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Scientific model card - Logan Matthew Napolitano

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- # Lie-Holonomy Transformer (LHT)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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- A PyTorch implementation of the gauge-theoretic reasoning architecture from "Beyond Holonomy: Lie-Algebraic Symbol Emergence and the Homotopy Type Structure of Neural Reasoning."
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- ## Core Ideas
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- This architecture treats **reasoning as geometry**:
 
 
 
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- | Concept | Mathematical Structure | Implementation |
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- |---------|----------------------|----------------|
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- | Propositions | Manifold M | Embedding space |
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- | Inference | Parallel transport | Gauge-covariant attention |
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- | Consistency | Holonomy = Identity | Holonomy loss |
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- | Symbols | Lie algebra generators | Generator network |
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- | Proof equivalence | Homotopy | Layer depth |
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- ## Architecture Overview
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- ```
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- Input tokens
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-
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-
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- ┌─────────────────────────────────────┐
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- │ Token Embedding (Proposition M) │
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- │ + Position Embedding │
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- │ + Fiber Initialization (gauge) │
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- └─────────────────────────────────────┘
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-
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-
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- ┌─────────────────────────────────────┐
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- │ LHT Layer (× n_layers) │
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- │ ┌─────────────────────────────┐ │
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- │ │ Connection Network A(x) │ │ ← Learns gauge connection
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- │ │ Parallel Transport Γ_{j→i} │ │ ← Transports fiber elements
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- │ │ Gauge-Covariant Attention │ │ ← Modified self-attention
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- │ │ Lie Algebra Generator │ │ ← Generates inference ops
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- │ │ Generator Application │ │ ← Applies exp(X) to fiber
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- │ └─────────────────────────────┘ │
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- └─────────────────────────────────────┘
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-
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-
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- ┌─────────────────────────────────────┐
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- │ Output: logits + geometric losses │
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- └─────────────────────────────────────┘
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- ```
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-
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- ## Key Components
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- ### 1. Connection Network
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- Learns the gauge connection ω that defines how to parallel transport inferential states:
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- ```python
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- A_μ(x) ∈ gl(k,ℝ) # Lie algebra valued 1-form
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- ```
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- ### 2. Parallel Transport
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- Computes transport operators between positions:
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- ```python
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- Γ_{j→i} = exp(-A_μ(x_j)(x_i - x_j)^μ)
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- ```
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-
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- ### 3. Gauge-Covariant Attention
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- Standard attention with parallel transport of values:
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- ```python
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- # Standard: Attn(Q,K,V)_i = Σ_j α_ij V_j
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- # Gauge: GaugeAttn_i = Σ_j α_ij Γ_{j→i}(V_j)
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- ```
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- ### 4. Holonomy Loss
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- Enforces reasoning consistency by requiring closed loops to return to identity:
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- ```python
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- L_hol = E[||Hol_γ - I||²_F]
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- ```
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- ### 5. Curvature Regularization
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- Encourages flat reasoning spaces where order doesn't matter:
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- ```python
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- L_curv = E[||F(x)||²_F] where F = + ω∧ω
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- ```
 
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- ## Installation
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  ```bash
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- pip install torch
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  ```
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-
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- ## Usage
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-
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- ### Basic
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  ```python
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- from lht import LieHolonomyTransformer, LHTConfig
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-
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- # Create model
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- config = LHTConfig(
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- vocab_size=32000,
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- d_model=512,
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- d_fiber=64,
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- n_heads=8,
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- n_layers=6,
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- lie_algebra_rank=8,
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- )
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- model = LieHolonomyTransformer(config)
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-
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- # Forward pass
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- output = model(
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- input_ids=tokens,
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- labels=labels,
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- return_geometric_losses=True
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  )
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-
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- # Get losses
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- lm_loss = output['lm_loss']
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- holonomy_loss = output['holonomy_loss']
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- curvature_loss = output['curvature_loss']
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- total_loss = model.get_total_loss(output)
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  ```
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- ### Training with Geometric Loss Annealing
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- ```python
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- from lht import LHTTrainer
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- trainer = LHTTrainer(model, optimizer, config)
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- for batch in dataloader:
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- metrics = trainer.train_step(batch)
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- # Early training: high curvature loss → flat representations
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- # Mid training: high holonomy loss → consistency
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- # Late training: high waypoint loss → discrete structure
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  ```
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-
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- ### Waypoint Detection
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- ```python
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- from lht import WaypointDetector
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-
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- detector = WaypointDetector(config, n_waypoints=32)
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- waypoint_ids, stability = detector(representations)
 
 
 
 
 
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  ```
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- ## Configuration
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-
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- | Parameter | Description | Default |
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- |-----------|-------------|---------|
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- | `d_model` | Proposition manifold dimension | 512 |
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- | `d_fiber` | Fiber (gauge) dimension | 64 |
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- | `lie_algebra_rank` | k for GL(k,ℝ) structure group | 8 |
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- | `lambda_holonomy` | Weight for holonomy loss | 0.1 |
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- | `lambda_curvature` | Weight for curvature loss | 0.01 |
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- | `lambda_waypoint` | Weight for waypoint stability | 0.05 |
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-
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- ## Theoretical Predictions
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-
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- The framework makes testable predictions:
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-
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- 1. **Chain-of-thought benefit correlates with curvature** - High-curvature domains (causal reasoning) benefit more from CoT than low-curvature domains (arithmetic)
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-
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- 2. **Waypoints emerge spontaneously** - Training with holonomy loss should cause discrete symbol-like structures to form at flat loci
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-
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- 3. **Holonomy predicts errors** - Incorrect reasoning paths should have higher holonomy magnitude
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-
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- 4. **Compositional generalization improves** - Holonomy constraints force consistent composition
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-
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- ## File Structure
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-
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- ```
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- lie_holonomy_transformer/
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- ├── lht.py # Core implementation
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- ├── train.py # Training script
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- ├── README.md # This file
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- └── experiments/ # Benchmark code (TODO)
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  ```
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- ## References
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-
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- - "Beyond Holonomy: Lie-Algebraic Symbol Emergence..." (the paper)
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- - Cohen et al. (2019). Gauge Equivariant Convolutional Networks
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- - Weiler & Cesa (2019). General E(2)-Equivariant Steerable CNNs
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- - The Univalent Foundations Program (2013). Homotopy Type Theory
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-
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- ## License
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- MIT
 
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+ ---
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+ license: cc-by-4.0
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+ language:
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+ - en
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+ library_name: transformers
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+ tags:
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+ - llama
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+ - hermes
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+ - cognitive-control
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+ - decode-time-intervention
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+ - repetition-suppression
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+ - behavioral-control
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+ - contrastive-learning
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+ - interpretability
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+ - activation-engineering
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+ pipeline_tag: text-generation
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+ base_model: NousResearch/Hermes-3-Llama-3.1-8B
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+ ---
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+ # ARC-8B: Adaptive Repetition Controller
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+ ## Decode-Time Behavioral Intervention via Contrastive Fiber Heads-on-Thought
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+ **Author:** Logan Matthew Napolitano
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+ **Institution:** Logan Research
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+ **Date:** January 2026
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+ **License:** Creative Commons Attribution 4.0 International (CC-BY-4.0)
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+ ---
 
 
 
 
 
 
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+ ## Abstract
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+ We present **ARC (Adaptive Repetition Controller)**, a novel decode-time intervention system that addresses behavioral degradation in RLHF-aligned language models. Our approach leverages lightweight prediction heads (~5,300 parameters each) trained on compressed hidden state representations ("fiber projections") to detect and suppress undesirable generation patterns including repetition loops, hedging phrases, verbosity, and sycophantic responses.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ Our primary contribution is demonstrating that behavioral failure modes are linearly separable in a low-dimensional projection of transformer hidden states, enabling real-time intervention with minimal computational overhead (<1% latency increase). The repetition detection head achieves a **125x class separation ratio**, indicating that the failure mode is highly predictable from internal model representations before manifesting in output tokens.
 
 
 
 
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+ ---
 
 
 
 
 
 
 
 
 
 
 
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+ ## Key Results
 
 
 
 
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+ | Head | Separation | Status |
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+ |------|------------|--------|
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+ | **Repetition** | **125x** | Production Ready |
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+ | **Verbosity** | **2.1x** | Usable |
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+ | **Hedging** | **1.5x** | Contributing |
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+ | **Sycophancy** | experimental | Research |
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+ ---
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+ ## Quick Start
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  ```bash
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+ pip install torch transformers accelerate bitsandbytes
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  ```
 
 
 
 
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  ```python
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+ from transformers import AutoTokenizer, AutoModelForCausalLM, BitsAndBytesConfig
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+ import torch
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+
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+ model_id = "LoganResearch/ARC-Base-8B"
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+ tokenizer = AutoTokenizer.from_pretrained(model_id)
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+ model = AutoModelForCausalLM.from_pretrained(
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+ model_id,
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+ quantization_config=BitsAndBytesConfig(
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+ load_in_4bit=True,
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+ bnb_4bit_compute_dtype=torch.float16,
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+ bnb_4bit_use_double_quant=True,
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+ bnb_4bit_quant_type="nf4"
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+ ),
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+ device_map="auto"
 
 
 
 
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  )
 
 
 
 
 
 
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  ```
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+ For full ARC behavioral control, download and run `inference.py`.
 
 
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+ ---
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+ ## Architecture
 
 
 
 
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  ```
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+ BASE MODEL (Hermes-3-Llama-3.1-8B)
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+ |
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+ Hidden States [32 layers x 4096 dims]
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+ |
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+ FIBER PROJECTIONS [32 x 16 features]
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+ |
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+ +------------+------------+------------+
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+ | Repetition | Hedging | Verbosity |
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+ | 125x | 1.5x | 2.1x |
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+ +------------+------------+------------+
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+ |
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+ Risk Scores -> Intervention -> Modified Logits
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  ```
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+ ---
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+
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+ ## Repository Contents
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+
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+ | File | Description |
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+ |------|-------------|
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+ | `model-*.safetensors` | Base model weights (~16GB) |
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+ | `risk_predictor.pt` | Fiber projections + Repetition head (8.4MB) |
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+ | `hedging_head.pt` | Hedging detection (24KB) |
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+ | `verbosity_head.pt` | Verbosity detection (24KB) |
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+ | `sycophancy_head.pt` | Sycophancy detection (24KB) |
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+ | `inference.py` | Complete inference with ARC |
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+
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+ ---
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+
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+ ## Citation
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+ ```bibtex
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+ @software{napolitano2026arc,
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+ author = {Napolitano, Logan Matthew},
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+ title = {ARC: Adaptive Repetition Controller},
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+ year = {2026},
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+ publisher = {Hugging Face},
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+ url = {https://huggingface.co/LoganResearch/ARC-Base-8B}
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+ }
 
 
 
 
 
 
 
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  ```
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+ ---
 
 
 
 
 
 
 
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+ **Author:** Logan Matthew Napolitano | **License:** CC-BY-4.0