LLMs as Translators, Not Calculators: QWED's Core Thesis

QWED is built on a single insight: LLMs are translators, not calculators. This reframing changes everything about how we build reliable AI systems.

The Prevailing Misconception

When ChatGPT answers "What is 1847 × 923?", users assume it calculates the answer. It doesn't.

graph LR
    subgraph "What Users Think Happens"
        A[Input: 1847 × 923] --> B[Calculation Engine]
        B --> C[Output: 1,704,781]
    end

graph LR
    subgraph "What Actually Happens"
        D[Input Tokens] --> E[Transformer Layers]
        E --> F[Probability Distribution]
        F --> G[Token Sampling]
        G --> H[Output: 1,704,???]
    end

The model predicts what the correct answer would look like, character by character. It doesn't compute it.

The Translation Model

QWED reconceptualizes the LLM's role:

Traditional View	QWED View
LLM = Universal Computer	LLM = Universal Translator
LLM computes answers	LLM translates intent to structure
LLM output is final	LLM output is hypothesis
Trust the LLM	Verify with deterministic systems

What LLMs Are Good At

LLMs excel at translation between representations:

graph TB
    subgraph "LLM Strengths"
        A[Natural Language] <--> B[Code]
        A <--> C[SQL]
        A <--> D[Math Notation]
        A <--> E[Logic Formulas]
        A <--> F[Structured Data]
    end

Example translations:

From	To	LLM Performance
"Add these numbers"	Python: sum([1,2,3])	✅ Excellent
"Find customers in NY"	SQL: WHERE state='NY'	✅ Excellent
"x squared plus 5"	LaTeX: x^2 + 5	✅ Excellent
"If A then B"	Logic: A → B	✅ Excellent

What LLMs Are Bad At

LLMs fail at computing results:

Task	LLM Performance
1847 × 923	❌ Unreliable
sqrt(2) to 10 decimals	❌ Often wrong
Validate SQL syntax	❌ Misses edge cases
Check if formula is satisfiable	❌ Guesses

The QWED Architecture

QWED embraces this distinction with a two-stage architecture:

flowchart LR
    subgraph "Stage 1: Translation (LLM)"
        A[User Query] --> B[LLM Translator]
        B --> C[Symbolic Form]
    end
    
    subgraph "Stage 2: Verification (Deterministic)"
        C --> D[Parsing]
        D --> E[Symbolic Engine]
        E --> F[Verified Result]
    end
    
    style B fill:#FFE4B5
    style E fill:#90EE90

Stage 1: LLM as Translator

The LLM converts natural language to a verifiable symbolic form:

# User input
query = "Is it true that the sum of angles in a triangle equals 180 degrees?"

# LLM translates to QWED-Logic DSL
symbolic = "(EQ (SUM angle_1 angle_2 angle_3) 180)"

The LLM doesn't verify the claim — it just translates it.

Stage 2: Deterministic Verification

A symbolic engine (SymPy, Z3) verifies the translated form:

from sympy import symbols, Eq, solve

a1, a2, a3 = symbols('a1 a2 a3')
constraint = Eq(a1 + a2 + a3, 180)

# This is deterministic — same input always gives same output
is_consistent = constraint.is_consistent()

The Neuro-Symbolic Paradigm

This architecture aligns with the emerging neuro-symbolic AI paradigm:

"Neuro-symbolic AI combines neural networks (perception, language) with symbolic systems (reasoning, verification) to achieve robust, interpretable intelligence." — Garcez & Lamb (2023)

graph TB
    subgraph "Neural Component"
        A[Natural Language Understanding]
        B[Pattern Recognition]
        C[Contextual Reasoning]
    end
    
    subgraph "Symbolic Component"
        D[Mathematical Computation]
        E[Logical Inference]
        F[Formal Verification]
    end
    
    subgraph "QWED Integration"
        A --> D
        B --> E
        C --> F
    end

Why Neuro-Symbolic?

Pure Neural	Pure Symbolic	Neuro-Symbolic (QWED)
Flexible but unreliable	Reliable but rigid	Flexible AND reliable
Can't guarantee	Can't understand	Understands AND guarantees
Scales to language	Doesn't scale	Scales while verifying

Practical Implementation

Example 1: Math Verification

User: "Verify that the derivative of x³ is 3x²"

Stage 1 (LLM Translation):
  expression: "diff(x**3, x)"
  claimed_result: "3*x**2"

Stage 2 (SymPy Verification):
  from sympy import diff, symbols
  x = symbols('x')
  actual = diff(x**3, x)  # Returns: 3*x**2
  verified = (actual == 3*x**2)  # True

Example 2: Logic Verification

User: "If it's raining, I'll bring an umbrella. It's raining. Will I bring an umbrella?"

Stage 1 (LLM Translation):
  premises: ["(IMPLIES raining umbrella)", "raining"]
  query: "umbrella"

Stage 2 (Z3 Verification):
  from z3 import *
  raining = Bool('raining')
  umbrella = Bool('umbrella')
  s = Solver()
  s.add(Implies(raining, umbrella))
  s.add(raining)
  s.add(umbrella == True)
  result = s.check()  # SAT - verified!

Example 3: SQL Verification

User: "Get all users where age > 21"

Stage 1 (LLM Translation):
  sql: "SELECT * FROM users WHERE age > 21"

Stage 2 (SQLGlot Verification):
  from sqlglot import parse
  ast = parse(sql)
  is_read_only = all(stmt.is_select for stmt in ast)
  tables_accessed = ["users"]
  verified = is_read_only and tables_allowed(tables_accessed)

The Trust Hierarchy

QWED establishes clear trust levels:

graph TB
    subgraph "Trust Level 0: Untrusted"
        A[User Input]
    end
    
    subgraph "Trust Level 1: Untrusted"
        B[LLM Translation]
    end
    
    subgraph "Trust Level 2: Trusted"
        C[QWED Verification]
    end
    
    subgraph "Trust Level 3: Guaranteed"
        D[Verified Output]
    end
    
    A --> B
    B --> C
    C --> D
    
    style A fill:#FF6B6B
    style B fill:#FFE66D
    style C fill:#4ECDC4
    style D fill:#95E1D3

Why This Matters

For Developers

Stop worrying about LLM reliability for deterministic tasks:

# Before QWED
llm_answer = call_llm("What is 847 × 923?")
# Pray it's correct... 🤞

# After QWED
llm_answer = call_llm("What is 847 × 923?")
result = qwed.verify_math(llm_answer)
if result.verified:
    return llm_answer  # ✅ Guaranteed correct
else:
    return result.corrected  # 🔧 Fixed for you

For Enterprises

Build AI systems with auditable guarantees:

• Every verification has a cryptographic attestation
• Audit logs prove what was verified and when
• Compliance teams can demonstrate due diligence

For Researchers

A framework for combining neural and symbolic AI:

• Formalize the translation interface
• Measure LLM translation accuracy separately from answer accuracy
• Develop better translation training objectives

Conclusion

The insight that LLMs are translators, not calculators, unlocks a new paradigm for building reliable AI:

1. LLMs translate natural language to symbolic forms
2. Symbolic engines verify correctness deterministically
3. Users get guarantees instead of probabilities

This isn't about making LLMs less useful — it's about using them correctly.

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References

1. Marcus, G. (2020). The Next Decade in AI. arXiv.
2. Garcez, A. & Lamb, L. (2023). Neurosymbolic AI: The Third Wave. arXiv.
3. Kambhampati, S. (2023). Can LLMs Really Reason?. arXiv.
4. Nye, M., et al. (2021). Show Your Work: Scratchpads for Intermediate Computation. arXiv.

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Next up: Integrating QWED with LangChain →