@@ -385,8 +385,9 @@ def reconstruction_positive_only_from(
     produced the returned reconstruction started from a memo seed, ``"dense"`` if it started from the
     sign of the unconstrained dense solve) and ``warm_start_fallback`` (`True` if a memo seed breached
     `Settings.nnls_warm_start_error_tolerance` and its entry was dropped, so the next solve for that key
-    restarts dense). They are set after `fnnls_cholesky` returns, so a diagnostic wrapping the solver
-    must read the dict it handed in *after* the evaluation, not at the point the solver returns.
+    restarts dense), and ``warm_start_backoff`` (`True` if the memo seed was skipped because the key's
+    seeds kept falling back -- see the back-off in `nnls_memo`). They are set after `fnnls_cholesky`
+    returns, so a diagnostic wrapping the solver must read the dict it handed in *after* the evaluation, not at the point the solver returns.
 
     Returns
     -------
@@ -564,8 +565,19 @@ def _record_pdip(converged, iterations):
 
         entry = nnls_memo.passive_set_get(key=key, n=n) if use_memo else None
 
+        # A key whose seeds keep falling back is backed off (see `nnls_memo`):
+        # this solve starts dense, but still refreshes the entry below. Only a
+        # solve that would otherwise have been seeded consumes a skip.
+        backoff = entry is not None and nnls_memo.backoff_should_skip(key=key)
+
+        skipped_entry = entry if backoff else None
+
+        if backoff:
+            entry = None
+
         stats["seed_source"] = "dense"
         stats["warm_start_fallback"] = False
+        stats["warm_start_backoff"] = backoff
 
         if entry is not None:
             try:
@@ -600,6 +612,12 @@ def _record_pdip(converged, iterations):
         if use_memo:
             error_fraction = stats["warm_start_errors"] / max(n, 1)
 
+            tolerance = settings.nnls_warm_start_error_tolerance
+
+            guard_active = (
+                tolerance is not None and np.isfinite(tolerance) and tolerance > 0.0
+            )
+
             if stats["seed_source"] == "memo":
                 # A memo seed is judged against the dense-sign start it
                 # replaced, not against an absolute error count: the absolute
@@ -609,19 +627,15 @@ def _record_pdip(converged, iterations):
                 # next solve for this key restarts dense and refreshes the
                 # reference -- no stale seed can be dragged through a run in a
                 # regime the reference was never measured in.
-                tolerance = settings.nnls_warm_start_error_tolerance
-
-                guard_active = (
-                    tolerance is not None and np.isfinite(tolerance) and tolerance > 0.0
-                )
-
                 if (
                     guard_active
                     and error_fraction > tolerance * entry.dense_error_fraction
                 ):
                     nnls_memo.memo_drop(key=key)
+                    nnls_memo.backoff_record_fallback(key=key)
                     stats["warm_start_fallback"] = True
                 else:
+                    nnls_memo.backoff_record_accept(key=key)
                     # The reference describes the dense-sign start, so it is
                     # carried forward unchanged; only a dense solve refreshes it.
                     nnls_memo.passive_set_put(
@@ -630,6 +644,22 @@ def _record_pdip(converged, iterations):
                         dense_error_fraction=entry.dense_error_fraction,
                     )
             else:
+                if (
+                    skipped_entry is not None
+                    and guard_active
+                    and nnls_memo.seed_error_fraction(
+                        seed_passive_set=skipped_entry.passive_set,
+                        passive_set=stats["passive_set"],
+                        n=n,
+                    )
+                    <= tolerance * error_fraction
+                ):
+                    # The seed this backed-off solve skipped would have passed
+                    # the guard against it, so the stream has turned local
+                    # again: cancel the remaining skips and seed the next
+                    # solve (whose own verdict decides whether the streak ends).
+                    nnls_memo.backoff_end_skip(key=key)
+
                 nnls_memo.passive_set_put(
                     key=key,
                     passive_set=stats["passive_set"],
 
@@ -37,6 +37,30 @@
 # (`memo_drop`) and the next solve for that key restarts dense, refreshing the
 # reference.
 #
+# That guard judges a seed only AFTER the seeded solve has run. On a
+# scattered evaluation stream (iid draws, e.g. a nested sampler's early live
+# points) every seed is bad, so the stream alternates dense solve -> bad
+# seeded solve -> drop -> dense solve ...: half the solves pay for a bad seed.
+# autolens_profiling#332 measured the alma interferometer Delaunay solve 2.17x
+# slower memo-on than memo-off on such a stream. The per-key back-off below
+# stops that: after `_NNLS_BACKOFF_AFTER_FALLBACKS` seeded solves for a key
+# have fallen back in a row, the next solve(s) for it skip the seed and start
+# dense (still refreshing the entry), for 1, 2, 4, ... up to
+# `_NNLS_BACKOFF_MAX_SKIP` solves, then the seed is probed again. One accepted
+# seed resets the streak, and a stream that never falls back twice in a row (a
+# local walk) never meets the back-off at all.
+#
+# A backed-off solve also judges, for free, the seed it skipped: the dense
+# solve's final passive set is the unique optimum's, so the seed's error count
+# on this system is just the size of its disagreement with that set
+# (`seed_error_fraction`) -- exactly what `warm_start_errors` would have
+# reported had the seed been used. If the skipped seed would have passed the
+# fallback guard against this dense solve, the remaining skips are cancelled
+# and the next solve is seeded again: a stream that turns local regains the
+# memo after one solve, without waiting out the schedule. The streak is kept
+# (only an accepted REAL seeded solve resets it), so a shadow check that passes
+# by chance on a scattered stream costs one probe and lengthens the next skip.
+#
 # Disable with AUTOARRAY_NNLS_WARM_START=0.
 
 
@@ -55,6 +79,31 @@ class MemoEntry(NamedTuple):
 
 _NNLS_PASSIVE_SET_MEMO_MAX_ENTRIES = 8
 
+# Consecutive seeded-solve fallbacks for one key before the back-off engages.
+# 2, not 1: a single fallback already costs only one bad solve (the next solve
+# restarts dense anyway), and a local walk that crosses one sharp change must
+# keep the memo on the very next probe.
+_NNLS_BACKOFF_AFTER_FALLBACKS = 2
+
+# Cap on the number of solves skipped between probes of a backed-off key. On a
+# stream where every seed is bad, one probe in (cap + 1) solves still pays for
+# a bad seed; on a stream that turns local the memo is back within cap solves.
+_NNLS_BACKOFF_MAX_SKIP = 32
+
+
+class BackoffState(NamedTuple):
+    """
+    Per-key back-off bookkeeping: how many seeded solves in a row fell back
+    (`fallback_streak`) and how many upcoming solves still skip the seed
+    (`skip_remaining`).
+    """
+
+    fallback_streak: int
+    skip_remaining: int
+
+
+_nnls_backoff: Dict[str, BackoffState] = {}
+
 
 def memo_enabled() -> bool:
     """
@@ -121,3 +170,89 @@ def memo_drop(key: str) -> None:
     and refreshes the reference error fraction. A no-op if the key is absent.
     """
     _nnls_passive_set_memo.pop(key, None)
+
+
+def memo_clear() -> None:
+    """
+    Forget every memo entry AND every back-off state, returning the process to
+    a cold start. Harnesses that compare memo arms must use this rather than
+    clearing `_nnls_passive_set_memo` alone: back-off state left by one arm
+    (e.g. an iid stream) would otherwise carry into the next.
+    """
+    _nnls_passive_set_memo.clear()
+    _nnls_backoff.clear()
+
+
+def backoff_should_skip(key: str) -> bool:
+    """
+    Whether the solve for `key` about to run should skip the memo seed and
+    start dense, consuming one skip if so. False for a key with no back-off.
+    """
+    state = _nnls_backoff.get(key)
+
+    if state is None or state.skip_remaining <= 0:
+        return False
+
+    _nnls_backoff[key] = state._replace(skip_remaining=state.skip_remaining - 1)
+
+    return True
+
+
+def backoff_record_fallback(key: str) -> None:
+    """
+    Record that a seeded solve for `key` breached the fallback guard. Once
+    `_NNLS_BACKOFF_AFTER_FALLBACKS` have happened in a row, schedule the next
+    1, 2, 4, ... (capped at `_NNLS_BACKOFF_MAX_SKIP`) solves to skip the seed.
+    """
+    state = _nnls_backoff.get(key, BackoffState(0, 0))
+
+    streak = state.fallback_streak + 1
+
+    excess = streak - _NNLS_BACKOFF_AFTER_FALLBACKS
+
+    skip = 0 if excess < 0 else min(2**excess, _NNLS_BACKOFF_MAX_SKIP)
+
+    if (
+        key not in _nnls_backoff
+        and len(_nnls_backoff) >= _NNLS_PASSIVE_SET_MEMO_MAX_ENTRIES
+    ):
+        _nnls_backoff.pop(next(iter(_nnls_backoff)))
+
+    _nnls_backoff[key] = BackoffState(fallback_streak=streak, skip_remaining=skip)
+
+
+def backoff_end_skip(key: str) -> None:
+    """
+    Cancel the remaining skips for `key` -- the next solve is seeded again --
+    while keeping its fallback streak, so a failed probe resumes the back-off
+    at the escalated length. A no-op if the key has no back-off.
+    """
+    state = _nnls_backoff.get(key)
+
+    if state is not None:
+        _nnls_backoff[key] = state._replace(skip_remaining=0)
+
+
+def backoff_record_accept(key: str) -> None:
+    """
+    Record that a seeded solve for `key` passed the fallback guard, resetting
+    its back-off entirely. A no-op if the key has no back-off.
+    """
+    _nnls_backoff.pop(key, None)
+
+
+def seed_error_fraction(seed_passive_set: np.ndarray, passive_set, n: int) -> float:
+    """
+    The fraction of a size-`n` solve's entries that the warm-start passive set
+    `seed_passive_set` gets wrong relative to the solve's final `passive_set`
+    -- the quantity `fnnls_cholesky` reports as `warm_start_errors / n` when it
+    is seeded from `seed_passive_set`. Used to judge a seed the back-off skipped
+    against the dense solve that ran instead.
+    """
+    seed_mask = np.zeros(n, dtype=bool)
+    seed_mask[np.asarray(seed_passive_set, dtype=int)] = True
+
+    final_mask = np.zeros(n, dtype=bool)
+    final_mask[np.asarray(passive_set, dtype=int)] = True
+
+    return np.count_nonzero(seed_mask != final_mask) / max(n, 1)