AbstractPhil/svae-freckles-4096-cifar10

--- dataset_info: features: - name: omega_map dtype: float32 shape: - 4 - 64 - 64 - name: label dtype: int32 - name: class_name dtype: string splits: - name: train num_examples: 50000 - name: test num_examples: 10000 license: mit task_categories: - image-classification tags: - svae - geometric-deep-learning - spectral-decomposition - svd - omega-tokens - cifar10 - precomputed-features pretty_name: "SVAE Freckles 4096 — CIFAR-10 Omega Tokens" size_categories: - 10K<n<100K --- # SVAE Freckles 4096 — CIFAR-10 Omega Tokens Precomputed spectral decomposition of CIFAR-10 through **Freckles v41** (256×256), a frozen Spectral Variational Autoencoder trained exclusively on synthetic noise. Each CIFAR-10 image is resized to 256×256, decomposed into 4096 patches (4×4 each), and passed through Freckles' encoder → SVD bottleneck. The 4 singular values per patch are stored as a **(4, 64, 64) omega map** — a 4-channel spatial representation of spectral energy. ## What's Inside | Field | Shape | Description | |-------|-------|-------------| | `omega_map` | `(4, 64, 64)` | Singular values per patch, laid out spatially. Channel 0 = S₀ (dominant mode), Channel 3 = S₃ (weakest mode). | | `label` | `int32` | CIFAR-10 class index (0–9) | | `class_name` | `string` | Human-readable class name | **Classes:** airplane, automobile, bird, cat, deer, dog, frog, horse, ship, truck ## How It Was Made ``` CIFAR-10 (32×32) → bilinear resize to 256×256 → Freckles v41 encoder (frozen, noise-trained, 2.5M params) → SVD: M = U · diag(S) · Vt per patch → S values (4 per patch) stored as (4, 64, 64) spatial map ``` - **Freckles version:** [v41_freckles_256](https://huggingface.co/AbstractPhil/geolip-SVAE) — trained on 16 synthetic noise types, never seen a real image - **Patch size:** 4×4 pixels → 64×64 grid = 4096 patches per image - **SVD:** FLEigh (geolip-core), fp64 precision, machine-epsilon orthogonality - **Normalization:** CIFAR-10 standard (mean=[0.4914, 0.4822, 0.4465], std=[0.2470, 0.2435, 0.2616]) ## Usage ```python from datasets import load_dataset import torch ds = load_dataset("AbstractPhil/svae-freckles-4096-cifar10") # Single sample sample = ds['train'][0] omega_map = torch.tensor(sample['omega_map']) # (4, 64, 64) label = sample['label'] # int class_name = sample['class_name'] # str print(f"Class: {class_name}, Omega map shape: {omega_map.shape}") print(f"S₀ range: [{omega_map[0].min():.2f}, {omega_map[0].max():.2f}]") ``` ### Train a classifier on omega tokens ```python from datasets import load_dataset import torch import torch.nn as nn ds = load_dataset("AbstractPhil/svae-freckles-4096-cifar10") # Stack into tensors train_omega = torch.tensor(ds['train']['omega_map']) # (50000, 4, 64, 64) train_labels = torch.tensor(ds['train']['label']) # (50000,) # A tiny CNN on the 4-channel omega image model = nn.Sequential( nn.Conv2d(4, 32, 3, stride=2, padding=1), nn.GELU(), nn.Conv2d(32, 64, 3, stride=2, padding=1), nn.GELU(), nn.Conv2d(64, 128, 3, stride=2, padding=1), nn.GELU(), nn.AdaptiveAvgPool2d(1), nn.Flatten(), nn.Linear(128, 10), ) ``` ## Omega Map Properties The 4 channels encode spectral energy at each SVD mode: | Channel | Mode | Typical Range | Energy Share | Description | |---------|------|---------------|--------------|-------------| | 0 | S₀ | 4.2–4.8 | ~43% | Dominant spectral structure | | 1 | S₁ | 3.6–4.2 | ~32% | Secondary structure | | 2 | S₂ | 2.5–3.2 | ~17% | Tertiary detail | | 3 | S₃ | 1.5–2.2 | ~7% | Fine structure / residual | The singular values are **post cross-attention** — Freckles' two-layer cross-attention has coordinated them across all 4096 patches before storage. ## Key Properties - **Resolution invariant:** Freckles produces identical spectral signatures regardless of input resolution - **Noise-trained:** The encoder has never seen a real image — all spectral knowledge comes from synthetic noise - **Lossless factorization:** SVD reconstruction error is ~1.5e-15 (machine epsilon) - **Perfect orthogonality:** U and Vt bases are orthogonal to ~3.4e-15 ## Related - **Model:** [AbstractPhil/geolip-SVAE](https://huggingface.co/AbstractPhil/geolip-SVAE) — Freckles, Johanna, Fresnel, Grandmaster checkpoints - **Library:** [AbstractEyes/geolip-core](https://github.com/AbstractEyes/geolip-core) — pip install geolip - **Research:** [Multimodal Geometric Fusion](https://huggingface.co/blog/AbstractPhil/multimodal-geometric-fusion) ## Citation ``` @misc{freckles-cifar10-omega, author = {AbstractPhil}, title = {SVAE Freckles 4096 — Precomputed Spectral Decomposition of CIFAR-10}, year = {2025}, publisher = {HuggingFace}, url = {https://huggingface.co/datasets/AbstractPhil/svae-freckles-4096-cifar10} } ```dataset_info: 特征: - 名称: omega_map 数据类型: float32 形状: - 4 - 64 - 64 - 名称: label 数据类型: int32 - 名称: class_name 数据类型: string 划分: - 名称: train 样本数: 50000 - 名称: test 样本数: 10000 许可证: MIT协议 任务类别: - 图像分类 标签: - svae - 几何深度学习 - 谱分解 - 奇异值分解（Singular Value Decomposition, SVD） - Omega Token（omega-tokens） - CIFAR-10 - 预计算特征 展示名称: "SVAE Freckles 4096 — CIFAR-10 Omega Token数据集" 样本量范围: - 10000 < 样本数 < 100000 # SVAE Freckles 4096 — CIFAR-10 Omega Token数据集 本数据集为通过**Freckles v41**（输入分辨率256×256）对CIFAR-10进行的预计算谱分解结果；Freckles v41是一个仅在合成噪声上训练得到的冻结谱变分自编码器（Spectral Variational Autoencoder, SVAE）。 每一张CIFAR-10图像先被双线性上采样至256×256分辨率，随后被分割为4096个4×4像素的图像块，再输入至Freckles的编码器→奇异值分解瓶颈模块。每个图像块对应的4个奇异值被存储为**(4, 64, 64)格式的Omega映射**——这是一种4通道的谱能量空间表征。 ## 数据字段说明 | 字段 | 形状 | 描述 | |-------|-------|-------------| | `omega_map` | `(4, 64, 64)` | 每个图像块的奇异值，按空间布局排列。通道0为主奇异值S₀，通道3为最弱奇异值S₃。 | | `label` | `int32` | CIFAR-10类别索引（0~9） | | `class_name` | `string` | 人类可读的类别名称 | **类别列表：** 飞机、汽车、鸟类、猫、鹿、狗、青蛙、马、船舶、卡车 ## 数据集构建流程 CIFAR-10（32×32）→ 双线性上采样至256×256 → 冻结的、仅在合成噪声上训练的Freckles v41编码器（参数量250万） → 对每个图像块执行奇异值分解：M = U · diag(S) · Vt → 将每个图像块的4个奇异值存储为(4, 64, 64)空间映射 - **Freckles版本：** [v41_freckles_256](https://huggingface.co/AbstractPhil/geolip-SVAE) — 在16种合成噪声类型上训练，从未接触过真实图像 - **图像块尺寸：** 4×4像素 → 64×64的网格 = 每张图像含4096个图像块 - **奇异值分解实现：** FLEigh（geolip-core库），fp64精度，机器epsilon级正交性 - **归一化方式：** CIFAR-10标准归一化（均值=[0.4914, 0.4822, 0.4465]，标准差=[0.2470, 0.2435, 0.2616]） ## 使用示例 python from datasets import load_dataset import torch ds = load_dataset("AbstractPhil/svae-freckles-4096-cifar10") # 加载单一样本 sample = ds['train'][0] omega_map = torch.tensor(sample['omega_map']) # 形状为(4, 64, 64) label = sample['label'] # 整数类型 class_name = sample['class_name'] # 字符串类型 print(f"类别：{class_name}，Omega映射形状：{omega_map.shape}") print(f"S₀取值范围：[{omega_map[0].min():.2f}, {omega_map[0].max():.2f}]") ### 在Omega Token上训练分类器 python from datasets import load_dataset import torch import torch.nn as nn ds = load_dataset("AbstractPhil/svae-freckles-4096-cifar10") # 将数据堆叠为张量 train_omega = torch.tensor(ds['train']['omega_map']) # 形状为(50000, 4, 64, 64) train_labels = torch.tensor(ds['train']['label']) # 形状为(50000,) # 针对4通道Omega图像的轻量卷积神经网络 model = nn.Sequential( nn.Conv2d(4, 32, 3, stride=2, padding=1), nn.GELU(), nn.Conv2d(32, 64, 3, stride=2, padding=1), nn.GELU(), nn.Conv2d(64, 128, 3, stride=2, padding=1), nn.GELU(), nn.AdaptiveAvgPool2d(1), nn.Flatten(), nn.Linear(128, 10), ) ## Omega映射属性 4个通道分别编码不同SVD模式下的谱能量： | 通道 | 奇异值模式 | 典型取值范围 | 能量占比 | 描述 | |---------|------|---------------|--------------|-------------| | 0 | S₀ | 4.2–4.8 | 约43% | 主导光谱结构 | | 1 | S₁ | 3.6–4.2 | 约32% | 次级结构 | | 2 | S₂ | 2.5–3.2 | 约17% | 三级细节 | | 3 | S₃ | 1.5–2.2 | 约7% | 精细结构/残差信号 | 该奇异值为**跨注意力后结果**——Freckles的双层跨注意力模块已在存储前对全部4096个图像块的奇异值进行了协同校准。 ## 核心属性 - **分辨率不变性：** Freckles可生成与输入分辨率无关的谱特征签名 - **噪声训练：** 编码器从未接触过真实图像——所有谱知识均来自合成噪声 - **无损分解：** SVD重构误差约为1.5e-15（机器epsilon级别） - **完美正交性：** U和Vt基的正交性误差约为3.4e-15 ## 相关资源 - **模型库：** [AbstractPhil/geolip-SVAE](https://huggingface.co/AbstractPhil/geolip-SVAE) — 包含Freckles、Johanna、Fresnel、Grandmaster等模型权重checkpoint - **工具库：** [AbstractEyes/geolip-core](https://github.com/AbstractEyes/geolip-core) — 可通过`pip install geolip`安装 - **相关研究：** [多模态几何融合](https://huggingface.co/blog/AbstractPhil/multimodal-geometric-fusion) ## 引用格式 @misc{freckles-cifar10-omega, author = {AbstractPhil}, title = {SVAE Freckles 4096 — Precomputed Spectral Decomposition of CIFAR-10}, year = {2025}, publisher = {HuggingFace}, url = {https://huggingface.co/datasets/AbstractPhil/svae-freckles-4096-cifar10} }