Building AI Agents: A Technical Deep Dive

Welcome to our technical deep dive into AI agents! This post covers the mathematical foundations and practical implementation.

The Attention Mechanism

At the heart of modern LLMs is the attention mechanism. The scaled dot-product attention is computed as:

$$ \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V $$

Where:

$Q$ = Query matrix
$K$ = Key matrix
$V$ = Value matrix
$d_k$ = Dimension of keys

Loss Functions

For training, we typically use cross-entropy loss. Given predictions $\hat{y}$ and labels $y$:

$$ \mathcal{L} = -\sum_{i} y_i \log(\hat{y}_i) $$

The gradient update follows: $\theta_{t+1} = \theta_t - \eta \nabla_\theta \mathcal{L}$

Code Example

Here's how to implement a simple agent in Python:

from adalflow import Generator, Agent

class SimpleAgent(Agent):
    def __init__(self, model="gpt-4"):
        self.generator = Generator(model=model)
    
    def run(self, query: str) -> str:
        response = self.generator(query)
        return response.text

Key Features

Our agent framework includes:

Tool Integration - Connect any Python function
Memory Systems - Short and long-term memory
Multi-agent Support - Coordinate multiple agents
Observability - Built-in tracing and debugging

Performance Metrics

Metric	Value
Latency (p50)	120ms
Latency (p99)	450ms
Success Rate	98.5%

Getting Started

Install AdalFlow:

pip install adalflow

Then import and use:

import adalflow as af

agent = af.Agent(model="claude-3")
result = agent.run("Explain quantum computing")

Mathematical Notes

The softmax function $\sigma(z)_i = \frac{e^{z_i}}{\sum_j e^{z_j}}$ ensures probabilities sum to 1.

Temperature $T$ controls randomness: higher $T$ → more uniform distribution.

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