SnakeByte[21]: The Token Arms Race: Architectures Behind Long-Context Foundation Models

OpenAI’s Idea Of A Computer Loving The Sunset

Sometimes I tell sky our story. I dont have to say a word. Words are useless in the cosmos; words are useless and absurd.

~ Jess Welles

First, i trust everyone is safe. Second, i am going to write about something that is evolving extremely quickly and we are moving into a world some are calling context engineering. This is beyond prompt engineering. Instead of this just being mainly a python based how-to use a library, i wanted to do some math and some business modeling, thus the name of the blog.

So the more i thought about this i was thinking in terms of how our world is now tokenized. (Remember the token economy ala the word that shall not be named BLOCKCHAIN. Ok, i said it much like saying CandyMan in the movie CandyMan except i dont think anyone will show up if you say blockchain five times).

The old days of crafting clever prompts are fading fast, some say prompting is obsolete. The future isn’t about typing the perfect input; it’s about engineering the entire context in which AI operates and feeding that back into the evolving system. This shift is a game-changer, moving us from toy demos to real-world production systems where AI can actually deliver on scale.

Prompt Engineering So Last Month

Think about it: prompts might dazzle in a controlled demo, but they crumble when faced with the messy reality of actual work. Most AI agents don’t fail because their underlying models are weak—they falter because they don’t see enough of the window and aperture, if you will, is not wide enough. They lack the full situational awareness needed to navigate complex tasks. That’s where context engineering steps in as the new core skill, the backbone of getting AI to handle real jobs effectively.

Words Have Meanings.

~ Dr. Mathew Aldridge

So, what does context engineering mean? It’s a holistic approach to feeding AI the right information at the right time, beyond just a single command. It starts with system prompts that shape the agent’s behavior and voice, setting the tone for how it responds. Then there’s user intent, which frames the actual goalnot just what you ask, but why you’re asking it. Short-term memory keeps multi-step logic and dialogue history alive, while long-term memory stores facts, preferences, and learnings for consistency. Retrieval-Augmented Generation (RAG) pulls in relevant data from APIs, databases, and documents, ensuring the agent has the latest context. Tool availability empowers agents to act not just answer by letting them execute tasks. Finally, structured outputs ensure responses are usable, cutting the fluff and delivering actionable results.

Vertically Trained Horizontally Chained

This isn’t theory; platforms like LangChain and Anthropic are already proving it at scale. They split complex tasks into sub-agents, each with a focused context window to avoid overload. Long chats get compressed via summarization, keeping token limits in check. Sandboxed environments isolate heavy state, preventing crashes, while memory is managed with embeddings, scratchpads, and smart retrieval systems. LangGraph orchestrates these agents with fine-grained control, and LangSmith’s tracing and testing tools evaluate every context tweak, ensuring reliability. It’s a far cry from the old string-crafting days of prompting.

Prompting involved crafting a response with a well-worded sentence. Context engineering is the dynamic design of systems, building full-stack pipelines that provide AI with the right input when it matters. This is what turns a flashy demo into a production-ready product. The magic happens not in the prompt, but in the orchestrated context that surrounds it. As we move forward, mastering this skill will distinguish innovators from imitators, enabling AI to solve real-world problems with precision and power. People will look at you quizzically. In this context, tokens are the food for Large Language Models and are orthogonal to tokens in a blockchain economy.

Slide The Transformers

Which brings us to the evolution of long-context transformers, examining key players, technical concepts, and business implications. NOTE: Even back in the days of the semantic web it was about context.

Foundation model development has entered a new frontier not just of model size, but of memory scale. We’re witnessing the rise of long-context transformers: architectures capable of handling hundreds of thousands and even millions of tokens in a single pass.

This shift is not cosmetic; it alters the fundamental capabilities and business models of LLM platforms. First, i’ll analyze the major players, their long-term strategies, and then we will run through some mathematical architecture powering these transformations. Finally getting down to the Snake Language on basic function implementations for very simple examples.

CompanyModelMax Context LengthTransformer VariantNotable Use Case
GoogleGemini 1.5 Pro2M tokensMixture-of-Experts + RoPEContext-rich agent orchestration
OpenAIGPT-4 Turbo128k tokensLLM w/ windowed attentionChatGPT + enterprise workflows
AnthropicClaude 3.5 Sonnet200k tokensConstitutional Sparse AttentionSafety-aligned memory agents
Magic.devLTM-2-Mini100M tokensSegmented Recurrence w/ CacheCodebase-wide comprehension
MetaLlama 4 Scout10M tokensOn-device, efficient RoPEEdge + multimodal inference
MistralMistral Large 2128k tokensSliding Window + Local AttentionGeneralist LLM APIs
DeepSeekDeepSeek V3128k tokensBlock Sparse TransformerMultilingual document parsing
IBMGranite Code/Instruct128k tokensOptimized FlashAttention-2Code generation & compliance

The Matrix Of The Token Grid Arms Race

Redefining Long Context

Here is my explanation and blurb that i researched on each of these:

  • Google – Gemini 1.5 Pro (2M tokens, Mixture-of-Experts + RoPE)
    Google’s Gemini 1.5 Pro is a heavyweight, handling 2 million tokens with a clever mix of Mixture-of-Experts and Rotary Positional Embeddings. It shines in context-rich agent orchestration, seamlessly managing complex, multi-step tasks across vast datasets—perfect for enterprise-grade automation.
  • OpenAI – GPT-4 Turbo (128k tokens, LLM w/ windowed attention)
    OpenAI’s GPT-4 Turbo packs 128k tokens into a windowed attention framework, making it a go-to for ChatGPT and enterprise workflows. Its strength lies in balancing performance and accessibility, delivering reliable responses for business applications with moderate context needs.
  • Anthropic – Claude 3.5 Sonnet (200k tokens, Constitutional Sparse Attention)
    Anthropic’s Claude 3.5 Sonnet offers 200k tokens with Constitutional Sparse Attention, prioritizing safety and alignment. It’s a standout for memory agents, ensuring secure, ethical handling of long conversations—a boon for sensitive industries like healthcare or legal.
  • Magic.dev – LTM-2-Mini (100M tokens, Segmented Recurrence w/ Cache)
    Magic.dev’s LTM-2-Mini pushes the envelope with 100 million tokens, using Segmented Recurrence and caching for codebase-wide comprehension. This beast is ideal for developers, retaining entire project histories to streamline coding and debugging at scale.
  • Meta – Llama 4 Scout (10M tokens, On-device, efficient RoPE)
    Meta’s Llama 4 Scout brings 10 million tokens to the edge with efficient RoPE, designed for on-device use. Its multimodal inference capability makes it a favorite for privacy-focused applications, from smart devices to defense systems, without cloud reliance.
  • Mistral – Mistral Large 2 (128k tokens, Sliding Window + Local Attention)
    Mistral Large 2 handles 128k tokens with Sliding Window and Local Attention, offering a versatile generalist LLM API. It’s a solid choice for broad applications, providing fast, efficient responses for developers and businesses alike.
  • DeepSeek – DeepSeek V3 (128k tokens, Block Sparse Transformer)
    DeepSeek V3 matches 128k tokens with a Block Sparse Transformer, excelling in multilingual document parsing. Its strength lies in handling diverse languages and formats, making it a go-to for global content analysis and translation tasks.
  • IBM – Granite Code/Instruct (128k tokens, Optimized FlashAttention-2)
    IBM’s Granite Code/Instruct leverages 128k tokens with Optimized FlashAttention-2, tailored for code generation and compliance. It’s a powerhouse for technical workflows, ensuring accurate, regulation-aware outputs for developers and enterprises.

Each of these companies is carving out their own window of context and capabilities for the tokens arms race. So what are some of the basic mathematics at work here for long context?

i’ll integrate Python code to illustrate key architectural ideas (RoPE, Sparse Attention, MoE, Sliding Window) and business use cases (MaaS, Agentic Platforms), using libraries like NumPy, PyTorch, and a mock agent setup. These examples will be practical and runnable in a Jupyter environment.

Rotary Positional Embeddings (RoPE) Extensions

Rotary Positional Embeddings (RoPE) is a technique for incorporating positional information into Transformer-based Large Language Models (LLMs). Unlike traditional methods that add positional vectors, RoPE encodes absolute positions with a rotation matrix and explicitly includes relative position dependency within the self-attention mechanism. This approach enhances the model’s ability to handle longer sequences and better understand token interactions across larger contexts. 

The core idea behind RoPE involves rotating the query and key vectors within the attention mechanism based on their positions in the sequence. This rotation encodes positional information and affects the dot product between query and key vectors, which is crucial for attention calculations. 

To allow for arbitrarily long context, models generalize RoPE using scaling factors and interpolation. Here is the set of basic equations:

    \[\text{RoPE}(x_i) = x_i \cos(\theta_i) + x_i^\perp \sin(\theta_i)\]

where \theta_i \propto \frac{1}{10000^{\frac{2i}{d}}}, extended by interpolation.

Here is some basic code implementing this process:

import numpy as np
import torch

def apply_rope(input_seq, dim=768, max_seq_len=1000000):
    """
    Apply Rotary Positional Embeddings (RoPE) to input sequence.
    Args:
        input_seq (torch.Tensor): Input tensor of shape (batch_size, seq_len, dim)
        dim (int): Model dimension (must be even)
        max_seq_len (int): Maximum sequence length for precomputing positional embeddings
    Returns:
        torch.Tensor: Input with RoPE applied, same shape as input_seq
    """
    batch_size, seq_len, dim = input_seq.shape
    assert dim % 2 == 0, "Dimension must be even for RoPE"
    
    # Compute positional frequencies for half the dimension
    theta = 10000 ** (-2 * np.arange(0, dim//2, 1) / (dim//2))
    pos = np.arange(seq_len)
    pos_emb = pos[:, None] * theta[None, :]
    pos_emb = np.stack([np.cos(pos_emb), np.sin(pos_emb)], axis=-1)  # Shape: (seq_len, dim//2, 2)
    pos_emb = torch.tensor(pos_emb, dtype=torch.float32).view(seq_len, -1)  # Shape: (seq_len, dim)

    # Reshape and split input for RoPE
    x = input_seq  # Keep original shape (batch_size, seq_len, dim)
    x_reshaped = x.view(batch_size, seq_len, dim//2, 2).transpose(2, 3)  # Shape: (batch_size, seq_len, 2, dim//2)
    x_real = x_reshaped[:, :, 0, :]  # Real part, shape: (batch_size, seq_len, dim//2)
    x_imag = x_reshaped[:, :, 1, :]  # Imaginary part, shape: (batch_size, seq_len, dim//2)

    # Expand pos_emb for batch dimension and apply RoPE
    pos_emb_expanded = pos_emb[None, :, :].expand(batch_size, -1, -1)  # Shape: (batch_size, seq_len, dim)
    out_real = x_real * pos_emb_expanded[:, :, ::2] - x_imag * pos_emb_expanded[:, :, 1::2]
    out_imag = x_real * pos_emb_expanded[:, :, 1::2] + x_imag * pos_emb_expanded[:, :, ::2]

    # Combine and reshape back to original
    output = torch.stack([out_real, out_imag], dim=-1).view(batch_size, seq_len, dim)
    return output

# Mock input sequence (batch_size=1, seq_len=5, dim=4)
input_tensor = torch.randn(1, 5, 4)
rope_output = apply_rope(input_seq=input_tensor, dim=4, max_seq_len=5)
print("RoPE Output Shape:", rope_output.shape)
print("RoPE Output Sample:", rope_output[0, 0, :])  # Print first token's output

You should have get the following output:

RoPE Output Shape: torch.Size([1, 5, 4])
RoPE Output Sample: tensor([ 0.6517, -0.6794, -0.4551,  0.3666])

The shape verifies the function’s dimensional integrity, ensuring it’s ready for downstream tasks. The sample gives a glimpse into the transformed token, showing RoPE’s effect. You can compare it to the raw input_tensor[0, 0, :] tto see the rotation (though exact differences depend on position and frequency).see the rotation (though exact differences depend on position and to see the rotation (though exact differences depend on position and frequency).

Sparse Attention Mechanisms:

Sparse attention mechanisms are techniques used in transformer models to reduce computational cost by focusing on a subset of input tokens during attention calculations, rather than considering all possible token interactions. This selective attention process enhances efficiency and allows models to handle longer sequences, making them particularly useful for natural language processing tasks like translation and summarization. 

In standard self-attention mechanisms, each token in an input sequence attends to every other token, resulting in a computational complexity that scales quadratically with the sequence length (O(n^2 d)). For long sequences, this becomes computationally expensive. Sparse attention addresses this by selectively attending to a subset of tokens, reducing the computational burden.  Complexity drops from O(n^2 d) to O(nd \sqrt{n}) or better using block or sliding windows.

Sparse attention mechanisms achieve this reduction in computation by reducing the number of interactions instead of computing attention scores for all possible token pairs, sparse attention focuses on a smaller, selected set of tokens. The downside is by focusing on a subset of tokens, sparse attention may potentially discard some relevant information, which could negatively impact performance on certain tasks. Also it gets more complex code-wise.

This is mock implementation using pytorch.

import torch
import torch.nn.functional as F

def sparse_attention(q, k, v, window_size=3):
    batch, num_heads, seq_len, head_dim = q.shape
    attn_scores = torch.matmul(q, k.transpose(-2, -1)) / (head_dim ** 0.5)
    # Apply sliding window mask
    mask = torch.triu(torch.ones(seq_len, seq_len), diagonal=1-window_size).bool()
    attn_scores.masked_fill_(mask, float('-inf'))
    attn_weights = F.softmax(attn_scores, dim=-1)
    return torch.matmul(attn_weights, v)

# Mock query, key, value tensors (batch=1, heads=2, seq_len=6, dim=4)
q = torch.randn(1, 2, 6, 4)
k = torch.randn(1, 2, 6, 4)
v = torch.randn(1, 2, 6, 4)
output = sparse_attention(q, k, v, window_size=3)
print("Sparse Attention Output Shape:", output.shape)

This should just print out the shape:

Sparse Attention Output Shape: torch.Size([1, 2, 6, 4])

The sparse_attention function implements a simplified attention mechanism with a sliding window mask, mimicking sparse attention patterns used in long-context transformers. It takes query (q), key (k), and value (v) tensors, computes attention scores, applies a mask to limit the attention window, and returns the weighted output. The shape torch.Size([1, 2, 6, 4]) indicates that the output tensor has the same structure as the input v tensor. This is expected because the attention mechanism computes a weighted sum of the value vectors based on the attention scores derived from q and k. The sliding window mask (defined by window_size=3) restricts attention to the current token and the previous 2 tokens (diagonal offset of 1-window_size), but it doesn’t change the output shape it only affects which scores contribute to the weighting. The output retains the full sequence length and head structure, ensuring compatibility with downstream layers in a transformer model. This shape signifies that for each of the 1 batch, 2 heads, and 6 tokens, the output is a 4-dimensional vector, representing the attended features after the sparse attention operation.

Mixture-of-Experts (MoE) + Routing

Mixture-of-Experts (MoE) is a machine learning technique that utilizes multiple specialized neural networks, called “experts,” along with a routing mechanism to process input data. The router, a gating network, determines which experts are most relevant for a given input and routes the data accordingly, activating only those specific experts. This approach allows for increased model capacity and computational efficiency, as only a subset of the model needs to be activated for each input. 

Key Components:

  • Experts: These are individual neural networks, each trained to be effective at processing specific types of data or patterns. They can be simple feedforward networks, or even more complex structures. 
  • Routing/Gating Network:This component acts as a dispatcher, deciding which experts are most appropriate for a given input. It typically uses a learned weighting or probability distribution to select the experts. 

This basic definition activates a sparse subset of experts:

    \[\text{MoE}(x) = \sum_{i=1}^k g_i(x) \cdot E_i(x)\]

(Simulating MoE with 2 of 4 experts):

import torch
import torch.nn as nn

class MoE(nn.Module):
    def __init__(self, num_experts=4, top_k=2):
        super().__init__()
        self.experts = nn.ModuleList([nn.Linear(4, 4) for _ in range(num_experts)])
        self.gate = nn.Linear(4, num_experts)
        self.top_k = top_k

    def forward(self, x):
        scores = self.gate(x)  # (batch, num_experts)
        _, top_indices = scores.topk(self.top_k, dim=-1)  # Select top 2 experts
        output = torch.zeros_like(x)
        for i in range(x.shape[0]):
            for j in top_indices[i]:
                output[i] += self.experts[j](x[i])
        return output / self.top_k

# Mock input (batch=2, dim=4)
x = torch.randn(2, 4)
moe = MoE(num_experts=4, top_k=2)
moe_output = moe(x)
print("MoE Output Shape:", moe_output.shape)

This should give you the output:

MoE Output Shape: torch.Size([2, 4])

The shape torch.Size([2, 4]) indicates that the output tensor has the same batch size and dimension as the input tensor x. This is expected because the MoE applies a linear transformation from each selected expert (all outputting 4-dimensional vectors) and averages them, maintaining the input’s feature space. The Mixture-of-Experts mechanism works by:

  • Computing scores via self.gate(x), producing a (2, 4) tensor that’s transformed to (2, num_experts) (i.e., (2, 4)).
  • Selecting the top_k=2 experts per sample using topk, resulting in indices for the 2 best experts out of 4.
  • Applying each expert’s nn.Linear(4, 4) to the input x[i], summing the outputs, and dividing by top_k to normalize the contribution.

The output represents the averaged transformation of the input by the two most relevant experts for each sample, tailored to the input’s characteristics as determined by the gating function.

Sliding Window + Recurrence for Locality

While A context window in an AI model refers to the amount of information (tokens in text) it can consider at any one time. The Locality emphasizes the importance of data points that are close together in a sequence. In many applications, recent information is more relevant than older information. For example, in conversations, recent dialogue contributes most to a coherent response.  The importance of that addition lies in effectively handling long contexts in large language models (LLMs) and optimizing inference. Strategies involve splitting the context into segments and managing the Key-Value (KV) cache using data structures like trees. 

Segmenting Context: For very long inputs, the entire context might not fit within the model’s memory or process efficiently as a single unit. Therefore, the context can be divided into smaller, manageable segments or chunks.

KV Cache: During LLM inference, the KV cache stores previously computed “keys” and “values” for tokens in the input sequence. This avoids recomputing attention mechanisms for already processed tokens, speeding up the generation process ergo the terminology.

This code splits context into segments with KV cache trees.

import torch

def sliding_window_recurrence(input_seq, segment_size=3, cache_size=2):
    """
    Apply sliding window recurrence with caching.
    Args:
        input_seq (torch.Tensor): Input tensor of shape (batch_size, seq_len, dim)
        segment_size (int): Size of each segment
        cache_size (int): Size of the cache
    Returns:
        torch.Tensor: Output with recurrence applied
    """
    batch_size, seq_len, dim = input_seq.shape
    output = []
    # Initialize cache with batch dimension
    cache = torch.zeros(batch_size, cache_size, dim)  # Shape: (batch_size, cache_size, dim)
    
    for i in range(0, seq_len, segment_size):
        segment = input_seq[:, i:i+segment_size]  # Shape: (batch_size, segment_size, dim)
        # Ensure cache and segment dimensions align
        if segment.size(1) < segment_size and i + segment_size <= seq_len:
            segment = torch.cat([segment, torch.zeros(batch_size, segment_size - segment.size(1), dim)], dim=1)
        # Mock recurrence: combine with cache
        combined = torch.cat([cache, segment], dim=1)[:, -segment_size:]  # Take last segment_size
        output.append(combined)
        # Update cache with the last cache_size elements
        cache = torch.cat([cache, segment], dim=1)[:, -cache_size:]

    return torch.cat(output, dim=1)

# Mock input (batch=1, seq_len=6, dim=4)
input_tensor = torch.randn(1, 6, 4)
recurrent_output = sliding_window_recurrence(input_tensor, segment_size=3, cache_size=2)
print("Recurrent Output Shape:", recurrent_output.shape)

The output should be:

Recurrent Output Shape: torch.Size([1, 6, 4])

The shape torch.Size([1, 6, 4]) indicates that the output tensor has the same structure as the input tensor input_tensor. This is intentional, as the function aims to process the entire sequence while applying a recurrent mechanism. Sliding Window Process:

  • The input sequence (length 6) is split into segments of size 3. With seq_len=6 and segment_size=3, there are 2 full segments (indices 0:3 and 3:6).
  • Each segment is combined with a cache (size 2) using torch.cat, and the last segment_size elements are kept (e.g., (2+3)=5 elements, sliced to 3).
  • The loop runs twice, appending segments and torch.cat(output, dim=1) reconstructs the full sequence length of 6.

For the Recurrence Effect the cache (initialized as (1, 2, 4)) carries over information from previous segments, mimicking a recurrent neural network’s memory. The output at each position reflects the segment’s data combined with the cache’s prior context, but the shape remains unchanged because the function preserves the original sequence length. In practical applicability for a long-context model, this output could feed into attention layers, where the recurrent combination enhances positional awareness across segments, supporting lengths like 10M tokens (e.g., Meta’s Llama 4 Scout).

So how do we make money? Here are some business model implications.

MemoryAsAService: MaaS class mocks token storage and retrieval with a cost model. For enterprise search, compliance, and document workflows, long-context models enable models to hold entire datasets in RAM, reducing RAG complexity.

Revenue lever: Metered billing based on tokens stored and tokens retrieved

Agentic Platforms and Contextual Autonomy: (With 10M+ token windows), AI agents can:

  • Load multiyear project timelines
  • Track legal/compliance chains of thought
  • Maintain psychological memory for coaching or therapy

Revenue lever: Subscription for persistent agent state memory

Embedded / Edge LLMs: Pruning the attention mimics on-device optimization.

What are you attentive to and where are you attentive to? This is very important for autonomy systems. Insect-like LLMS? Models uses hardware-tuned attention pruning to run on-device without cloud support.

Revenue lever:

  • Hardware partnerships (Qualcomm, Apple, etc.)
  • Private licensing for defense/healthcare

Developer Infrastructure: Codebase Memory tracks repo events. Can Haz Logs? Devops on steroids. Analyize repos based on quality and deployment size.

Revenue lever: Developer SaaS pricing by repo or engineering team size (best fewest ups the revenue per employee and margin).

Magic.dev monetizes 100M-token memory by creating LLM-native IDEs that retain architecture history, unit tests, PRs, and stack traces. Super IDE’s for Context Engineering?

Here are some notional mappings for catalyst:

Business EdgeMathematical Leverage
Persistent memoryAttention cache, memory layers, LRU gating
Low latencySliding windows, efficient decoding
Data privacyOn-device + quantized attention ops
Vertical domain AIMoE + sparse fine-tuning adapters

Closing

In this token-maximized world, the architectural arms race is becoming a memory computation problem. The firms that master the blend of:

  • Efficient inference at high context length
  • Agentic memory persistence
  • Economically viable context scaling will win not just on benchmark scores, but on unit economics, retention, and defensibility.

In the world of AI business models, context is the new (i couldnt think of a buzzword please help me LazyWebTM)? Also I believe that William Gibson was right. Got More Ram?

Until Then.

#iwishyouwater

Ted ℂ. Tanner Jr. (@tctjr) / X

MUZAK TO BLOG BY: Jesse Welles, Pilgrim. If you havent listened to Jesse Welles you are missing out. He is our present-day Bob Dylan. Look him up on youtube out in the field and under the power lines.

Considerations for NoSQL and Map Reducing Machine Learning Algorithms

The Machine Is Learning

The past couple of weeks have been rather tumultus for me and several others.  I wont go into details and “kiss and tell” but suffice to say it is has led me to the land of “Free Agency”.

As such over the past couple of weeks I have met several people and have been discussing items such as Big Data, Semantics, Hadoop, NoSQL, Data Science <<insert favorite bingo buzzword here>>. One issue that I see over and over concerns the usage of different distributed compute frameworks. Saying “Hadoop” is not a panacea for your Big Data problems.  One must understand the problem your trying to solve.  Many people fall prey to the “new shiny thing” paradigm.  On the issue of BigData concerns if you want to scale horizontal go with a NoSQL solution – if it is necessary.  The NoSQL database is implemented as a data grid for processing (mapReduce, queries, CRUD, etc.).  Most big websites and players that have moved towards non-relational datastores include LinkedIn, Amazon, Digg and Twitter. One of the main reasons for using NoSQL solutions is relational databases place computation on reads, which is considered wrong for large-scale web applications such as Digg etc.

Aspects of this behavior are:
• The serial nature of applications1 often waiting for I/O from the data store which does no good to scalability and low response times.
• Huge amounts of data and a high growth factor lead Twitter towards facilitating Cassandra, which is designed to operate with large scale data.
• Furthermore, operational costs of running and maintaining systems like Twitter et al escalate. Web applications of this size therefore “need a system that can grow in a more automated fashion and be highly available.”.

Amazon’s James Hamilton agrees:

“Scale-first applications are those that absolutely must scale without bound and being able to do this without restriction is much more important than more features. These applications are exemplified by very high scale web sites such as Facebook, MySpace, Gmail, Yahoo, and Amazon.com. Some of these sites actually do make use of relational databases but many do not. The common theme across all of these services is that scale is more important than features and none of them could possibly run on a single RDBMS.”

Ok so lets assume you have your high availability horizontal scale framework (HAHSF)  in place and you are harvesting, ingressing and egressing data.  Now what?  You must figure out the DataScience strategy and what to do with the data.  Otherwise its like hoarding – your just harvesting and storing it, which by definition means that you need to do some type of statistics, machine learning or data mining.  Here is where I believe most people get slightly sideways.  Map Reduction is not Hadoop.  Map Reducing of Machine Learning algorithms are at the forefront of what is occurring within scale applications.

Machine Learning Review

For a refresher I would suggest breaking out that Grey Book called Machine Learning by Professor Mitchell or Haykin’s, Neural Network tome.  So lets start with something we all probably learned in one of your AI or machine learning classes.  Remember the Back-Propagation Network?  If not here is the diagram for a refresher:

Essentially the system is a linear combination of weights with a trigonometric function that provides a threshold then the error is fed back the the weights are changed.  There are three types of neurons in a neural network that is created BP ANN algorithm:
  • Input neurons

For discrete input attributes, an input neuron typically represents a single state from the input attribute. This includes missing values, if the training data contains nulls for that attribute. A discrete input attribute that has more than two states generates one input neuron for each state, and one input neuron for a missing state, if there are any nulls in the training data. A continuous input attribute generates two input neurons: one neuron for a missing state, and one neuron for the value of the continuous attribute itself. Input neurons provide inputs to one or more hidden neurons.

  • Hidden neurons

Hidden neurons receive inputs from input neurons and provide outputs to output neurons.

  • Output neurons

Output neurons represent predictable attribute values for the data mining model. For discrete input attributes, an output neuron typically represents a single predicted state for a predictable attribute, including missing values. For example, a binary predictable attribute produces one output node that describes a missing or existing state, to indicate whether a value exists for that attribute. A Boolean column that is used as a predictable attribute generates three output neurons: one neuron for a true value, one neuron for a false value, and one neuron for a missing or existing state.

A neuron receives input from other neurons, or from other data, depending on which layer of the network it is in. An input neuron receives inputs from the original data. Hidden neurons and output neurons receive inputs from the output of other neurons in the neural network. Inputs establish relationships between neurons, and the relationships serve as a path of analysis for a specific set of cases.

Each input has a value assigned to it, called the weight, which describes the relevance or importance of that particular input to the hidden neuron or the output neuron. The greater the weight that is assigned to an input, the more relevant or important the value of that input. Weights can be negative, which implies that the input can inhibit, rather than activate, a specific neuron. The value of each input is multiplied by the weight to emphasize the importance of an input for a specific neuron. For negative weights, the effect of multiplying the value by the weight is to deemphasize the importance.

Each neuron has a simple non-linear function assigned to it, called the activation function, which describes the relevance or importance of a particular neuron to that layer of a neural network. Hidden neurons use a hyperbolic tangent function (tanh) for their activation function, whereas output neurons use a sigmoid function for activation. Both functions are nonlinear, continuous functions that allow the neural network to model nonlinear relationships between input and output neurons.

Map Reducing The Algorithm

Now here is where the world of real time systems and distributed systems collide.  Suppose we have a epoch and we have an error propagated back and we need to update the weights?  We need to map reduce this functionality to fully gain benefit from the map reduction – hadoop-it-izing magic.  As a specific note the performance that results depends intimately on the design choices underlying the MapReduce implementation, and how well those choices support the data processing pattern of the respective Machine Learning algorithm.

However, not only does Hadoop not support static reference to shared content across map tasks, as far as I know the implementation also prevented us from adding this feature. In Hadoop, each map task runs in its own Java Virtual Machine (JVM), leaving no access to a shared memory space across multiple map tasks running on the same node. Hadoop does provide some minimal support for sharing parameters in that its streaming mode allows the distribution of a file to all compute nodes (once per machine) that can be referenced by a map task. In this way, data can be shared across map tasks without incurring redundant transfer costs. However, this work-around requires that the map task be written as a separate applications, furthermore, it still requires that each map task load a distinct copy of its parameters into the heap of its JVM.  That said almost all ML learning algorithms and particularly ANN are commonly done with stochastic or direct gradient descent/ascent (depending on sign), which poses a challenge to parallelization.

The problem is that in every step of gradient ascent, the algorithm updates a common set of parameters (e.g. the update matrix for the weights in the BPANN case). When one gradient ascent step (involving one training sample) is updating W , it has to lock down this matrix, read it, compute the gradient, update W , and finally release the lock. This “lock-release” block creates a bottleneck for parallelization; thus, instead of stochastic gradient ascent many methods use a batch method which greatly slows the process down and takes away from the real time aspect.  Work arounds that I have personally seen used and help create are memory mapped shared functions (think signal processing and CPU shared memory modules) which allows a pseudo persistence to occur and the weights to be updated at and paralleled at “epoch time”.   As we reduce the latencies of the networked systems we are starting to get back to some of the very problems that plagued real time parallel signal processing systems – the disc i/o and disc read-write heads are starting to become the bottlneck.  So you move to solid state devices or massive in memory systems.  That does not solve the map reduction problem of machine learning algorithms.  That said over the past years the Apache Foundation and more specifically the Mahout project has been busy adding distributed algorithms to its arsenal.  Of particular interest is the Singular value decomposition which is the basis kernel for processes such as Latent Semantic Indexing and the like.  Even given the breadth of additions fundamental computational blocks such as Kohonen networks and the algorithm mentioned here – Backpropagation are not in the arsenal.  Some good stuff such as an experimental Hidden Markov Model are there.

That said I really do believe we will start to see more of a signal processing architecture on the web.  Just maybe “cycle-stealing” via true grids will make comeback?

Go Big Or Go Home!

@jaxsoncreole

Probablistic Databases For Predictive Content

The Other PDF To You

The Probability Something Will Happen

 

Digital Remote for Your Life

Well folks we are going to shift gears here a little and get back to some hardcore Ideas2Bank discussions concerning technologies.  As of late I have been interested once again in Finding-Not-Searching types of behaviors.  Affinity based systems are once again on the rise.  I will go so far as to say the Age of Affinity is here.  TechCrunch did a writeup recently concerning relevance.  At the end it turned into a pitch for Quora.  However it did have some good ideas concerning continuum of Personalization functionality from complete serendipity to exact personalized context aware information constructs based on geo-location.  I have always been a fan of “lean back” technologies.   Technologies that essentially enable a digital remote for your life.  These types of systems have two common themes: 1) ease of use 2) The probability of usage

Predictive Content and Probability

In today’s world we are trying to create predictive, context aware systems based on the wrong models.  For today’s database architecture: 1) An item either is in the database or is not 2) A tuple either is in the query answer or is not.   This applies to all state-of-the-art data models across the board.  In a probablistic database we have a different construct altogether which is a better fit for the flow of content. For a content prediction event driven system we can assume the events are precise and have no ambiguity. Instead, it is the future event stream that is unknown and the matching of a pattern at some point in the future is predicted with some probability.   When, Where and How are the operatives for this type of predictive event, f(Wh,Wr,H) if you will.  Also note I mentioned the word stream.   I believe given the current and future infrastructures for processing we are bringing back some of the same analogies for large array signal processing frameworks.  The probablistic database models set up extremely well for these types of event processing mechanics.

For a probabilistic database we have:

  • “An item belongs to the database” is a probabilistic event.
  • “A tuple is an answer to a query” is a probabilistic event
  • Can be extended to all data models; we discuss only probabilistic relational data

Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database).  In complex event processing systems, events from the environment are correlated and aggregated to form higher level events. Uncertainty in the events may be due to a variety of factors including imprecision in the event sensors or generators (eg streams), and corruption of the communication channel possibly dropping events, which can be measured with entropy metrics.  These attributes lend themselves well to fusion systems and the social stream architectures.   Given we are looking at heterogenous data sources that set up for collisions and data source integrity these types of databases hold great promise.    In addition many of these types of database architectures build upon Finite State Machine mechanics for event processing in operating systems.  Of further interest the data is usually imprecise.

Probalistic Databases address types of imprecision whereas:

  • Data is precise, query answers are imprecise
  • User has limited understanding of the data
  • User has limited understanding of the schema
  • User has personal preferences

Notice a “trend” here?  This sets up very well for content flow predictions.  In addition these types of systems hold well for principled semantics for complex queries.  This provides context for the queries where the data is usually imprecise.  Data integration and data hygiene are paramount in social stream systems.  Where data accuracy is important most companies spend 85% of workload cleansing data.  We could use probabilistic information to reason about soundness, completeness, and overlap of sources (think linked data here).  I have listed some of the main sources of research in Probabilistic databases herewith.  As far as I know there are no publicly commercial applications as of yet for this technology.  My bet is we will see some very soon integrated with some of the other NoSQL like technologies.

For a list of current research projects see:

Until Then,

Go Big Or Go Home!

@jaxsoncreole