The key to call graph construction

For an OOP programming language, the key challenge in call graph construction is handling the virtual call, as it may involve multiple target methods, as shown in the following table¹.

The method call and method signature

Let’s take Java as an example; a method call may have this form.

Motivations

There is a type of problem where you are given an array $arr$ and $Q$ queries. Each query is represented as $query(l, r)$, which asks for the sum of the elements in the subarray $[l, r]$, i.e., $arr[l] + arr[l + 1] + … + arr[r]$.

If we handle each query using a brute-force approach, the time complexity will be $O(N)$. Thus, solving $Q$ queries would require $O(NQ)$. Is there a more efficient approach?

Intro

What’s Multi-Head Attention (MHA)

In last post I have explained how the self-attention mechanism works. Today let’s take a step further and explore multi-head attention (MHA), which is the full version of self-attention as described in the original paper¹. Since I have covered most of the foundation concepts in last post, this post will be short. :)

Previously, we mentioned that the self-attention mechanism has three import matrices.

$$ \mathbf Q,\mathbf K,\mathbf V\in\mathcal{R}^{n\times d} $$

Motivation

The current RAG techniques can not answer the global questions about the corpus. For example, we may want to know what is the topic of the corpus. Usually, the answer does not exist in the corpus but needs to understand the whole corpus and give summarization. Such global questions are called query-focused summarization (QFS) problems in this paper¹. A naive RAG technique can not handle such a situation.

And it’s unrealistic to put all the text in the corpus in the context window of LLM. Even if we could, the LLM may miss the information in the middle of the context window.

Motivations

The model’s performance is related to the model’s parameter. The bigger the model is, the more performant it will be. However, the computational cost also increases. To mitigate this problem, various forms of conditional computation have been proposed to increase model performance without a proportional increase in computational costs¹.

Today I would like to share the Sparsely-Gated Mixture-of-Experts Layer (MoE) as proposed in this paper.¹

MoE architecture

There are $n$ experts in the MoE layer (denoted as $E_1, E_2, …, E_n$) and they are controlled by a gating network $G$. The output of the gating network $G$ is a vector with length $n$.

Intro

If you could understand this statement: Python function is a first-class function, then I believe you should have no problem understanding the Python decorator too. This statement means that the function is also a value, just like any other primitive types (int, str, float, etc), and can be passed as arguments to function or returned as function outputs.

You may heard of the technical term - high-order function, which means that its arguments contain a function or (and) it returns a function. So we know that the Python decorator is a kind of high-order function.

Motivation

A language solves 2 subproblems.

1. Mapping sentence prefixes to fixed-size representation.
2. Using these representations to predict the next token in the context.

The $k\texttt{NN-LM}$ proposed in this hypothesis that representation learning problem may be easier than the prediction problem

kNN-LM

The following graph demonstrates the idea behind the $k\texttt{NN-LM}$ model.

Data Preparation

To use the $k\texttt{NN-LM}$, we need to preprocess the documents in the corpus. The preprocessing procedure can be divided into some steps. Take the following sentence as an example.

What’ is KNN Algorithm