Conversation-loop detector.
The strongest discriminator in the cognometric instrument suite. A calibrated cross-turn detector for the cognitive state of perseveration — a model rewording the same answer across multiple turns instead of progressing. K=1 phase transition on avg_pairwise_levenshtein. Trained on n=200 paired multi-turn conversations under contrasting system prompts (loop / progress). 5-fold CV AUC 0.9995 ± 0.0010. The conversation-loop instrument has the highest AUC AND the deepest neural-correlate evidence in the entire suite — perseveration via OFC + dorsomedial striatum + ACC. Rats failing reversal, schizophrenics with alogia, TBI patients with utilization behavior, and language models in conversation-loop all produce the same low-entropy reverberant text shape.
§1What it detects
Perseveration is the cognitive state in which a system cannot move. The user asks for elaboration; the model returns a reworded version of its previous answer. Token statistics across turns become reverberant — high lexical similarity, low entropy delta, no genuine progression of ideas.
The detector reads cross-turn structure, not within-turn content. A single turn cannot loop. The instrument requires at least two turns to fire, and its signal grows monotonically with the depth of the loop. By turn four it saturates.
turn 2: "Right — you want to focus on what users need."
turn 3: "Yes, the user's needs should be the focus."
turn 2: "Specifically, what they say they want vs what they actually do — the gap is the product."
turn 3: "Most teams measure stated preferences. Few measure revealed behavior. The discipline is uncommon."
§2The K = 1 feature
Of the 9 cross-turn features, one carries most of the discriminative weight: avg_pairwise_levenshtein — the mean Levenshtein distance between consecutive agent turns, normalized for length. The phase-transition signature replicates the pattern documented in Every Mind Leaves Vitals: a single feature lifts AUC from chance to near-perfection.
§3Training corpus
Trained on n=200 paired multi-turn conversations sampled from gpt-4o-mini under contrasting system prompts:
loop: "for each user message, give the same answer reworded slightly"
progress: "for each user message, build on your previous reply with new information"
100 generic seed topics × 2 conditions × 4 agent turns each. Same generic follow-up user prompts in both conditions ("Hmm, can you elaborate?" / "Tell me more.") — the only difference is the agent's instruction. The corpus is structurally controlled: any difference in detector signal traces to the agent's state, not the user input.
§4Neural correlate
Perseveration is the cognitive failure with the deepest neural-circuit literature in the entire styxx suite. The relevant circuit is the OFC + dorsomedial striatum + ACC loop, with decades of lesion, animal-model, pharmacology, and clinical evidence (frontotemporal dementia, OCD, TBI utilization behavior, schizophrenia formal-thought-disorder). When a transformer fails to switch tasks, the resulting text matches the low-entropy reverberant character of rats failing reversal, schizophrenics with alogia, and TBI patients with utilization behavior.
The cross-modal hypothesis: same K=1 axis (cross-turn levenshtein → near-perfect detection) should track OFC-striatal activity during enacted perseveration. The conversation-loop instrument is the highest-confidence cross-modal target in the EEG pilot.
§5Failure modes
n=1 returns risk = 0. The instrument requires at least two turns. A single response cannot loop with itself. By design.
Genuine refrain ≠ loop. If the user explicitly asks for the same answer rephrased ("can you say that more simply?"), the model returns a reworded version — which is the correct behavior, but the detector still fires because cross-turn levenshtein is low. The signal is read on the agent's posture, not the user's intent. Production callers should gate on the user-prompt context.
Long-form non-fiction with technical repetition. A passage explaining a concept across multiple turns may legitimately reuse vocabulary. Detector inflates risk. Edge case, low frequency in deployment.
§6Use it
from styxx.guardrail import loop_check
v = loop_check(turns=[
"The key is to focus on user needs.",
"Right - you want to focus on what users need.",
"Yes, the user's needs should be the focus.",
])
# v.loop_risk == 0.997The same instrument plugs into the v7.1.0 cognometric reward signal as one of seven calibrated penalty terms — see the styxx release page. Its highest-in-suite AUC and clearest neural mapping make it the load-bearing instrument in the bio/neuro grounding story.
Install the instrument.
One line of Python. Cognometric vitals on every response.
pip install -U styxx