The Black Box of Language: How Large Language Models Capture Meaning in Semantic Geometry

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Introduction: From Words to Geometry

When you type a sentence into a large language model (LLM), something remarkable happens. What began as ordinary human language is transformed into an abstract geometry, a mathematical landscape where words, phrases, and concepts take shape as points and curves in high-dimensional space.

This “semantic geometry” is the hidden terrain that allows the model to generate fluent answers, connect distant ideas, and even mimic reasoning. It isn’t a dictionary or a database of facts. Instead, it’s a statistical map of how words relate to one another, learned through exposure to billions of examples.

But here lies the great puzzle: how exactly is this geometry captured inside the artificial neural network (ANN)? We know the sequence of steps at a high level — language → tokens → embeddings → semantic geometry → weights and biases → probability maps. We know the process involves countless adjustments to billions of parameters during training. Yet no one can point to a specific place in the network and say, “Here is where the meaning of cat lives” or “this neuron contains the relationship between gravity and falling.”

Instead, what we see is a black box. The knowledge is everywhere and nowhere, smeared across the network in a way that is cumulative, multiplexed, and distributed. This essay explores that mystery in plain English — how LLMs translate language into semantic geometry, why the final configuration of weights is so hard to interpret, and what this tells us about the limits of our current understanding of intelligence.

Section 1: Breaking Down the Journey — From Language to Numbers

Let’s start simple. Computers cannot understand words directly. They only manipulate numbers. So when we feed text into an LLM, the first job is to turn words into numerical form.

Tokens: Words (or pieces of words) are chopped into “tokens.” For example, the sentence The cat sat on the mat might become [The] [cat] [sat] [on] [the] [mat]. But tokens can be smaller than words: “unbelievable” might become [un] [believ] [able].
Embeddings: Each token is assigned a vector — a string of numbers like [0.12, -0.56, 0.87, ...]. This is called an embedding. Think of it as the “address” of the token in a multidimensional space.
Semantic Geometry: When many tokens are embedded, a landscape emerges. Words with similar meanings end up near each other. “Cat” is close to “dog,” but far from “astronomy.” This arrangement is not designed by hand; it emerges statistically from training.

At this stage, we already have something powerful: a geometry of meaning. But embeddings alone don’t make a language model. They are just the entryway. The real action happens when these vectors are processed by the network.

Section 2: The Neural Network as a Landscape of Adjustments

An artificial neural network is a massive web of simple units called neurons. Each neuron takes in numbers, applies a simple transformation, and passes the result forward. Neurons are connected by weights (scalars) and adjusted by biases (offsets).

The key is this: training changes the weights and biases. When the model makes a wrong prediction during training, the error is measured, and the network slightly adjusts its weights to reduce future errors. This process is called backpropagation.

Now imagine doing this billions of times, across billions of tokens, sentences, and contexts. Each tiny adjustment is like carving a groove into clay. Over time, the clay becomes a sculpture. The weights and biases in the final network are that sculpture — a cumulative record of countless relationships between tokens.

But here’s the catch: the record is not stored in one place. It is distributed across the entire network. No single neuron holds the meaning of “gravity.” Instead, meaning is encoded in patterns of activation spread over many neurons, the way a hologram stores an image across its whole surface.

This is where the idea of multiplexing comes in. Just as a single radio wave can carry multiple signals by layering frequencies, a single ANN configuration can hold billions of overlapping relationships at once. The network’s weights are a giant multiplexed storage system, holding not individual facts but a dense statistical structure.

Section 3: Why the Record is Cumulative and Distributed

To understand why this cumulative, distributed storage happens, let’s use an analogy.

Imagine you are teaching a child the meaning of words by giving examples. You tell them:

“A cat is an animal.”
“A dog is an animal.”
“A cat chases mice.”
“Dogs bark.”

Each new sentence adds to the child’s mental map. But the child doesn’t create a separate box in their brain labeled “cat.” Instead, they weave the word “cat” into a network of relationships. The meaning is cumulative: it builds from many overlapping associations.

An LLM works the same way. Every time a token appears, the network slightly adjusts its weights. These adjustments aren’t stored as “facts,” but as changes to a distributed landscape. Over billions of examples, the landscape becomes rich enough that the model can predict what word is likely to come next in almost any context.

Thus, the “record” of meaning isn’t a table of facts. It’s a statistical field woven into the network itself.

Section 4: The Black Box Problem

Here we arrive at the central mystery. We know how training works. We can write down the equations. We can measure the final weights. Yet we cannot say where a particular piece of knowledge is stored.

For example, suppose the model “knows” that Paris is the capital of France. Where is that information in the network? It’s not in one neuron. It’s not even in one layer. Instead, it is smeared across many connections, distributed in a way that resists human interpretation.

This is why researchers talk about the “black box” nature of neural networks. We see the inputs and outputs, but the middle remains obscure.

Some progress has been made:

Activation studies: By testing which neurons activate for certain inputs, researchers have identified partial clusters of meaning (so-called “concept neurons”).
Linear probes: By training simple models on frozen embeddings, researchers can extract directions in the geometry that correspond to concepts (like gender or tense).
Attention maps: By visualizing which tokens the model “pays attention to,” we get a glimpse of the internal reasoning process.

Yet these are fragments. The overall system remains opaque. The knowledge is everywhere and nowhere — distributed like ripples in a pond.

Section 5: Multiplexing as a Way to Think About It

The best metaphor for how LLMs store meaning may be multiplexing.

In telecommunications, multiplexing allows many signals to be carried on a single channel. For example, radio waves can carry multiple stations at once by layering them at different frequencies.

Similarly, a trained ANN carries billions of relationships at once in its weights. The “frequency spectrum” here is the multidimensional parameter space. Each new training example modifies that space slightly, without erasing the old ones. Over time, the network becomes a multiplexed configuration — a single system that encodes many signals simultaneously.

This explains why it is so hard to isolate a single piece of knowledge. Each “signal” (relationship between tokens) is not stored in isolation, but interwoven with others. To pull out one thread is to tug on the whole fabric.

Section 6: Why We Don’t Know Where the Knowledge Lives

Why can’t we just read the weights like a book? After all, we know the numbers.

The problem is interpretability. Neural networks do not store information in human-readable form. They don’t have a dictionary of words or a table of facts. Instead, they have a web of numbers whose meaning only emerges through collective behavior.

It’s like trying to read a human brain neuron by neuron. The brain knows what a cat is, but no single neuron contains “catness.” Instead, catness is a pattern that emerges across millions of neurons.

In LLMs, the same principle applies. Knowledge is emergent, not localized. It is statistical, not symbolic. This is both the strength and the weakness of neural networks. It makes them incredibly powerful at capturing patterns, but also incredibly difficult to interpret.

Section 7: The Pipeline Summarized

To pull the threads together, let’s walk the pipeline step by step:

Language → Tokens
Words are chopped into tokens.
Tokens → Embeddings
Each token is turned into a vector in a high-dimensional space.
Embeddings → Semantic Geometry
Relationships between words form a landscape of meaning.
Semantic Geometry → ANN Weights
The network processes embeddings through layers of neurons. Training adjusts weights and biases to capture statistical relationships.
Weights → Statistical Map
The final weights encode billions of overlapping relationships in a distributed, multiplexed form.
Statistical Map → Probability Algorithm
At runtime, the model uses this map to predict the next word with high probability, generating fluent text.

And the black box? It is step 4 and 5: how semantic geometry is encoded into weights. We see the process, but we do not fully understand the representation.

Section 8: What This Mystery Means for AI

This black box raises profound questions:

Limits of Control: If we cannot see how knowledge is stored, can we truly control what the model knows or does?
Trust and Safety: Without interpretability, ensuring alignment with human values is harder.
Scientific Insight: Cracking the black box might reveal new principles of intelligence — artificial and biological.

In some ways, the mystery is not a bug but a feature. It shows that intelligence, whether natural or artificial, may inherently involve distributed, emergent patterns that defy reduction to simple rules.

Section 9: Analogies to Biology

It’s worth noting that biology faces the same puzzle. In the human brain, memories are not localized in single neurons. They are distributed across networks. Similarly, in genetics, information is not just in DNA, but also in epigenetic and regulatory systems that interact in complex ways.

Just as we cannot point to a single cell and say “this contains your memory of Paris,” we cannot point to a single weight and say “this contains the meaning of Paris.” The information is woven into the whole.

This suggests that distributed, cumulative encoding may be a universal feature of systems that learn from data.

Section 10: Toward the Future

Researchers are actively working to open the black box. Approaches include:

Mechanistic interpretability: Reverse-engineering neural circuits within models.
Sparse models: Designing architectures where knowledge is more localized.
Hybrid systems: Combining neural networks with symbolic reasoning.

But even if we never fully open the box, understanding that meaning is distributed and multiplexed is a step forward. It helps us see LLMs not as databases, but as geometrical engines of probability — machines that carve meaning into the shape of space.

Conclusion: The Beauty of the Black Box

Large language models translate language into geometry. They capture billions of relationships between tokens in a cumulative, distributed, multiplexed fashion. We can describe the pipeline. We can measure the outputs. But the exact way embeddings become encoded in weights remains a mystery.

Perhaps this is not surprising. After all, intelligence itself — human or machine — may always be partly opaque. What matters is that the black box works: it generates coherent language, connects ideas, and reveals the hidden geometry of meaning.

In plain English: the magic of LLMs is not that they memorize facts, but that they sculpt a landscape of meaning in which words live as geometry. And though we cannot yet map every valley and peak of that landscape, we are beginning to glimpse the contours of a new kind of knowledge — one that is everywhere and nowhere at once.