The Illusion of Incremental Learning in Large Language Models
Large Language Models (LLMs) have captivated many with their ability to generate coherent, context-aware responses. This often gives users the impression that these models are learning and improving with each interaction and offers the illusion of incremental learning. But beneath the surface, these models simulate short-term understanding, without actually modifying their internal parameters.
In this post, we’ll explore both incremental learning and the underlying maths used for LLMs to create this illusion. We’ll also examine why true incremental learning isn’t implemented in LLMs, as it poses significant security and functionality risks.
What is Incremental Learning?
Incremental learning is a form of continuous learning where a model updates its internal parameters with new data on the fly. This allows the model to adapt and refine its knowledge base in real time without retraining from scratch.
Mathematically, this can be viewed as an optimisation problem where the model minimises a loss function L over new data Dnew, while maintaining knowledge from previously learned data Dold.
This can be represented as:
In incremental learning, this update happens continuously, with the model retaining new information while preserving previously learned knowledge. This allows a machine learning model to evolve with new information over time.
The Maths Behind LLMs: Context Vectors
LLMs, however, do not employ incremental learning. Instead, they rely on expanding the context vector to give the illusion that they are adapting to past interactions. In simpler terms, LLMs use a sliding window of relevant text that acts as a temporary memory.
The process of generating responses involves two key steps:
Encoding Input into a Context Vector: LLMs encode the input text into a high-dimensional representation, often referred to as a context vector. This vector holds information about the current conversation.
The model uses an attention mechanism to compute this vector. Let’s assume we have an input sequence of tokens x1,x2,…,xnx1,x2,…,xn. Each token is represented by an embedding vector, and the attention mechanism calculates a weighted sum of these embeddings, where the weights depend on the relevance of each token to the rest of the sequence.
Mathematically, the attention score for each token is computed using a scaled dot-product attention mechanism:
This produces a context vector that summarises the input sequence, and this context is used to generate the next response.
Using Context to Predict the Next Token: Once the model has encoded the input into a context vector, it uses it to predict the next word or token in the sequence. The model does this by maximising the probability of the next token xn+1xn+1 given the previous tokens x1,x2,…,xnx1,x2,…,xn. This is done using:
This context-based prediction makes the model’s response appear as though it is learning from the conversation, but in reality, it is simply responding based on the temporary context window.
Why LLMs Don’t Use Incremental Learning: The Security and Hack Risk
Despite the utility of incremental learning in many fields, LLMs deliberately avoid it, primarily due to security concerns.
Implementing incremental learning in public-facing models like GPT would expose the model to severe vulnerabilities. A model that learns from every user interaction could be hacked or manipulated by feeding it malicious or biased content. Over time, these biased inputs could corrupt the model’s internal knowledge, leading it to produce inaccurate or even harmful responses. This risk is one of the reasons why LLMs are not designed to update their weights based on individual interactions.
An example of the dangers of this approach is Microsoft’s chatbot Tay. Tay was designed to learn from user interactions on Twitter. However, within hours of its launch, users flooded it with offensive and inappropriate content, causing Tay to "learn" these behaviours and reflect them in its responses. The experiment was quickly shut down, but it highlighted how susceptible incremental learning can be to malicious inputs in a real-world setting.
The Role of Context Expansion in LLMs
Instead of learning incrementally, LLMs rely on expanding their context window, which temporarily captures past information to create a coherent response. This temporary context does not change the underlying model parameters, preserving the integrity of the model while still providing short-term "awareness."
For example, when you have a conversation with an LLM, the model uses tokens from earlier in the conversation to create the context vector for generating responses. This is why it seems like the model remembers what was said earlier, but the context only persists within that session. Once the conversation ends, the model discards the context, and future interactions are treated as new conversations.
This approach maintains model safety while still allowing for sophisticated, context-aware responses.
Large language models are incredibly powerful tools, but they do not engage in true incremental learning. Instead, they rely on expanding context vectors to simulate learning during conversations. This design ensures that the models remain secure and robust, avoiding the risks of hackable incremental learning systems. As AI continues to evolve, striking a balance between adaptive learning and security will remain a key challenge, but for now, context expansion remains a safe and effective solution.
Understanding the mathematical underpinnings of these models is crucial for appreciating both their potential and their limitations. LLMs, while impressive, are not learning in real time — they are simply leveraging the magic of context vectors to give the appearance of it.
