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+
+######################################################################
+
+2024 Jan 07 21:37:48 (from mygpt.py)
+
+
+# This is one order of magnitude more complicated than I expected, not
+# elegant, slow, hopefully not buggy
+
+
+def flash_back_time_src(N, H, t0, t1, CL, CH, proba, device):
+    # starting flash backs
+    fb_start = (torch.rand(N, CH, t1 - t0, device=device) <= proba).long()
+    fb_start[:, :, -CL:] = 0
+    fb_start[:, :, :CL] = 0
+
+    # Remove series longer than CL
+    fb_body = fb_start.clone()
+    fb_body[:, :, CL + 1 :] -= fb_start[:, :, : -(CL + 1)]
+    fb_body = fb_body.cumsum(dim=2)
+    fb_start = fb_start * (fb_body == 1)
+
+    # Set a origin source time (starting time of the chunck to copy
+    # here) We set it as the current time minus a multiple of CL to be
+    # consistent with the "rolling" caterpillar
+    t = torch.arange(fb_start.size(2), device=fb_start.device)[None, None, :]
+    src_time = fb_start * (
+        t
+        - CL
+        * (
+            1
+            + (
+                torch.rand(fb_start.size(), device=fb_start.device) * (t // CL - 1)
+            ).long()
+        )
+    )
+    src_time[:, :, CL:] -= src_time.clone()[:, :, :-CL]
+    src_time = src_time.cumsum(dim=2)
+
+    src_head = fb_start * torch.randint(H, fb_start.size(), device=fb_start.device)
+    src_head[:, :, CL:] -= src_head.clone()[:, :, :-CL]
+    src_head = src_head.cumsum(dim=2)
+
+    # combine
+    src_delta = fb_start.clone()
+    src_delta[:, :, CL:] -= fb_start[:, :, :-CL]
+    src_delta = src_delta.cumsum(dim=2)
+    src_delta[:, :, CL:] -= CL * fb_start[:, :, :-CL]
+    src_time += src_delta.cumsum(dim=2) - 1
+
+    return src_time, src_head
+
+
+def insert_flash_back(rec_V, V, rec_K, K, t0, t1, CL, proba):
+    N, H, CH = V.size(0), V.size(1), rec_V.size(1)
+
+    fbt, fbh = flash_back_time_src(N, H, t0, t1, CL, CH, proba, rec_V.device)
+
+    fbt_V = fbt[:, :, :, None]
+    fbh_V = fbh[:, :, :, None]
+    t = fbt_V.clamp(min=0)
+    n = torch.arange(V.size(0), device=V.device)[:, None, None, None]
+    d = torch.arange(V.size(3), device=V.device)[None, None, None, :]
+    q = V[:, :, t0:t1][n, fbh_V, t, d]
+    rec_V[:, :, t0:t1] = q * (fbt_V >= 0) + rec_V[:, :, t0:t1] * (fbt_V < 0)
+
+    fbt_K = fbt[:, :, :, None]
+    fbh_K = fbh[:, :, :, None]
+    t = fbt_K.clamp(min=0)
+    n = torch.arange(K.size(0), device=K.device)[:, None, None, None]
+    d = torch.arange(K.size(3), device=K.device)[None, None, None, :]
+    q = K[:, :, t0:t1][n, fbh_K, t, d]
+    rec_K[:, :, t0:t1] = q * (fbt_K >= 0) + rec_K[:, :, t0:t1] * (fbt_K < 0)
+
+
+######################################################################