diff --git a/arrayjit/lib/cuda_backend.cudajit.ml b/arrayjit/lib/cuda_backend.cudajit.ml
index 7d8fc68a..16db6903 100644
--- a/arrayjit/lib/cuda_backend.cudajit.ml
+++ b/arrayjit/lib/cuda_backend.cudajit.ml
@@ -30,10 +30,6 @@ type device = {
   cross_stream_candidates : ctx_array Hashtbl.M(Tn).t;
       (** Freshly created arrays that might be shared across streams. The map can both grow and
           shrink. See the explanation on top of this file. *)
-  cross_stream_shared : Hash_set.M(Tn).t;
-      (** Tensor nodes known to be cross-stream shared. This set can only grow. *)
-  non_cross_stream : Hash_set.M(Tn).t;
-      (** Tensor nodes known to not be cross-stream shared. This set can only grow. *)
   owner_stream_subordinal : int Hashtbl.M(Tn).t;
       (** The streams owning the given nodes. This map can only grow. *)
 }
@@ -77,7 +73,6 @@ let is_done event = Cu.Delimited_event.query event
 let will_wait_for context event = Cu.Delimited_event.wait context.stream.cu_stream event
 let sync event = Cu.Delimited_event.synchronize event
 let all_work stream = Cu.Delimited_event.record stream.cu_stream
-
 let scheduled_merge_node stream = Option.map ~f:snd stream.merge_buffer
 
 let is_initialized, initialize =
@@ -152,8 +147,6 @@ let get_device ~(ordinal : int) : device =
           copy_merge_buffer_capacity;
           released = Atomic.make false;
           cross_stream_candidates = (Hashtbl.create (module Tn) : ctx_array Hashtbl.M(Tn).t);
-          cross_stream_shared = Hash_set.create (module Tn);
-          non_cross_stream = Hash_set.create (module Tn);
           owner_stream_subordinal = Hashtbl.create (module Tn);
         }
       in
@@ -275,9 +268,7 @@ let%diagn2_l_sexp rec device_to_device (tn : Tn.t) ~into_merge_buffer ~(dst : co
         ~src:s_arr.ptr ~src_ctx:src.ctx dst.stream.cu_stream
   in
   if
-    same_device
-    && (src.stream.subordinal = dst.stream.subordinal
-       || Hash_set.mem dst.stream.device.cross_stream_shared tn)
+    same_device && (src.stream.subordinal = dst.stream.subordinal || Tn.known_shared_cross_stream tn)
   then false
   else
     match Map.find src.ctx_arrays tn with
@@ -559,10 +550,11 @@ let link_proc ~prior_context ~name ~(params : (string * param_source) list) ~ctx
         work;
       } )
 
-let%diagn2_sexp alloc_if_needed ctx stream ~key ~data:node ctx_arrays =
+let%track3_sexp alloc_if_needed ctx stream ~key ~data:node ctx_arrays =
   if is_in_context node && not (Map.mem ctx_arrays key) then (
-    [%log Tn.debug_name key, "read_only", (node.read_only : bool)];
-    let default () =
+    [%log2 Tn.debug_name key, "read_only", (node.read_only : bool)];
+    [%log3 (key : Tn.t)];
+    let default () : ctx_array =
       set_ctx ctx;
       let ptr = Cu.Deviceptr.mem_alloc ~size_in_bytes:(Tn.size_in_bytes key) in
       { ptr; tracking = None }
@@ -570,13 +562,13 @@ let%diagn2_sexp alloc_if_needed ctx stream ~key ~data:node ctx_arrays =
     let add_new () = Map.add_exn ctx_arrays ~key ~data:(default ()) in
     let device = stream.device in
     if node.read_only then
-      if Hash_set.mem device.non_cross_stream key then add_new ()
+      if Tn.known_non_cross_stream key then add_new ()
       else (
         if Hashtbl.mem device.cross_stream_candidates key then
-          Hash_set.add device.cross_stream_shared key;
+          Tn.update_memory_sharing key Tn.Shared_cross_stream 40;
         let data = Hashtbl.find_or_add device.cross_stream_candidates key ~default in
         Map.add_exn ctx_arrays ~key ~data)
-    else if Hash_set.mem device.cross_stream_shared key then (
+    else if Tn.known_shared_cross_stream key then (
       if Hashtbl.mem device.owner_stream_subordinal key then
         if Hashtbl.find_exn device.owner_stream_subordinal key <> stream.subordinal then
           raise
@@ -587,7 +579,7 @@ let%diagn2_sexp alloc_if_needed ctx stream ~key ~data:node ctx_arrays =
       let data = Hashtbl.find_exn device.cross_stream_candidates key in
       Map.add_exn ctx_arrays ~key ~data)
     else (
-      Hash_set.add device.non_cross_stream key;
+      Tn.update_memory_sharing key Tn.Per_stream 41;
       Hashtbl.remove device.cross_stream_candidates key;
       add_new ()))
   else ctx_arrays
diff --git a/arrayjit/lib/tnode.ml b/arrayjit/lib/tnode.ml
index 12a70e99..97bc4f86 100644
--- a/arrayjit/lib/tnode.ml
+++ b/arrayjit/lib/tnode.ml
@@ -132,16 +132,13 @@ let log_debug_info ~from_log_level tn =
         | (lazy (Some nd)) -> Nd.log_debug_info ~from_log_level nd
       else [%log "<not-in-yet>"]]]
 
-(** The one exception to "most local" is the sharing property: defaults to [Shared_cross_stream]. *)
+(** The one exception to "most local" is that the sharing property is kept at [Unset]. *)
 let default_to_most_local tn provenance =
   match tn.memory_mode with
   | None | Some (Effectively_constant, _) -> tn.memory_mode <- Some (Virtual, provenance)
   | Some (Never_virtual, _) -> tn.memory_mode <- Some (Local, provenance)
   | Some (Device_only, _) -> tn.memory_mode <- Some (Local, provenance)
-  | Some (Materialized, _) -> tn.memory_mode <- Some (On_device Shared_cross_stream, provenance)
-  | Some (On_device Unset, _) -> tn.memory_mode <- Some (On_device Shared_cross_stream, provenance)
-  | Some (Hosted (Changed_on_devices Unset), _) ->
-      tn.memory_mode <- Some (Hosted (Changed_on_devices Shared_cross_stream), provenance)
+  | Some (Materialized, _) -> tn.memory_mode <- Some (On_device Unset, provenance)
   | Some ((Virtual | Local | On_device _ | Hosted _), _) -> ()
 
 let is_virtual_force tn provenance =
@@ -194,6 +191,18 @@ let known_not_param tn =
       true
   | _ -> false
 
+let known_shared_cross_stream tn =
+  match tn.memory_mode with
+  | Some ((On_device Shared_cross_stream | Hosted (Changed_on_devices Shared_cross_stream)), _) ->
+      true
+  | _ -> false
+
+let known_non_cross_stream tn =
+  match tn.memory_mode with
+  | Some ((On_device Per_stream | Hosted (Changed_on_devices Per_stream)), _) ->
+      true
+  | _ -> false
+
 let mode_is_unspecified tn =
   match tn.memory_mode with
   | None | Some ((Never_virtual | Effectively_constant), _) -> true
@@ -246,7 +255,7 @@ let update_memory_sharing tn sharing provenance =
            [%string
              "Tnode.update_memory_sharing: update %{prov2#Int} -> %{provenance#Int} for \
               %{debug_name tn} -- change from non-shared to shared is currently not permitted"]
-  | Some ((On_device _ | Device_only | Materialized), _), Shared_cross_stream ->
+  | Some ((On_device _ | Device_only | Materialized), _), _ ->
       tn.memory_mode <- Some (On_device sharing, provenance)
   | Some (Hosted (Changed_on_devices Per_stream), prov2), Shared_cross_stream ->
       raise
diff --git a/bin/hello_world.ml b/bin/hello_world.ml
index d1c4ec47..32556541 100644
--- a/bin/hello_world.ml
+++ b/bin/hello_world.ml
@@ -11,7 +11,7 @@ module Rand = Arrayjit.Rand.Lib
 let hello1 () =
   Rand.init 0;
   let module Backend = (val Arrayjit.Backends.fresh_backend ()) in
-  Utils.set_log_level 2;
+  (* Utils.set_log_level 2; *)
   (* Utils.settings.output_debug_files_in_build_directory <- true; *)
   let stream = Backend.(new_stream @@ get_device ~ordinal:0) in
   let ctx = Backend.init stream in