|
| 1 | +--- |
| 2 | +layout: post |
| 3 | +title: "Welcome to the Blog" |
| 4 | +date: 2026-01-13 |
| 5 | +categories: general |
| 6 | +--- |
| 7 | + |
| 8 | +Welcome to my AI research blog! This is a space where I'll share thoughts on machine learning theory, deep learning, and the latest developments in AI research. |
| 9 | + |
| 10 | +## What to Expect |
| 11 | + |
| 12 | +Posts will cover topics such as: |
| 13 | + |
| 14 | +- **Learning Theory**: Understanding generalization, sample complexity, and the theoretical foundations of ML |
| 15 | +- **Optimization**: Gradient descent dynamics, convergence analysis, and loss landscapes |
| 16 | +- **Neural Networks**: Architectures, expressivity, and training dynamics |
| 17 | +- **Research Insights**: Commentary on interesting papers and emerging trends |
| 18 | + |
| 19 | +## Code Examples |
| 20 | + |
| 21 | +Posts may include code snippets. Here's a simple example: |
| 22 | + |
| 23 | +```python |
| 24 | +import torch |
| 25 | +import torch.nn as nn |
| 26 | + |
| 27 | +class SimpleNetwork(nn.Module): |
| 28 | + def __init__(self, input_dim: int, hidden_dim: int, output_dim: int): |
| 29 | + super().__init__() |
| 30 | + self.layers = nn.Sequential( |
| 31 | + nn.Linear(input_dim, hidden_dim), |
| 32 | + nn.ReLU(), |
| 33 | + nn.Linear(hidden_dim, output_dim), |
| 34 | + ) |
| 35 | + |
| 36 | + def forward(self, x: torch.Tensor) -> torch.Tensor: |
| 37 | + return self.layers(x) |
| 38 | +``` |
| 39 | + |
| 40 | +## Math Support |
| 41 | + |
| 42 | +Jekyll with Kramdown supports LaTeX-style math. For example, the cross-entropy loss: |
| 43 | + |
| 44 | +$$ |
| 45 | +\mathcal{L}(\theta) = -\frac{1}{N} \sum_{i=1}^{N} \sum_{c=1}^{C} y_{i,c} \log(\hat{y}_{i,c}) |
| 46 | +$$ |
| 47 | + |
| 48 | +Stay tuned for more content! |
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