Optimize partial trace definition

pytensor/link/jax/dispatch/scan.py

@@ -209,18 +209,28 @@ def jax_funcify_Scan(op: Scan, **kwargs):
             ):
                 if init_state is not None:
                     # MIT-SOT and SIT-SOT: The final output should be as long as the input buffer
-                    trace = jnp.atleast_1d(trace)
-                    init_state = jnp.expand_dims(
-                        init_state, range(trace.ndim - init_state.ndim)
-                    )
-                    full_trace = jnp.concatenate([init_state, trace], axis=0)
                     buffer_size = buffer.shape[0]
+                    if trace.shape[0] > buffer_size:
+                        # Trace is longer than buffer, keep just the last `buffer.shape[0]` entries
+                        partial_trace = trace[-buffer_size:]
+                    else:
+                        # Trace is shorter than buffer, this happens when we keep the initial_state
+                        if init_state.ndim < buffer.ndim:
+                            init_state = init_state[None]
+                        if (
+                            n_init_needed := buffer_size - trace.shape[0]
+                        ) < init_state.shape[0]:
+                            # We may not need to keep all the initial states
+                            init_state = init_state[-n_init_needed:]
+                        partial_trace = jnp.concatenate([init_state, trace], axis=0)
                 else:
                     # NIT-SOT: Buffer is just the number of entries that should be returned
-                    full_trace = jnp.atleast_1d(trace)
                     buffer_size = buffer
+                    partial_trace = (
+                        trace[-buffer_size:] if trace.shape[0] > buffer else trace
+                    )
 
-                partial_trace = full_trace[-buffer_size:]
+                assert partial_trace.shape[0] == buffer_size
                 partial_traces.append(partial_trace)
 
             return partial_traces