// Paradigm Bridge · Applied Mathematics for AI

Point us at your
most expensive
operations.

Mathematical methods and products that find and eliminate bottlenecks across AI pipelines and quantitative finance. Drop-in where possible, deep integration where it matters — no retraining required.

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θ correct error P(t) · PRM800K · r=0.9994 0 1
Works with
Anthropic
LLM judge · eval harness
🤗
Hugging Face
PRM800K · TRL · datasets
PyTorch
underlying framework
Ray Tune
HPO callback · early stopping
W&B
training monitoring
LangChain
RAG pipeline integration
EleutherAI
Pythia training suite
QuantConnect
backtesting acceleration
Products
Design-partner preview

Governor

A control layer for multi-agent systems

Agent swarms chain calls — one agent’s output feeds the next. When an agent goes wrong early, the rest confidently build on its garbage and you pay full price for all of it. Governor watches each agent’s health, catches the cascade as it starts to spread, and throttles the doomed work before it finishes — so you spend less, or spend the same budget on a better answer.

Built on Reasoning Chain Selection (r=0.9994, below) — the same P(t) signal, generalized from ranking reasoning chains to governing coupled agents. The method is validated; Governor is its productized form.
See Governor → Become a design partner
WatchOne-sided per-agent health — falls on degradation, ignores outperformance, doesn’t wash out slow drift.
DetectSelf-calibrating: learns the normal coupling between agents, fires when it breaks. No threshold to tune.
ActThrottle, not kill — a continuous dial on the failing branch. Bank the freed budget or reallocate it.
FitsLangGraph-first: reads your StateGraph edges as the coupling map. A wrapper, not a rewrite.
Next off the portfolio Caustic Retrieval — RAG routing Backtesting acceleration Adaptive risk OMS
Selected Results
Outside model
Live
−43.7%
zero accuracy loss · McNemar p=0.73 · n=500
Caustic Retrieval
Geometric query routing that determines which region of your corpus is relevant before any search occurs. 97% of RAG pipeline cost is corpus-side — that is where the savings land.
INTEGRATION
Drop in front of any RAG pipeline. Lightweight classifier on BGE-large embeddings. No retraining.
HOW TO USE
eval_harness.py · 27,671 cached judge entries · contact for access
Outside model
Live
92.7%
compute reduction · −0.008 coverage loss
Inference Stopping
P(t) monitors each reasoning chain during generation and stops ones showing degrading health early — before they waste compute on a chain that will be discarded anyway.
INTEGRATION
Callback in any sampling loop. Fires when P(t) drops below θ=0.40.
HOW TO USE
Paper_2_power_metric_inference.py · public on GitHub
Outside model
Live
0.9994
vs 0.529 baseline · 100% classification · in-sample
Reasoning Chain Selection
P(t) final health score ranks N candidate chains and selects the best — using the full trajectory, not just the last few steps. Zero additional model calls required.
INTEGRATION
Plug into any best-of-N loop. Requires step-level quality signal (PRM or confidence proxy).
HOW TO USE
Paper_18_Chain_v2.py · α=0.5 · θ=0.65 · public on GitHub
Inside model
Live
32/35
LCBench datasets · 37–45% compute saved
HPO Acceleration
P(t) early stopping outperforms successive halving on non-stationary learning curve datasets — the regime that characterizes most real training runs. Kills losers early, frees budget for promising configs.
INTEGRATION
Ray Tune or Optuna callback. Requires per-epoch validation metric stream.
HOW TO USE
Paper_7_power_metric_hpo.py · public on GitHub
Inside model
Live
97→1%
14 model variants · 70M–12B · 2 training regimes · α=0.6
Scaling Law Reliability
Adaptive baseline detects regime changes before you commit to expensive training runs. Validated across all 7 standard Pythia sizes plus 7 deduped variants — two independent training regimes. 13 of 14 variants hit 0% unreliability. 89.2% MAE reduction.
INTEGRATION
Run on early checkpoints before committing full training budget. No architecture changes.
HOW TO USE
Paper_3_scaling_UPDATED.py · public on GitHub
Inside model
Preliminary
−50%
91% alignment retained · simulation on published curves
Token Generation Cost
P(t) V2 + V9 detect the recall phase onset and plateau in token generation alignment trajectories, enabling mean pooling over only the high-signal window. Addresses the linear-in-T limitation identified by Wang et al. (2026).
INTEGRATION
Requires hidden state access during generation. Seeking Qwen3-14B validation partners.
STATUS
Simulation validated · real hidden-state validation in progress
Backtesting
Harness in progress
37–45%
compute saved · validated on HPO benchmarks
Backtesting Acceleration
P(t) prunes underperforming strategies early before they consume the full historical window. Same mechanism validated on 32/35 LCBench HPO datasets — structurally identical problem. Kill losers early, reallocate compute to viable strategies.
INTEGRATION
Callback in any backtesting framework — QuantConnect, Backtrader, or bespoke. Fires when strategy P(t) drops below threshold.
STATUS
Dedicated harness in progress · contact for early access
Live Trading
Available on request
Dynamic
real-time adaptive risk sizing · OMS layer
Adaptive Risk Allocation
P(t) as a real-time position sizing signal. When P(t) is high, allocate more. When it drops, cut exposure. Built on the patent-pending GBM + Ornstein-Uhlenbeck machinery — efficiency and win rate modeled as coupled stochastic processes.
INTEGRATION
OMS layer or risk engine plugin. Compatible with prop shop and quant fund infrastructure. NDA available.
STATUS
Patent pending · implementation available on request
Domain agnostic
Live
Same math
ML · finance · any sequential process
One Framework, Every Domain
The same P(t) signal that reduces RAG cost by 43.7% and accelerates HPO applies directly to strategy evaluation and live risk management. The patterns repeat. The math transfers.
INTEGRATION
Any sequential process with observable performance signal. No domain-specific tuning required.
HOW TO USE
21 papers · all code public · github.com/HauntedKernel/power-metric
Papers & Code
ML PIPELINE
01Training Health MonitoringReal · Pythia
02Inference Stopping (92.7% reduction)Real · GSM8K
03Scaling Law Reliability (97→1%)Real · 14 variants
04Per-Domain Training HealthReal · Pythia
05LIF Identity — Wiener-Hopf ProofTheory
06FlashAttention StackSim
07HPO Acceleration (32/35 LCBench)Real · LCBench
08Early Exit via LIF ThresholdSim
09Checkpoint SelectionSim
10Speculative DecodingSim
11MoE RoutingSim
12RLHF Reward Hacking DetectionSim
13Continual Learning (~89% retention)Sim
1498% Compute Waste Synthesis ↗Zenodo
16INGENIOUS + P(t) (+1.88–2.96% at scale)Real · Pythia
17Verifier Health Monitoring ↗Zenodo
INFERENCE + RETRIEVAL
18Chain Selection — r=0.9994 on PRM800KReal · 30,500 chains
21Caustic Retrieval + Adaptive Token PoolingReal + Sim
QUANT FINANCE
—Backtesting AccelerationIn progress
—Adaptive Risk Allocation OMSPatent pending
THEORETICAL FOUNDATION
05LIF ≡ P(t) via Wiener-Hopf (ε < 10⁻¹⁶)Theory
—Noether NESS Foundation (Paper 22)Drafting
VIEW ALL ON GITHUB →
FILE WHAT IT DOES STATUS LINK
Paper_21_caustic_retrieval.py Caustic Retrieval harness — 27,671 judge cache entries, IPW-corrected, MATH-500 + GSM8K LIVE GitHub ↗
Paper_18_Chain_v2.py Reasoning chain selection on PRM800K — r=0.9994, α=0.5, fixed neutral init LIVE GitHub ↗
Paper_2_power_metric_inference.py Inference stopping — kills bad chains early, 92.7% compute reduction LIVE GitHub ↗
Paper_7_power_metric_hpo.py HPO acceleration — P(t) early stopping, Ray Tune / Optuna callback LIVE GitHub ↗
Paper_3_scaling_UPDATED.py Scaling law reliability — 97→1% unreliable, 14 Pythia variants, α=0.6 LIVE GitHub ↗
Paper_1_power_metric_training.py Training health monitoring — Pythia empirical, checkpoint callback LIVE GitHub ↗
Paper_4_power_metric_mixing.py Per-domain training health — per-source signals LIVE GitHub ↗
Paper_16_ingenious.py INGENIOUS + P(t) — data selection + stopping, +1.88–2.96% at scale LIVE GitHub ↗
Paper_5_power_metric_lif_identity.py LIF identity proof — Wiener-Hopf, ε < 10⁻¹⁶ LIVE GitHub ↗
Paper_8_power_metric_early_exit.py Early exit via LIF threshold firing LIVE GitHub ↗
Paper_12_power_metric_rlhf.py RLHF reward hacking detection LIVE GitHub ↗
Paper_13_Catastrophic.py Continual learning forgetting detection LIVE GitHub ↗
VIEW FULL REPO ON GITHUB →