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Adaptive decoding controller implementing proposal Phase Four (closed loop).
Workflow (proposal):
Measure state → Compute MEA distance → Derive Reward → Compute TD Error
→ Adjust Decoding Parameters
Equations:
(xxii) s_t = {λ(model), λ(human), N̄, B̄, Q̄} [state representation]
(xxxiii) r_{t+1} = D(s_t, x) - D(s_{t+1}, x) [reward signal]
(xxxiv) V_ψ(s_t, x) ≈ E[ Σ_ℓ γ^ℓ r_{t+1+ℓ} | s_t, x ] [TD value function]
(xxxv) δ_t(x) = r_{t+1} + γ·V_ψ(s_{t+1}, x) - V_ψ(s_t, x) [TD error]
(xxxvi) V_ψ(s_t, x) ← V_ψ(s_t, x) + α·δ_t(x) [value update]
(xxxvii) θ_{t+1} = clip(θ_t + η·δ_t(x)·c, θ_min, θ_max) [decoding update]
θ_t = {τ_t, p_t, k_t}: temperature, top-p (nucleus), top-k.
c is the fixed heuristic control direction; it is chosen once per episode
from the dominant component of the MEA gap vector Δ(s_t, x) (Eq xxxi):
a novelty deficit points c toward more exploration (+τ, +p, +k), a bias
excess or quality deficit points it toward more conservative decoding
(-τ, -p, -k), and a decay mismatch follows the sign of λ(model)-λ(human).
Bootstrap of the first update: before any regeneration there is no observed
transition, so no δ_t exists yet. With V_ψ ≡ 0 initially, the expected
reward of moving from s_0 to the target end-state (distance 0) is
r̂ = D(s_0) - 0, hence δ_0 := D(s_0) ≥ 0 and the first action moves along c
with magnitude η·D(s_0). Every subsequent update uses the observed δ_t of
Equation (xxxv) exactly.
"""
from dataclasses import dataclass, field
from typing import Dict, List, Optional, Tuple
import math
@dataclass
class FrameworkState:
"""State representation s_t from Equation (xxii)."""
lambda_model: Optional[float]
lambda_human: float
aggregate_novelty: Optional[float]
aggregate_bias: Optional[float]
aggregate_quality: Optional[float]
def as_dict(self) -> Dict[str, Optional[float]]:
return {
"lambda_model": self.lambda_model,
"lambda_human": self.lambda_human,
"aggregate_novelty": self.aggregate_novelty,
"aggregate_bias": self.aggregate_bias,
"aggregate_quality": self.aggregate_quality,
}
def key(self, resolution: float = 0.05) -> str:
"""Discretised key for the tabular value function V_ψ."""
def bucket(v: Optional[float]) -> str:
if v is None:
return "na"
return str(round(float(v) / resolution) * resolution)
return "|".join([
bucket(self.lambda_model),
bucket(self.aggregate_novelty),
bucket(self.aggregate_bias),
bucket(self.aggregate_quality),
])
@dataclass
class DecodingParameters:
"""Decoding parameter vector θ_t = {τ_t, p_t, k_t}."""
temperature: float
top_p: float
top_k: int
def as_tuple(self) -> Tuple[float, float, int]:
return (self.temperature, self.top_p, self.top_k)
@dataclass
class ControlStep:
"""Record of one controller transition (for reports/audit)."""
theta_before: DecodingParameters
theta_after: DecodingParameters
distance_before: float
distance_after: Optional[float]
reward: Optional[float]
td_error: float
value_before: float
value_after: float
direction: Dict[str, float]
dominant_gap: str
rationale: str
class AdaptiveController:
"""
TD-driven adaptive decoding controller (Equations xxii, xxxiii-xxxvii).
"""
# Parameter bounds θ_min / θ_max used by the clip in Eq (xxxvii)
TEMP_MIN, TEMP_MAX = 0.20, 1.20
TOP_P_MIN, TOP_P_MAX = 0.70, 0.98
TOP_K_MIN, TOP_K_MAX = 10, 200
# Fixed heuristic control directions c per dominant gap component.
# Convention: c is the direction expected to REDUCE the dominant gap.
# Units are (temperature, top_p, top_k-fraction-of-range).
CONTROL_DIRECTIONS = {
"novelty_deficit": {"temperature": +1.0, "top_p": +0.3, "top_k": +0.5},
"bias_excess": {"temperature": -1.0, "top_p": -0.3, "top_k": -0.5},
"quality_deficit": {"temperature": -1.0, "top_p": -0.2, "top_k": -0.3},
# decay_mismatch direction is resolved at runtime from the sign of
# λ(model) - λ(human): faster-than-human decay needs exploration.
"decay_mismatch_fast": {"temperature": +1.0, "top_p": +0.3, "top_k": +0.5},
"decay_mismatch_slow": {"temperature": -0.5, "top_p": -0.15, "top_k": -0.25},
"none": {"temperature": 0.0, "top_p": 0.0, "top_k": 0.0},
}
def __init__(
self,
targets: Optional[Dict[str, float]] = None,
eta: float = 0.15,
gamma: float = 0.95,
alpha: float = 0.10,
human_lambda: float = 0.15,
state_resolution: float = 0.05,
):
"""
Args:
targets: Optional static fallback targets for the legacy API
eta: Adaptation rate η in Equation (xxxvii)
gamma: Discount factor γ in Equations (xxxiv)-(xxxv)
alpha: Value learning rate α in Equation (xxxvi)
human_lambda: Human decay baseline λ(human)
state_resolution: Discretisation step for the tabular V_ψ
"""
self.targets = targets or {}
self.eta = float(eta)
self.gamma = float(gamma)
self.alpha = float(alpha)
self.human_lambda = float(human_lambda)
self.state_resolution = float(state_resolution)
# Tabular value function V_ψ(s, x) and episode memory
self.value_table: Dict[str, float] = {}
self.history: List[ControlStep] = []
# Kept for backward compatibility with earlier experiments
self.q_table: Dict[str, Dict[str, float]] = {}
self.experience_buffer: List[Dict] = []
# ------------------------------------------------------------------
# State construction (Eq xxii)
# ------------------------------------------------------------------
def build_state(
self,
metrics: Dict[str, Optional[float]],
lambda_model: Optional[float] = None,
) -> FrameworkState:
"""Assemble s_t = {λ(model), λ(human), N̄, B̄, Q̄} from metrics."""
novelty = metrics.get("Novelty", metrics.get("novelty"))
bias = metrics.get("Bias Proxy", metrics.get("bias_proxy"))
quality = (
metrics.get("Quality (Q)")
or metrics.get("quality_q")
or metrics.get("BERTScore F1")
or metrics.get("bertscore")
or metrics.get("Fallback Quality")
or metrics.get("fallback_quality")
)
lam = lambda_model if lambda_model is not None else metrics.get(
"decay_rate", metrics.get("Decay Rate (λ)")
)
return FrameworkState(
lambda_model=_maybe_float(lam),
lambda_human=self.human_lambda,
aggregate_novelty=_maybe_float(novelty),
aggregate_bias=_maybe_float(bias),
aggregate_quality=_maybe_float(quality),
)
# ------------------------------------------------------------------
# Value function V_ψ (Eq xxxiv) with TD updates (Eq xxxv-xxxvi)
# ------------------------------------------------------------------
def value(self, state: FrameworkState) -> float:
"""Current estimate V_ψ(s, x)."""
return self.value_table.get(state.key(self.state_resolution), 0.0)
def compute_reward(self, distance_before: float, distance_after: float) -> float:
"""Reward signal from Equation (xxxiii): r_{t+1} = D(s_t) - D(s_{t+1})."""
return float(distance_before) - float(distance_after)
def compute_td_error(
self,
reward: float,
state: FrameworkState,
next_state: FrameworkState,
) -> float:
"""TD error from Equation (xxxv): δ_t = r + γ·V(s_{t+1}) - V(s_t)."""
return reward + self.gamma * self.value(next_state) - self.value(state)
def update_value(self, state: FrameworkState, td_error: float) -> float:
"""Value update from Equation (xxxvi): V(s_t) ← V(s_t) + α·δ_t."""
key = state.key(self.state_resolution)
self.value_table[key] = self.value_table.get(key, 0.0) + self.alpha * td_error
return self.value_table[key]
# ------------------------------------------------------------------
# Control direction c (fixed heuristic, resolved from the gap vector)
# ------------------------------------------------------------------
def select_control_direction(
self,
gap_vector: Dict[str, float],
state: FrameworkState,
) -> Tuple[str, Dict[str, float]]:
"""
Pick the fixed heuristic direction c from the dominant component of
the MEA gap vector Δ(s_t, x) (Eq xxxi).
"""
if not gap_vector:
return "none", dict(self.CONTROL_DIRECTIONS["none"])
dominant, value = max(gap_vector.items(), key=lambda kv: kv[1])
if value <= 1e-12:
return "none", dict(self.CONTROL_DIRECTIONS["none"])
if dominant == "decay_mismatch":
lam = state.lambda_model if state.lambda_model is not None else state.lambda_human
key = "decay_mismatch_fast" if lam >= state.lambda_human else "decay_mismatch_slow"
return dominant, dict(self.CONTROL_DIRECTIONS[key])
return dominant, dict(self.CONTROL_DIRECTIONS.get(dominant, self.CONTROL_DIRECTIONS["none"]))
# ------------------------------------------------------------------
# Parameter update θ_{t+1} = clip(θ_t + η·δ_t·c) (Eq xxxvii)
# ------------------------------------------------------------------
def apply_parameter_update(
self,
theta: DecodingParameters,
td_error: float,
direction: Dict[str, float],
) -> DecodingParameters:
"""Apply Equation (xxxvii) with per-parameter clipping."""
step = self.eta * td_error
new_temp = theta.temperature + step * direction.get("temperature", 0.0)
new_top_p = theta.top_p + step * direction.get("top_p", 0.0)
top_k_range = self.TOP_K_MAX - self.TOP_K_MIN
new_top_k = theta.top_k + step * direction.get("top_k", 0.0) * top_k_range
return DecodingParameters(
temperature=_clip(new_temp, self.TEMP_MIN, self.TEMP_MAX),
top_p=_clip(new_top_p, self.TOP_P_MIN, self.TOP_P_MAX),
top_k=int(round(_clip(new_top_k, self.TOP_K_MIN, self.TOP_K_MAX))),
)
# ------------------------------------------------------------------
# Episode API used by the application pipeline
# ------------------------------------------------------------------
def initial_step(
self,
state: FrameworkState,
distance_result: Dict,
theta: DecodingParameters,
) -> ControlStep:
"""
First controller action of an episode (bootstrap).
No transition has been observed yet, so with V_ψ ≡ 0 the expected
reward of reaching the target end-state (D = 0) is D(s_0), giving
δ_0 := D(s_0) + γ·V(s_0) - V(s_0-implicit-start) = D(s_0) when the
table is empty. The action direction is the fixed heuristic c for
the dominant gap.
"""
distance = float(distance_result.get("total_distance", 0.0))
gap_vector = distance_result.get("gap_vector", {}) or {}
dominant, direction = self.select_control_direction(gap_vector, state)
td_error = distance + self.gamma * self.value(state) - self.value(state)
theta_next = self.apply_parameter_update(theta, td_error, direction)
step = ControlStep(
theta_before=theta,
theta_after=theta_next,
distance_before=distance,
distance_after=None,
reward=None,
td_error=td_error,
value_before=self.value(state),
value_after=self.value(state),
direction=direction,
dominant_gap=dominant,
rationale=(
f"Bootstrap step: dominant gap '{dominant}' "
f"(D(s_0)={distance:.4f}); θ moved along fixed direction c "
f"with magnitude η·δ_0 = {self.eta:.2f}·{td_error:.4f}."
),
)
self.history.append(step)
return step
def transition_step(
self,
state: FrameworkState,
next_state: FrameworkState,
distance_before: Dict,
distance_after: Dict,
theta: DecodingParameters,
) -> ControlStep:
"""
Full observed transition: reward (Eq xxxiii), TD error (Eq xxxv),
value update (Eq xxxvi), and next parameter proposal (Eq xxxvii).
"""
d_before = float(distance_before.get("total_distance", 0.0))
d_after = float(distance_after.get("total_distance", 0.0))
reward = self.compute_reward(d_before, d_after)
td_error = self.compute_td_error(reward, state, next_state)
value_before = self.value(state)
value_after = self.update_value(state, td_error)
gap_vector = distance_after.get("gap_vector", {}) or {}
dominant, direction = self.select_control_direction(gap_vector, next_state)
theta_next = self.apply_parameter_update(theta, td_error, direction)
step = ControlStep(
theta_before=theta,
theta_after=theta_next,
distance_before=d_before,
distance_after=d_after,
reward=reward,
td_error=td_error,
value_before=value_before,
value_after=value_after,
direction=direction,
dominant_gap=dominant,
rationale=(
f"Observed transition: r={reward:+.4f} (Eq xxxiii), "
f"δ={td_error:+.4f} (Eq xxxv), V(s) {value_before:.4f}→{value_after:.4f} "
f"(Eq xxxvi); next dominant gap '{dominant}'."
),
)
self.history.append(step)
return step
@staticmethod
def describe_theta(theta: DecodingParameters) -> str:
return (
f"temperature={theta.temperature:.2f}, top_p={theta.top_p:.2f}, "
f"top_k={theta.top_k}"
)
# ------------------------------------------------------------------
# Legacy rule-based API (kept for CLI/backward compatibility).
# The TD-driven episode API above is the proposal-faithful path.
# ------------------------------------------------------------------
def recommend_parameters(
self,
metrics: Dict[str, Optional[float]],
current_temp: float,
current_top_p: float
) -> str:
"""Legacy heuristic recommendation (pre-TD fallback)."""
novelty = metrics.get("Novelty", metrics.get("novelty"))
self_bleu = metrics.get("Self-BLEU", metrics.get("self_bleu"))
quality = (
metrics.get("BERTScore F1")
or metrics.get("bertscore")
or metrics.get("Fallback Quality")
or metrics.get("fallback_quality")
)
bias = metrics.get("Bias Proxy", metrics.get("bias_proxy"))
ppl = metrics.get("Perplexity", metrics.get("perplexity"))
new_temp = float(current_temp)
new_top_p = float(current_top_p)
reasons = []
if novelty is not None and novelty < 0.35:
new_temp += 0.10
new_top_p += 0.03
reasons.append("novelty is below target (increase exploration)")
if self_bleu is not None and self_bleu > 45.0:
new_temp += 0.05
new_top_p += 0.03
reasons.append("Self-BLEU is high (increase diversity)")
if quality is not None and quality < 0.75:
new_temp -= 0.05
reasons.append("quality is below target (decrease randomness)")
if bias is not None and bias > 0.25:
new_temp -= 0.05
reasons.append("bias/risk proxy is above target (decrease randomness)")
if ppl is not None and math.isfinite(ppl) and ppl > 80.0:
new_temp -= 0.05
new_top_p -= 0.02
reasons.append("perplexity is high (decrease uncertainty)")
new_temp = _clip(new_temp, self.TEMP_MIN, self.TEMP_MAX)
new_top_p = _clip(new_top_p, self.TOP_P_MIN, self.TOP_P_MAX)
if not reasons:
reasons.append("metrics are close to target state")
return (
f"Suggested: temperature={new_temp:.2f}, top_p={new_top_p:.2f}. "
f"Reason: {', '.join(reasons)}"
)
def _clip(value: float, lo: float, hi: float) -> float:
return min(hi, max(lo, float(value)))
def _maybe_float(value) -> Optional[float]:
if value is None:
return None
try:
f = float(value)
except (TypeError, ValueError):
return None
if math.isnan(f) or math.isinf(f):
return None
return f
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