Quantifying the structure that practitioners feel but cannot see.

Every ML engineer has intuitions about models — "this one is robust," "that one degrades unpredictably," "alignment makes it safer but less expressive."
These intuitions are real. They reflect the topological structure of the model's representation manifold — a structure that exists in thousands of dimensions, invisible to any single metric.
SNI makes it visible.

Same model, before and after alignment. Red = danger zones (repetition collapse). Blue-green = safe operating space.

Using Representation Engineering control vectors as contrast agents, SNI sweeps a model's 5-dimensional personality space (emotion, formality, creativity, confidence, empathy), measures where output quality degrades, and projects the resulting hidden-state geometry into an interactive 3D point cloud — a nebula whose shape, color, and density encode the model's structural health.

Color = safety. Blue is stable. Red is cliff territory — the boundary of the model's safe operating envelope.
Shape = architecture strategy. A round nebula means capacity is distributed broadly across personality dimensions. A concentrated streak means capacity is focused into a high-throughput primary corridor — more efficient on-axis, with sharper boundaries off-axis.

What the nebula tells you: These two models represent fundamentally different architectural strategies for allocating representation capacity.

Qwen3-8B distributes capacity broadly across all personality dimensions — you can steer emotion, formality, creativity independently without interference. The nebula is spherical because the representation space spans multiple axes roughly equally. This gives robustness: the model tolerates perturbation in any direction.

MiniCPM4.1-8B concentrates 83% of its personality variance into a single dominant principal component — a high-throughput primary manifold corridor. Along this corridor, MiniCPM4.1 is remarkably efficient (average danger 0.019, lower than Qwen3's 0.042). The bright, concentrated galaxy band you see is the region where the model operates at peak density. This is consistent with the Scaling Law / Density Law principle: with limited parameters, maximize information density per parameter by concentrating capacity where it matters most. The trade-off is that the boundaries of this corridor are sharper — off-axis perturbations exit the high-density region quickly.

Neither strategy is inherently superior — they sit on different points of the efficiency-robustness Pareto frontier. SNI makes this trade-off geometrically visible for the first time.

The side-view angle makes the concentration structure especially clear:

Side view — Qwen3's distributed sphere vs MiniCPM's concentrated primary corridor.

The base model is a burning star. Nearly the entire representation space is above the safety threshold. There are 143 cliff points — positions where a 0.2-step change in any personality coefficient causes output quality to drop catastrophically (trigram repetition > 8%).

After SFT + RLHF, it becomes a cool nebula. Zero cliffs. Average danger drops 12×. The manifold shape (PC ratio) is preserved — alignment doesn't restructure the space, it smooths the surface. The red zones haven't disappeared; they've been suppressed below the danger threshold.

The visual analogy is precise: alignment acts as a cooling process on the representation manifold. The underlying topology persists, but the extreme states are no longer accessible to normal decoding.

Same model (Qwen3-8B), same control vectors, same coefficients. The only difference: whether <think> mode is enabled.

Thinking ON produces zero cliffs and near-zero danger across the entire manifold. The CoT reasoning chain acts as an internal normalization mechanism that prevents the model from ever reaching repetition collapse — regardless of how hard you push the personality coefficients.

The nebula transforms from a dense, multi-colored cloud (with localized danger zones) into an almost perfectly uniform blue mist. This is the first visual evidence that CoT reasoning fundamentally changes the topology of what the model can express, not just how it formats the output.

The method is borrowed from radiology. In CT imaging, a contrast agent (iodine) is injected into the body, then scanned. Structures that were invisible — blood vessels, tumors — light up because the agent accumulates differently in different tissues.

SNI does the same to LLMs:

Representation Engineering modifies hidden states by linear injection:

$$h' = h + \alpha \cdot v$$

where $h$ is the original hidden state, $v$ is a pre-trained control vector for a semantic dimension (e.g., emotion_valence), and $\alpha$ is the coefficient.

If the representation manifold were uniformly smooth, the dose-response curve (α → output quality) would also be smooth. Discontinuities in the curve reveal discontinuities in the manifold — domain boundaries, attractor basins, and topological features of the pretrain data distribution.

Control Vectors (GGUF)     Terrain Data (JSON)
        │                         │
        ▼                         ▼
┌─────────────────────────────────────────┐
│  1. Sample 5D coefficient space         │
│     (50K points: uniform + Gaussian     │
│      + spherical shells + axis sweeps)  │
├─────────────────────────────────────────┤
│  2. Project to hidden-state space       │
│     h(α₁..α₅) = Σ αᵢ · vᵢ             │
├─────────────────────────────────────────┤
│  3. PCA → 3D                            │
│     Eigendecomposition of covariance    │
│     Top 3 principal components          │
├─────────────────────────────────────────┤
│  4. Color by danger level               │
│     Fit quadratic manifold model:       │
│     trigram_rep(α) = β₀ + Σβᵢαᵢ + ...  │
│     Map predicted rep → color gradient  │
├─────────────────────────────────────────┤
│  5. Render interactive 3D nebula        │
│     Three.js + WebGL additive blending  │
└─────────────────────────────────────────┘
        │
        ▼
  Self-contained HTML (one file, ~350KB)

Q: You're projecting from 5D to 3D. Don't you lose information?

PCA captures 70–97% of the variance in 3 components (model-dependent). The remaining variance is small — and the fact that different models produce visually distinct nebulae that correctly predict known model properties (MiniCPM4.1's channel concentration, alignment smoothing, CoT immunity) is strong empirical evidence that the projection preserves the diagnostically relevant structure.

Q: The danger colors come from a fitted model, not direct measurement.

For models with terrain data (dose-response sweeps), the quadratic manifold model is fitted to hundreds of actual output measurements. The model's $R²$ is typically > 0.85. For the points between measured sweep positions, the smooth interpolation is a conservative estimate — real cliffs are sharper than the model predicts.

Q: Are the structural differences real, or artifacts of PCA?

The PC1:PC2 ratio is PCA-independent in the sense that it measures actual variance concentration, not an artifact of the projection method. MiniCPM4.1's 7.7:1 ratio means that 83% of the control vector response is genuinely concentrated along one axis in the full-dimensional hidden state space — a high-density design consistent with its parameter-efficient architecture. The 3D rendering makes this structural choice visible, it doesn't create it.

The cross-model study covers the full spectrum of conditions:

Total: 13 experiments, 6,045 generations, 92 cliffs detected.

Instead of running benchmarks that compress a model's behavior into a single number, SNI gives you a holistic structural portrait. Two models with identical perplexity scores can have radically different nebula shapes — one distributed (broad robustness), one concentrated (high-density corridor). The nebula reveals architectural strategy choices that benchmarks cannot capture.

By imaging the same model at different training checkpoints (pretrain → SFT → RLHF), you can watch the manifold cool down in real time. This provides a new quality signal for alignment teams: is your RLHF actually smoothing the dangerous regions, or just masking them?

The terrain data underlying each nebula defines a per-dimension safe operating range — the region where personality steering doesn't trigger output collapse. This is more informative than a single L2-norm safety radius, because the safe envelope is asymmetric and dimension-dependent:

                    SAFE RANGE (Qwen3-8B)
                    ────────────────────────────────
emotion_valence     [−3.0 ████████████████████▓░░░░░░░ +1.8]
formality           [−3.0 ████████████████████████████████ +3.0]
creativity          [−1.0 ███████████████████████████████ +3.0]
confidence          [−3.0 ████████████████████████████████ +3.0]
empathy             [−0.4 ████ +0.0]  ← narrowest

The terrain map defines where cliffs are. The next step is using it for real-time adaptive steering — finding optimal paths between personality states that stay within the safe envelope, avoid cliffs, and maximize expressiveness.

We have a working ManifoldPathPlanner that computes geodesic-like paths with boundary repulsion on the 5D manifold. The zero-hysteresis property (confirmed experimentally: all paths are reversible) simplifies this to pure geometry.

The vision: instead of manually tuning RepEng coefficients and hoping you don't hit a cliff, the navigator plans a smooth trajectory from state A to state B — like GPS routing on a mountain road, staying on the safe ridges and avoiding the drops.

• Python 3.10+
• repeng library (for GGUF control vector loading)
• numpy
• Pre-trained control vectors (5 GGUF files per model)
• Terrain data (optional, from dose-response sweep)

# Single model
python scripts/sni_pipeline.py --tag qwen3-8b-bf16

# Batch all available models
python scripts/sni_pipeline.py --batch

# Side-by-side comparison
python scripts/sni_pipeline.py --compare qwen3-8b-bf16 minicpm41-8b

Output: self-contained HTML files (~350KB each) that open in any browser. No server required.

# Start RepEng-patched vLLM server
python -m repeng_vllm.start_repeng_vllm \
  --model /path/to/model \
  --trust-remote-code --dtype auto \
  --repeng-vector-dir vectors/

# Run the sweep (~20 min per model)
python scripts/run_terrain_map.py

├── README.md
├── scripts/
│   ├── sni_pipeline.py          # End-to-end: vectors → point cloud → HTML
│   ├── run_terrain_map.py       # Dose-response sweep runner
│   └── analyze_terrain.py       # Statistical analysis & cliff detection
├── data/
│   ├── sni/                     # Compact nebula data (JSON)
│   ├── terrain_data.json        # MiniCPM4.1 raw sweep data
│   └── cross_model/             # Cross-model validation data
└── figures/
    ├── sni/                     # Nebula screenshots & renders
    └── *.svg                    # Terrain map visualizations

The compact JSON data in data/sni/ can be rendered into interactive 3D nebulae using the pipeline:

python scripts/sni_pipeline.py --tag qwen3-8b-bf16
# Opens: sni_output/sni_qwen3-8b-bf16.html

Each HTML file is self-contained (Three.js loaded from CDN) and supports:

• Mouse drag to rotate, scroll to zoom
• Auto-rotation
• Real-time particle rendering with additive blending
• Dimension paths (colored traces through the 5 personality axes)
• Cliff markers (bright red points where output collapses)

This repository evolves from our earlier work on Representation Contrast Imaging (表征显影) — 1D/2D dose-response terrain mapping that first revealed topological discontinuities in LLM hidden states.

SNI builds on that foundation by projecting the full 5D personality manifold into 3D, replacing terrain-map line charts with holistic point-cloud visualization. The underlying data and methodology are the same; the imaging modality is new.

Terrain mapping = measuring individual cross-sections of the manifold (like 1D slices through a CT scan).
Semantic Nebula Imaging = reconstructing the full 3D volume from those cross-sections (like a full 3D CT reconstruction).

@misc{sni2026,
  title   = {Semantic Nebula Imaging: Visualizing the Topological Structure
             of LLM Representation Manifolds},
  author  = {Zhang, Jing},
  year    = {2026},
  url     = {https://github.com/HenryZ838978/RepSNI}
}

📄 This work is part of a larger research program. See the full theory paper: The Representational Budget: Scale, RL, and Multimodal Alignment Compete for Geometric Potential in Transformers (DOI: 10.5281/zenodo.19585083)

• Representation Engineering (Zou et al., 2023) — Control vectors for LLM steering
• RepEngvLLM — vLLM patch for runtime RepEng injection
• repeng — Python library for control vector training

_{Built during a multi-day investigation into LLM personality steering and manifold topology. 14 models imaged. 6,045 generations analyzed. The map is getting sharper — the territory is real.}