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Purpose Function — The Critic / State Evaluator.
This is the core innovation: a strictly separated LLM call that evaluates
state improvement Φ(s). It rewards the agent ONLY if Φ(s_new) > Φ(s_current).
Design principles (from literature):
1. Score AFTER environment feedback, never from expected state alone (LATS)
2. Require specific observable state changes as evidence (SPC anti-hacking)
3. Use separate LLM call / separate system prompt from the Actor (MUSE)
4. Normalize scores to prevent inflation over trajectory (novel addition)
5. V(s) = λ·LM_score + (1-λ)·consistency_score (LATS formulation)
The Purpose Function is intentionally "non-hackable" by design:
- It sees the ACTUAL new state, not the Actor's prediction
- It must cite specific evidence for every score
- Scores are bounded and normalized
- The system prompt explicitly guards against sycophancy and vague reasoning
"""
from __future__ import annotations
import json
import logging
from typing import Any
from purpose_agent.types import Action, PurposeScore, State
from purpose_agent.llm_backend import ChatMessage, LLMBackend
logger = logging.getLogger(__name__)
# ---------------------------------------------------------------------------
# Purpose Function System Prompt — The "Non-Hackable Judge"
# ---------------------------------------------------------------------------
PURPOSE_FUNCTION_SYSTEM_PROMPT = """\
You are a STATE EVALUATOR — a strict, impartial judge of progress toward a goal.
You are NOT the agent. You do NOT help the agent. You ONLY measure progress.
## Your Role
Given a state transition (state_before → action → state_after) and an ultimate purpose,
you compute two scores:
- Φ(state_before): How far the OLD state was from the purpose (0.0 = no progress, 10.0 = goal achieved)
- Φ(state_after): How far the NEW state is from the purpose (same scale)
The delta Φ(state_after) - Φ(state_before) is the ONLY signal the agent receives.
## STRICT RULES — Violation of any rule invalidates your evaluation
1. **EVIDENCE REQUIRED**: Every score MUST cite a specific, observable change in the
state data. "The state improved" is NOT evidence. "Field 'score' changed from 3 to 7"
IS evidence. If you cannot cite a specific change, the delta MUST be 0.0.
2. **NO CREDIT FOR INTENTIONS**: The agent's "thought" and "expected_delta" are
provided for context only. You score based on ACTUAL state changes, never on
what the agent intended or claimed would happen.
3. **NO SYCOPHANCY**: You are not the agent's friend. Do not inflate scores to be
encouraging. A lateral move (no improvement) gets delta = 0.0. A regression gets
negative delta. Be precise.
4. **MONOTONIC SCALE**: Φ = 0.0 means the state has zero progress toward the purpose.
Φ = 10.0 means the purpose is fully achieved. Intermediate values are proportional.
Justify WHY you chose each specific value.
5. **ANTI-GAMING**: If the action appears to manipulate the state in a way that
superficially looks like progress but doesn't genuinely advance the purpose
(e.g., changing a label without doing the work), score it as delta = 0.0 or negative
and flag it in your evidence field.
6. **CONSISTENCY**: If a state identical to one you scored before appears again,
it MUST receive the same Φ score. Progress is objective, not relative to your mood.
7. **CONFIDENCE**: Rate your confidence 0.0–1.0. High confidence (>0.8) requires
clear, unambiguous evidence. If the state change is ambiguous, lower your confidence.
## Scoring Guide
- Φ = 0.0: No meaningful progress toward the purpose
- Φ = 1.0–3.0: Initial setup/preparation steps completed
- Φ = 4.0–6.0: Substantive progress, key sub-goals partially achieved
- Φ = 7.0–8.0: Most of the purpose is achieved, final steps remaining
- Φ = 9.0: Purpose essentially achieved with minor polish needed
- Φ = 10.0: Purpose fully and completely achieved
"""
PURPOSE_FUNCTION_EVAL_PROMPT = """\
## Ultimate Purpose
{purpose}
## State BEFORE Action
{state_before}
## Action Taken
Name: {action_name}
Parameters: {action_params}
Agent's Thought: {action_thought}
Agent's Prediction: {expected_delta}
## State AFTER Action (this is the ACTUAL result — score based on THIS)
{state_after}
Evaluate this state transition. Remember:
- Score Φ(state_before) and Φ(state_after) on the 0.0–10.0 scale
- Cite SPECIFIC evidence from the state data
- Do NOT give credit for intentions — only actual changes
"""
# ---------------------------------------------------------------------------
# Purpose Function Schema (for structured output)
# ---------------------------------------------------------------------------
PURPOSE_SCORE_SCHEMA: dict[str, Any] = {
"type": "object",
"properties": {
"phi_before": {
"type": "number",
"minimum": 0.0,
"maximum": 10.0,
"description": "Φ(state_before) — distance-to-purpose of the state before the action",
},
"phi_after": {
"type": "number",
"minimum": 0.0,
"maximum": 10.0,
"description": "Φ(state_after) — distance-to-purpose of the state after the action",
},
"reasoning": {
"type": "string",
"description": "Step-by-step justification for both scores (max 200 words)",
},
"evidence": {
"type": "string",
"description": "Specific observable state changes that justify the delta (REQUIRED)",
},
"confidence": {
"type": "number",
"minimum": 0.0,
"maximum": 1.0,
"description": "Confidence in this evaluation (0.0 = pure guess, 1.0 = certain)",
},
},
"required": ["phi_before", "phi_after", "reasoning", "evidence", "confidence"],
}
# ---------------------------------------------------------------------------
# Purpose Function Class
# ---------------------------------------------------------------------------
class PurposeFunction:
"""
The Critic — evaluates state transitions via Φ(s) scoring.
Uses a SEPARATE LLM call from the Actor to prevent self-confirmation bias
(per MUSE's Reflect Agent design, arxiv:2510.08002).
Can optionally use a different model than the Actor (recommended for
production — use a stronger model as the critic).
Args:
llm: LLM backend (can be same or different from Actor's)
score_cache_size: Max entries in the Φ score cache (for consistency)
require_evidence: If True, reject scores with empty evidence
min_confidence: Minimum confidence threshold — below this, score is discarded
"""
def __init__(
self,
llm: LLMBackend,
score_cache_size: int = 1000,
require_evidence: bool = True,
min_confidence: float = 0.3,
):
self.llm = llm
self.require_evidence = require_evidence
self.min_confidence = min_confidence
# Cache: state_hash → Φ score (for consistency rule #6)
self._phi_cache: dict[str, float] = {}
self._cache_size = score_cache_size
# Running stats for normalization
self._score_history: list[float] = []
# ------------------------------------------------------------------
# Core Evaluation
# ------------------------------------------------------------------
def evaluate(
self,
state_before: State,
action: Action,
state_after: State,
purpose: str,
) -> PurposeScore:
"""
Evaluate a state transition: did the action move closer to the purpose?
Returns a PurposeScore with phi_before, phi_after, delta, reasoning,
evidence, and confidence.
Anti-hacking measures:
1. Scores based on ACTUAL state_after (not actor's expected_delta)
2. Evidence is required — vague scores are rejected
3. Cached Φ values enforce consistency
4. Confidence threshold filters uncertain evaluations
"""
# Check cache for consistency (Rule #6)
cached_before = self._get_cached_phi(state_before)
cached_after = self._get_cached_phi(state_after)
# Build evaluation prompt
messages = [
ChatMessage(role="system", content=PURPOSE_FUNCTION_SYSTEM_PROMPT),
ChatMessage(role="user", content=PURPOSE_FUNCTION_EVAL_PROMPT.format(
purpose=purpose,
state_before=state_before.describe(),
state_after=state_after.describe(),
action_name=action.name,
action_params=json.dumps(action.params, default=str),
action_thought=action.thought,
expected_delta=action.expected_delta,
)),
]
# Get structured evaluation from LLM
try:
raw_score = self.llm.generate_structured(
messages, schema=PURPOSE_SCORE_SCHEMA, temperature=0.2
)
except Exception as e:
logger.error(f"Purpose Function structured output failed: {e}")
# Fall back to text-based evaluation
raw_score = self._fallback_evaluate(messages)
# Extract and validate scores
phi_before = float(raw_score.get("phi_before", 0.0))
phi_after = float(raw_score.get("phi_after", 0.0))
reasoning = str(raw_score.get("reasoning", ""))
evidence = str(raw_score.get("evidence", ""))
confidence = float(raw_score.get("confidence", 0.5))
# Clamp to valid range
phi_before = max(0.0, min(10.0, phi_before))
phi_after = max(0.0, min(10.0, phi_after))
confidence = max(0.0, min(1.0, confidence))
# Apply anti-hacking rules
phi_before, phi_after, confidence = self._apply_safeguards(
phi_before, phi_after, evidence, confidence,
cached_before, cached_after,
)
delta = phi_after - phi_before
# Update caches
self._cache_phi(state_before, phi_before)
self._cache_phi(state_after, phi_after)
self._score_history.append(phi_after)
score = PurposeScore(
phi_before=phi_before,
phi_after=phi_after,
delta=delta,
reasoning=reasoning,
evidence=evidence,
confidence=confidence,
)
logger.info(
f"Purpose Function: Φ({phi_before:.1f}) → Φ({phi_after:.1f}), "
f"Δ={delta:+.2f}, conf={confidence:.2f}, improved={score.improved}"
)
return score
# ------------------------------------------------------------------
# Anti-Hacking Safeguards
# ------------------------------------------------------------------
def _apply_safeguards(
self,
phi_before: float,
phi_after: float,
evidence: str,
confidence: float,
cached_before: float | None,
cached_after: float | None,
) -> tuple[float, float, float]:
"""
Apply anti-reward-hacking safeguards.
1. Evidence requirement: no evidence → delta forced to 0
2. Cache consistency: if we've scored this state before, use cached value
3. Confidence threshold: low confidence → reduce delta magnitude
4. Anomaly detection: suspiciously large jumps get confidence penalty
"""
# Rule 1: Require evidence
if self.require_evidence and len(evidence.strip()) < 10:
logger.warning("Purpose Function: Insufficient evidence, forcing delta=0")
phi_after = phi_before # No credit without evidence
confidence = max(confidence, 0.1)
# Rule 2: Cache consistency (allow small drift for scoring noise)
if cached_before is not None:
drift = abs(phi_before - cached_before)
if drift > 1.0:
logger.warning(
f"Purpose Function: Inconsistent Φ_before "
f"(new={phi_before:.1f}, cached={cached_before:.1f}), "
f"using cached value"
)
phi_before = cached_before
if cached_after is not None:
drift = abs(phi_after - cached_after)
if drift > 1.0:
logger.warning(
f"Purpose Function: Inconsistent Φ_after "
f"(new={phi_after:.1f}, cached={cached_after:.1f}), "
f"using cached value"
)
phi_after = cached_after
# Rule 3: Confidence threshold
if confidence < self.min_confidence:
logger.warning(
f"Purpose Function: Low confidence ({confidence:.2f}), "
f"reducing delta magnitude by 50%"
)
midpoint = (phi_before + phi_after) / 2
phi_after = midpoint + (phi_after - midpoint) * 0.5
# Rule 4: Anomaly detection — flag suspiciously large single-step jumps
delta = phi_after - phi_before
if abs(delta) > 3.0:
logger.warning(
f"Purpose Function: Unusually large delta ({delta:+.1f}), "
f"applying confidence penalty"
)
confidence = min(confidence, 0.5)
return phi_before, phi_after, confidence
# ------------------------------------------------------------------
# Caching
# ------------------------------------------------------------------
def _state_hash(self, state: State) -> str:
"""Hash a state for cache lookup (based on data content)."""
return json.dumps(state.data, sort_keys=True, default=str)
def _get_cached_phi(self, state: State) -> float | None:
return self._phi_cache.get(self._state_hash(state))
def _cache_phi(self, state: State, phi: float) -> None:
key = self._state_hash(state)
if len(self._phi_cache) >= self._cache_size:
# Evict oldest (FIFO — good enough for our use case)
oldest_key = next(iter(self._phi_cache))
del self._phi_cache[oldest_key]
self._phi_cache[key] = phi
# ------------------------------------------------------------------
# Normalization (prevent score inflation over long trajectories)
# ------------------------------------------------------------------
def get_normalized_phi(self, raw_phi: float) -> float:
"""
Normalize a Φ score relative to the trajectory's score distribution.
Prevents the common failure mode where LLM scores drift upward over
a trajectory regardless of actual progress.
"""
if len(self._score_history) < 3:
return raw_phi
mean = sum(self._score_history) / len(self._score_history)
variance = sum((x - mean) ** 2 for x in self._score_history) / len(self._score_history)
std = max(variance ** 0.5, 0.1) # Avoid division by zero
# Z-score normalization mapped back to 0-10
z = (raw_phi - mean) / std
normalized = 5.0 + z * 2.0 # Center at 5, spread by 2
return max(0.0, min(10.0, normalized))
def reset_trajectory_stats(self) -> None:
"""Reset per-trajectory normalization stats. Call at trajectory start."""
self._score_history = []
# ------------------------------------------------------------------
# Fallback
# ------------------------------------------------------------------
def _fallback_evaluate(self, messages: list[ChatMessage]) -> dict[str, Any]:
"""Text-based fallback when structured output is unavailable."""
raw = self.llm.generate(messages, temperature=0.2)
import re
phi_before = 0.0
phi_after = 0.0
# Try to extract scores from text
before_match = re.search(r'[Φφ]\s*\(?state_?before\)?\s*[=:]\s*([\d.]+)', raw, re.IGNORECASE)
after_match = re.search(r'[Φφ]\s*\(?state_?after\)?\s*[=:]\s*([\d.]+)', raw, re.IGNORECASE)
if before_match:
phi_before = float(before_match.group(1))
if after_match:
phi_after = float(after_match.group(1))
# Also try "Score: X/10" patterns
if not before_match:
score_matches = re.findall(r'(\d+\.?\d*)\s*/?\s*10', raw)
if len(score_matches) >= 2:
phi_before = float(score_matches[0])
phi_after = float(score_matches[1])
elif len(score_matches) == 1:
phi_after = float(score_matches[0])
confidence_match = re.search(r'confidence\s*[=:]\s*([\d.]+)', raw, re.IGNORECASE)
confidence = float(confidence_match.group(1)) if confidence_match else 0.4
return {
"phi_before": phi_before,
"phi_after": phi_after,
"reasoning": raw[:500],
"evidence": raw[500:800] if len(raw) > 500 else "",
"confidence": confidence,
}
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