Upload README.md with huggingface_hub
Browse files
README.md
CHANGED
|
@@ -1,197 +1,250 @@
|
|
| 1 |
-
# CTM Experiments
|
| 2 |
|
| 3 |
-
|
| 4 |
|
| 5 |
-
**
|
| 6 |
|
| 7 |
-
##
|
| 8 |
|
| 9 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 10 |
|
| 11 |
-
|
| 12 |
-
|
| 13 |
-
|
| 14 |
-
|
| 15 |
-
|
| 16 |
-
|
| 17 |
-
|
| 18 |
-
|
| 19 |
-
| **Jigsaw** | Classify shuffled patches | Part-whole integration |
|
| 20 |
-
|
| 21 |
-
## Results Summary
|
| 22 |
-
|
| 23 |
-
| Experiment | Accuracy | Notes |
|
| 24 |
-
|------------|----------|-------|
|
| 25 |
-
| **MNIST** | **97.9%** | Digit classification, 5 min training |
|
| 26 |
-
| **Parity-16** | **99.0%** | 16-bit cumulative parity |
|
| 27 |
-
| **QAMNIST** | **100%** | Multi-step arithmetic (3-5 digits, 3-5 ops) |
|
| 28 |
-
| **Brackets** | **94.7%** | Stack-like reasoning for `(()[])` vs `([)]` |
|
| 29 |
-
| **Object Tracking** | **100%** | Quadrant prediction from motion (4 classes) |
|
| 30 |
-
| **Velocity Prediction** | **100%** | Direction prediction (9 classes) |
|
| 31 |
-
| **Position Prediction** | **93.8%** | Exact position (256 classes, 16x16 grid) |
|
| 32 |
-
| **Transfer Learning** | **94.5%** | Parity→Brackets (core frozen) |
|
| 33 |
-
| **Maze Solving** | **Visualized** | Pretrained model inference on 15x15 mazes |
|
| 34 |
-
| **Jigsaw MNIST** | **92%** | Classify digits from shuffled patches (no positional encoding) |
|
| 35 |
-
|
| 36 |
-
## Key Findings
|
| 37 |
-
|
| 38 |
-
### 1. Architecture Matters More Than Scale
|
| 39 |
-
|
| 40 |
-
Early experiments showed 50% accuracy on parity (random guessing). The fix wasn't more parameters - it was using the **correct architecture**:
|
| 41 |
-
|
| 42 |
-
| Parameter | Wrong | Correct (Official) |
|
| 43 |
-
|-----------|-------|-------------------|
|
| 44 |
-
| `n_synch_out` | 512 | **32** |
|
| 45 |
-
| `n_synch_action` | 512 | **32** |
|
| 46 |
-
| `synapse_depth` | 4 (U-NET) | **1** (linear) |
|
| 47 |
-
|
| 48 |
-
The official parity implementation uses surprisingly small synchronization dimensions with a linear synapse - this is critical for learning.
|
| 49 |
-
|
| 50 |
-
### 2. "Thinking Longer" = Higher Accuracy
|
| 51 |
-
|
| 52 |
-

|
| 53 |
-
|
| 54 |
-
CTM accuracy improves with more internal iterations:
|
| 55 |
-
- **Tick 0**: 7% (random)
|
| 56 |
-
- **Tick 10-11**: 100% (peak)
|
| 57 |
-
- **Final tick**: 98%
|
| 58 |
-
|
| 59 |
-
Harder tasks need more "thinking time" - parity peaks at tick 35.
|
| 60 |
-
|
| 61 |
-
### 3. Transfer Learning Works
|
| 62 |
-
|
| 63 |
-
Pretrained parity model transfers to brackets:
|
| 64 |
-
- **Baseline**: 52.5% (random)
|
| 65 |
-
- **After transfer**: 94.5% (core frozen, only backbone/output trained)
|
| 66 |
-
|
| 67 |
-
The iterative counting learned for parity transfers to stack tracking for brackets - matching from-scratch performance with only 37.7% of parameters trainable.
|
| 68 |
-
|
| 69 |
-
### 4. Maze Solving "The Hard Way"
|
| 70 |
-
|
| 71 |
-
CTM solves mazes by outputting action trajectories (Up/Down/Left/Right/Wait), not pixel masks:
|
| 72 |
-
- **Step accuracy**: 60%+ after 2000 iterations
|
| 73 |
-
- Uses auto-extending curriculum (loss only on trajectory up to first error)
|
| 74 |
-
- Demonstrates sequential reasoning capability
|
| 75 |
-
|
| 76 |
-

|
| 77 |
-
|
| 78 |
-
*CTM "thinking" through a 15x15 maze: blue = predicted path, red = attention focus, green = start position. The attention heatmap shows where CTM looks at each internal tick (T=75 iterations).*
|
| 79 |
-
|
| 80 |
-
## Detailed Results
|
| 81 |
-
|
| 82 |
-
### MNIST Digit Classification (97.9%)
|
| 83 |
-
|
| 84 |
-

|
| 85 |
-
|
| 86 |
-
CTM learns digit classification in ~5 minutes on RTX 4070 Ti.
|
| 87 |
-
|
| 88 |
-
### Parity-16 Cumulative Parity (99.0%)
|
| 89 |
-
|
| 90 |
-

|
| 91 |
|
| 92 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 93 |
|
| 94 |
-
###
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 95 |
|
| 96 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 97 |
|
| 98 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 99 |
|
| 100 |
-
###
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 101 |
|
| 102 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 103 |
|
| 104 |
-
|
| 105 |
-
|
| 106 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 107 |
|
| 108 |
-
|
| 109 |
-
|
| 110 |
-
|
| 111 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 112 |
|
| 113 |
-
|
| 114 |
|
| 115 |
-
|
|
|
|
|
|
|
| 116 |
|
| 117 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
| 118 |
|
| 119 |
-
|
|
|
|
| 120 |
|
| 121 |
-
|
|
|
|
| 122 |
|
| 123 |
-
|
| 124 |
-
|
| 125 |
-
|
| 126 |
-
- **Results**: [`experiments/results/`](continuous-thought-machines/experiments/results/)
|
| 127 |
|
| 128 |
-
|
|
|
|
|
|
|
|
|
|
| 129 |
|
| 130 |
-
|
| 131 |
-
Classify bracket strings as valid or invalid: `(()[])` vs `([)]`
|
| 132 |
|
| 133 |
-
|
|
|
|
|
|
|
|
|
|
| 134 |
|
| 135 |
-
|
| 136 |
-
Predict properties of a moving dot from 5 video frames (16x16 grid).
|
| 137 |
|
| 138 |
-
|
| 139 |
-
|
| 140 |
-
.
|
| 141 |
-
.
|
| 142 |
-
. . . . . . . . . . . . . . . * . . . .
|
| 143 |
-
. . . . . . . . . . . . . . . . . . . *
|
| 144 |
-
```
|
| 145 |
|
| 146 |
-
|
| 147 |
-
| Task | Classes | Accuracy | Notes |
|
| 148 |
-
|------|---------|----------|-------|
|
| 149 |
-
| **Quadrant** | 4 | 100% | TL/TR/BL/BR - easiest |
|
| 150 |
-
| **Velocity** | 9 | 100% | 8 directions + stationary |
|
| 151 |
-
| **Position** | 256 | 93.8% | Exact cell (16x16) - hardest |
|
| 152 |
|
| 153 |
-
|
| 154 |
|
| 155 |
-
|
| 156 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 157 |
|
| 158 |
-
|
| 159 |
-
Run pretrained maze model on small-mazes dataset to visualize CTM's "thinking" process:
|
| 160 |
|
| 161 |
-
|
| 162 |
-
python -m tasks.mazes.analysis.run \
|
| 163 |
-
--actions viz \
|
| 164 |
-
--checkpoint checkpoints/mazes/ctm_mazeslarge_D=2048_T=75_M=25.pt \
|
| 165 |
-
--dataset_for_viz small-mazes
|
| 166 |
-
```
|
| 167 |
|
| 168 |
-
|
| 169 |
|
| 170 |
-
|
| 171 |
-
|
|
|
|
|
|
|
| 172 |
|
| 173 |
-
|
| 174 |
-
|
| 175 |
-
|
| 176 |
-
│ 1 │ 2 │ 3 │ 4 │ │12 │ 7 │ 2 │15 │
|
| 177 |
-
├───┼───┼───┼───┤ ├───┼───┼───┼───┤
|
| 178 |
-
│ 5 │ 6 │ 7 │ 8 │ => │ 4 │11 │ 9 │ 1 │
|
| 179 |
-
├───┼───┼───┼───┤ ├───┼───┼───┼───┤
|
| 180 |
-
│ 9 │10 │11 │12 │ │ 6 │ 3 │14 │ 5 │
|
| 181 |
-
├───┼───┼───┼───┤ ├───┼───┼───┼───┤
|
| 182 |
-
│13 │14 │15 │16 │ │16 │ 8 │10 │13 │
|
| 183 |
-
└───┴─��─┴───┴───┘ └───┴───┴───┴───┘
|
| 184 |
-
```
|
| 185 |
|
| 186 |
-
|
| 187 |
|
| 188 |
-
|
| 189 |
|
| 190 |
-
|
| 191 |
|
| 192 |
-
|
|
|
|
| 193 |
|
| 194 |
-
##
|
| 195 |
|
| 196 |
-
- [
|
| 197 |
-
- [Original
|
|
|
|
|
|
| 1 |
+
# CTM Experiments - Continuous Thought Machine Models
|
| 2 |
|
| 3 |
+
Experimental checkpoints trained on the [Continuous Thought Machine](https://github.com/SakanaAI/continuous-thought-machines) architecture by Sakana AI.
|
| 4 |
|
| 5 |
+
**These are community experiments on the original work - not official SakanaAI models.**
|
| 6 |
|
| 7 |
+
## Paper Reference
|
| 8 |
|
| 9 |
+
> **Continuous Thought Machines**
|
| 10 |
+
>
|
| 11 |
+
> Sakana AI
|
| 12 |
+
>
|
| 13 |
+
> [arXiv:2505.05522](https://arxiv.org/abs/2505.05522)
|
| 14 |
+
>
|
| 15 |
+
> [Interactive Demo](https://pub.sakana.ai/ctm/) | [Blog Post](https://sakana.ai/ctm/)
|
| 16 |
|
| 17 |
+
```bibtex
|
| 18 |
+
@article{sakana2025ctm,
|
| 19 |
+
title={Continuous Thought Machines},
|
| 20 |
+
author={Sakana AI},
|
| 21 |
+
journal={arXiv preprint arXiv:2505.05522},
|
| 22 |
+
year={2025}
|
| 23 |
+
}
|
| 24 |
+
```
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 25 |
|
| 26 |
+
## Core Insight
|
| 27 |
+
|
| 28 |
+
CTM's key innovation: **accuracy improves with more internal iterations**. The model "thinks longer" to reach better answers. This enables CTM to learn algorithmic reasoning that feedforward networks struggle with.
|
| 29 |
+
|
| 30 |
+
## Models
|
| 31 |
+
|
| 32 |
+
| Model | File | Size | Task | Accuracy | Description |
|
| 33 |
+
|-------|------|------|------|----------|-------------|
|
| 34 |
+
| MNIST | `ctm-mnist.pt` | 1.3M | Digit classification | 97.9% | 10-class MNIST |
|
| 35 |
+
| Parity-16 | `ctm-parity-16.pt` | 2.5M | Cumulative parity | 99.0% | 16-bit sequences |
|
| 36 |
+
| Parity-64 | `ctm-parity-64.pt` | 66M | Cumulative parity | 58.6% | 64-bit sequences (custom config) |
|
| 37 |
+
| Parity-64 Official | `ctm-parity-64-official.pt` | 21M | Cumulative parity | 57.7% | 64-bit sequences (official config) |
|
| 38 |
+
| QAMNIST | `ctm-qamnist.pt` | 39M | Multi-step arithmetic | 100% | 3-5 digits, 3-5 ops |
|
| 39 |
+
| Brackets | `ctm-brackets.pt` | 6.1M | Bracket matching | 94.7% | Valid/invalid `(()[])` |
|
| 40 |
+
| Tracking-Quadrant | `ctm-tracking-quadrant.pt` | 6.7M | Motion quadrant | 100% | 4-class prediction |
|
| 41 |
+
| Tracking-Position | `ctm-tracking-position.pt` | 6.7M | Exact position | 93.8% | 256-class (16x16 grid) |
|
| 42 |
+
| Transfer | `ctm-transfer-parity-brackets.pt` | 2.5M | Transfer learning | 94.5% | Parity core to brackets |
|
| 43 |
+
| Jigsaw MNIST | `ctm-jigsaw-mnist.pt` | 19M | Jigsaw puzzle solving | 92.3% | Reassemble 2x2 shuffled MNIST |
|
| 44 |
+
| Rotation MNIST | `ctm-rotation-mnist.pt` | 4.2M | Rotation prediction | 89.1% | Predict rotation angle (4 classes) |
|
| 45 |
+
| Brackets Transfer | `ctm-brackets-transfer-depth4.pt` | 6.1M | Transfer learning | 95.1% | Parity→Brackets (depth 4 synapse) |
|
| 46 |
+
| Dual-Task | `ctm-dual-task-brackets-parity.pt` | 2.8M | Multi-task | 86.1% | Brackets (94%) + Parity (78%) jointly |
|
| 47 |
+
| Parity-64 | `ctm-parity-64-8x8.pt` | 4.1M | Long parity | 58.6% | 64-bit (8x8) cumulative parity |
|
| 48 |
+
| Parity-144 | `ctm-parity-144-12x12.pt` | 4.1M | Long parity | 51.7% | 144-bit (12x12) cumulative parity |
|
| 49 |
+
|
| 50 |
+
## Model Configurations
|
| 51 |
+
|
| 52 |
+
### MNIST CTM
|
| 53 |
+
```python
|
| 54 |
+
config = {
|
| 55 |
+
"iterations": 15,
|
| 56 |
+
"memory_length": 10,
|
| 57 |
+
"d_model": 128,
|
| 58 |
+
"d_input": 128,
|
| 59 |
+
"heads": 2,
|
| 60 |
+
"n_synch_out": 16,
|
| 61 |
+
"n_synch_action": 16,
|
| 62 |
+
"memory_hidden_dims": 8,
|
| 63 |
+
"out_dims": 10,
|
| 64 |
+
"synapse_depth": 1,
|
| 65 |
+
}
|
| 66 |
+
```
|
| 67 |
|
| 68 |
+
### Parity-16 CTM
|
| 69 |
+
```python
|
| 70 |
+
config = {
|
| 71 |
+
"iterations": 50,
|
| 72 |
+
"memory_length": 25,
|
| 73 |
+
"d_model": 256,
|
| 74 |
+
"d_input": 32,
|
| 75 |
+
"heads": 8,
|
| 76 |
+
"synapse_depth": 8,
|
| 77 |
+
"out_dims": 16, # cumulative parity
|
| 78 |
+
}
|
| 79 |
+
```
|
| 80 |
|
| 81 |
+
### Parity-64 Official CTM
|
| 82 |
+
```python
|
| 83 |
+
config = {
|
| 84 |
+
"iterations": 75,
|
| 85 |
+
"memory_length": 25,
|
| 86 |
+
"d_model": 1024,
|
| 87 |
+
"d_input": 64,
|
| 88 |
+
"heads": 8,
|
| 89 |
+
"n_synch_out": 32,
|
| 90 |
+
"n_synch_action": 32,
|
| 91 |
+
"synapse_depth": 1, # linear synapse (official)
|
| 92 |
+
"out_dims": 64, # cumulative parity
|
| 93 |
+
}
|
| 94 |
+
```
|
| 95 |
|
| 96 |
+
### QAMNIST CTM
|
| 97 |
+
```python
|
| 98 |
+
config = {
|
| 99 |
+
"iterations": 10,
|
| 100 |
+
"memory_length": 30,
|
| 101 |
+
"d_model": 1024,
|
| 102 |
+
"d_input": 64,
|
| 103 |
+
"synapse_depth": 1,
|
| 104 |
+
"heads": 4,
|
| 105 |
+
"n_synch_out": 32,
|
| 106 |
+
"n_synch_action": 32,
|
| 107 |
+
}
|
| 108 |
+
```
|
| 109 |
|
| 110 |
+
### Brackets CTM
|
| 111 |
+
```python
|
| 112 |
+
config = {
|
| 113 |
+
"iterations": 30,
|
| 114 |
+
"memory_length": 15,
|
| 115 |
+
"d_model": 256,
|
| 116 |
+
"d_input": 64,
|
| 117 |
+
"heads": 4,
|
| 118 |
+
"n_synch_out": 32,
|
| 119 |
+
"n_synch_action": 32,
|
| 120 |
+
"out_dims": 2, # valid/invalid
|
| 121 |
+
}
|
| 122 |
+
```
|
| 123 |
|
| 124 |
+
### Tracking CTM
|
| 125 |
+
```python
|
| 126 |
+
config = {
|
| 127 |
+
"iterations": 20,
|
| 128 |
+
"memory_length": 15,
|
| 129 |
+
"d_model": 256,
|
| 130 |
+
"d_input": 64,
|
| 131 |
+
"heads": 4,
|
| 132 |
+
"n_synch_out": 32,
|
| 133 |
+
"n_synch_action": 32,
|
| 134 |
+
}
|
| 135 |
+
```
|
| 136 |
|
| 137 |
+
### Jigsaw MNIST CTM
|
| 138 |
+
```python
|
| 139 |
+
config = {
|
| 140 |
+
"iterations": 30,
|
| 141 |
+
"memory_length": 20,
|
| 142 |
+
"d_model": 512,
|
| 143 |
+
"d_input": 128,
|
| 144 |
+
"heads": 8,
|
| 145 |
+
"n_synch_out": 32,
|
| 146 |
+
"n_synch_action": 32,
|
| 147 |
+
"synapse_depth": 1,
|
| 148 |
+
"out_dims": 24, # 4 tiles x 6 permutation options
|
| 149 |
+
"backbone_type": "jigsaw",
|
| 150 |
+
}
|
| 151 |
+
```
|
| 152 |
|
| 153 |
+
### Rotation MNIST CTM
|
| 154 |
+
```python
|
| 155 |
+
config = {
|
| 156 |
+
"iterations": 20,
|
| 157 |
+
"memory_length": 15,
|
| 158 |
+
"d_model": 256,
|
| 159 |
+
"d_input": 64,
|
| 160 |
+
"heads": 4,
|
| 161 |
+
"n_synch_out": 32,
|
| 162 |
+
"n_synch_action": 32,
|
| 163 |
+
"synapse_depth": 1,
|
| 164 |
+
"out_dims": 4, # 0°, 90°, 180°, 270°
|
| 165 |
+
"backbone_type": "rotation",
|
| 166 |
+
}
|
| 167 |
+
```
|
| 168 |
|
| 169 |
+
## Usage
|
| 170 |
|
| 171 |
+
```python
|
| 172 |
+
import torch
|
| 173 |
+
from huggingface_hub import hf_hub_download
|
| 174 |
|
| 175 |
+
# Download model
|
| 176 |
+
model_path = hf_hub_download(
|
| 177 |
+
repo_id="vincentoh/ctm-experiments",
|
| 178 |
+
filename="ctm-mnist.pt"
|
| 179 |
+
)
|
| 180 |
|
| 181 |
+
# Load checkpoint
|
| 182 |
+
checkpoint = torch.load(model_path, map_location="cpu")
|
| 183 |
|
| 184 |
+
# Initialize CTM with matching config
|
| 185 |
+
from models.ctm import ContinuousThoughtMachine
|
| 186 |
|
| 187 |
+
model = ContinuousThoughtMachine(**config)
|
| 188 |
+
model.load_state_dict(checkpoint['model_state_dict'])
|
| 189 |
+
model.eval()
|
|
|
|
| 190 |
|
| 191 |
+
# Inference
|
| 192 |
+
with torch.no_grad():
|
| 193 |
+
output = model(input_tensor)
|
| 194 |
+
```
|
| 195 |
|
| 196 |
+
## Training Details
|
|
|
|
| 197 |
|
| 198 |
+
- **Hardware**: NVIDIA RTX 4070 Ti SUPER
|
| 199 |
+
- **Framework**: PyTorch
|
| 200 |
+
- **Optimizer**: AdamW
|
| 201 |
+
- **Training time**: 5 minutes (MNIST) to 17 hours (QAMNIST)
|
| 202 |
|
| 203 |
+
## Key Findings
|
|
|
|
| 204 |
|
| 205 |
+
1. **Architecture > Scale**: Small sync dimensions (32) with linear synapses work better than large/deep variants
|
| 206 |
+
2. **"Thinking Longer" = Higher Accuracy**: CTM accuracy improves with more internal iterations
|
| 207 |
+
3. **Transfer Learning Works**: Parity-trained core transfers to brackets with 94.5% accuracy
|
| 208 |
+
4. **Architectural Limits**: CTM has a ~58% ceiling on 64-bit parity regardless of hyperparameters
|
|
|
|
|
|
|
|
|
|
| 209 |
|
| 210 |
+
## Parity Scaling Experiments
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 211 |
|
| 212 |
+
We tested CTM on increasingly long parity sequences to find where it breaks down:
|
| 213 |
|
| 214 |
+
| Sequence | Grid | Accuracy | vs Random | Status |
|
| 215 |
+
|----------|------|----------|-----------|--------|
|
| 216 |
+
| 16 | 4x4 | **99.0%** | +49.0% | ✅ Solved |
|
| 217 |
+
| 36 | 6x6 | **66.3%** | +16.3% | ⚠️ Degraded |
|
| 218 |
+
| 64 | 8x8 | **58.6%** | +8.6% | ❌ Struggling |
|
| 219 |
+
| 64 (official) | 8x8 | **57.7%** | +7.7% | ❌ Same ceiling |
|
| 220 |
+
| 144 | 12x12 | **51.7%** | +1.7% | ❌ Random |
|
| 221 |
|
| 222 |
+
**Key insight**: The ~58% ceiling for parity-64 is an **architectural limit**, not a hyperparameter issue. Both custom config (d_model=512, synapse_depth=4) and official config (d_model=1024, synapse_depth=1) achieve essentially the same accuracy.
|
|
|
|
| 223 |
|
| 224 |
+
### Why CTM Fails on Long Parity
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 225 |
|
| 226 |
+
Parity requires **strict sequential computation**: process bit 1 before bit 2 before bit 3... CTM's attention-based "thinking" is fundamentally parallel - all positions attend simultaneously. The model can learn approximate sequential patterns for short sequences (~64 steps), but this breaks down for longer sequences.
|
| 227 |
|
| 228 |
+
**CTM excels at:**
|
| 229 |
+
- Moderate sequence lengths (< 64 elements)
|
| 230 |
+
- Local dependencies (brackets: track depth, not full history)
|
| 231 |
+
- Parallelizable structure (MNIST: patches contribute independently)
|
| 232 |
|
| 233 |
+
**CTM struggles with:**
|
| 234 |
+
- Long strict sequential dependencies (parity-144)
|
| 235 |
+
- Tasks requiring O(n) sequential steps where n > ~64
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 236 |
|
| 237 |
+
## License
|
| 238 |
|
| 239 |
+
MIT License (same as original CTM repository)
|
| 240 |
|
| 241 |
+
## Acknowledgments
|
| 242 |
|
| 243 |
+
- [Sakana AI](https://sakana.ai/) for the Continuous Thought Machine architecture
|
| 244 |
+
- Original [CTM Repository](https://github.com/SakanaAI/continuous-thought-machines)
|
| 245 |
|
| 246 |
+
## Links
|
| 247 |
|
| 248 |
+
- [Experiment Repository](https://github.com/bigsnarfdude/ctm-experiments)
|
| 249 |
+
- [Original Paper](https://arxiv.org/abs/2505.05522)
|
| 250 |
+
- [Interactive Demo](https://pub.sakana.ai/ctm/)
|