’s-eye-view panoptic segmentation using monocular frontal view images. IEEE Robotics and Automation Letters, 2022.   
+[26] Z. Li, W. Wang, H. Li, E. Xie, C. Sima, T. Lu, Q. Yu, and J. Dai. BEVFormer: Learning bird’s-eye-view representation from multi-camera images via spatiotemporal transformers. In Proceedings of the European Conference on Computer Vision (ECCV), 2022.   
+[27] J. Schrittwieser, I. Antonoglou, T. Hubert, K. Simonyan, L. Sifre, S. Schmitt, A. Guez, E. Lockhart, D. Hassabis, T. Graepel, T. Lillicrap, and D. Silver. Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model. In Nature, 2020.   
+[28] W. Zhou, S. Bajracharya, and D. Held. PLAS: Latent Action Space for Offline Reinforcement Learning. In Proceedings of the Conference on Robot Learning (CoRL), 2020.   
+[29] T. Yu, G. Thomas, L. Yu, S. Ermon, J. Zou, S. Levine, C. Finn, and T. Ma. MOPO: Model-based Offline Policy Optimization. In Advances in Neural Information Processing Systems (NeurIPS), 2020.   
+[30] P. Englert, A. Paraschos, M. P. Deisenroth, and J. Peters. Probabilistic model-based imitation learning. Adaptive Behavior, 21(5):388–403, 2013.   
+[31] R. Kidambi, J. Chang, and W. Sun. Mobile: Model-based imitation learning from observation alone. Advances in Neural Information Processing Systems, 34, 2021.   
+[32] M. Babaeizadeh, C. Finn, D. Erhan, R. H. Campbell, and S. Levine. Stochastic variational video prediction. In Proceedings of the International Conference on Learning Representations (ICLR), 2018.   
+[33] E. Denton and R. Fergus. Stochastic Video Generation with a Learned Prior. In Proceedings of the International Conference on Machine Learning (ICML), 2018.   
+[34] J.-Y. Franceschi, E. Delasalles, M. Chen, S. Lamprier, and P. Gallinari. Stochastic latent residual video prediction. In Proceedings of the International Conference on Machine Learning (ICML), 2020.   
+[35] N. Lee, W. Choi, P. Vernaza, C. B. Choy, P. H. S. Torr, and M. K. Chandraker. DESIRE: distant future prediction in dynamic scenes with interacting agents. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.   
+[36] N. Rhinehart, R. McAllister, K. M. Kitani, and S. Levine. PRECOG: prediction conditioned on goals in visual multi-agent settings. Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2019.   
+[37] H. Zhao, J. Gao, T. Lan, C. Sun, B. Sapp, B. Varadarajan, Y. Shen, Y. Shen, Y. Chai, C. Schmid, C. Li, and D. Anguelov. TNT: Target-driven trajectory prediction. In Proceedings of the Conference on Robot Learning (CoRL), 2020.   
+[38] T. Salzmann, B. Ivanovic, P. Chakravarty, and M. Pavone. Trajectron $^ { + + }$ : Dynamically-feasible trajectory forecasting with heterogeneous data. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   
+[39] N. Rhinehart, R. McAllister, and S. Levine. Deep imitative models for flexible inference, planning, and control. In Proceedings of the International Conference on Learning Representations (ICLR), 2020.   
+[40] D. P. Kingma and M. Welling. Auto-encoding variational bayes. Proceedings of the International Conference on Learning Representations (ICLR), 2014.   
+[41] L.-C. Chen, G. Papandreou, F. Schroff, and H. Adam. Rethinking Atrous Convolution for Semantic Image Segmentation. arXiv preprint arXiv:1706.05587, 2017.   
+[42] C. Godard, O. Mac Aodha, M. Firman, and G. J. Brostow. Digging into self-supervised monocular depth prediction. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), October 2019.   
+[43] T. Karras, S. Laine, and T. Aila. A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.   
+[44] I. Loshchilov and F. Hutter. Decoupled Weight Decay Regularization. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   
+[45] CARLA Team. CARLA Autonomous Driving Leaderboard. https://leaderboard.carla. org/get_started/, 2019.   
+[46] M. Toromanoff, E. Wirbel, and F. Moutarde. End-to-end model-free reinforcement learning for urban driving using implicit affordances. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   
+[47] D. Chen, B. Zhou, V. Koltun, and P. Krähenbühl. Learning by cheating. In Conference on Robot Learning, pages 66–75, 2020.   
+[48] A. Prakash, K. Chitta, and A. Geiger. Multi-modal fusion transformer for end-to-end autonomous driving. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 7077–7087, 2021.   
+[49] T. Madl, K. Chen, D. Montaldi, and R. Trappl. Computational cognitive models of spatial memory in navigation space: A review. Neural Networks, 65:18–43, 2015.   
+[50] R. A. Epstein, E. Z. Patai, J. B. Julian, and H. J. Spiers. The cognitive map in humans: spatial navigation and beyond. Nature Neuroscience, 20(11):1504–1513, 2017.   
+[51] J. L. Park, P. A. Dudchenko, and D. I. Donaldson. Navigation in real-world environments: New opportunities afforded by advances in mobile brain imaging. Frontiers in Human Neuroscience, 12, 2018.   
+[52] CARLA Team. CARLA Maps. https://carla.readthedocs.io/en/latest/core_ map/, 2022.   
+[53] M. Henaff, A. Canziani, and Y. LeCun. Model-Predictive Policy Learning with Uncertainty Regularization for Driving in Dense Traffic. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   
+[54] B. Cheng, M. D. Collins, Y. Zhu, T. Liu, T. S. Huang, H. Adam, and L. Chen. Panoptic-deeplab: A simple, strong, and fast baseline for bottom-up panoptic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   
+[55] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.
+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See Section 5 and Section 6.   
+(b) Did you describe the limitations of your work? [Yes] See Section 7.   
+(c) Did you discuss any potential negative societal impacts of your work? [No]   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Section 3.   
+(b) Did you include complete proofs of all theoretical results? [Yes] See Appendix B.
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See https://github.com/wayveai/mile.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendix C and Appendix D.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] See Section 5.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Section 4.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes]   
+(b) Did you mention the license of the assets? [Yes]   
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] See https://github.com/wayveai/mile.   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/dev/Zk1SbbdZwS/Zk1SbbdZwS_content_list.json

@@ -0,0 +1,1294 @@
+[
+    {
+        "type": "text",
+        "text": "Model-Based Imitation Learning for Urban Driving ",
+        "text_level": 1,
+        "bbox": [
+            184,
+            122,
+            812,
+            148
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anthony $\\mathbf { H } \\mathbf { u } ^ { 1 , 2 }$ Gianluca Corrado1 Nicolas Griffiths1 Zak Murez1 Corina Gurau1 ",
+        "bbox": [
+            184,
+            199,
+            813,
+            217
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Hudson Yeo1 Alex Kendall1 Roberto Cipolla2 Jamie Shotton1 ",
+        "bbox": [
+            212,
+            234,
+            782,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1Wayve, UK. 2University of Cambridge, UK. research@wayve.ai ",
+        "bbox": [
+            334,
+            270,
+            663,
+            300
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            335,
+            535,
+            352
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "An accurate model of the environment and the dynamic agents acting in it offers great potential for improving motion planning. We present MILE: a Model-based Imitation LEarning approach to jointly learn a model of the world and a policy for autonomous driving. Our method leverages 3D geometry as an inductive bias and learns a highly compact latent space directly from high-resolution videos of expert demonstrations. Our model is trained on an offline corpus of urban driving data, without any online interaction with the environment. MILE improves upon prior state-of-the-art by $31 \\%$ in driving score on the CARLA simulator when deployed in a completely new town and new weather conditions. Our model can predict diverse and plausible states and actions, that can be interpretably decoded to bird’s-eye view semantic segmentation. Further, we demonstrate that it can execute complex driving manoeuvres from plans entirely predicted in imagination. Our approach is the first camera-only method that models static scene, dynamic scene, and ego-behaviour in an urban driving environment. The code and model weights are available at https://github.com/wayveai/mile. ",
+        "bbox": [
+            233,
+            368,
+            766,
+            575
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            604,
+            310,
+            622
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "From an early age we start building internal representations of the world through observation and interaction [1]. Our ability to estimate scene geometry and dynamics is paramount to generating complex and adaptable movements. This accumulated knowledge of the world, part of what we often refer to as common sense, allows us to navigate effectively in unfamiliar situations [2]. ",
+        "bbox": [
+            174,
+            637,
+            823,
+            693
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we present MILE, a Model-based Imitation LEarning approach to jointly learn a model of the world and a driving policy. We demonstrate the effectiveness of our approach in the autonomous driving domain, operating on complex visual inputs labelled only with expert action and semantic segmentation. Unlike prior work on world models [3, 4, 5], our method does not assume access to a ground truth reward, nor does it need any online interaction with the environment. Further, previous environments in OpenAI Gym [3], MuJoCo [4], and Atari [5] were characterised by simplified visual inputs as small as $6 4 \\times 6 4$ images. In contrast, MILE operates on high-resolution camera observations of urban driving scenes. ",
+        "bbox": [
+            174,
+            698,
+            825,
+            809
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Driving inherently requires a geometric understanding of the environment, and MILE exploits 3D geometry as an important inductive bias by first lifting image features to 3D and pooling them into a bird’s-eye view $\\mathrm { ( B e V ) }$ representation. The evolution of the world is modelled by a latent dynamics model that infers compact latent states from observations and expert actions. The learned latent state is the input to a driving policy that outputs vehicle control, and can additionally be decoded to BeV segmentation for visualisation and as a supervision signal. ",
+        "bbox": [
+            174,
+            815,
+            825,
+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Our method also relaxes the assumption made in some recent work [6, 7] that neither the agent nor its actions influence the environment. This assumption rarely holds in urban driving, and therefore MILE is action-conditioned, allowing us to model how other agents respond to ego-actions. We show that our model can predict plausible and diverse futures from latent states and actions over long time horizons. It can even predict entire driving plans in imagination to successfully execute complex driving manoeuvres, such as negotiating a roundabout, or swerving to avoid a motorcyclist (see videos in the supplementary material). ",
+        "bbox": [
+            174,
+            92,
+            825,
+            188
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We showcase the performance of our model on the driving simulator CARLA [8], and demonstrate a new state-of-the-art. MILE achieves a $31 \\%$ improvement in driving score with respect to previous methods [9, 10] when tested in a new town and new weather conditions. Finally, during inference, because we model time with a recurrent neural network, we can maintain a single state that summarises all the past observations and then efficiently update the state when a new observation is available. We demonstrate that this design decision has important benefits for deployment in terms of latency, with negligible impact on the driving performance. ",
+        "bbox": [
+            174,
+            194,
+            825,
+            292
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To summarise the main contributions of this paper: ",
+        "bbox": [
+            174,
+            297,
+            508,
+            313
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We introduce a novel model-based imitation learning architecture that scales to the visual complexity of autonomous driving in urban environments by leveraging 3D geometry as an inductive bias. Our method is trained solely using an offline corpus of expert driving data, and does not require any interaction with an online environment or access to a reward, offering strong potential for real-world application.   \n• Our camera-only model sets a new state-of-the-art on the CARLA simulator, surpassing other approaches, including those requiring LiDAR inputs.   \n• Our model predicts a distribution of diverse and plausible futures states and actions. We demonstrate that it can execute complex driving manoeuvres from plans entirely predicted in imagination. ",
+        "bbox": [
+            217,
+            324,
+            825,
+            474
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            494,
+            321,
+            512
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our work is at the intersection of imitation learning, 3D scene representation, and world modelling. ",
+        "bbox": [
+            176,
+            526,
+            821,
+            541
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Imitation learning. Despite that the first end-to-end method for autonomous driving was envisioned more than 30 years ago [11], early autonomous driving approaches were dominated by modular frameworks, where each module solves a specific task [12, 13, 14]. Recent years have seen the development of several end-to-end self-driving systems that show strong potential to improve driving performance by predicting driving commands from high-dimensional observations alone. Conditional imitation learning has proven to be one successful method to learn end-to-end driving policies that can be deployed in simulation [15] and real-world urban driving scenarios [16]. Nevertheless, difficulties of learning end-to-end policies from high-dimensional visual observations and expert trajectories alone have been highlighted [17]. ",
+        "bbox": [
+            174,
+            556,
+            825,
+            681
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Several works have attempted to overcome such difficulties by moving past pure imitation learning. DAgger [18] proposes iterative dataset aggregation to collect data from trajectories that are likely to be experienced by the policy during deployment. NEAT [19] additionally supervises the model with BeV semantic segmentation. ChauffeurNet [20] exposes the learner to synthesised perturbations of the expert data in order to produce more robust driving policies. Learning from All Vehicles (LAV) [10] boosts sample efficiency by learning behaviours from not only the ego vehicle, but from all the vehicles in the scene. Roach [9] presents an agent trained with supervision from a reinforcement learning coach that was trained on-policy and with access to privileged information. ",
+        "bbox": [
+            174,
+            688,
+            825,
+            799
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3D scene representation. Successful planning for autonomous driving requires being able to understand and reason about the 3D scene, and this can be challenging from monocular cameras. One common solution is to condense the information from multiple cameras to a single bird’s-eye representation of the scene. This can be achieved by lifting each image in 3D (by learning a depth distribution of features) and then splatting all frustums into a common rasterised BeV grid [21, 22, 23]. An alternative approach is to rely on transformers to learn the direct mapping from image to bird’s-eye view [24, 25, 26], without explicitly modelling depth. ",
+        "bbox": [
+            174,
+            814,
+            825,
+            911
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "World models. Model-based methods have mostly been explored in a reinforcement learning setting and have been shown to be extremely successful [3, 27, 5]. These methods assume access to a reward, and online interaction with the environment, although progress has been made on fully offline reinforcement learning [28, 29]. Model-based imitation learning has emerged as an alternative to reinforcement learning in robotic manipulation [30] and OpenAI Gym [31]. Even though these methods do not require access to a reward, they still require online interaction with the environment to achieve good performance. ",
+        "bbox": [
+            174,
+            92,
+            825,
+            188
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Learning the latent dynamics of a world model from image observations was first introduced in video prediction [32, 33, 34]. Most similar to our approach, [4, 5] additionally modelled the reward function and optimised a policy inside their world model. Contrarily to prior work, our method does not assume access to a reward function, and directly learns a policy from an offline dataset. Additionally, previous methods operate on simple visual inputs, mostly of size $6 4 \\times 6 4$ . In contrast, MILE is able to learn the latent dynamics of complex urban driving scenes from high resolution $6 0 0 \\times 9 6 0$ input observations, which is important to ensure small details such as traffic lights can be perceived reliably. ",
+        "bbox": [
+            173,
+            194,
+            825,
+            305
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Trajectory forecasting. The goal of trajectory forecasting is to estimate the future trajectories of dynamic agents using past physical states (e.g. position, velocity), and scene context (e.g. as an offline HD map) [35, 36, 37, 38]. World models build a latent representation of the environment that explains the observations from the sensory inputs of the ego-agent (e.g. camera images) conditioned on their actions. While trajectory forecasting methods only model the dynamic scene, world models jointly reason on static and dynamic scenes. The future trajectories of moving agents is implicitly encoded in the learned latent representation of the world model, and could be explicitly decoded given we have access to future trajectory labels. ",
+        "bbox": [
+            174,
+            327,
+            825,
+            438
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "[35, 37, 38] forecast the future trajectory of moving agents, but did not control the ego-agent. They focused on the prediction problem and not on learning expert behaviour from demonstrations. [39] inferred future trajectories of the ego-agent from expert demonstrations, and conditioned on some specified goal to perform new tasks. [36] extended their work to jointly model the future trajectories of moving agents as well as of the ego-agent. ",
+        "bbox": [
+            174,
+            444,
+            823,
+            513
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our proposed model jointly models the motion of other dynamics agents, the behaviour of the ego-agent, as well as the static scene. Contrary to prior work, we do not assume access to ground truth physical states (position, velocity) or to an offline HD map for scene context. Our approach is the first camera-only method that models static scene, dynamic scene, and ego-behaviour in an urban driving environment. ",
+        "bbox": [
+            174,
+            520,
+            825,
+            590
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 MILE: Model-based Imitation LEarning ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            616,
+            545,
+            633
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present MILE: our method that learns to jointly control an autonomous vehicle and model the world and its dynamics. An overview of the architecture is presented in Figure 1 and the full description of the network can be found in Appendix C. We begin by defining the generative model (Section 3.1), and then derive the inference model (Section 3.2). Section 3.3 and Section 3.4 describe the neural networks that parametrise the inference and generative models respectively. Finally, in Section 3.5 we show how our model can predict future states and actions to drive in imagination. ",
+        "bbox": [
+            174,
+            651,
+            825,
+            734
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 Probabilistic Generative Model ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            758,
+            429,
+            773
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let $\\mathbf { o } _ { 1 : T }$ be a sequence of $T$ video frames with associated expert actions $\\mathbf { a } _ { 1 : T }$ and ground truth $\\mathbf { B e V }$ semantic segmentation labels $\\mathbf { y } _ { 1 : T }$ . We model their evolution by introducing latent variables $\\mathbf { s } _ { 1 : T }$ that govern the temporal dynamics. The initial distribution is parameterised as $\\mathbf { s } _ { 1 } \\sim \\mathcal { N } ( \\mathbf { 0 } , I )$ , and we additionally introduce a variable ${ \\bf h } _ { 1 } \\sim \\delta ( { \\bf 0 } )$ that serves as a deterministic history. The transition consists of (i) a deterministic update $\\mathbf { h } _ { t + 1 } = f _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } )$ that depends on the past history $\\mathbf { h } _ { t }$ and past state $\\mathbf { s } _ { t }$ , followed by (ii) a stochastic update $\\mathbf { \\dot { s } } _ { t + 1 } \\sim \\mathcal { N } ( \\mu _ { \\theta } ( \\mathbf { \\bar { h } } _ { t + 1 } , \\mathbf { a } _ { t } ) , \\sigma _ { \\theta } ( \\mathbf { \\bar { h } } _ { t + 1 } , \\mathbf { a } _ { t } ) \\bar { \\mathbf { I } } )$ , where we parameterised $\\mathbf { s } _ { t }$ as a normal distribution with diagonal covariance. We model these transitions with neural networks: $f _ { \\theta }$ is a gated recurrent cell, and $\\left( \\mu _ { \\boldsymbol { \\theta } } , \\sigma _ { \\boldsymbol { \\theta } } \\right)$ are multi-layer perceptrons. The full probabilistic model is given by Equation (1). ",
+        "bbox": [
+            174,
+            786,
+            825,
+            911
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/07c5c0627aa498a160e9e555c211525e8cedbd640c19afee53a2015c017c24c2.jpg",
+        "image_caption": [
+            "Figure 1: Architecture of MILE. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            171,
+            87,
+            821,
+            371
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "(i) The goal is to infer the latent dynamics $\\left( \\mathbf { h } _ { 1 : T } , \\mathbf { s } _ { 1 : T } \\right)$ that generated the observations $\\mathbf { o } _ { 1 : T }$ , the expert actions $\\mathbf { a } _ { 1 : T }$ and the bird’s-eye view labels $\\mathbf { y } _ { 1 : T }$ . The latent dynamics contains a deterministic history $\\mathbf { h } _ { t }$ and a stochastic state $\\mathbf { s } _ { t }$ .   \n(ii) The inference model, with parameters $\\phi$ , estimates the posterior distribution of the stochastic state $\\begin{array} { r } { q ( \\mathbf { s } _ { t } | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } ) \\sim \\mathcal { N } ( \\mu _ { \\phi } ( \\mathbf { h } _ { t } , \\mathbf { a } _ { t - 1 } , \\mathbf { x } _ { t } ) , \\sigma _ { \\phi } ( \\mathbf { h } _ { t } , \\mathbf { \\bar { a } } _ { t - 1 } , \\mathbf { x } _ { t } ) I ) } \\end{array}$ with $\\mathbf { x } _ { t } = e _ { \\phi } ( \\mathbf { o } _ { t } )$ . $e _ { \\phi }$ is the observation encoder that lifts image features to 3D, pools them to bird’s-eye view, and compresses to a 1D vector.   \n(iii) The generative model, with parameters $\\theta$ , estimates the prior distribution of the stochastic state $p ( \\mathbf { s } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) \\sim \\mathcal { N } ( \\mu _ { \\theta } ( \\mathbf { h } _ { t } , \\hat { \\mathbf { a } } _ { t - 1 } ) , \\sigma _ { \\theta } ( \\mathbf { h } _ { t } , \\hat { \\mathbf { a } } _ { t - 1 } ) \\bar { \\mathbf { I } } )$ , with $\\mathbf h _ { t } = f _ { \\theta } ( \\mathbf h _ { t - 1 } , \\mathbf s _ { t - 1 } )$ the deterministic transition, and $\\hat { \\mathbf { a } } _ { t - 1 } = \\pi _ { \\theta } ( \\mathbf h _ { t - 1 } , \\mathbf s _ { t - 1 } )$ the predicted action. It additionally estimates the distributions of the observation $p ( \\mathbf { o } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) \\sim \\mathcal { N } ( g _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) , I )$ , the bird’s-eye view segmentation $p ( \\mathbf { y } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) \\sim \\mathrm { C a t e g o r i c a l } ( l _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) )$ , and the action $p ( \\mathbf { a } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) \\dot { } \\sim$ Laplace $( \\pi _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) , \\mathbf { 1 } )$ .   \n(iv) In the diagram, we represented our model observing inputs for $T = 2$ timesteps, and then imagining future latent states and actions for one step. ",
+        "bbox": [
+            197,
+            398,
+            826,
+            611
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c0da990903799102d7a9e78ac900a2d6efab1ab0bd326bee3fd534be1e0fceea.jpg",
+        "text": "$$\n\\left\\{ \\begin{array} { l l } { \\mathbf { h } _ { 1 } } & { \\sim \\delta ( \\mathbf { 0 } ) } \\\\ { \\mathbf { s } _ { 1 } } & { \\sim \\mathcal { N } ( \\mathbf { 0 } , I ) } \\\\ { \\mathbf { h } _ { t + 1 } } & { = f _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) } \\\\ { \\mathbf { s } _ { t + 1 } } & { \\sim \\mathcal { N } ( \\mu _ { \\theta } ( \\mathbf { h } _ { t + 1 } , \\mathbf { a } _ { t } ) , \\sigma _ { \\theta } ( \\mathbf { h } _ { t + 1 } , \\mathbf { a } _ { t } ) I ) } \\\\ { \\mathbf { o } _ { t } } & { \\sim \\mathcal { N } ( g _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) , I ) } \\\\ { \\mathbf { y } _ { t } } & { \\sim \\mathrm { C a t e g o r i c a l } ( l _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) ) } \\\\ { \\mathbf { a } _ { t } } & { \\sim \\mathrm { L a p l a c e } ( \\pi _ { \\theta } ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) , \\mathbf { 1 } ) } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            659,
+            647,
+            777
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with $\\delta$ the Dirac delta function, $g _ { \\theta }$ the image decoder, $l _ { \\theta }$ the $\\mathbf { B e V }$ decoder, and $\\pi _ { \\theta }$ the policy, which will be described in Section 3.4. ",
+        "bbox": [
+            173,
+            782,
+            821,
+            811
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 Variational Inference ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            827,
+            361,
+            842
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Following the generative model described in Equation (1), we can factorise the joint probability as: ",
+        "bbox": [
+            168,
+            852,
+            823,
+            868
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d1cb4927a9045335238cf22db4369842953fba808d52440bdda971bbb97866ab.jpg",
+        "text": "$$\np ( \\mathbf { o } _ { 1 : T } , \\mathbf { y } _ { 1 : T } , \\mathbf { a } _ { 1 : T } , \\mathbf { h } _ { 1 : T } , \\mathbf { s } _ { 1 : T } ) = \\prod _ { t = 1 } ^ { T } p ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } , \\mathbf { a } _ { t - 1 } ) p ( \\mathbf { o } _ { t } , \\mathbf { y } _ { t } , \\mathbf { a } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            228,
+            872,
+            767,
+            916
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with ",
+        "bbox": [
+            173,
+            92,
+            205,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c72f502241eaa42cfedb3d1380b3f3c29fbfb93617a8aeef51388183cb7f9331.jpg",
+        "text": "$$\n\\begin{array} { r l } & { p ( \\mathbf { h } _ { t } , \\mathbf { s } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } , \\mathbf { a } _ { t - 1 } ) = p ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) p ( \\mathbf { s } _ { t } | \\mathbf { h } _ { t } , \\mathbf { a } _ { t - 1 } ) } \\\\ & { \\qquad p ( \\mathbf { o } _ { t } , \\mathbf { y } _ { t } , \\mathbf { a } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) = p ( \\mathbf { o } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) p ( \\mathbf { y } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) p ( \\mathbf { a } _ { t } | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            284,
+            109,
+            712,
+            147
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given that $\\mathbf { h } _ { t }$ is deterministic according to Equation (1), we have $p ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) = \\delta ( \\mathbf { h } _ { t } - \\mathbf { \\tilde { k } }$ $f _ { \\theta } ( \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) )$ . Therefore, in order to maximise the marginal likelihood of the observed data $p ( \\mathbf { o } _ { 1 : T } , \\mathbf { y } _ { 1 : T } , \\mathbf { a } _ { 1 : T } )$ , we need to infer the latent variables $\\mathbf { s } _ { 1 : T }$ . We do this through deep variational inference by introducing a variational distribution $q _ { H , S }$ defined and factorised as follows: ",
+        "bbox": [
+            176,
+            156,
+            821,
+            213
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/14f7abee89e25852c1508639cc3b5ade2912b6215b4ae99dd28f068fb86b8d5d.jpg",
+        "text": "$$\nq _ { H , S } \\triangleq q ( \\mathbf { h } _ { 1 : T } , \\mathbf { s } _ { 1 : T } | \\mathbf { o } _ { 1 : T } , \\mathbf { a } _ { 1 : T - 1 } ) = \\prod _ { t = 1 } ^ { T } q ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) q ( \\mathbf { s } _ { t } | \\mathbf { o } _ { \\le t } , \\mathbf { a } _ { < t } )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            254,
+            228,
+            740,
+            272
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "with $q ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) = p ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } )$ , the Delta dirac function defined above, and $q ( { \\bf h } _ { 1 } ) = \\delta ( { \\bf 0 } )$ We parameterise this variational distribution with a neural network with weights $\\phi$ . By applying Jensen’s inequality, we can obtain a variational lower bound on the log evidence: ",
+        "bbox": [
+            174,
+            280,
+            825,
+            323
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/532e29f8a4988f4a02a597c596491ef9d8fb42cc941dc350d4abd53d42269136.jpg",
+        "text": "$$\n\\begin{array} { r l } { \\log p \\big ( \\mathbf { o } _ { 1 : T } , \\mathbf { y } _ { 1 : T } , \\mathbf { a } _ { 1 : T } \\big ) \\geq } & { \\mathcal { L } \\big ( \\mathbf { o } _ { 1 : T } , \\mathbf { y } _ { 1 : T } , \\mathbf { a } _ { 1 : T } ; \\theta , \\phi \\big ) } \\\\ { \\triangleq } & { \\displaystyle \\sum _ { t = 1 } ^ { T } \\mathbb { E } _ { q ( \\mathbf { h } _ { 1 : t } , \\mathbf { s } _ { 1 : t } | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } ) } \\left[ \\underbrace { \\log p \\big ( \\mathbf { o } _ { t } \\big | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } \\big ) } _ { \\mathrm { i m a g e r e c o n s t u r a t i o n } } + \\underbrace { \\log p \\big ( \\mathbf { y } _ { t } \\big | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } \\big ) } _ { \\mathrm { b i f i ^ { * } \\times \\mathrm { e y r e s e p u r a t i o n } } } + \\underbrace { \\log p \\big ( \\mathbf { a } _ { t } \\big | \\mathbf { h } _ { t } , \\mathbf { s } _ { t } \\big ) } _ { \\mathrm { a c t i o n } } \\right] } \\\\ & { \\displaystyle - \\sum _ { t = 1 } ^ { T } \\mathbb { E } _ { q ( \\mathbf { h } _ { 1 : t - 1 } , \\mathbf { s } _ { 1 : t - 1 } | \\mathbf { o } _ { \\leq t - 1 } , \\mathbf { a } _ { < t - 1 } ) } \\left[ \\underbrace { D _ { \\mathrm { K L } } \\Big ( q \\big ( \\mathbf { s } _ { t } \\big | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } \\big ) \\big | | \\ p \\big ( \\mathbf { s } _ { t } \\big | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } \\big ) \\Big ) } _ { \\mathrm { o r } \\mathrm { e x t } \\big ( \\mathbf { y } + \\mathbf { s } _ { t } , \\mathbf { a } _ { < t } \\big ) } \\right] \\enspace ( \\mathbf { s } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            189,
+            344,
+            807,
+            463
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "{zposterior and prior matching ",
+        "bbox": [
+            571,
+            462,
+            705,
+            473
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Please refer to Appendix B for the full derivation. We model $q ( \\mathbf { s } _ { t } | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } )$ as a Gaussian distribution so that the Kullback-Leibler (KL) divergence can be computed in closed-form. Given that the image observations $\\mathbf { o } _ { t }$ are modelled as Gaussian distributions with unit variance, the resulting loss is the mean-squared error. Similarly, the action being modelled as a Laplace distribution and the $\\mathbf { B e V }$ labels as a categorical distribution, the resulting losses are, respectively, $L _ { 1 }$ and cross-entropy. The expectations over the variational distribution can be efficiently approximated with a single sequence sample from $q _ { H , S }$ , and backpropagating gradients with the reparametrisation trick [40]. ",
+        "bbox": [
+            173,
+            484,
+            825,
+            583
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 Inference Network $\\phi$ ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            598,
+            356,
+            613
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The inference network, parameterised by $\\phi$ , models $q ( \\mathbf { s } _ { t } | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } )$ , which approximates the true posterior $p ( \\mathbf { s } _ { t } | \\mathbf { o } _ { \\leq t } , \\mathbf { a } _ { < t } )$ . It is constituted of two elements: the observation encoder $e _ { \\phi }$ , that embeds input images, route map and vehicle control sensor data to a low-dimensional vector, and the posterior network $\\left( \\mu _ { \\phi } , \\sigma _ { \\phi } \\right)$ , that estimates the probability distribution of the Gaussian posterior. ",
+        "bbox": [
+            173,
+            625,
+            825,
+            680
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3.1 Observation Encoder ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            694,
+            374,
+            708
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The state of our model should be compact and low-dimensional in order to effectively learn dynamics. Therefore, we need to embed the high resolution input images to a low-dimensional vector. Naively encoding this image to a 1D vector similarly to an image classification task results in poor performance as shown in Section 5.2. Instead, we explicitly encode 3D geometric inductive biases in the model. ",
+        "bbox": [
+            173,
+            718,
+            825,
+            773
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Lifting image features to 3D. Since autonomous driving is a geometric problem where it is necessary to reason on the static scene and dynamic agents in 3D, we first lift the image features to 3D. More precisely, we encode the image inputs $\\mathbf { \\sigma } _ { \\mathbf { o } _ { t } } ~ \\in ~ \\mathbb { R } ^ { 3 \\times H \\times W }$ with an image encoder to extract features $\\mathbf { u } _ { t } \\in \\dot { \\mathbb { R } } ^ { C _ { e } \\times H _ { e } \\times W _ { e } }$ . Then similarly to Philion and Fidler [21], we predict a depth probability distribution for each image feature along a predefined grid of depth bins $\\mathbf { \\dot { d } } _ { t } \\in \\mathbb { R } ^ { D \\times \\dot { H } _ { e } , \\times \\mathbf { \\dot { W } } _ { e } }$ . Using the depth probability distribution, the camera intrinsics $K$ and extrinsics $M$ , we can lift the image features to 3D: L $\\mathrm { i f t } ( \\mathbf { \\bar { u } } _ { t } , \\mathbf { d } _ { t } , K ^ { - 1 } , M ) ) \\in \\mathbb { R } ^ { C _ { e } \\times D \\times H _ { e } \\times D _ { e } \\times 3 }$ . ",
+        "bbox": [
+            173,
+            779,
+            825,
+            877
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Pooling to BeV. The 3D feature voxels are then sum-pooled to $\\mathbf { B e V }$ space using a predefined grid with spatial extent $H _ { b } \\times W _ { b }$ and spatial resolution $b _ { \\mathrm { r e s } }$ . The resulting feature is $\\mathbf { \\breve { b } } _ { t } \\in \\mathbb { R } ^ { C _ { e } \\times H _ { b } \\times \\mathbf { \\breve { W } } _ { b } }$ . ",
+        "bbox": [
+            173,
+            883,
+            823,
+            911
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Mapping to a 1D vector. In traditional computer vision tasks (e.g. semantic segmentation [41], depth prediction [42]), the bottleneck feature is usually a spatial tensor, in the order of $1 0 ^ { 5 } - 1 0 ^ { \\bar { 6 } }$ features. Such high dimensionality is prohibitive for a world model that has to match the distribution of the priors (what it thinks will happen given the executed action) to the posteriors (what actually happened by observing the image input). Therefore, using a convolutional backbone, we compress the $\\mathbf { B e V }$ feature $\\mathbf { b } _ { t }$ to a single vector $\\mathbf { x } _ { t } ^ { \\prime } \\in \\mathbb { R } ^ { C ^ { \\prime } }$ . As shown in Section 5.2, we found it critical to compress in $\\mathbf { B e V }$ space rather than directly in image space. ",
+        "bbox": [
+            173,
+            92,
+            825,
+            190
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Route map and speed. We provide the agent with a goal in the form of a route map [9], which is a small grayscale image indicating to the agent where to navigate at intersections. The route map is encoded using a convolutional module resulting in a 1D feature $\\mathbf { r } _ { t }$ . The current speed is encoded with fully connected layers as $\\mathbf { m } _ { t }$ . At each timestep $t$ , the observation embedding $\\mathbf { x } _ { t }$ is the concatenation of the image feature, route map feature and speed feature: $\\mathbf { x } _ { t } = [ \\mathbf { x } _ { t } ^ { \\prime } , \\mathbf { r } _ { t } , \\mathbf { m } _ { t } ] \\in \\mathbb { R } ^ { C }$ , with $C = 5 1 2$ ",
+        "bbox": [
+            174,
+            196,
+            825,
+            267
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3.2 Posterior Network ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            295,
+            352,
+            309
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The posterior network $\\left( \\mu _ { \\phi } , \\sigma _ { \\phi } \\right)$ estimates the parameters of the variational distribution ${ q ( \\mathbf { s } _ { t } | \\bar { \\mathbf { o } } _ { \\le t } , \\mathbf { a } _ { < t } ) \\ \\sim \\ \\mathcal { N } \\left( \\mu _ { \\phi } ( \\mathbf { \\bar { h } } _ { t } , \\mathbf { a } _ { t - 1 } , e _ { \\phi } ( \\mathbf { o } _ { t } ) ) , \\sigma _ { \\phi } ( \\mathbf { \\bar { h } } _ { t } , \\mathbf { \\bar { a } } _ { t - 1 } , e _ { \\phi } ( \\mathbf { o } _ { t } ) ) I \\right) }$ with $\\mathbf h _ { t } \\ = \\ f _ { \\theta } ( \\mathbf h _ { t - 1 } , \\mathbf s _ { t - 1 } )$ . Note that $\\mathbf { h } _ { t }$ was inferred using $f _ { \\theta }$ because we have assumed that $\\mathbf { h } _ { t }$ is deterministic, meaning that $q ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) = p ( \\mathbf { h } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) = \\delta { \\bigl ( } \\mathbf { h } _ { t } - f _ { \\theta } { \\bigl ( } \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } { \\bigr ) } { \\bigr ) }$ . The dimension of the Gaussian distribution is equal to 512. ",
+        "bbox": [
+            174,
+            324,
+            826,
+            393
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4 Generative Network $\\theta$ ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            424,
+            366,
+            439
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The generative network, parameterised by $\\theta$ , models the latent dynamics $\\left( \\mathbf { h } _ { 1 : T } , \\mathbf { s } _ { 1 : T } \\right)$ as well as the generative process of $\\left( \\mathbf { o } _ { 1 : T } , \\mathbf { y } _ { 1 : T } , \\mathbf { a } _ { 1 : T } \\right)$ . It comprises a gated recurrent cell $f _ { \\theta }$ , a prior network $\\left( \\mu _ { \\boldsymbol { \\theta } } , \\sigma _ { \\boldsymbol { \\theta } } \\right)$ , an image decoder $g _ { \\theta }$ , a BeV decoder $l _ { \\theta }$ , and a policy $\\pi _ { \\theta }$ . ",
+        "bbox": [
+            174,
+            455,
+            825,
+            498
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The prior network estimates the parameters of the Gaussian distribution   \n$p ( \\mathbf { s } _ { t } | \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } ) \\ \\sim \\ { \\mathcal { N } } \\left( \\mu _ { \\theta } ( \\mathbf { h } _ { t } , { \\hat { \\mathbf { a } } } _ { t - 1 } ) , \\sigma _ { \\theta } ( \\mathbf { h } _ { t } , { \\hat { \\mathbf { a } } } _ { t - 1 } ) I \\right)$ with $\\mathbf h _ { t } \\ = \\ f _ { \\theta } ( \\mathbf h _ { t - 1 } , \\mathbf s _ { t - 1 } )$ and $\\hat { { \\bf a } } _ { t - 1 } =$ $\\pi _ { \\theta } ( \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } )$ . Since the prior does not have access to the ground truth action $\\mathbf { a } _ { t - 1 }$ , the latter is estimated with the learned policy $\\hat { \\mathbf { a } } _ { t - 1 } = \\pi _ { \\theta } ( \\mathbf h _ { t - 1 } , \\mathbf s _ { t - 1 } )$ . ",
+        "bbox": [
+            174,
+            503,
+            825,
+            560
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The Kullback-Leibler divergence loss between the prior and posterior distributions can be interpreted as follows. Given the past state $\\left( \\mathbf { h } _ { t - 1 } , \\mathbf { s } _ { t - 1 } \\right)$ , the objective is to predict the distribution of the next state $\\mathbf { s } _ { t }$ . As we model an active agent, this transition is decomposed into (i) action prediction and (ii) next state prediction. This transition estimation is compared to the posterior distribution that has access to the ground truth action $\\mathbf { a } _ { t - 1 }$ , and the image observation $\\mathbf { o } _ { t }$ . The prior distribution tries to match the posterior distribution. This divergence matching framework ensures the model predicts actions and future states that explain the observed data. The divergence of the posterior from the prior measures how many nats of information were missing from the prior when observing the posterior. At training convergence, the prior distribution should be able to model all action-state transitions from the expert dataset. ",
+        "bbox": [
+            173,
+            565,
+            825,
+            704
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The image and $\\mathbf { B e V }$ decoders have an architecture similar to StyleGAN [43]. The prediction starts as a learned constant tensor, and is progressively upsampled to the final resolution. At each resolution, the latent state is injected in the network with adaptive instance normalisation. This allows the latent states to modulate the predictions at different resolutions. The policy is a multi-layer perceptron. Please refer to Appendix C for a full description of the neural networks. ",
+        "bbox": [
+            174,
+            710,
+            825,
+            780
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.5 Imagining Future States and Actions ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            810,
+            467,
+            825
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our model can imagine future latent states by using the learned policy to infer actions $\\hat { \\mathbf { a } } _ { T + i } =$ $\\pi _ { \\boldsymbol { \\theta } } ( \\mathbf { h } _ { T + i } , \\mathbf { s } _ { T + i } )$ , predicting the next deterministic state $\\mathbf { h } _ { T + i + 1 } = f _ { \\theta } ( \\mathbf { h } _ { T + i } , \\mathbf { s } _ { T + i } )$ and sampling from the prior distribution $\\mathbf { s } _ { T + i + 1 } \\sim \\mathcal { N } ( \\mu _ { \\theta } ( \\mathbf { h } _ { T + i + 1 } , \\hat { \\mathbf { a } } _ { T + i } ) , \\sigma _ { \\theta } ( \\mathbf { h } _ { T + i + 1 } , \\hat { \\mathbf { a } } _ { T + i } ) I ) ,$ for $i \\geq 0$ . This process can be iteratively applied to generate sequences of longer futures in latent space, and the predicted futures can be visualised through the decoders. ",
+        "bbox": [
+            174,
+            842,
+            825,
+            911
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/da07eb0091ac0158fa551bd6dba8b66bbe3d83a8658a3a3fd659e33b6fecdb3a.jpg",
+        "table_caption": [
+            "Table 1: Driving performance on a new town and new weather conditions in CARLA. Metrics are averaged across three runs. We include reward signals from past work where available. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm. Reward</td></tr><tr><td>CILRS [17]</td><td>7.8± 0.3</td><td>10.3 ± 0.0</td><td>76.2 ± 0.5</td><td></td><td></td></tr><tr><td>LBC [47]</td><td>12.3 ± 2.0</td><td>31.9 ± 2.2</td><td>66.0 ± 1.7</td><td></td><td></td></tr><tr><td>TransFuser [48]</td><td>31.0 ± 3.6</td><td>47.5 ± 5.3</td><td>76.8 ± 3.9</td><td></td><td></td></tr><tr><td>Roach [9]</td><td>41.6 ± 1.8</td><td>96.4 ± 2.1</td><td>43.3 ± 2.8</td><td>4236 ± 468</td><td>0.34 ± 0.05</td></tr><tr><td>LAV[10]</td><td>46.5 ± 3.0</td><td>69.8 ± 2.3</td><td>73.4±2.2</td><td></td><td></td></tr><tr><td>MILE</td><td>61.1 ± 3.2</td><td>97.4 ± 0.8</td><td>63.0± 3.0</td><td>7621 ± 460</td><td>0.67 ± 0.02</td></tr><tr><td>Expert</td><td>88.4 ± 0.9</td><td>97.6 ± 1.2</td><td>90.5 ± 1.2</td><td>8694 ±88</td><td>0.70 ± 0.01</td></tr></table>",
+        "bbox": [
+            197,
+            126,
+            795,
+            250
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Experimental Setting ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            272,
+            383,
+            290
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Dataset. The training data was collected in the CARLA simulator with an expert reinforcement learning (RL) agent [9] that was trained using privileged information as input $\\mathrm { B e V }$ semantic segmentations and vehicle measurements). This RL agent generates more diverse runs and has greater driving performance than CARLA’s in-built autopilot [9]. ",
+        "bbox": [
+            174,
+            304,
+            825,
+            359
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We collect data at $2 5 \\mathrm { H z }$ in four different training towns (Town01, Town03, Town04, Town06) and four weather conditions (ClearNoon, WetNoon, HardRainNoon, ClearSunset) for a total of 2.9M frames, or 32 hours of driving data. At each timestep, we save a tuple $\\left( \\mathbf { o } _ { t } , \\mathbf { r o u t e } _ { t } , \\mathbf { s p e e d } _ { t } , \\mathbf { a } _ { t } , \\mathbf { y } _ { t } \\right)$ , with $\\mathbf { o } _ { t } \\in \\mathbb { R } ^ { 3 \\times 6 0 0 \\times 9 6 0 }$ the forward camera RGB image, route $\\mathbf { \\Phi } _ { t } \\in \\mathbb { R } ^ { 1 \\times 6 4 \\times 6 4 }$ the route map (visualized as an inset on the top right of the RGB images in Figure 2), $\\mathbf { s p e e d } _ { t } \\in \\mathbb { R }$ the current velocity of the vehicle, $\\mathbf { a } _ { t } \\in \\mathbb { R } ^ { 2 }$ the action executed by the expert (acceleration and steering), and $\\mathbf { y } _ { t } \\in \\mathbb { R } ^ { C _ { b } \\times \\mathbf { \\bar { 1 } 9 2 } \\times 1 9 2 }$ the $\\mathbf { B e V }$ semantic segmentation. There are $C _ { b } = 8$ semantic classes: background, road, lane marking, vehicles, pedestrians, and traffic light states (red, yellow, green). In urban driving environments, the dynamics of the scene do not contain high frequency components, which allows us to subsample frames at $\\mathrm { 5 H z }$ in our sequence model. ",
+        "bbox": [
+            173,
+            366,
+            825,
+            505
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Training. Our model was trained for 50, 000 iterations on a batch size of 64 on 8 V100 GPUs, with training sequence length $T = 1 2$ . We used the AdamW optimiser [44] with learning rate $1 0 ^ { - 4 }$ and weight decay 0.01. ",
+        "bbox": [
+            174,
+            520,
+            825,
+            563
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Metrics. We report metrics from the CARLA challenge [45] to measure on-road performance: route completion, infraction penalty, and driving score. These metrics are however very coarse, as they only give a sense of how well the agent performs with hard penalties (such as hitting virtual pedestrians). Core driving competencies such as lane keeping and driving at an appropriate speed are obscured. Therefore we also report the cumulative reward of the agent. At each timestep the reward [46] penalises the agent for deviating from the lane center, for driving too slowly/fast, or for causing infractions. It measures how well the agent drives at the timestep level. In order to account for the length of the simulation (due to various stochastic events, it can be longer or shorter), we also report the normalised cumulative reward. More details on the experimental setting is given in Appendix D. ",
+        "bbox": [
+            174,
+            577,
+            825,
+            703
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5 Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            722,
+            266,
+            738
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1 Driving Performance ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            753,
+            359,
+            768
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our model inside the CARLA simulator on a town and weather conditions never seen during training. We picked Town05 as it is the most complex testing town, and use the 10 routes of Town05 as specified in the CARLA challenge [45], in four different weather conditions. Table 1 shows the comparison against prior state-of-the-art methods: CILRS [17], LBC [47], TransFuser [48], Roach [9], and LAV [10]. We evaluate these methods using their publicly available pre-trained weights. ",
+        "bbox": [
+            174,
+            779,
+            825,
+            863
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "MILE outperforms previous works on all metrics, with a $31 \\%$ relative improvement in driving score with respect to LAV. Even though some methods have access to additional sensor information such as LiDAR (TransFuser [48], LAV [10]), our approach demonstates superior performance while only using RGB images from the front camera. Moreover, we observe that our method almost doubles the cumulative reward of Roach (which was trained on the same dataset) and approaches the performance of the privileged expert. ",
+        "bbox": [
+            174,
+            869,
+            825,
+            911
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/08a3b3160e37655d4fdfe16e2361d8e6a9498101e329bde66e0561a13dde691b.jpg",
+        "table_caption": [
+            "Table 2: Ablation studies. We report driving performance on a new town and new weather conditions in CARLA. Results are averaged across three runs. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm.Reward</td></tr><tr><td>Single frame, no 3D</td><td>51.8 ± 3.0</td><td>78.3 ± 3.0</td><td>68.3 ± 2.8</td><td>1878± 296</td><td>0.20 ± 0.04</td></tr><tr><td>Single frame</td><td>59.6 ± 3.6</td><td>94.5 ± 0.6</td><td>64.7 ± 3.3</td><td>6630 ± 168</td><td>0.60 ± 0.01</td></tr><tr><td>No 3D</td><td>63.0 ±1.5</td><td>91.5± 5.5</td><td>69.1 ± 2.8</td><td>4564 ± 1791</td><td>0.40 ± 0.15</td></tr><tr><td>No prior/post. matching</td><td>63.3 ± 2.2</td><td>91.5 ± 5.0</td><td>68.7 ± 1.8</td><td>6084 ± 1429</td><td>0.55 ± 0.07</td></tr><tr><td>No segmentation</td><td>55.0 ± 3.3</td><td>92.5 ± 2.4</td><td>60.9 ± 3.9</td><td>7183 ±107</td><td>0.64 ± 0.02</td></tr><tr><td>MILE</td><td>61.1 ± 3.2</td><td>97.4 ± 0.8</td><td>63.0±3.0</td><td>7621 ± 460</td><td>0.67 ± 0.02</td></tr><tr><td>Expert</td><td>88.4± 0.9</td><td>97.6 ± 1.2</td><td>90.5 ± 1.2</td><td>8694 ±88</td><td>0.70 ± 0.01</td></tr></table>",
+        "bbox": [
+            173,
+            126,
+            821,
+            256
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
+            277,
+            823,
+            319
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 Ablation Studies ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            335,
+            328,
+            349
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We next examine the effect of various design decisions in our approach. ",
+        "bbox": [
+            176,
+            359,
+            642,
+            375
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3D geometry. We compare our model to the following baselines. Single frame that predicts the action and BeV segmentation from a single image observation. Single frame, no 3D which is the same model but without the 3D lifting step. And finally, No $3 D$ which is MILE without 3D lifting. As shown in Table 2, in both cases, there is a significant drop in performance when not modelling 3D geometry. For the single frame model, the cumulative reward drops from 6084 to 1878. For MILE, the reward goes from 7621 to 4564. These results highlights the importance of the 3D geometry inductive bias. ",
+        "bbox": [
+            174,
+            388,
+            825,
+            486
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Probabilistic modelling. At any given time while driving, there exist multiple possible valid behaviours. For example, the driver can slightly adjust its speed, decide to change lane, or decide what is a safe distance to follow behind a vehicle. A deterministic driving policy cannot model these subtleties. In ambiguous situations where multiple choices are possible, it will often learn the mean behaviour, which is valid in certain situations (e.g. the mean safety distance and mean cruising speed are reasonable choices), but unsafe in others (e.g. in lane changing: the expert can change lane early, or late; the mean behaviour is to drive on the lane marking). We compare MILE with a No prior/post. matching baseline that does not have a Kullback-Leibler divergence loss between the prior and posterior distributions, and observe this results in a drop in cumulative reward from 7621 to 6084. ",
+        "bbox": [
+            173,
+            500,
+            825,
+            625
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 Fully Recurrent Inference in Closed-Loop Driving ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            640,
+            562,
+            655
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We compare the closed-loop performance of our model with two different strategies: ",
+        "bbox": [
+            178,
+            665,
+            725,
+            680
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(i) Reset state: for every new observation, we re-initialise the latent state and recompute the new state $\\left[ h _ { T } , s _ { T } \\right]$ , with $T$ matching the training sequence length. ",
+        "bbox": [
+            202,
+            690,
+            820,
+            719
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "(ii) Fully recurrent: the latent state is initialised at the beginning of the evaluation, and is recursively updated with new observations. It is never reset, and instead, the model must have learned a representation that generalises to integrating information for orders of magnitude more steps than the $T$ used during training. ",
+        "bbox": [
+            207,
+            720,
+            821,
+            776
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows that our model can be deployed with recurrent updates, matching the performance of the Reset state approach, while being much more computationally efficient $7 \\times$ faster from $6 . 2 \\mathrm { H z }$ with $T = 1 2$ of fixed context to $4 3 . 0 \\mathrm { H z }$ with a fully recurrent approach). A hypothesis that could explain why the Fully recurrent deployment method works well is because the world model has learned to always discard all past information and rely solely on the present input. To test this hypothesis, we add Gaussian noise to the past latent state during deployment. If the recurrent network is simply discarding all past information, its performance should not be affected. However in Table 3, we see that the cumulative reward significantly decreases, showing our model does not simply discard all past context, but actively makes use of it. ",
+        "bbox": [
+            173,
+            786,
+            825,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2a3fa117a5ed6e20258e51853df66b79935d9adca219ab3118189f028747e59b.jpg",
+        "table_caption": [
+            "Table 3: Comparison of two deployment methods. (i) Reset state: for each new observation a fresh state is computed from a zero-initialised latent state using the last $T$ observations, and (ii) Fully recurrent: the latent state is recurrently updated with new observations. We report driving performance on an unseen town and unseen weather conditions in CARLA. Frequency is in Hertz. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Driving Score</td><td>Route</td><td>Infraction</td><td>Reward</td><td>Norm. Reward</td><td>Freq.</td></tr><tr><td>Reset state</td><td>61.1 ± 3.2</td><td>97.4± 0.8</td><td>63.0±3.0</td><td>7621± 460</td><td>0.67 ± 0.02</td><td>6.2</td></tr><tr><td>Fully recurrent</td><td>62.1 ± 0.5</td><td>93.5± 4.8</td><td>66.6 ± 3.4</td><td>7532±1122</td><td>0.67 ± 0.04</td><td>43.0</td></tr><tr><td>Recurrent+noise</td><td>48.8± 1.8</td><td>81.1 ± 7.0</td><td>61.5± 6.4</td><td>3603± 780</td><td>0.35 ± 0.07</td><td>43.0</td></tr></table>",
+        "bbox": [
+            173,
+            154,
+            828,
+            227
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.4 Long Horizon, Diverse Future Predictions ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            239,
+            504,
+            256
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our model can imagine diverse futures in the latent space, which can be decoded to $\\mathbf { B e V }$ semantic segmentation for interpretability. Figure 2 shows examples of multi-modal futures predicted by MILE. ",
+        "bbox": [
+            174,
+            265,
+            823,
+            308
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/677bd3a03b6da96fa3ba6da7de23bced3e4d3e99f2c17bccb368ab61eef57a21.jpg",
+        "image_caption": [
+            "Figure 2: Qualitative example of multi-modal predictions, for 8 seconds in the future. BeV segmentation legend: black $=$ ego-vehicle, white $=$ background, gray $=$ road, dark gray=lane marking, blue $=$ vehicles, cyan $=$ pedestrians, green/yellow/red $=$ traffic lights. Ground truth labels (GT) outside the field-of-view of the front camera are masked out. In this example, we visualise two distinct futures predicted by the model: 1) (top row) driving through the green light, 2) (bottom row) stopping because the model imagines the traffic light turning red. Note the light transition from green, to yellow, to red, and also at the last frame $t + 8 . 0 8$ how the traffic light in the left lane turns green. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            319,
+            825,
+            450
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 Insights from the World Model ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            574,
+            464,
+            590
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6.1 Latent State Dimension ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            604,
+            377,
+            619
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In our model, we have set the latent state to be a low-dimensional 1D vector of size 512. In dense image reconstruction however, the bottleneck feature is often a 3D spatial tensor of dimension (channel, height, width). We test whether it is possible to have a 3D tensor as a latent probabilistic state instead of a 1D vector. We change the latent state to have dimension $2 5 6 \\times 1 2 \\times 1 2$ (40k distributions), $1 2 8 \\times 2 4 \\times 2 4$ (80k distributions), and $6 4 \\times 4 8 \\times 4 8$ $1 6 0 \\mathrm { k }$ distributions, which is the typical bottleneck size in dense image prediction). Since the latent state is now a spatial tensor, we adapt the recurrent network to be convolutional by switching the fully-connected operations with convolutions. We evaluate the model in the reset state and fully recurrent setting and report the results in Figure 3. ",
+        "bbox": [
+            173,
+            631,
+            826,
+            756
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/16fd01ca573e3503e5c25413c1cd039bc7dd449aa748b36ec6b74a51c5a92d1b.jpg",
+        "image_caption": [
+            "Figure 3: Analysis on the latent state dimension. We report closed-loop driving performance in a new town and new weather in CARLA. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            305,
+            768,
+            694,
+            885
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In the reset state setting, performance decreases as the dimensionality of the latent state increases. Surprisingly, even though the latent space is larger and has more capacity, driving performance is negatively impacted. This seems to indicate that optimising the prior and posterior distributions in the latent space is difficult, and especially more so as dimensionality increases. The prior, which is a multivariate Gaussian distribution needs to match the posterior, another multivariate Gaussian distribution. What makes this optimisation tricky is that the two distributions are non-stationary and change over time during the course of training. The posterior needs to extract the relevant information from the high-resolution images and incorporate it in the latent state in order to reconstruct BeV segmentation and regress the expert action. The prior has to predict the transition that matches the distribution of the posterior. ",
+        "bbox": [
+            174,
+            90,
+            825,
+            229
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Even more intriguing is when we look at the results in the fully recurrent deployment setting. When deployed in a fully recurrent manner in the simulator, without resetting the latent state, the model needs to discard information that is no longer relevant and continuously update its internal state with new knowledge coming from image observations. In our original latent state dimension of 512, there is almost no different in driving performance between the two deployment modes. The picture is dramatically different when using a higher dimensional spatial latent state. For all the tested dimensions, there is a large gap between the two deployment settings. This result seems to indicate that the world model operating on high-dimensional spatial states has not optimally learned this behaviour, contrarily to the one operating on low-dimensional vector states. ",
+        "bbox": [
+            174,
+            236,
+            825,
+            361
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6.2 Driving in Imagination ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            377,
+            372,
+            391
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Humans are believed to build an internal model of the world in order to navigate in it [49, 50, 51]. Since the stream of information they perceive is often incomplete and noisy, their brains fill missing information through imagination. This explains why it is possible for them to continue driving when blinded by sunlight for example. Even if no visual observations are available for a brief moment, they can still reliably predict their next states and actions to exhibit a safe driving behaviour. We demonstrate that similarly, MILE can execute accurate driving plans entirely predicted from imagination, without having access to image observations. We qualitatively show that it can perform complex driving maneuvers such as navigating a roundabout, marking a pause a stop sign, or swerving to avoid a motorcyclist, using an imagined plan from the model (see supplementary material). ",
+        "bbox": [
+            174,
+            401,
+            825,
+            526
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Quantitatively, we measure how accurate the predicted plans are by operating in the fully recurrent setting. We alternate between the observing mode where the model can see image observations, and the imagining mode where the model has to imagine the next states and actions, similarly to a driver that temporarily loses sight due to sun glare. In Appendix A.1 we show that our model can retain the same driving performance with up to $30 \\%$ of the drive in imagining mode. This demonstrates that the model can imagine driving plans that are accurate enough for closed loop driving. Further, it shows that the latent state of the world model can seamlessly switch between the observing and imagining modes. The evolution of the latent state is predicted from imagination when observations are not available, and updated with image observations when they become accessible. ",
+        "bbox": [
+            174,
+            534,
+            825,
+            657
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "7 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            676,
+            299,
+            694
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We presented MILE: a Model-based Imitation LEarning approach for urban driving, that jointly learns a driving policy and a world model from offline expert demonstrations alone. Our approach exploits geometric inductive biases, operates on high-dimensional visual inputs, and sets a new state-of-the-art on the CARLA simulator. MILE can predict diverse and plausible future states and actions, allowing the model to drive from a plan entirely predicted from imagination. ",
+        "bbox": [
+            174,
+            708,
+            823,
+            777
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "An open problem is how to infer the driving reward function from expert data, as this would enable explicit planning in the world model. Another exciting avenue is self-supervision in order to relax the dependency on the bird’s-eye view segmentation labels. Self-supervision could fully unlock the potential of world models for real-world driving and other robotics tasks. ",
+        "bbox": [
+            174,
+            784,
+            823,
+            839
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. We would like to thank Vijay Badrinarayanan, Przemyslaw Mazur, and Oleg Sinavski for insightful research discussions. We are also grateful to Lorenzo Bertoni, Lloyd Russell, Juba Nait Saada, Thomas Uriot, and the anonymous reviewers for their helpful feedback and comments on the paper. ",
+        "bbox": [
+            176,
+            854,
+            823,
+            911
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "References   \n[1] H. B. Barlow. Unsupervised learning. Neural computation, 1(3):295–311, 1989.   \n[2] D. M. Wolpert and M. Kawato. Multiple paired forward and inverse models for motor control. Neural networks, 11(7-8):1317–1329, 1998.   \n[3] D. Ha and J. Schmidhuber. Recurrent world models facilitate policy evolution. In Advances in Neural Information Processing Systems (NeurIPS), 2018.   \n[4] D. Hafner, T. Lillicrap, I. Fischer, R. Villegas, D. Ha, H. Lee, and J. Davidson. Learning Latent Dynamics for Planning from Pixels. In Proceedings of the International Conference on Machine Learning (ICML), 2019.   \n[5] D. Hafner, T. Lillicrap, M. Norouzi, and J. Ba. Mastering atari with discrete world models. Proceedings of the International Conference on Learning Representations (ICLR), 2021.   \n[6] D. Chen, V. Koltun, and P. Krähenbühl. Learning to drive from a world on rails. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 15590– 15599, 2021.   \n[7] V. Sobal, A. Canziani, N. Carion, K. Cho, and Y. LeCun. Separating the world and ego models for self-driving. arXiv preprint arXiv:2204.07184, 2022.   \n[8] A. Dosovitskiy, G. Ros, F. Codevilla, A. Lopez, and V. Koltun. CARLA: An Open Urban Driving Simulator. In Proceedings of the Conference on Robot Learning (CoRL), pages 1–16, 2017.   \n[9] Z. Zhang, A. Liniger, D. Dai, F. Yu, and L. Van Gool. End-to-end urban driving by imitating a reinforcement learning coach. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 15222–15232, 2021.   \n[10] D. Chen and P. Krähenbühl. Learning from all vehicles. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022.   \n[11] D. A. Pomerleau. ALVINN: An autonomous land vehicle in a neural network. Advances in Neural Information Processing Systems (NeurIPS), 1, 1988.   \n[12] A. Bacha, C. Bauman, R. Faruque, M. Fleming, C. Terwelp, C. Reinholtz, D. Hong, A. Wicks, T. Alberi, D. Anderson, et al. Odin: Team VictorTango’s Entry in the DARPA Urban Challenge. Journal of Field Robotics, 25(8):467–492, 2008.   \n[13] D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel. Practical search techniques in path planning for autonomous driving. Ann Arbor, 1001(48105):18–80, 2008.   \n[14] J. Leonard, J. How, S. Teller, M. Berger, S. Campbell, G. Fiore, L. Fletcher, E. Frazzoli, A. Huang, S. Karaman, et al. A perception-driven autonomous urban vehicle. Journal of Field Robotics, 25(10):727–774, 2008.   \n[15] F. Codevilla, M. Müller, A. López, V. Koltun, and A. Dosovitskiy. End-to-end driving via conditional imitation learning. In Proceedings of the International Conference on Robotics and Automation (ICRA), 2018.   \n[16] J. Hawke, R. Shen, C. Gurau, S. Sharma, D. Reda, N. Nikolov, P. Mazur, S. Micklethwaite, N. Griffiths, A. Shah, et al. Urban Driving with Conditional Imitation Learning. In Proceedings of the International Conference on Robotics and Automation (ICRA), pages 251–257, 2020.   \n[17] F. Codevilla, E. Santana, A. M. López, and A. Gaidon. Exploring the Limitations of Behavior Cloning for Autonomous Driving. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 9329–9338, 2019.   \n[18] S. Ross, G. Gordon, and D. Bagnell. A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning. In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), pages 627–635, 2011.   \n[19] K. Chitta, A. Prakash, and A. Geiger. NEAT: Neural Attention Fields for End-to-End Autonomous Driving. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2021.   \n[20] M. Bansal, A. Krizhevsky, and A. Ogale. ChauffeurNet: Learning to drive by imitating the best and synthesizing the worst. In Proceedings of Robotics: Science and Systems (RSS), 2019.   \n[21] J. Philion and S. Fidler. Lift, splat, shoot: Encoding images from arbitrary camera rigs by implicitly unprojecting to 3d. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   \n[22] A. Saha, O. Mendez, C. Russell, and R. Bowden. Enabling Spatio-temporal aggregation in Birds-Eye-View Vehicle Estimation. In Proceedings of the International Conference on Robotics and Automation (ICRA), 2021.   \n[23] A. Hu, Z. Murez, N. Mohan, S. Dudas, J. Hawke, V. Badrinarayanan, R. Cipolla, and A. Kendall. FIERY: Future Instance Prediction in Bird’s-Eye View From Surround Monocular Cameras. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 15273–15282, 2021.   \n[24] L. Peng, Z. Chen, Z. Fu, P. Liang, and E. Cheng. Bevsegformer: Bird’s eye view semantic segmentation from arbitrary camera rigs. arXiv preprint arXiv:2203.04050, 2022.   \n[25] N. Gosala and A. Valada. Bird’s-eye-view panoptic segmentation using monocular frontal view images. IEEE Robotics and Automation Letters, 2022.   \n[26] Z. Li, W. Wang, H. Li, E. Xie, C. Sima, T. Lu, Q. Yu, and J. Dai. BEVFormer: Learning bird’s-eye-view representation from multi-camera images via spatiotemporal transformers. In Proceedings of the European Conference on Computer Vision (ECCV), 2022.   \n[27] J. Schrittwieser, I. Antonoglou, T. Hubert, K. Simonyan, L. Sifre, S. Schmitt, A. Guez, E. Lockhart, D. Hassabis, T. Graepel, T. Lillicrap, and D. Silver. Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model. In Nature, 2020.   \n[28] W. Zhou, S. Bajracharya, and D. Held. PLAS: Latent Action Space for Offline Reinforcement Learning. In Proceedings of the Conference on Robot Learning (CoRL), 2020.   \n[29] T. Yu, G. Thomas, L. Yu, S. Ermon, J. Zou, S. Levine, C. Finn, and T. Ma. MOPO: Model-based Offline Policy Optimization. In Advances in Neural Information Processing Systems (NeurIPS), 2020.   \n[30] P. Englert, A. Paraschos, M. P. Deisenroth, and J. Peters. Probabilistic model-based imitation learning. Adaptive Behavior, 21(5):388–403, 2013.   \n[31] R. Kidambi, J. Chang, and W. Sun. Mobile: Model-based imitation learning from observation alone. Advances in Neural Information Processing Systems, 34, 2021.   \n[32] M. Babaeizadeh, C. Finn, D. Erhan, R. H. Campbell, and S. Levine. Stochastic variational video prediction. In Proceedings of the International Conference on Learning Representations (ICLR), 2018.   \n[33] E. Denton and R. Fergus. Stochastic Video Generation with a Learned Prior. In Proceedings of the International Conference on Machine Learning (ICML), 2018.   \n[34] J.-Y. Franceschi, E. Delasalles, M. Chen, S. Lamprier, and P. Gallinari. Stochastic latent residual video prediction. In Proceedings of the International Conference on Machine Learning (ICML), 2020.   \n[35] N. Lee, W. Choi, P. Vernaza, C. B. Choy, P. H. S. Torr, and M. K. Chandraker. DESIRE: distant future prediction in dynamic scenes with interacting agents. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.   \n[36] N. Rhinehart, R. McAllister, K. M. Kitani, and S. Levine. PRECOG: prediction conditioned on goals in visual multi-agent settings. Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2019.   \n[37] H. Zhao, J. Gao, T. Lan, C. Sun, B. Sapp, B. Varadarajan, Y. Shen, Y. Shen, Y. Chai, C. Schmid, C. Li, and D. Anguelov. TNT: Target-driven trajectory prediction. In Proceedings of the Conference on Robot Learning (CoRL), 2020.   \n[38] T. Salzmann, B. Ivanovic, P. Chakravarty, and M. Pavone. Trajectron $^ { + + }$ : Dynamically-feasible trajectory forecasting with heterogeneous data. In Proceedings of the European Conference on Computer Vision (ECCV), 2020.   \n[39] N. Rhinehart, R. McAllister, and S. Levine. Deep imitative models for flexible inference, planning, and control. In Proceedings of the International Conference on Learning Representations (ICLR), 2020.   \n[40] D. P. Kingma and M. Welling. Auto-encoding variational bayes. Proceedings of the International Conference on Learning Representations (ICLR), 2014.   \n[41] L.-C. Chen, G. Papandreou, F. Schroff, and H. Adam. Rethinking Atrous Convolution for Semantic Image Segmentation. arXiv preprint arXiv:1706.05587, 2017.   \n[42] C. Godard, O. Mac Aodha, M. Firman, and G. J. Brostow. Digging into self-supervised monocular depth prediction. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), October 2019.   \n[43] T. Karras, S. Laine, and T. Aila. A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.   \n[44] I. Loshchilov and F. Hutter. Decoupled Weight Decay Regularization. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   \n[45] CARLA Team. CARLA Autonomous Driving Leaderboard. https://leaderboard.carla. org/get_started/, 2019.   \n[46] M. Toromanoff, E. Wirbel, and F. Moutarde. End-to-end model-free reinforcement learning for urban driving using implicit affordances. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   \n[47] D. Chen, B. Zhou, V. Koltun, and P. Krähenbühl. Learning by cheating. In Conference on Robot Learning, pages 66–75, 2020.   \n[48] A. Prakash, K. Chitta, and A. Geiger. Multi-modal fusion transformer for end-to-end autonomous driving. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 7077–7087, 2021.   \n[49] T. Madl, K. Chen, D. Montaldi, and R. Trappl. Computational cognitive models of spatial memory in navigation space: A review. Neural Networks, 65:18–43, 2015.   \n[50] R. A. Epstein, E. Z. Patai, J. B. Julian, and H. J. Spiers. The cognitive map in humans: spatial navigation and beyond. Nature Neuroscience, 20(11):1504–1513, 2017.   \n[51] J. L. Park, P. A. Dudchenko, and D. I. Donaldson. Navigation in real-world environments: New opportunities afforded by advances in mobile brain imaging. Frontiers in Human Neuroscience, 12, 2018.   \n[52] CARLA Team. CARLA Maps. https://carla.readthedocs.io/en/latest/core_ map/, 2022.   \n[53] M. Henaff, A. Canziani, and Y. LeCun. Model-Predictive Policy Learning with Uncertainty Regularization for Driving in Dense Traffic. In Proceedings of the International Conference on Learning Representations (ICLR), 2019.   \n[54] B. Cheng, M. D. Collins, Y. Zhu, T. Liu, T. S. Huang, H. Adam, and L. Chen. Panoptic-deeplab: A simple, strong, and fast baseline for bottom-up panoptic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.   \n[55] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016. ",
+        "bbox": [
+            171,
+            77,
+            828,
+            917
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            37,
+            828,
+            916
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            64,
+            828,
+            920
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Checklist ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            89,
+            254,
+            106
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "1. For all authors... ",
+        "bbox": [
+            214,
+            116,
+            339,
+            130
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See Section 5 and Section 6.   \n(b) Did you describe the limitations of your work? [Yes] See Section 7.   \n(c) Did you discuss any potential negative societal impacts of your work? [No]   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
+        "bbox": [
+            238,
+            136,
+            825,
+            227
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "2. If you are including theoretical results... ",
+        "bbox": [
+            214,
+            231,
+            493,
+            244
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Section 3.   \n(b) Did you include complete proofs of all theoretical results? [Yes] See Appendix B. ",
+        "bbox": [
+            238,
+            248,
+            825,
+            280
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "3. If you ran experiments... ",
+        "bbox": [
+            212,
+            285,
+            393,
+            299
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See https://github.com/wayveai/mile.   \n(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendix C and Appendix D.   \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] See Section 5.   \n(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Section 4. ",
+        "bbox": [
+            238,
+            303,
+            825,
+            435
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... ",
+        "bbox": [
+            222,
+            439,
+            823,
+            454
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "(a) If your work uses existing assets, did you cite the creators? [Yes]   \n(b) Did you mention the license of the assets? [Yes]   \n(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] See https://github.com/wayveai/mile.   \n(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   \n(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A] ",
+        "bbox": [
+            238,
+            458,
+            823,
+            579
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "5. If you used crowdsourcing or conducted research with human subjects... ",
+        "bbox": [
+            214,
+            583,
+            705,
+            598
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   \n(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   \n(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] ",
+        "bbox": [
+            238,
+            602,
+            825,
+            691
+        ],
+        "page_idx": 13
+    }
+]