This is to share Q&As in order to understand how LLMs work. Naturally I used some LLM tool (Google Gemini) to generate the answers.

<1>About the general transformer structure of LLMs, how does the training process differ from the working process when user inputs prompts and gets replies?

Feature Training Process Working (Inference) Process Primary Goal To optimize the model’s weights(W) so it accurately predicts the next token. To generate a coherent output sequence based on the prompt using the fixed weights.

Input Data Flow Parallel Processing: All tokens in a training sequence (e.g., a sentence) are fed into the transformer simultaneously. Sequential (Auto-Regressive): The model processes the initial prompt in parallel, but then generates the reply one token at a time, feeding its own output back in as the next input.

Context Masking Uses a Causal Mask (or Look-Ahead Mask) to prevent the model from “cheating” by seeing future tokens when predicting the current one. The mask is applied implicitly during sequential generation, as the model physically has no future tokens to look at.

Weight Status Trainable: Weights are constantly updated using the optimizer (e.g., Adam or SGD). Fixed/Frozen: Weights are constant and read-only. No learning or updating occurs.

Core Mechanism Loss Calculation & Backpropagation:Calculates loss (error) between the prediction and the true next token, then uses backpropagation to adjust weights. Next-Token Sampling/Decoding: Calculates the probability distribution (softmax) over the vocabulary and selects the next token.

  1. Training Process: Learning the Language The training process is about optimizing the billions of parameters within the transformer’s self-attention and feed-forward layers. A. Data Flow (Parallel) During training, the transformer processes long sequences of text in parallel. For instance, given the sequence, “The quick brown fox jumps over the lazy dog,” the model is trained to make predictions at every single position simultaneously: • Predict quick given “The” • Predict brown given “The quick” • Predict fox given “The quick brown” • …and so on. B. Backpropagation
  2. Forward Pass: The parallel predictions are made.
  3. Loss Calculation: A Loss Function (usually cross-entropy loss) measures the difference between the model’s predicted token probabilities and the true next token.
  4. Backward Pass: Backpropagation calculates the gradient of the loss with respect to every single weight in the model.

  5. Optimization: An Optimizer (e.g., Adam) uses these gradients to slightly adjust the weights () to minimize the loss.

  6. Working (Inference) Process: Generating the Reply The working process (often called inference or decoding) uses the final, trained weights to generate new, original content. A. Data Flow (Auto-Regressive) The generation is sequential (auto-regressive), meaning it relies on its own previously generated output:
  7. Initial Prompt Processing (Parallel): The user’s entire prompt is processed at once to establish context.
  8. Token 1 Generation: The model predicts the first token of the reply.
  9. Token 2 Generation: The original prompt plus the newly generated Token 1 are fed back into the model to predict Token 2.
  10. Iteration: This cycle repeats until the model generates a special end-of-sequence (EOS) token or reaches a set length limit. B. Decoding and Sampling The final step uses decoding strategies (like temperature sampling or beam search) on the output probabilities (softmax) to select the next word, allowing the model to produce creative and contextually relevant responses without changing any of its learned parameters.

<2>In the inference process, is it true that the system has multiple candidate tokens to choose from to output the first token? But it chooses the most likely one based on the softmax calculation.

That’s partially true, but requires clarification on how the choice is made based on the softmax calculation.

It is true that the system considers multiple candidate tokens (in fact, it considers every token in its vocabulary) for the first output token. However, it only chooses the single most likely one if it is using a specific decoding strategy called greedy decoding.

🎲 Candidate Tokens and Softmax

  1. The Candidates During inference, the model takes the user’s prompt, processes it through the transformer layers, and its final layer outputs a vector of logits. This vector has a score for every single token in the model’s vocabulary (which can be 50,000+ tokens). The softmax function converts these raw logits into a probability distribution where every token is assigned a probability of being the next word, and these probabilities sum to 1. Every token is a candidate.

  2. The Choice (Decoding Strategy) The way the model selects the final token is determined by the decoding strategy: Decoding Strategy How the Choice is Made Characteristics Greedy Decoding Chooses the token with the highest probability (P=max). Deterministic and Conservative. Often leads to repetitive or sub-optimal text, as it never explores slightly less likely but better-fitting sequences.

Sampling (Temperature Sampling) Samples the token randomly based on the probability distribution. Creative and Stochastic. Allows lower-probability tokens to be selected, increasing novelty but risking incoherence. The Temperature hyperparameter controls how sharply the probabilities are weighted.

Beam Search Tracks the top k most likely sequences at each step (where is the beam width). It maintains parallel candidate sequences and chooses the sequence with the highest total probability at the end. Optimizing for Quality. Aims for a higher-quality output sequence than greedy search by looking several steps ahead, but it’s more computationally expensive.

Therefore, while the model calculates the probability for every candidate via softmax, whether it chooses only the single most likely one depends entirely on whether it is configured to use greedy decoding. Most production LLMs use sampling (often with techniques like Top-K or Nucleus sampling) to balance quality and creativity.

<3>About the general transformer structure of LLMs, how the training process differs from the working process when user inputs prompts and gets replies?

We need multiple layers in Large Language Models (LLMs) because they allow the model to learn and represent increasingly complex and abstract features of language, enabling sophisticated reasoning and generation capabilities.This structure is the basis of deep learning.

🧱 The Principle of Deep Learning Using a single layer would only allow the model to learn simple, linear relationships. By stacking layers in the Transformer architecture, the model learns a hierarchy of representations:

  1. Early Layers (Shallow Abstraction) 🔎 The initial layers of the transformer focus on local and surface-level features. These layers primarily learn: • Syntax: Basic grammatical structure (e.g., subject-verb agreement). • Token Relationships: Simple dependencies between adjacent words (e.g., “fast” modifies “car”). • Word Sense: Distinguishing between different meanings of a word based on immediate context.

  2. Middle Layers (Mid-Level Abstraction) 🗺️ As information passes through the middle layers, the features become more abstract and contextual. These layers integrate information learned in the lower layers to understand: • Phrases and Clauses: The meaning of multi-word expressions (e.g., understanding the idiom “kick the bucket”). • Coreference Resolution: Identifying that pronouns (“he,” “it”) refer back to a specific noun earlier in the text. • Sentiment: Determining the overall positive or negative tone of a sentence or paragraph.

  3. Deep Layers (High-Level Abstraction) 💡 The deepest layers synthesize all the information to grasp the overall meaning, intent, and structure of the entire document. These layers are crucial for complex tasks: • Contextual Reasoning: Understanding relationships between widely separated sentences across different paragraphs. • Topic Modeling: Identifying the central themes and subtopics of the entire text. • Logical Inference: Enabling the model to make logical jumps, answer complex questions, and write coherent, long-form prose.

📈 Necessity for LLM Scale For an LLM to perform tasks like summarizing a 50-page document or generating complex, functional code, it needs a huge capacity to store and process complex patterns. More layers provide this architectural depth necessary to move from simple word-to-word relationships to comprehensive, world-knowledge representations, which is the definition of a powerful LLM.

<4>How many layers does an LLM typically have?

There is no single fixed number of layers an LLM typically has, as the count varies dramatically based on its size and generation. However, modern, state-of-the-art LLMs generally range from tens to over a hundred layers.

The number of layers is a key component of the model’s overall size, or depth, which is usually measured by its total number of parameters.

📊 Layer Counts of Notable LLM Families The term “layer” in the Transformer architecture typically refers to a single Transformer Block, which contains one Multi-Head Attention mechanism and one Feed-Forward Network.

Here is a look at the approximate number of layers in some famous LLM families, demonstrating the trend toward deeper models: LLM Model Family Approximate Number of Parameters Approximate Number of Layers (Blocks) Original GPT 117 Million 12 BERT-Base 110 Million 12 GPT-3 175 Billion 96 LLaMA 2 70B 70 Billion 80 LLaMA 3 8B 8 Billion 32 Megatron-Turing NLG 530 Billion 105

📈 The Importance of Depth The shift from 12 layers (in early models) to 80-100+ layers in large-scale LLMs is crucial because depth is necessary for:

  1. Hierarchical Feature Learning: As discussed previously, each layer learns increasingly complex and abstract features. Deep models can capture long-range dependencies and intricate reasoning.

  2. Model Capacity: A greater number of layers increases the total parameter count, giving the model more “space” to store the vast amount of knowledge and linguistic patterns learned from the huge training datasets. In current research, while the total number of parameters continues to grow, there is also intense focus on making each layer more efficient rather than just blindly stacking more of them.

<5> My understanding of using multiple layers in LLMs or deep learning is that it helps build an implicit function which embeds nonlinearity and maps user input to a generated word (token) with minimised error. Is it true?

That’s an excellent and highly accurate summary of the core purpose of using multiple layers in deep learning, especially LLMs! 👍 Your understanding is fundamentally true, but we can slightly refine the terminology to capture the full scope of what those layers achieve:

🎯 The Core Purpose of Multiple Layers The deep structure of an LLM or any deep neural network is built to achieve two primary, interconnected goals:

  1. Nonlinearity (The “Deep” Part) 〰️ • It is true: Each layer, after performing a linear transformation (matrix multiplication by weights), applies a non-linear activation function (like ReLU, GELU, or Swish). • The Benefit: Without these non-linearities, stacking layers would simply result in one combined giant linear transformation, no matter how many layers you use. The non-linearities allow the network to model highly complex, curved, and non-linear relationships in the data—which is essential because real-world data (like language) is inherently non-linear. This is what gives the network the power to approximate any continuous function (the Universal Approximation Theorem).

  2. Hierarchical Feature Representation (The “Embedding” Part) 🗺️ • It is true: The layers implicitly build a function that transforms the input. This process is called feature extraction or representation learning. • The Benefit: Multiple layers create a hierarchy: shallow layers learn simple, local features (e.g., word syntax), and deep layers learn abstract, global features (e.g., context, intent, reasoning). The final, high-level representation (or embedding) is a complex encoding that captures the full meaning of the user’s input, making the final prediction more accurate.

  3. Mapping and Minimizing Error (The “Function” Part) ⬇️ • It is true: The entire model acts as a single, massive, differentiable function. It takes the input and produces an output (the probability distribution over the next tokens). • The Benefit: The model’s weights are adjusted during training (via gradient descent) specifically to minimize the prediction error (loss) between its generated probabilities and the true next word. The multiple layers provide the capacity and flexibility necessary for this function to map virtually any input to its most accurate output. In summary, you are correct: multiple layers build a complex, non-linear, implicit function that hierarchically extracts meaningful features from the input to minimize prediction error. About the 2nd purpose, has it been proven that different layers play different roles (e.g., from local features to global features)? Any maths behind this? Yes, the idea that different layers in an LLM or deep learning model play different hierarchical roles—moving from local/low-level features to global/abstract/high-level features—is well-established and extensively supported by both empirical evidence and mathematical theory. This concept is often referred to as hierarchical representation learning.

🔬 Empirical Evidence of Layer Roles Researchers use various visualization and probing techniques to analyze what each layer “sees” or focuses on: • Computer Vision (CV): This is where the concept was first clearly demonstrated. In Convolutional Neural Networks (CNNs): o Layer 1: Detects simple edges and colors (local features). o Middle Layers: Detects textures, patterns, and parts (e.g., eyes, wheels, doors). o Final Layers: Detects entire objects and complex scenes (global features). • Large Language Models (LLMs) & NLP: Similar hierarchical behavior is observed: o Shallow Layers: Tend to focus on syntactic features (e.g., part-of-speech tags, subject-verb agreement, immediate dependencies). o Mid-Layers: Focus on semantic and discourse features (e.g., coreference resolution, phrase meaning, sentiment analysis). o Deep Layers: Focus on high-level, abstract reasoning (e.g., answering questions, logical inference, contextual relationships over long spans of text). This empirical evidence is often gathered by “probing” the internal activations of different layers and training a simple linear classifier to predict a specific linguistic property (like POS tag or sentiment) based on that layer’s output. If the linear classifier is highly accurate, it suggests that feature has been robustly encoded by that layer.

📐 Mathematical Principle: The Role of Non-Linearity The mathematical reason that deep layers are required to build these complex features lies in the power of composition of functions.

Composition of Functions The entire deep network is a single, composite function , where each layer applies a non-linear transformation : The output of the entire network is: where represents the operation of layer . • Low-Level Features: is a direct, relatively simple non-linear function of the raw input . • High-Level Features: is a function of a function of a function… of the raw input. This mathematical composition allows the model to build up representations that are exponentially more complex than a single layer could achieve. The Universal Approximation Theorem (UAT) While the UAT often refers to width (the number of neurons in a single layer), the practical relevance of depth is that a deeper network can often represent certain classes of functions far more efficiently than a shallow, very wide network. Mathematically, many functions (especially those related to symmetry, hierarchy, and composition) require an exponential number of parameters to be approximated accurately by a shallow network, but only a polynomial number of parameters (or fewer) when using a deep network. This efficiency is the fundamental mathematical reason we need multiple layers.

<6> In the transformer structure of LLMs, what is the purpose of using the self-attention scheme?

The self-attention mechanism is the single most important innovation in the Transformer architecture, and its purpose is to enable the LLM to understand the context and dependencies between all tokens in a sequence, regardless of their position. Simply put, self-attention allows the model to answer the question: “When processing this word, which other words in the entire input sequence are most relevant?”

🔍 Key Purposes of Self-Attention

  1. Capturing Long-Range Dependencies (Context) Before Transformers, models like RNNs or LSTMs had to process sequences sequentially, making it difficult to maintain context over long distances (the vanishing gradient problem). Self-attention solves this: • Parallel Processing: Self-attention processes all tokens simultaneously. For every token, it calculates an attention score with every other token in the sequence. • Distance Agnostic: It connects the most relevant words directly, regardless of whether they are two words apart or two hundred words apart. This allows the model to build a global understanding of the entire text in a single step.
  2. Contextualizing Word Meaning Self-attention allows the model to create contextualized embeddings. A single word can have multiple meanings, and the meaning depends entirely on its surrounding context. • Example: Consider the word “bank” in two sentences:
  3. “The financial bank raised its rates.”
  4. “The children played near the river bank.” • When processing “bank” in the first sentence, self-attention assigns high scores (high relevance) to words like “financial” and “rates,” leading to an embedding that represents the money-lending institution. • In the second sentence, it assigns high scores to words like “river” and “played,” leading to an embedding that represents the edge of a river.
  5. Coreference Resolution Self-attention is fundamental to resolving coreference, where pronouns refer back to specific nouns. • Example: “The engineer designed the bridge, and he was proud of it.” o When the model processes the pronoun “he,” self-attention assigns a high relevance score to “engineer.” o When it processes “it,” it assigns a high relevance score to “bridge.” By combining these three elements, the self-attention mechanism generates a weighted representation of the entire sequence for every single token, resulting in rich, deeply contextualized embeddings that are essential for high-quality language understanding and generation.

<7>Then what is the multi-head attention scheme?

The multi-head attention scheme is an enhancement to the self-attention mechanism, designed to improve the model’s ability to focus on different aspects of the input simultaneously, thereby enriching its understanding of the context.1 It’s essentially running several different self-attention calculations in parallel and then combining the results.2

💡 Purpose of Multi-Head Attention Instead of performing a single, large attention function, the input is split into 3$H$ (the number of heads) smaller pieces.4 The main purposes are:

  1. Modeling Diverse Relationships: Each “head” learns to focus on a different kind of relationship within the same sequence. For example: o Head 1 might focus on syntactic relationships (e.g., subject-verb agreement).5 o Head 2 might focus on coreference (e.g., linking a pronoun to its antecedent). o Head 3 might focus on semantic relevance (e.g., words related by theme or topic).
  2. Increased Representational Power: By combining these diverse perspectives, the model generates a richer, more comprehensive contextual embedding for each token than a single attention mechanism could achieve.6
  3. Stability and Speed: Running smaller attention calculations in parallel is often more stable and computationally efficient than running one large calculation.

📐 How It Works The multi-head process involves three main steps:7

  1. Splitting and Projection • The input vectors (Query 8$\mathbf{Q}$, Key 9$\mathbf{K}$, and Value 10$\mathbf{V}$) are linearly projected 11$H$ times using different, learned weight matrices for each head.12 • This creates 13$H$ separate, smaller sets of 14$\mathbf{Q}_h, \mathbf{K}_h, \mathbf{V}_h$.15 If the original dimension was $D$, each head works with vectors of dimension $D/H$.
  2. Parallel Attention • The scaled dot-product attention function is executed independently and in parallel for each of the $H$ projected sets of $\mathbf{Q}, \mathbf{K}, \mathbf{V}$. • This results in 16$H$ different output matrices, 17$\text{Attention}_1$ through 18$\text{Attention}_H$.19
  3. Concatenation and Final Projection • The 20$H$ output matrices are concatenated back together along the dimension that was split (restoring the original dimension 21$D$).22 • This concatenated result is then passed through one final linear projection layer to combine the distinct knowledge captured by each head into the final, consolidated output representation.23 This final output is the enriched contextual vector that is passed to the next component (the Feed-Forward Network or the next Transformer layer).24

<8>Do we lose information if we split the input into small pieces? Cannot we do this multi-head attention on the original data?

That’s an insightful question that touches on the fundamental mechanics of the multi-head attention mechanism! The answer is that no, we don’t lose information when splitting the input, because the process involves projection, not physical division of the data. You could do the attention on the original data, but splitting it into multiple heads is done to increase the model’s analytical power and efficiency.

  1. No Information Loss (Projection vs. Splitting) The input to the multi-head attention layer (the vectors) is not physically divided or chopped up. Instead, the input vectors are linearly projected into smaller, lower-dimensional subspaces. • Original Data: Each token has an embedding of dimension (e.g., ). • Projection: For heads, the -dimensional vector is multiplied by different weight matrices. Each matrix projects the dimensions down to dimensions (e.g., ). • Complete Information: Crucially, the full input information is available to each of the heads, but each head learns a different, specialized way to filter or compress that information into its lower-dimensional space. No data is thrown away. The projected results are then concatenated back together at the end, recovering the original dimension before the final linear layer combines the results.

  2. Why Use Multi-Head Over Single-Head? While you could certainly perform a single self-attention mechanism on the full -dimensional vectors (this is what is called Single-Head Attention), using multiple heads provides several significant benefits: • Diverse Feature Learning: A single large attention layer might struggle to optimize for multiple tasks simultaneously (e.g., syntax, semantics, and coreference). By splitting into heads, each head learns to specialize in a different aspect of the input data, providing different perspectives on the context. • Robustness: If one head fails to capture a relationship, the other heads can compensate, making the overall mechanism more robust. • Computational Efficiency (Parallelism): The calculations for each small attention head can be executed independently and in parallel on modern GPU hardware. This makes the multi-head mechanism faster and more scalable than trying to perform one massive attention matrix calculation. • Representational Capacity: The final linear projection layer, which combines the results, learns the optimal way to weight and integrate the different types of information captured by each head, ultimately yielding a richer and more contextually powerful output vector than a single large head could achieve.

<9>In the transformer structure of LLMs, we have the self-attention scheme in each layer. Why don’t we do the self-attention in the first layer only? Do we need self-attention scheme in later layers?

It’s an insightful question about the repeated use of attention. The short answer is: Yes, we absolutely need the self-attention scheme in every subsequent layer because each layer’s attention mechanism operates on increasingly rich and abstract contextual embeddings created by the layers preceding it.1 You need self-attention in later layers to build the hierarchical understanding necessary for complex language tasks.

🏗️ Why Attention Must Be Layered (Hierarchical Context) The primary reason for repeating the self-attention mechanism in every Transformer block is to facilitate hierarchical feature learning and contextual refinement.

  1. Input to Layer 1: The first layer’s attention operates on the raw input tokens (embeddings) and Positional Encodings. It builds simple, direct connections (e.g., subject to verb) and resolves immediate ambiguities (e.g., word sense).2 \(\text{Output}_1 = \text{Attention}(\text{Input\_Tokens})\)
  2. Input to Layer 2: The input to the second layer’s attention block is the enriched contextual embedding ($\text{Output}_1$) created by the first layer and the Feed-Forward Network (FFN). $\text{Output}_1$ is no longer just a word; it’s a vector representing the word plus the context captured by the first layer.
  3. Refining Contextual Connections: The second layer’s attention uses this richer input to build more complex and abstract connections. For example, it might connect a pronoun in one sentence to its antecedent in another, or link two semantically related ideas across a long passage. \(\text{Output}_2 = \text{Attention}(\text{Output}_1)\) If you only performed attention in the first layer, the deeper layers would only apply simple, feed-forward transformations to the initial, flat context. They would be unable to perform the deep, long-range contextual reasoning required to understand complex language, reasoning, and coherence across large documents.

🎯 The Role of Deep Attention • Layer 1 Attention: Focuses on local dependencies (syntax, immediate phrases). • Deep Layer Attention: Focuses on global dependencies (discourse, logical structure, cross-sentence coreference, and theme). Each successive attention layer refines the contextual vector, integrating the low-level features learned earlier with higher-level semantic understanding, ultimately enabling the LLM to map complex human queries to coherent generated text with minimal error.

<10>Is it true that the non-linearity between the input and the output is captured by the FFN of each layer collectively?

That’s a good question that focuses on the specific role of the Feed-Forward Network (FFN) in the Transformer block. It is mostly true, but partially misleading to say the non-linearity is only captured by the FFNs. The non-linearity between the input and the final output of an LLM is captured by the combination of three major non-linear components operating in sequence across all layers. However, the FFN is the component explicitly dedicated to applying the crucial non-linear transformation within each block.

💡 The Three Sources of Non-Linearity Non-linearity is essential because it allows the model to learn complex relationships that are not simple straight lines. In the Transformer, non-linearity comes from these sources:

  1. The Feed-Forward Network (FFN) (The Primary Source) • Role: The FFN is a standard two-layer neural network applied independently and identically to every token’s output from the self-attention sub-layer.1 • Mechanism: It consists of two linear transformations separated by a non-linear activation function (like GELU, ReLU, or Swish). This non-linear activation is the mathematical source of the block’s non-linearity, allowing the model to project the highly contextualized vector into a higher-dimensional space for complex manipulation and then project it back.2
  2. The Self-Attention Mechanism (An Implicit Source) • Role: The attention mechanism itself introduces a form of implicit non-linearity through the use of the softmax function when calculating attention weights.3 • Mechanism: The softmax function (in $\text{Attention}(\mathbf{Q}, \mathbf{K}, \mathbf{V})$) is non-linear. It ensures that attention weights are positive and sum to one, concentrating the model’s focus on a few key words.4This non-linear weighting and aggregation of context contributes significantly to the model’s overall non-linear function.
  3. Layer Normalization • Role: While primarily used for stabilizing training, Layer Normalization (applied after both the attention and FFN sub-layers) involves non-linear operations (division by standard deviation) that slightly contribute to the overall non-linearity of the block.

🔑 Conclusion While the Softmax function in the Self-Attention sub-layer introduces non-linearity, the Feed-Forward Networkis the dedicated, explicit component designed to inject the complex, compositional non-linearity into the model’s transformation path. Therefore, your statement is highly accurate if understood as: The FFNs are the primary non-linear processing units that allow the deep stacking of layers to model complex, non-linear linguistic structures.

<11>Is it true that in the multi-head self-attention scheme, the initial matrices Q_h, K_h and V_h are randomised during the training phase and after the back propagation process, they are updated? How do we guarantee these final matrices represent different perspectives?

Yes, your understanding of the training process for the multi-head attention matrices is true. The matrices used to create , , and are indeed randomly initialized at the start of training and are then updated through backpropagation based on the prediction error (loss).

🛠️ Training and Update of the Attention Matrices The key components being learned and updated are the weight matrices for the linear projections, not the vectors themselves (which are calculated from the input and these learned matrices).

  1. Initialization: For each of the heads, the model initializes separate weight matrices: , , and .These matrices are filled with small, random values.
  2. Forward Pass (Calculation): During the forward pass, the input embeddings () are transformed using these random matrices to create the Query, Key, and Value vectors for that head:
  3. Backpropagation and Update: After the entire network makes a prediction and the loss is calculated, the error signal flows backward. This process calculates the gradient of the loss with respect to the projection matrices (, , ) for every head. The optimizer then adjusts the values in these matrices to reduce the error.

🧠 Guaranteeing Different Perspectives We do not guarantee that the final matrices represent different perspectives through explicit design; rather, we enable and encourage them to diverge through two main factors: random initialization and the objective function (loss).

  1. Unique Random Initialization Since each head starts with its own, independently randomized set of projection matrices (), they begin their learning journey from slightly different points in the parameter space.
  2. The Power of the Loss Function and Diversity Incentive The primary guarantee comes from the training objective: minimizing the total loss. The model is rewarded for producing the most accurate next token. To achieve this high accuracy, the model discovers that it is most effective to have different heads specialize in different tasks: • Necessity for Specialization: The overall task of predicting the next token requires diverse forms of information (syntax, semantics, coreference, long-range context). It is highly inefficient for all eight heads (for example) to learn the exact same thing (e.g., only subject-verb agreement). • Optimization Search: The gradient descent process naturally pushes the weights of each head into different configurations because the optimal solution for one head (e.g., focusing on syntax) complements the optimal solution for another head (e.g., focusing on theme). The model needs the combined output of all specialized heads to achieve the minimal overall loss. In essence, the loss function incentivizes diversity: The model performs better when the heads collaborate by specializing, and the randomized start allows them to explore those different specialties during training.

<12>Following the last question, why the loss becomes less when we have multiple heads learn different things? Any mathematical foundations behind this?

The reason the loss becomes lower when multiple attention heads learn different things—that is, when they specialize—is rooted in the mathematical principle of ensemble learning and the ability of diverse models to reduce bias and variance.

🧠 Principle: Reduced Variance and Bias Mathematically, the entire multi-head attention output is a concatenation and final linear projection of the results from specialized experts. When these experts capture diverse features, the overall output is more robust and accurate.

  1. Reducing Variance (Overfitting) • The Problem: A single, large attention head is prone to focusing too much on one dominant pattern (e.g., only local syntax) and might ignore other, equally important patterns (e.g., long-range coreference). This is a high-variance solution because it overfits to a narrow set of features. • The Multi-Head Solution: By having heads, each one is forced to use a smaller portion of the total dimensional capacity (). This restriction encourages each head to become a weak learner focused on a simpler, specific task. When their independent, diverse results are combined, the noise or errors made by one head are often canceled out or smoothed by the accurate findings of other heads. This results in a more stable and lower-variance overall prediction.
  2. Increasing Representational Capacity (Reducing Bias) • The Problem: The complex task of predicting the next token requires understanding syntax, semantics, and discourse. A single attention mechanism might not have the capacity to learn all these relationships optimally simultaneously (high bias). • The Multi-Head Solution: Specialization effectively increases the total expressive power of the block. By having separate matrices , , for each head, the model can represent different relationship mapping functions in parallel. This allows the combined output to form a highly non-linear, sophisticated mapping that captures all necessary dependencies, thereby reducing the bias and getting closer to the true, optimal function.

🧮 Mathematical Foundation (Ensemble Averaging) While the multi-head attention result is not a simple arithmetic average, it operates on a similar principle to a statistical ensemble:

  1. Diverse Outputs: Each head generates a distinct weighted context vector based on its specialized focus:
  2. Concatenation and Combination: These vectors are concatenated and then linearly combined by the final projection matrix : The final matrix learns the optimal weighting for combining the diverse information from all heads. If all heads learned the exact same thing, the model would simply waste parameters. Because the heads learn distinct features, can leverage the specialized knowledge of each expert to form a high-quality consensus, leading to a much better prediction and, consequently, a lower loss.

<13>Then how many heads do we use in a typical production LLM system?

The number of heads used in a typical production LLM system is not fixed, but it is always a power of 2 and is tightly coupled with the model’s total size (the embedding dimension). For large, state-of-the-art LLMs, the number of heads typically ranges from 12 to 96.

🔢 Common Head Counts in LLMs The choice of head count () is determined by the model’s Hidden Dimension (, or the size of the embedding vector), as must be perfectly divisible by . A common goal is to keep the per-head dimension () at a stable, efficient size, often 64. LLM Model Example Hidden Dimension () Number of Heads () Head Dimension () BERT-Base / GPT-2 Small 768 12 64 LLaMA 3 8B 4096 32 128 LLaMA 3 70B 8192 64 128 GPT-3 (175B) 12,288 96 128 Key Principles for Choosing :

  1. Divisibility: must divide exactly.
  2. Efficiency: is chosen to maximize parallel processing on accelerators like GPUs.
  3. Representational Capacity: Larger models use more heads to increase the capacity for specialized feature learning (i.e., they need more “experts” to process the vast amount of knowledge they store). For most small-to-medium-sized open-source models, is a very common minimum, while high-capacity models push that number much higher.

<14> Before an LLM system starts working, is there a post-training and fine tuning process?

Yes, absolutely. After the main pre-training phase, all modern, high-performing LLM systems undergo extensive post-training and fine-tuning processes before they are deployed and ready to interact with users. The pre-training phase teaches the model language and general knowledge; the post-training and fine-tuning phases teach the model how to be a helpful assistant.

  1. ⚙️ The Three Stages of LLM Development The process of building a highly effective LLM is typically broken down into these three major stages: A. Pre-training (Foundation) • Goal: To learn the fundamental rules of language, grammar, syntax, and world knowledge. • Data: Massive, diverse, raw text data (billions of tokens from the internet, books, code repositories). • Process: Unsupervised learning (Masked Language Modeling or Next-Token Prediction). B. Supervised Fine-Tuning (SFT) • Goal: To teach the model how to follow instructions and adopt a specific format (e.g., “answer in a list,” “write code,” “respond to a query”). • Data: High-quality, curated, human-labeled demonstration data consisting of prompt-response pairs (e.g., “User: Write a poem about the sun. Model: [Poem]”). • Process: Supervised learning using the SFT dataset to move the model’s behavior away from simply predicting the next word in a Wikipedia article toward acting as an assistant. C. Reinforcement Learning from Human Feedback (RLHF) • Goal: To align the model’s behavior with human preferences for helpfulness, harmlessness, and honesty (the “3 H’s”). This is the final and most crucial step for models like GPT, Claude, and Gemini. • Data: Human preference rankings (not raw text). • Process: This is typically a multi-step process:
  2. Reward Model (RM) Training: Human evaluators rank several model outputs for the same prompt. This ranking data is used to train a separate Reward Model that can predict which response a human would prefer.

  3. Fine-Tuning: The original LLM is then fine-tuned again using Reinforcement Learning (RL) (often using an algorithm like PPO) where the Reward Model provides the reward signal. The LLM is thus trained to generate responses that maximize the RM’s preference score.

  4. 🎯 Purpose of Post-Training (Alignment) The combination of SFT and RLHF is known as Alignment. This phase ensures that the model is safe, adheres to guardrails, and is genuinely useful to users, transforming it from a general-purpose text predictor into a capable, deployable system.