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A novel mathematical framework that treats L1 and L2 (English) as
competing attractor fields in acoustic feature space.
The child's actual speech production is modeled as a state vector S in
high-dimensional acoustic space. Two attractor points -- A_L1 (L1 target)
and A_L2 (English target) -- exert competing pulls. The Contrastive Interference
Index (CII) measures where S falls between these attractors.
Supports multiple L1 languages: Bhojpuri, Hindi, Bangla, Odia.
Definitions:
CII(S) = d(S, A_L2) / (d(S, A_L1) + d(S, A_L2))
where d is weighted Mahalanobis distance.
CII = 0 -> perfect L2 (English) production
CII = 1 -> pure L1 transfer
CII = 0.5 -> equal pull from both languages
Per-dimension decomposition:
CII_phoneme, CII_prosody, CII_rhythm, CII_voice, CII_fluency
Trajectory prediction:
CII(t) = CII_0 * exp(-lambda * t) + CII_inf
Author: Neil Shankar Ray, IIT Patna
"""
from __future__ import annotations
import math
from dataclasses import dataclass, field
from typing import Any
import numpy as np
from scipy.optimize import curve_fit
# ββ Attractor definitions ββββββββββββββββββββββββββββββββββββββββββββββββ
# Each attractor is a dict of feature_name -> (expected_value, weight, natural_std)
# natural_std is used to normalize deviations (Mahalanobis-style)
# Per-L1 attractors: what L1-dominant speech sounds like for each language
L1_ATTRACTORS: dict[str, dict[str, tuple[float, float, float]]] = {
"bho": { # Bhojpuri: 6 vowels, strong retroflex, syllable-timed
"f1_mean": (620, 1.0, 80), "f2_mean": (1350, 1.0, 150),
"vowel_space_area": (130000, 1.2, 30000), "phoneme_accuracy": (0.45, 1.5, 0.15),
"interference_score": (70, 1.0, 15),
"npvi_v": (32, 1.3, 8), "percent_v": (58, 1.0, 5), "prosodic_score": (35, 1.0, 12),
"speech_rate_syl": (3.2, 0.8, 0.8), "pause_to_speech": (0.35, 0.8, 0.1),
"delta_c": (25, 1.0, 8),
"hnr": (11, 0.7, 4), "jitter": (0.025, 0.7, 0.01), "voice_quality_score": (55, 0.8, 12),
"fluency_score": (25, 1.2, 10), "coarticulation_index": (0.35, 1.0, 0.15),
"cognitive_load": (60, 0.8, 15),
},
"hin": { # Hindi: 10 vowels, retroflex, better English exposure typically
"f1_mean": (590, 1.0, 80), "f2_mean": (1400, 1.0, 150),
"vowel_space_area": (170000, 1.2, 35000), "phoneme_accuracy": (0.55, 1.5, 0.15),
"interference_score": (55, 1.0, 15),
"npvi_v": (35, 1.3, 8), "percent_v": (55, 1.0, 5), "prosodic_score": (42, 1.0, 12),
"speech_rate_syl": (3.5, 0.8, 0.8), "pause_to_speech": (0.30, 0.8, 0.1),
"delta_c": (30, 1.0, 8),
"hnr": (12, 0.7, 4), "jitter": (0.022, 0.7, 0.01), "voice_quality_score": (58, 0.8, 12),
"fluency_score": (32, 1.2, 10), "coarticulation_index": (0.40, 1.0, 0.15),
"cognitive_load": (52, 0.8, 15),
},
"ben": { # Bangla: 7 vowels, retroflex, strong nasalization
"f1_mean": (610, 1.0, 80), "f2_mean": (1380, 1.0, 150),
"vowel_space_area": (145000, 1.2, 30000), "phoneme_accuracy": (0.48, 1.5, 0.15),
"interference_score": (65, 1.0, 15),
"npvi_v": (30, 1.3, 8), "percent_v": (57, 1.0, 5), "prosodic_score": (38, 1.0, 12),
"speech_rate_syl": (3.3, 0.8, 0.8), "pause_to_speech": (0.33, 0.8, 0.1),
"delta_c": (27, 1.0, 8),
"hnr": (11, 0.7, 4), "jitter": (0.024, 0.7, 0.01), "voice_quality_score": (56, 0.8, 12),
"fluency_score": (28, 1.2, 10), "coarticulation_index": (0.37, 1.0, 0.15),
"cognitive_load": (58, 0.8, 15),
},
"ori": { # Odia: 6 vowels, strong retroflex, similar to Bhojpuri
"f1_mean": (615, 1.0, 80), "f2_mean": (1340, 1.0, 150),
"vowel_space_area": (135000, 1.2, 30000), "phoneme_accuracy": (0.47, 1.5, 0.15),
"interference_score": (68, 1.0, 15),
"npvi_v": (33, 1.3, 8), "percent_v": (57, 1.0, 5), "prosodic_score": (36, 1.0, 12),
"speech_rate_syl": (3.2, 0.8, 0.8), "pause_to_speech": (0.34, 0.8, 0.1),
"delta_c": (26, 1.0, 8),
"hnr": (11, 0.7, 4), "jitter": (0.024, 0.7, 0.01), "voice_quality_score": (55, 0.8, 12),
"fluency_score": (26, 1.2, 10), "coarticulation_index": (0.36, 1.0, 0.15),
"cognitive_load": (59, 0.8, 15),
},
}
DEFAULT_L1_CODE = "bho"
# English L2 attractor (what native-like English sounds like)
ATTRACTOR_L2: dict[str, tuple[float, float, float]] = {
# Phoneme features
"f1_mean": (480, 1.0, 80), # wider vowel space
"f2_mean": (1650, 1.0, 150), # broader F2 range
"vowel_space_area": (280000, 1.2, 40000), # larger VSA (12+ vowels)
"phoneme_accuracy": (0.88, 1.5, 0.08), # high accuracy
"interference_score": (10, 1.0, 8), # low interference
# Prosody features
"npvi_v": (62, 1.3, 8), # stress-timed
"percent_v": (42, 1.0, 5), # lower vocalic proportion
"prosodic_score": (82, 1.0, 10), # high nativeness
# Rhythm features
"speech_rate_syl": (5.0, 0.8, 0.8), # natural rate
"pause_to_speech": (0.18, 0.8, 0.06), # less pausing
"delta_c": (55, 1.0, 10), # high consonantal variability
# Voice quality features
"hnr": (18, 0.7, 4), # clear voice
"jitter": (0.012, 0.7, 0.005), # low jitter
"voice_quality_score": (80, 0.8, 8), # good quality
# Fluency features
"fluency_score": (70, 1.2, 12), # strong connected speech
"coarticulation_index": (0.75, 1.0, 0.12), # smooth coarticulation
"cognitive_load": (20, 0.8, 10), # low effort
}
# ββ Feature groupings for per-dimension CII ββββββββββββββββββββββββββββββ
DIMENSION_FEATURES: dict[str, list[str]] = {
"phoneme": ["f1_mean", "f2_mean", "vowel_space_area", "phoneme_accuracy", "interference_score"],
"prosody": ["npvi_v", "percent_v", "prosodic_score"],
"rhythm": ["speech_rate_syl", "pause_to_speech", "delta_c"],
"voice": ["hnr", "jitter", "voice_quality_score"],
"fluency": ["fluency_score", "coarticulation_index", "cognitive_load"],
}
# ββ Result dataclasses βββββββββββββββββββββββββββββββββββββββββββββββββββ
@dataclass
class DimensionCII:
name: str
cii: float # 0-1
severity: str # "Low", "Mild", "Moderate", "High", "Critical"
distance_to_l1: float
distance_to_l2: float
features_used: list[str]
bar: str # visual bar e.g. "ββββββββββ"
@dataclass
class TrajectoryPrediction:
cii_initial: float # CII_0
cii_residual: float # CII_inf (asymptotic floor)
decay_rate: float # lambda
predicted_cii_8w: float # predicted CII at 8 weeks
weeks_to_moderate: float | None # weeks to reach CII < 0.5
weeks_to_mild: float | None # weeks to reach CII < 0.3
confidence: str # "high", "moderate", "low"
@dataclass
class CIFResult:
overall_cii: float
overall_severity: str
dimensions: list[DimensionCII]
state_vector: dict[str, float]
trajectory: TrajectoryPrediction | None
methodology: str
# ββ Core math ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _weighted_mahalanobis(
state: dict[str, float],
attractor: dict[str, tuple[float, float, float]],
features: list[str],
) -> float:
"""Compute weighted Mahalanobis-style distance from state to attractor.
For each feature:
contribution = weight * ((state_val - attractor_val) / sigma)^2
Distance = sqrt(sum of contributions)
This normalizes each feature by its natural standard deviation (sigma)
so that all features contribute proportionally regardless of unit scale.
The weight further controls clinical importance.
"""
total = 0.0
n_used = 0
for feat in features:
if feat not in state or feat not in attractor:
continue
s_val = state[feat]
a_val, weight, sigma = attractor[feat]
if sigma <= 0:
continue
normalized_diff = (s_val - a_val) / sigma
total += weight * (normalized_diff ** 2)
n_used += 1
if n_used == 0:
return 0.0
# Normalize by number of features so dimensions with more features
# don't dominate the overall CII
return math.sqrt(total / n_used)
def _compute_cii(d_l1: float, d_l2: float) -> float:
"""CII = d(S, A_L2) / (d(S, A_L1) + d(S, A_L2))
Returns 0 when speech is at the English attractor,
1 when at the L1 attractor.
"""
denominator = d_l1 + d_l2
if denominator < 1e-10:
return 0.5 # equidistant / no signal
return d_l2 / denominator
def _classify_severity(cii: float) -> str:
if cii >= 0.75:
return "Critical"
elif cii >= 0.60:
return "High"
elif cii >= 0.45:
return "Moderate"
elif cii >= 0.25:
return "Mild"
else:
return "Low"
def _make_bar(cii: float, width: int = 10) -> str:
"""Generate visual bar: ββββββββββ"""
filled = max(0, min(width, round(cii * width)))
empty = width - filled
return "\u2588" * filled + "\u2591" * empty
# ββ Trajectory prediction ββββββββββββββββββββββββββββββββββββββββββββββββ
def _exponential_decay(t: np.ndarray, cii_0: float, lam: float, cii_inf: float) -> np.ndarray:
"""CII(t) = CII_0 * exp(-lambda * t) + CII_inf"""
return cii_0 * np.exp(-lam * t) + cii_inf
def predict_trajectory(
historical_ciis: list[tuple[float, float]], # [(week_number, cii_value), ...]
current_cii: float,
) -> TrajectoryPrediction:
"""Fit exponential decay to historical CII values and predict future.
If insufficient history, uses population-level defaults for lambda.
"""
confidence = "low"
if len(historical_ciis) >= 4:
# Enough data to fit the curve
try:
t_data = np.array([h[0] for h in historical_ciis])
cii_data = np.array([h[1] for h in historical_ciis])
# Initial guesses
p0 = [cii_data[0], 0.05, 0.15]
bounds = ([0, 0.001, 0], [1.5, 0.5, 0.8])
popt, pcov = curve_fit(_exponential_decay, t_data, cii_data, p0=p0, bounds=bounds, maxfev=5000)
cii_0, lam, cii_inf = popt
confidence = "high" if len(historical_ciis) >= 8 else "moderate"
except (RuntimeError, ValueError):
# Fit failed, use defaults
cii_0 = current_cii
lam = 0.034 # population average
cii_inf = 0.12
confidence = "low"
elif len(historical_ciis) >= 2:
# Minimal data β estimate lambda from two-point slope
t1, c1 = historical_ciis[0]
t2, c2 = historical_ciis[-1]
dt = t2 - t1
if dt > 0 and c1 > c2 and c1 > 0.15:
lam = -math.log(max(0.01, (c2 - 0.12) / (c1 - 0.12))) / dt
lam = max(0.005, min(0.3, lam))
else:
lam = 0.034
cii_0 = current_cii
cii_inf = 0.12
confidence = "low"
else:
# No history β use population defaults
cii_0 = current_cii
lam = 0.034
cii_inf = 0.12
confidence = "low"
# Predict at 8 weeks from now
predicted_8w = cii_0 * math.exp(-lam * 8) + cii_inf
# Weeks to reach moderate (CII < 0.5)
weeks_to_moderate = None
if current_cii >= 0.5 and cii_inf < 0.5:
target = 0.5 - cii_inf
if cii_0 > 0 and target > 0 and target < cii_0:
weeks_to_moderate = round(-math.log(target / cii_0) / lam, 1)
# Weeks to reach mild (CII < 0.3)
weeks_to_mild = None
if current_cii >= 0.3 and cii_inf < 0.3:
target = 0.3 - cii_inf
if cii_0 > 0 and target > 0 and target < cii_0:
weeks_to_mild = round(-math.log(target / cii_0) / lam, 1)
return TrajectoryPrediction(
cii_initial=round(cii_0, 4),
cii_residual=round(cii_inf, 4),
decay_rate=round(lam, 4),
predicted_cii_8w=round(max(cii_inf, predicted_8w), 4),
weeks_to_moderate=weeks_to_moderate,
weeks_to_mild=weeks_to_mild,
confidence=confidence,
)
# ββ Feature extraction from pipeline results βββββββββββββββββββββββββββββ
def _extract_state_vector(profile: dict[str, Any]) -> dict[str, float]:
"""Extract the acoustic state vector S from pipeline results.
Maps every relevant score/measurement from the 10-layer pipeline
into the feature space defined by the attractors.
"""
state: dict[str, float] = {}
# ββ From phoneme_analysis ββ
pa = profile.get("phoneme_analysis", {})
state["phoneme_accuracy"] = float(pa.get("overall_accuracy", 0))
state["interference_score"] = float(pa.get("interference_score", 50))
state["vowel_space_area"] = float(pa.get("vowel_space_area", 0))
formant_means = pa.get("formant_means", {})
state["f1_mean"] = float(formant_means.get("f1", 0))
state["f2_mean"] = float(formant_means.get("f2", 0))
# If phoneme_analysis formants are zero, try feature_extraction
if state["f1_mean"] == 0:
fe = profile.get("feature_extraction", {})
praat = fe.get("parselmouth", {})
formants = praat.get("formants", {})
state["f1_mean"] = float(formants.get("f1_mean", 0))
state["f2_mean"] = float(formants.get("f2_mean", 0))
if state["vowel_space_area"] == 0:
state["vowel_space_area"] = float(formants.get("vowel_space_area", 0))
# ββ From prosodic_profile ββ
pp = profile.get("prosodic_profile", {})
rhythm = pp.get("rhythm", {})
state["npvi_v"] = float(rhythm.get("npvi_v", 0))
state["percent_v"] = float(rhythm.get("percent_v", 50))
state["delta_c"] = float(rhythm.get("delta_c", 0))
state["prosodic_score"] = float(pp.get("prosodic_score", 50))
state["speech_rate_syl"] = float(pp.get("speech_rate_syl_per_sec", 0))
state["pause_to_speech"] = float(pp.get("pause_to_speech_ratio", 0))
# ββ From voice_quality ββ
vq = profile.get("voice_quality", {})
breathiness = vq.get("breathiness", {})
creakiness = vq.get("creakiness", {})
state["hnr"] = float(breathiness.get("hnr", 0))
state["jitter"] = float(creakiness.get("jitter_local", 0))
state["voice_quality_score"] = float(vq.get("overall_quality_score", 50))
# ββ From connected_speech ββ
cs = profile.get("connected_speech", {})
state["fluency_score"] = float(cs.get("fluency_score", 0))
state["coarticulation_index"] = float(cs.get("coarticulation_index", 0))
# ββ From morpheme_boundary ββ
mb = profile.get("morpheme_boundary", {})
cog = mb.get("cognitive_load", {})
state["cognitive_load"] = float(cog.get("score", 50))
return state
# ββ Main entry point βββββββββββββββββββββββββββββββββββββββββββββββββββββ
def compute_cif(
profile: dict[str, Any],
l1_code: str = DEFAULT_L1_CODE,
historical_ciis: list[tuple[float, float]] | None = None,
) -> dict[str, Any]:
"""Compute the Contrastive Interference Field analysis.
Args:
profile: Full pipeline result dict from _run_full_pipeline
l1_code: L1 language code ("bho", "hin", "ben", "ori")
historical_ciis: Optional list of (week, cii) tuples for trajectory fitting
Returns:
Dict suitable for JSON serialization containing full CIF analysis.
"""
state = _extract_state_vector(profile)
attractor_l1 = L1_ATTRACTORS.get(l1_code, L1_ATTRACTORS[DEFAULT_L1_CODE])
from modules.l1_targets import get_l1_profile
l1_profile = get_l1_profile(l1_code)
l1_display_name = l1_profile.display_name
# ββ Per-dimension CII ββ
dimensions: list[DimensionCII] = []
dimension_ciis: list[float] = []
dimension_weights: list[float] = []
for dim_name, features in DIMENSION_FEATURES.items():
d_l1 = _weighted_mahalanobis(state, attractor_l1, features)
d_l2 = _weighted_mahalanobis(state, ATTRACTOR_L2, features)
cii = _compute_cii(d_l1, d_l2)
# Weight dimensions by their clinical importance for overall CII
# Phoneme and rhythm deviations are the most perceptually salient
dim_weight = {
"phoneme": 1.5,
"prosody": 1.3,
"rhythm": 1.2,
"voice": 0.7,
"fluency": 1.3,
}.get(dim_name, 1.0)
dimensions.append(DimensionCII(
name=dim_name,
cii=round(cii, 4),
severity=_classify_severity(cii),
distance_to_l1=round(d_l1, 4),
distance_to_l2=round(d_l2, 4),
features_used=features,
bar=_make_bar(cii),
))
dimension_ciis.append(cii)
dimension_weights.append(dim_weight)
# ββ Overall CII (weighted average of dimension CIIs) ββ
w_arr = np.array(dimension_weights)
c_arr = np.array(dimension_ciis)
overall_cii = float(np.average(c_arr, weights=w_arr))
# ββ Trajectory prediction ββ
trajectory = None
if historical_ciis is not None:
trajectory = predict_trajectory(historical_ciis, overall_cii)
else:
# Still provide a default prediction using population lambda
trajectory = predict_trajectory([], overall_cii)
result = CIFResult(
overall_cii=round(overall_cii, 4),
overall_severity=_classify_severity(overall_cii),
dimensions=dimensions,
state_vector={k: round(v, 4) for k, v in state.items()},
trajectory=trajectory,
methodology=(
f"Contrastive Interference Field (CIF) Model v2.0 -- "
f"Weighted Mahalanobis distance from L1 ({l1_display_name}) and L2 (English) "
f"attractor points in 17-dimensional acoustic feature space. "
f"CII = d(S,A_L2) / (d(S,A_L1) + d(S,A_L2)). "
f"Trajectory: CII(t) = CII_0 * exp(-lambda*t) + CII_inf."
),
)
# Serialize to dict
return _serialize_cif(result)
def _serialize_cif(result: CIFResult) -> dict[str, Any]:
"""Convert CIFResult to a JSON-serializable dict."""
return {
"overall_cii": result.overall_cii,
"overall_severity": result.overall_severity,
"dimensions": [
{
"name": d.name.capitalize(),
"cii": d.cii,
"severity": d.severity,
"distance_to_l1": d.distance_to_l1,
"distance_to_l2": d.distance_to_l2,
"features_used": d.features_used,
"bar": d.bar,
}
for d in result.dimensions
],
"state_vector": result.state_vector,
"trajectory": {
"cii_initial": result.trajectory.cii_initial,
"cii_residual": result.trajectory.cii_residual,
"decay_rate": result.trajectory.decay_rate,
"predicted_cii_8w": result.trajectory.predicted_cii_8w,
"weeks_to_moderate": result.trajectory.weeks_to_moderate,
"weeks_to_mild": result.trajectory.weeks_to_mild,
"confidence": result.trajectory.confidence,
} if result.trajectory else None,
"methodology": result.methodology,
}
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