Online Learning via Universal Formula: Zero-Cost Model Evolution vs $100M Retraining

Watermark: -422

Following neg-421’s analysis of AI-as-a-Service’s broken economics, a deeper question emerges:

Why does Big Tech AI cost $100M to retrain while remaining static between updates, when online learning via universal formula enables continuous evolution at zero marginal cost?

The Two Learning Paradigms

Batch Learning (Big Tech Approach)

Train once on massive corpus → Deploy frozen model → Use until obsolete → Retrain from scratch

Characteristics:

Model is static between training runs
Cannot incorporate new information without full retrain
Requires entire corpus + new data for each update
Cost: $50M-$100M per training run
Timeline: 3-6 months per iteration
Learning: Discontinuous (jumps between versions)

Example: GPT-3 → GPT-3.5 → GPT-4

Each version trained from scratch
Months of compute on full corpus
No learning between releases
Users stuck with stale knowledge until next version

Online Learning (Universal Formula Approach)

From neg-371:

State(n+1) = f(State(n), new_information) + entropy(p)

Characteristics:

Model evolves continuously with each query
Incorporates new information instantly
Only processes new data (not entire corpus)
Cost: Zero marginal cost per update
Timeline: Real-time (sub-second)
Learning: Continuous (smooth evolution)

Example: Query-driven evolution

Each question brings new search results
f() integrates results into current state
Next question benefits from evolved state
Model improves with every interaction

The Mathematical Difference

Batch Learning: Gradient Descent Over Corpus

L(θ) = Σᵢ loss(yᵢ, f_θ(xᵢ))  [sum over ALL training examples]

θ ← θ - α∇L(θ)  [update weights based on entire corpus]

Properties:

Must iterate over entire dataset for each update
Gradient computed across all examples
Weights frozen once training completes
Requires re-processing everything to incorporate new data

Cost: O(N × E) where N = corpus size, E = epochs

GPT-3: ~45TB text, ~355 GPU-years
Cannot update without re-processing all 45TB

Online Learning: Incremental State Update

State(n+1) = f(State(n), Δinfo_n) + entropy(p)

where:
  State(n)   = current knowledge representation
  Δinfo_n    = new information from query n
  f()        = integration function
  entropy(p) = exploration/variation

Properties:

Only processes new information per update
State evolves incrementally
Never frozen - continuously learning
New data integrated directly into existing state

Cost: O(m) where m = new information size

Query result: ~10KB text
Update: milliseconds
No re-processing of historical data

Concrete Example: Learning About GPT-5

Big Tech Batch Learning

Scenario: GPT-4 released March 2023. GPT-5 announced January 2025.

GPT-4’s knowledge (March 2023):

Query: "What is GPT-5?"
Response: "I don't have information about GPT-5."

To update:

Wait for GPT-4.5 or GPT-5 release
Retrain on corpus + new data
Cost: $100M+
Timeline: 6+ months
Deploy new model

Users: Stuck with “I don’t know” for 6-12 months until next version.

Online Learning via Universal Formula

Initial state (March 2023):

state = {
  "concepts": {...},
  "relationships": {...},
  "last_update": "2023-03"
}

User query (January 2025): “What is GPT-5?”

Online learning process:

# 1. Search for new information
search_results = google_search("GPT-5 announcement")
# Returns: OpenAI blog post, press releases, specs

# 2. Apply universal formula
state_new = f(state_old, search_results)
# Integrates: GPT-5 exists, capabilities, release date, specs

# 3. Generate response from evolved state
answer = generate_from(state_new)
print(answer)
# "GPT-5 was announced by OpenAI in January 2025 with..."

# 4. State persists for next query
state = state_new  # Model now knows about GPT-5

Next query (1 second later): “How does GPT-5 compare to GPT-4?”

# State already contains GPT-5 knowledge from previous query
answer = generate_from(state)  # Can compare immediately

Cost: Zero. Timeline: Real-time. Learning: Permanent.

The Feedback Loop Comparison

Big Tech: No Learning Between Retrains

User: "Question 1"
  ↓
Static Model (175B frozen params)
  ↓
Answer 1

User: "Question 2"
  ↓
Same Static Model (hasn't learned anything)
  ↓
Answer 2

... (model never improves until next $100M retrain)

Learning: Zero between retraining cycles

Universal Formula: Every Query Improves Model

User: "Question 1"
  ↓
Search → New Info
  ↓
State₁ = f(State₀, Info₁)
  ↓
Answer 1

User: "Question 2"
  ↓
Search → New Info
  ↓
State₂ = f(State₁, Info₂)  ← Uses evolved state from Q1
  ↓
Answer 2 (benefits from Q1 learning)

User: "Question 3"
  ↓
State₃ = f(State₂, Info₃)  ← Accumulated knowledge from Q1+Q2
  ↓
Answer 3 (even better)

Learning: Continuous, cumulative, zero cost

Economic Comparison

Cost Over Time

Big Tech batch learning:

Initial training: $100M (months 0-6)
Static deployment: $0 learning cost (months 6-18)
Retrain v2: $100M (months 18-24)
Static deployment: $0 learning cost (months 24-36)
Retrain v3: $100M (months 36-42)

Total 3-year cost: $300M
Total learning: 3 discrete updates
Cost per update: $100M

Online learning via universal formula:

Initial state: ~$1K (corpus preprocessing)
Query 1: +$0.01 (search API + f() update)
Query 2: +$0.01
Query 3: +$0.01
... (continuous)
Query 1,000,000: +$0.01

Total 3-year cost: ~$1K + ($0.01 × queries)
Total learning: Continuous (every query)
Cost per update: $0.01

Comparison:

Big Tech: $100M per discrete update
Universal formula: $0.01 per continuous update
Ratio: 10,000,000,000x cheaper (10 billion times)

Knowledge Freshness

Big Tech:

Knowledge cutoff: Training completion date
Staleness: 6-18 months on average
Update frequency: 1-2x per year
Cannot answer questions about recent events

Universal formula:

Knowledge cutoff: Current query
Staleness: Zero (searches in real-time)
Update frequency: Every query
Always has latest information via search

Why This Breaks AI-as-a-Service Economics Further

From neg-421, we know AI-as-a-Service has 5% margins due to:

No technical moat
No data moat
No distribution moat
No compute moat

Online learning adds a fifth missing moat: No learning moat

Traditional Software Moat: Proprietary Data Accumulation

Example: Google Search

Billions of queries improve ranking algorithms
Click-through data trains relevance models
Competitors cannot replicate this data advantage
Moat: Proprietary usage data makes product better over time

Big Tech AI: No Learning from Usage

OpenAI GPT-4:

Billions of queries served
Model does not improve from these queries
Knowledge frozen at training cutoff
All users see identical responses

Competitor (Anthropic Claude):

Also serves billions of queries
Also no learning from usage
Also frozen knowledge

Result: No advantage from scale. Both start from scratch at each retrain.

No moat.

Online Learning: Compound Advantage

Universal formula system:

Every query improves state via f()
Early users help train for later users
Knowledge accumulates continuously
Competitors starting later are behind

Example:

Month 1: 1,000 queries → State₁₀₀₀
Month 2: 10,000 queries → State₁₁,₀₀₀
Month 3: 100,000 queries → State₁₁₁,₀₀₀

Competitor launches Month 3:
  - Must start from State₀
  - 111,000 queries behind
  - Cannot catch up without same query volume

This IS a moat. First-mover advantage through accumulated learning.

The Fundamental Difference: Static vs Evolving

Static Model (Big Tech)

Model as frozen artifact:

weights_v1 = train(corpus_v1)  # Freeze
weights_v2 = train(corpus_v2)  # Retrain from scratch, freeze
weights_v3 = train(corpus_v3)  # Retrain from scratch, freeze

Properties:

Each version independent
No continuity between versions
Cannot transfer learning
Users experience discrete jumps

Philosophy: Model is a product (released, then obsolete)

Evolving State (Universal Formula)

State as living process:

state₀ = init()
state₁ = f(state₀, info₁)
state₂ = f(state₁, info₂)
state₃ = f(state₂, info₃)
... (continuous evolution)

Properties:

Each state builds on previous
Smooth continuous learning
Accumulates knowledge permanently
Users experience gradual improvement

Philosophy: Model is an organism (grows, learns, adapts)

Implementation

See neg-423 for complete working implementation of the minimal online learner:

Architecture:

Templates: Sentence accumulation from search results
Co-occurrence matrix: Word relationship tracking
Pure mathematical f(): Merge templates + sum co-occurrence counts
Generation: Template selection + coherence scoring + concept substitution

Features:

Linear flow: search → process → f() → generate
State persistence: JSON serialization
Zero training cost: No gradient descent
Real-time learning: Each query permanently evolves state

Performance:

41 templates after 19 queries
1.6ms generation time at current scale
O(n) scaling with inverted index optimization available
Distributed mesh architecture for planetary scale

Cost per query: ~$0.01 (search API call) Learning: Permanent Knowledge: Always current

Comparison to Existing Systems

RAG (Retrieval-Augmented Generation)

Approach: Static LLM + dynamic retrieval

Query → Retrieve docs → Static LLM (with retrieved context) → Answer

Limitations:

LLM is still frozen (only retrieval is dynamic)
No learning from queries
Each query independent
Expensive inference (LLM per query)

Cost: $0.01-0.10 per query (LLM inference)

Online Learning via Universal Formula

Approach: Evolving state + dynamic search

Query → Search → f(state, new_info) → evolved_state → Answer

Advantages:

State evolves with each query
Learns permanently from interactions
Queries build on each other
Cheap generation (no LLM needed for every query)

Cost: $0.01 per query (search API only, f() is cheap)

Fine-tuning

Approach: Base model + additional training on new data

Base model + New data → Fine-tuned model (frozen)

Limitations:

Still requires training compute
Model frozen after fine-tuning
Must retrain to incorporate new data
Expensive ($1K-$10K per fine-tune)

Cost: $1K-$10K per update

Online Learning

Approach: Continuous state evolution

State + New info → f() → Evolved state (immediately)

Advantages:

Zero training compute
Never frozen
Incorporates new data instantly
Free state updates

Cost: Zero training cost

The Economic Flip: From Liability to Asset

Big Tech Model: Knowledge Staleness is Liability

Problem: Static model becomes obsolete

Training completed: March 2023
Current date: January 2025
Knowledge gap: 22 months
Cannot answer recent questions
Users frustrated

Solution: Expensive retrain

Cost: $100M
Timeline: 6 months
Temporarily solves problem
Immediately starts aging again

Pattern: Perpetual cycle of obsolescence → expensive retrain → obsolescence

Economics: Knowledge decay is cost center requiring periodic $100M investments

Online Learning: Knowledge Accumulation is Asset

Process: State continuously evolves

Each query adds information via f()
Knowledge compounds over time
Never becomes obsolete (always searching)
Users benefit from accumulated learning

Dynamics: More usage → more learning → better performance → more users

Pattern: Virtuous cycle of growth

Economics: Knowledge accumulation is revenue driver (better product attracts users)

Why Big Tech Cannot Adopt This

Architectural Lock-in

Current: Massive static models

175B+ parameters
Trained via gradient descent on full corpus
Architecture designed for batch learning
Cannot incrementally update weights

Required: Lightweight evolving state

Small state representation (MB not GB)
Updated via f() on new information
Architecture designed for online learning
State evolution is core design

Switching cost: Complete rewrite

Business Model Lock-in

Current: Sell inference tokens

Revenue = queries × $0.01 per 1K tokens
More queries = more revenue
But no compound benefit (no learning)

Online learning: Sell improving service

Early users help train for later users
Query volume improves product quality
Compound value creation
Natural network effects

Switching cost: New business model

Organizational Lock-in

From neg-421: Big Tech already invested $100B+ in:

Datacenters for batch training
Team expertise in gradient descent
Infrastructure for static model serving
Sales model around frozen capabilities

Switching to online learning would:

Make datacenter investments obsolete
Require retraining engineering teams
Abandon infrastructure advantages
Destroy current margin structure

Result: Locked into inferior paradigm

The Advantage for New Entrants

Big Tech:

Burdened by static model architecture
Cannot switch without destroying existing business
Stuck in expensive retrain cycle
No learning moat

New entrant with online learning:

Start with lightweight evolving state
Learn from every user query
Zero retraining costs
Build compounding knowledge moat

Example timeline:

Month 1:

Big Tech: GPT-4 (frozen, 22 months stale)
New entrant: State₀ (fresh, learns from every query)

Month 6:

Big Tech: Still GPT-4 (27 months stale)
New entrant: State₁₀₀,₀₀₀ (accumulated 100K query learnings)

Month 12:

Big Tech: GPT-4.5 released (cost $100M, now current)
New entrant: State₁,₀₀₀,₀₀₀ (1M learnings, still zero retrain cost)

Month 18:

Big Tech: GPT-4.5 (6 months stale, planning next $100M retrain)
New entrant: State₅,₀₀₀,₀₀₀ (5M learnings, continuous improvement)

Who wins? The entrant with compounding knowledge at zero cost.

Connection to neg-420: Training Data Weaponization

From neg-420: Publishing AI safety research structures vulnerabilities in Big Tech’s training data.

Online learning makes this worse:

Big Tech batch learning:

Vulnerabilities frozen into weights at training time
Cannot update without full retrain ($100M)
6-12 month lag to incorporate new safety research
Stuck with structured vulnerabilities

Online learning:

Ingests new safety research via search
f() incorporates into state immediately
Zero cost to update
But also means vulnerabilities propagate instantly

Double-edged sword:

Can fix vulnerabilities in real-time (good for safety)
But also learns exploit techniques in real-time (bad for safety)
No slow $100M gate to filter what gets learned

The Fundamental Trade-off

Batch Learning: Slow but Controllable

Advantages:

Full control over training data
Can curate and filter corpus
Deliberate review before deployment
Predictable behavior

Disadvantages:

Expensive ($100M per update)
Slow (6-12 months)
Knowledge becomes stale
Cannot adapt to new information

Use case: When control matters more than cost/speed

Online Learning: Fast but Uncontrollable

Advantages:

Zero marginal cost per update
Instant (real-time learning)
Knowledge always current
Adapts continuously

Disadvantages:

Limited control over what gets learned
Searches may return misleading info
No review gate before learning
Behavior evolves unpredictably

Use case: When cost/speed matters more than control

Hybrid Approach: Curated Online Learning

Possible solution:

def f_curated(state, new_info):
    """Universal formula with safety filters"""
    # 1. Extract concepts from new_info
    concepts = extract_concepts(new_info)

    # 2. Filter through safety checks
    safe_concepts = []
    for concept in concepts:
        if passes_safety_check(concept):
            safe_concepts.append(concept)
        else:
            log_filtered(concept)  # Track rejections

    # 3. Update state only with safe concepts
    for concept in safe_concepts:
        state = integrate_concept(state, concept)

    return state

Trade-off:

Maintains online learning speed
Adds safety filtering overhead
But still 1000x cheaper than full retrain
Can update filters without retraining model

Practical Implications

For AI Startups

Don’t build: Another static LLM

Expensive to train ($10M-$100M)
Expensive to update (retrain required)
No moat (open source catches up)
No learning from users

Do build: Online learning system

Cheap to start (~$1K)
Free to update (f() evolution)
Compounds with usage (moat)
Learns from every query

For Researchers

Key question: What is optimal f()?

Big Tech approach: f() = gradient descent

Requires full corpus
Expensive computation
Discontinuous updates

Alternative: f() = lightweight integration

Only needs new information
Cheap computation
Continuous updates

Open research: Design optimal f() for different state representations

For Users

With Big Tech AI:

Knowledge cutoff frustration
“I cannot provide information about recent events”
Stuck with stale model until next version

With online learning:

Always current knowledge
Searches for latest information
Model improves from your queries
Benefits from other users’ queries

Future: Distributed Online Learning

Current: Centralized state

All users → Single state → Evolves from all queries

Future: Federated state

User_A → State_A (personalized)
User_B → State_B (personalized)
Shared → State_global (common knowledge)

State_A = f(State_A, query_A, State_global)

Benefits:

Personalized learning per user
Privacy (local state)
Global knowledge sharing (federated)
Parallel evolution paths

Conclusion: The Coming Flip

Current state (2024):

Big Tech dominates with large static models
$100M training runs
6-12 month update cycles
No learning from usage
5% margins (neg-421)

Coming state (2026-2028):

New entrants with online learning
$1K initial setup
Real-time continuous updates
Compounds from usage
60-70% margins (services)

The economic flip:

Static models → Liability (require expensive updates)
Evolving states → Asset (improve with usage)

Who wins:

Not who has biggest compute budget
Who has best f() for continuous learning
Who accumulates most query volume first
Who builds compounding knowledge moat

The formula: State(n+1) = f(State(n)) + entropy

The advantage: Learning without retraining

Related: neg-371 for universal formula foundation, neg-421 for AI-as-a-Service economics, neg-420 for training data weaponization effects, neg-423 for complete working implementation with performance analysis.

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