Reasoning Model · Axiom Vertex

Glossary

Terms of the AI model and of Axiom Vertex that this model uses.

Agentic system
A system of several AI agents that coordinate through an orchestrator toward one goal.
AI agent
An active system that wraps an AI model with memory, goals and software tools and works in a loop, searching, reading and acting, to plan and carry out a task.
AI model
The model that processes data and generates text, predictions or insights. It is the core that an AI agent wraps with memory, goals and tools.
Attention
The operation by which each token reads from the tokens before it. The token's query is compared with their keys, softmax turns the comparisons into weights, and the output is the sum of their values weighted by those weights.
Attention head
One of the parallel attention computations in a layer. Each head has its own queries, keys and values and can attend to a different part of the context.
Attention sink
A token, usually the first, that receives a large share of the attention of later tokens whatever its meaning. Attention weights must add up to 100 percent, and the sink gives a head a place to put weight that no other token earns.
Autoregressive generation
Generation in which a model produces one token at a time, each conditioned on all the tokens before it.
CAG, cache-augmented generation
Loads the knowledge into the context once and reuses the stored key-value cache for every query, so that no retrieval step is needed. It is limited by the size of the context window, and the cache is rebuilt when the documents change.
Compute fabric
The dedicated hyperdimensional compute environment of a Virtual Organization. Axiom Vertex enables an AI model to reason on it over the Virtual Organization's validated records.
Context hash
A hash of the exact bytes of the context records. Identical records in identical order give the same hash, so the hash identifies the context that the model read.
Context window
The tokens that a model reads when it produces the next token, here the validated context records followed by the question. Its length is limited by the model.
Continuous embedding
A vector of real numbers that represents data, such as an image or a passage of text, as a point in a learned space.
Convolutional network
A neural network that detects patterns in a grid, such as the pixels of an image, by sliding small filters across it.
Coordinate
The permanent location of a record on the compute fabric. It is a deterministic function of the record's content, so any party that holds the same bytes recomputes the same coordinate.
Data storage
The dedicated storage of a Virtual Organization, in which its validated data and their sealed validation proofs are held. It takes one of three forms, a managed silo (a dedicated bucket on Cloudflare R2), a bucket that the customer names with an approved provider (Cloudflare R2 or AWS S3), or on-premises storage. The customer owns the data plane, and EdgeManager is the control plane.
Decision model
A model that returns a probability for each of a set of allowed answers, and a confidence, and writes no text. Jev from TypeSafe AI is an example.
Denoised sequence
The output of a diffusion model after its noise has been removed step by step.
Device-generated data
Camera, LiDAR, depth, radar, ultrasonic, inertial, tactile and joint-sensor readings, with operation, safety, metering and lifecycle records, validated at their own ingest gateway.
Diffusion model
A model that generates data by starting from noise and removing it in steps. Diffusion models generate images, video and audio, and diffusion language models apply the process to text.
Drift-free context
Context whose records are validated and returned as the same bytes for the same query, so the AI model reads an identical context on every run.
Embedding
The vector of numbers that represents a token in a form that a model computes with. The model shown uses 896 numbers for each token.
Expressway fabric
The physically separate network fabric, InfiniBand with RDMA, for high-throughput accelerators and top-tier GPUs. It keeps their traffic apart from standard Ethernet traffic, so a burst on one fabric does not slow the other.
Feed-forward network
The part of a transformer layer that transforms each token's vector on its own after attention.
Forge
The creation of a record's validation proof in StateFlow, in which the record's coordinate is computed from its content.
Gating
A step after retrieval that lets a system answer only when the retrieved records support an answer, and abstain when they do not.
Geodesic Context Engine
The engine that assembles context for an AI model from the validated records of a Virtual Organization, built to support reasoning over long-form context at hyperscale. For a query vector it finds the closest records and returns each with its index key, ledger proof hash and similarity score.
Graph neural network
A neural network that works on a graph of nodes and relations, passing messages along the relations to learn from connected records.
Greedy decoding
Choosing the most probable token at every step.
Hidden state
The vector that represents a token inside the model after each layer.
Hub
The part of Axiom Vertex that holds the Root System Laws and applies them to every record.
Hybrid RAG
Retrieval-augmented generation combined with keyword search, reranking and gating. A decision model can rerank the top candidates and, given a "not stated" option, decline when the answer is not in the documents.
Hyperdimensional tier
The size class of the hyperdimensional vectors by which records are compared, from AI Quant at 4,096 dimensions upward. An AI model is registered at the tier that matches the size of its embeddings.
Hypergeometric Ledger
The ledger of a Virtual Organization that stores validation states and leaves the underlying data payloads in the owner's storage. For each validated record it commits the Merkle proof, the entry in the proof of validation history and the ledger record that links them.
Ingest gateway
The entry point where the platform checks the source, structure and content of data before the data is accepted. Federated, AI-generated and device-generated data each pass their own gateway.
JEPA, joint embedding predictive architecture
A model that learns by predicting the representation of missing or future parts of its input in a learned representation space, and not the raw data. V-JEPA 2 applies it to video.
KAG, knowledge-augmented generation
Builds a knowledge graph of entities and relations linked to the source text and plans a question as steps over the graph. A graph takes time to build and to maintain.
Key-value cache
The stored keys and values of the tokens already read, which a model reuses and does not recompute.
Knowledge graph
A network of entities and the relations between them, linked to the source text.
Language model
A model trained to predict the next token of text. Large, small and multimodal language models write text one token at a time.
Latent vector
A vector inside a model that encodes meaning in a learned space and not in the form of the original data.
Layer
One repeated block of a transformer, made of attention and a feed-forward network. The model shown has 24 layers.
Logit
The raw score that a model assigns to a token before softmax. A larger logit means a more probable token.
Model vocabulary
The set of tokens that a model can read and write. The model shown has 151,936 tokens.
Orchestrator
The component of an agentic system that assigns work to the agents and combines their results under policy.
Platform vocabulary
The vocabulary that the platform maintains and shares with every Virtual Organization. It is built from a curated corpus of sources that the platform is entitled to use, it is separate from the data of every Virtual Organization, and it is released in attested versions. The vocabulary resolves the words of a question to coordinates.
Predictive world model
A model that learns how an environment evolves, from video and from the actions of a system that acts in it, and predicts what comes next so that the system can plan actions.
Project (domain)
The level of a Virtual Organization at which the validated records of one body of work are committed. A project is one domain, and its name is fixed at creation.
Proof of validation history
A hash chain in the Hypergeometric Ledger. Each commit appends one entry, which places the record at a specific position in the sequence of commitments.
Query vector
A vector that represents a query. The AI application sends it to the Geodesic Context Engine, which returns the closest records, each with its index key, ledger proof hash and similarity score.
Query, key and value
The three vectors that each token produces in an attention head. A token's query is compared with the keys of the tokens before it to decide how much to read from each token's value. The query asks, the key offers a match and the value supplies the content.
RAG, retrieval-augmented generation
Cuts documents into chunks stored as vectors and adds the chunks closest to the query by vector similarity to the prompt. A poor retrieval produces a poor answer.
Reasoning bridge
The coordinator of the query resolution of one sector of a Virtual Organization. It receives a query, decomposes it into sub-tasks, routes the sub-tasks to its runners, executes them, recomposes their outputs into one validated coordinate and commits the proof to the Hypergeometric Ledger.
Reranking
Reordering retrieved candidates with a second, more precise model so that the best candidates come first.
Retrieved context
Context assembled by retrieval, as in retrieval-augmented generation. The records that reach the model can differ between runs when the index changes, when approximate search or reranking returns a different set or order, or when an older version of a record ranks first.
Root System Laws (RS Laws)
The Root System Laws govern and enforce validation and dimensional laws on the architecture. The Hub applies the RS Laws validation when a validation proof is forged and enforces the RS Laws dimensional when a record is used. A record that fails any law is refused.
RRM Harness
The Relational Reasoning Model Harness, the bridge between text and coordinates. It resolves the words of a request to validated coordinates and passes them to the reasoning bridges.
Runner
The unit that executes the sub-tasks of a reasoning bridge. It returns an output coordinate with a proof.
Sampling
Choosing the next token at random in proportion to its probability, after temperature and top-k or top-p have reshaped the probabilities. What is sampled is the next token.
Softmax
The function that turns a list of scores into probabilities that are positive and add up to 100 percent. Larger scores receive larger probabilities.
StateFlow
The validation stage in which the validation proof of a record is forged. It is organized in layers of validation checkpoints, and a record that fails any checkpoint is refused.
Temperature
A setting that divides the logits before softmax. Below 1 the probabilities concentrate on the most probable tokens, above 1 they spread out, and as it approaches 0 the choice approaches greedy decoding.
Time-series model
A model of values ordered in time, such as telemetry and sensor readings, used for forecasting and anomaly detection.
Token
The unit of text that a model reads and writes, such as a word, a part of a word or a symbol. Each token has a numeric identifier in the model's vocabulary.
Tokenizer
The component that splits text into tokens and gives each token its identifier. It belongs to the model.
Top-k
Sampling limited to the k most probable tokens. The number is k, the count of tokens kept, so 5 keeps five candidates. The probabilities of the kept tokens are then scaled to add up to 100 percent.
Top-p
Sampling limited to the smallest group of most probable tokens whose probabilities add up to at least p, also called nucleus sampling. The number is p, a share between 0 and 1, so 0.9 keeps the tokens that together hold 90 percent. The probabilities of the kept tokens are then scaled to add up to 100 percent.
Transformer
The neural network architecture, built from layers of attention and feed-forward networks, that underlies today's language models.
Typed decision
An answer returned in a fixed type, such as a choice from a list, a score on a scale or a yes or no probability, as a decision model does.
Validation proof (datum)
An unforgeable, immutable, re-derivable mathematical identity for one record. It is the record's coordinate sealed by its Merkle leaf, it carries the record's entry in the proof of validation history, and it is committed to the Hypergeometric Ledger and stored with the validated data.
Virtual Organization (VO)
The isolated tenant of the platform. Each Virtual Organization has its own compute fabric, its own Hypergeometric Ledger and its own data storage.
Vision model
A model that works on pixel grids, such as images and video frames. Convolutional networks and vision transformers are vision models.

Guide

How to read this model, and what it shows about an AI model that reasons, trains and operates on Axiom Vertex.

What this model shows

The model follows one question through an AI model, from the validated records that the model reads to the answer that it writes, and sets the result beside the same question over retrieved context. It lets a technical reader see, step by step, where Axiom Vertex acts and where the AI model's own computation begins.

How to use it

What is being sampled

An AI model that writes text produces one token at a time. At each step it holds a score, a logit, for every token in its vocabulary. Softmax turns the scores into probabilities that add up to 100 percent, and sampling then chooses the next token from those probabilities. The step repeats until the answer is complete.

The controls shape the choice. Temperature divides the scores before softmax. Below 1 the most probable tokens gain weight and the choice becomes more predictable, and above 1 the probabilities spread out. Top-k keeps only the k most probable tokens, so a value of 5 keeps five candidates. Top-p keeps the fewest tokens whose probabilities add up to at least p, so a value of 0.9 keeps the tokens that together hold 90 percent. In both cases the kept probabilities are scaled to add up to 100 percent again, and the next token is drawn from them.

In this model the answer is produced by greedy decoding, which always takes the most probable token, so the controls change the display on stage 9 and not the answer. Sampling is the AI model's own setting, and on the standard request path the platform forwards it as sent.

What to look for

Integrity. Every record and the question is validated at its ingest gateway before the AI model reads it, and each receives a validation proof (stage 1). The context hash identifies the exact bytes that the model reads. With drift-free context the context hash is identical from run to run, and in this model's runs every internal value and the answer are identical too (stages 6 to 11). With retrieved context the hash changes when the records change, and the answer can change with it. The platform guarantees the context, and the quality of the answer remains the model's.

Operations. The customer hosts and executes the AI model on the customer's own infrastructure, and the platform validates the data around it. Context assembly is a separate query that the AI application sends (stage 5), so the model, its serving stack and its sampling settings stay as they are. The same mechanism serves AI models that use tokens and AI models that do not, and the AI agents built on them (stage 12). The organization's data stays in its own storage, and each Virtual Organization is an isolated tenant with its own compute fabric, ledger and storage.

Performance and scale. At scale the work is divided by sector. Six reasoning bridges, one for each sector of an organization's data, reason independently, and the runners within a bridge execute in parallel; a query across the organization is recomposed from the results of the bridges into one (stage 4). The platform's verification tests confirm that runner capacity holds exactly under concurrent load, that the full reasoning pipeline proposes the expected runners with a verifying proof at every hyperdimensional tier, and that the reasoning bridges route each query to the correct runner, identically on repeat (stage 12). The check on a model's internal state costs the same whether the model has 8 billion or 405 billion parameters, so the verification layer does not become more expensive as an organization adopts larger models.

Reasoning, training and operating at scale

Reasoning. A query is resolved within the sector in which its coordinate falls, and a query across the organization is recomposed from the bridges that contributed. The work spreads across the bridges as data arrives.

Training. Training data is validated before it is used. The organization trains its model on its own infrastructure, and the resulting checkpoint is forged, validated and recorded with an attestation that binds the trained model to its data and its training record. The model that is trained, the data that trained it and the context that it later reads are each identified by proofs that a third party can check with the owner's authorization.

Operation. Each Virtual Organization operates on its own compute fabric, so organizations scale independently of one another. Within an organization, capacity grows as data arrives and the reasoning bridges divide the work by sector. The practical limits are the organization's own storage and compute capacity.

About the model shown

The model runs a small open AI model, Qwen2.5-0.5B-Instruct, so that every internal value can be shown. The mechanisms are the same for AI models of any size, and the statements about scale rest on the platform's verification tests.

Sources

Top-k sampling follows Fan, Lewis and Dauphin (2018), and top-p sampling follows Holtzman and others (2020). The attention computation follows Vaswani and others (2017). The statements about scale follow the platform's verification tests.