LOS ANGELES, CA, January 15, 2026 /24-7PressRelease/ -- In the current landscape of artificial intelligence, the Transformer architecture is ubiquitous. It powers the Large Language Models (LLMs) that have reshaped industries, from coding to content creation. However, for many practitioners, the specific mathematical choices within the "Attention Mechanism", the heart of the Transformer, remain a black box. Why use a dot product? Why Softmax? Are these arbitrary engineering hacks, or are they theoretical necessities?

Neel Somani, a researcher with a background in quantitative finance and formal methods, argues that the Transformer architecture is not a random collection of components. Instead, he demonstrates that by starting with a small set of reasonable, minimalist assumptions, one recovers the standard Transformer attention mechanism.

By understanding these foundational assumptions, researchers can identify which parts of the architecture are theoretically mandated and which are merely design choices ripe for disruption.

The Problem with Predecessors: Why Attention Exists

To understand Neel Somani's derivation, one must first revisit the limitations of the Recurrent Neural Network (RNN). Classic RNNs process sequences token by token. They rely on a "hidden state", essentially a vector that acts as an accumulator of everything the model has seen so far.

The flaw in this approach is the "vanishing gradient" or long-range dependence problem. If a crucial piece of context appears at the start of a 10,000-token sequence, its signal dilutes as the RNN processes subsequent tokens. The model essentially forgets.

Somani posits that an ideal model should not rely on a decaying memory. Instead, it should look at all previously seen tokens simultaneously to predict the next one, weighting them by relevance. This requires computing a relevance score between the current position ($i$) and every other position ($j$).

The goal is to determine the simplest mathematical constraints that turn this concept into a functional architecture.

The Derivation: Five Assumptions That Build the Transformer

Somani approaches this by looking at the output vector at a specific position. He utilizes the Deep Sets theorem (Zaheer et al., 2017) to enforce permutation symmetry. Simply put, once the relevance scores are calculated, the output shouldn't depend on the order in which the context pairs are processed.

From this starting point, Neel Somani outlines five specific assumptions that narrow the infinite possibilities of functions down to the specific architecture used by GPT-4 and Claude today.

Assumption 1: Simplicity via the Identity Function

The Deep Sets theorem allows for complex transformation functions ($rho$) on the output. However, Somani notes that complex transformations often destroy information or create scaling issues.

The Constraint: Somani assumes $rho$ is the identity function.

The Result: The model sums the weighted inputs directly, rather than mapping them into a different manifold or dimension. This keeps the structure interpretable and preserves the information

Assumption 2: Relevance-Contribution Proportionality

How does the "relevance" of a token relate to its "contribution" to the answer?

The Constraint: Somani assumes a linear relationship. If a token's relevance score is scaled by a factor of $k$, its contribution to the output should scale by the same factor.

The Result: This assumption makes the function separable. It splits the mathematics into two distinct parts: a scalar that measures importance (magnitude) and a vector that determines the content being contributed.

Assumption 3: Linear Change of Coordinates

What function should be used to process the content vector ($v$)?

The Constraint: To keep the model efficient, Somani assumes $v$ is a linear transformation of the embedding.

The Result: This justifies the learned weight matrices found in Transformers. Each token contributes a linearly transformed version of its embedding, weighted by its relevance score.

Assumption 4: Efficient, Parallelizable Scoring
Perhaps the most critical constraint involves hardware. A fully general relevance function would require looking at all tokens at once, creating an $O(N^2)$ computational bottleneck that is slow to calculate sequentially.

The Constraint: The relevance function ($u$) must be built from tensor operations (linear projections, inner products) that are highly parallelizable on GPUs.

The Result: This necessitates the use of the dot product for similarity. It implies that we first project the input into "Query" and "Key" vectors, and then take their inner product to find their similarity.

Assumption 5: Normalization

Finally, raw dot products can vary wildly in scale.

The Constraint: The relevance scores must measure relative importance. If all scores increase uniformly, the ranking shouldn't change.

The Result: This motivates a differentiable normalization function. While there are options like Gumbel-Softmax, the standard Softmax is the most practical choice. To prevent large vector dimensions from skewing the Softmax, the logits are scaled, resulting in the famous "Scaled Dot-Product Attention."

The Implications for Future Architectures
Neel Somani's derivation serves as a proof of concept: if you accept these five specific assumptions, you must use the Transformer architecture. There is no other mathematical conclusion.

However, Somani's work also implies a disruptive corollary. While some constraints (like parallelizability) are non-negotiable for modern hardware, others are arbitrary.

Does the transformation function have to be the identity?
Must relevance be strictly proportional to contribution?
Is the dot product the only efficient way to measure similarity?

By identifying which parts of the Transformer are theoretically forced and which are choices, researchers can begin to explore new architectures. For example, Somani points out that while the derivation begins by assuming permutation invariance, Transformers explicitly re-inject positional encodings later, a contradiction that suggests there may be more elegant ways to handle sequence order.

About Neel Somani
Neel Somani is a researcher and entrepreneur operating at the intersection of machine learning and formal methods. A graduate of UC Berkeley with a triple major in Computer Science, Mathematics, and Business, Somani began his career researching computer security before moving to quantitative finance at Citadel.

In 2022, he founded Eclipse, an Ethereum Layer 2 solution powered by the Solana Virtual Machine (SVM), which raised $65 million to accelerate blockchain throughput. Currently, Somani is focused on philanthropy and machine learning research, exploring the theoretical underpinnings of neural architectures to drive the next generation of AI innovation.

Explore the Future of AI
Understanding the "why" behind AI architecture is the first step toward building what comes next. Whether you are a researcher looking to break the constraints of the Transformer or a developer integrating these models into enterprise solutions, staying grounded in first principles is essential.

To learn more visit: https://neelsomani.com

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