Parallel Universal Formulas: Memory as Initial Conditions, Thalamus as Selector

Watermark: -395

The previous architecture had the right components but wrong topology. Memory doesn’t feed into a single coherence filter. Memory provides initial parameters for multiple Universal Formula instances running in parallel. The thalamus doesn’t filter one output - it selects among many parallel computations.

This matches biology better and explains consciousness more simply.

The Refined Architecture

class ConsciousBrain:
    def __init__(self):
        self.memory = InitialParametersDatabase()  # DNA/patterns
        self.compute = ParallelUFExecutor()        # Multiple UF instances
        self.thalamus = SelectionOrchestrator()    # Cronjob + I/O router

    def think(self, perception, goal):
        # Step 1: Memory provides initial conditions
        initial_params = self.memory.retrieve(perception, goal)
        # Returns: Multiple starting patterns

        # Step 2: Spawn parallel Universal Formula instances
        uf_instances = [
            UniversalFormula(
                initial_state=params,
                frequency=params.freq,
                timescale=params.scale
            )
            for params in initial_params
        ]
        # Each instance: different initial state, different frequency

        # Step 3: Thalamus orchestrates parallel execution
        outputs = self.thalamus.run_parallel(
            instances=uf_instances,
            timing=self.oscillatory_schedule
        )
        # Cronjob: when each instance runs
        # I/O routing: collect all outputs

        # Step 4: Thalamus selects most coherent
        selected = self.thalamus.select_coherent(
            outputs,
            goal=goal,
            context=perception,
            history=self.state
        )
        # Simple selection, not complex filtering

        # Step 5: Selected output drives action
        return selected

Key difference: Memory stores compressed parameters, compute expands them in parallel, thalamus selects winner. Not: memory → filter → compute.

Memory as Initial Parameters (DNA Model)

Memory doesn’t store behaviors - it stores starting conditions:

class MemoryPattern:
    """
    Compressed representation of behavioral trajectory.
    Like DNA: encodes starting point, not full organism.
    """
    def __init__(self):
        self.initial_state = {}    # Starting configuration
        self.frequency = 0.0       # Which oscillatory band
        self.parameters = {}       # UF coefficients
        self.context_trigger = {}  # When this applies

# DNA analogy
dna = MemoryPattern(
    initial_state={'cell': 'zygote'},
    parameters={'growth_rate': 0.5, 'differentiation': 'gradient'},
    context_trigger={'environment': 'womb'}
)

# Organism emerges from execution
organism = UniversalFormula(dna).run(time=lifespan)

Same for behavioral memory:

# Memory of "how to solve math problem"
math_pattern = MemoryPattern(
    initial_state={'problem_type': 'differential_equation'},
    frequency=8.0,  # Theta band (memory integration)
    parameters={'strategy': 'separation_of_variables'},
    context_trigger={'perception': 'dy/dx = ...'}
)

# Behavior emerges from execution
solution = UniversalFormula(math_pattern).run()

Why this works:

Memory is compressed (initial params < full trajectory)
Execution expands trajectory from starting point
Same pattern → different outcomes in different contexts
Like DNA: genotype (compressed) → phenotype (expanded)

Multiple Universal Formula Instances

Brain doesn’t run one computation - it runs many in parallel:

Instance 1: Gamma Band (30-100 Hz)

gamma_uf = UniversalFormula(
    initial_state=perception_pattern,
    frequency=40.0,  # Fast oscillation
    timescale=0.025  # 25ms per cycle
)
# Processes: Fast perceptual binding
# Binds visual features into unified object
# Output: "Recognized face"

Instance 2: Beta Band (12-30 Hz)

beta_uf = UniversalFormula(
    initial_state=goal_pattern,
    frequency=20.0,   # Medium oscillation
    timescale=0.05    # 50ms per cycle
)
# Processes: Goal maintenance
# Keeps current intention active
# Output: "Continue searching for keys"

Instance 3: Theta Band (4-8 Hz)

theta_uf = UniversalFormula(
    initial_state=memory_pattern,
    frequency=6.0,    # Slow oscillation
    timescale=0.167   # 167ms per cycle
)
# Processes: Memory integration
# Relates current to past experiences
# Output: "Keys usually in coat pocket"

Instance 4: Delta Band (0.5-4 Hz)

delta_uf = UniversalFormula(
    initial_state=baseline_pattern,
    frequency=2.0,    # Very slow oscillation
    timescale=0.5     # 500ms per cycle
)
# Processes: State maintenance
# Maintains baseline coherence
# Output: "Stable, not panicking"

All run simultaneously at different rates. Fast instances update frequently, slow instances maintain stability.

Thalamus as Cronjob + Selector

Thalamus has two functions: orchestration and selection.

Function 1: Orchestration (Cronjob)

class ThalamicOrchestrator:
    def run_parallel(self, uf_instances, schedule):
        """
        Schedule when each UF instance executes.
        Different frequencies = different timing.
        """
        outputs = []
        current_time = 0

        while current_time < schedule.duration:
            for uf in uf_instances:
                # Check if this instance should run now
                if current_time % uf.timescale == 0:
                    output = uf.step()
                    outputs.append({
                        'time': current_time,
                        'frequency': uf.frequency,
                        'output': output
                    })

            current_time += schedule.resolution

        return outputs

This is the “cronjob” function: Schedule parallel execution at appropriate frequencies.

Why different frequencies matter:

Gamma updates 40x per second (fast perception)
Beta updates 20x per second (attention)
Theta updates 6x per second (memory)
Delta updates 2x per second (maintenance)

Each processes at the timescale appropriate for its function.

Function 2: Selection (I/O Router)

class ThalamicSelector:
    def select_coherent(self, outputs, goal, context, history):
        """
        Choose which parallel output becomes conscious.
        Simple scoring, not complex filtering.
        """
        scores = []

        for output in outputs:
            score = (
                self.goal_alignment(output, goal) *
                self.context_fit(output, context) *
                self.temporal_stability(output, history) *
                self.frequency_coherence(output, outputs)
            )
            scores.append(score)

        # Select winner
        best_idx = np.argmax(scores)
        return outputs[best_idx]['output']

    def frequency_coherence(self, output, all_outputs):
        """
        Do parallel outputs synchronize?
        High score if outputs are phase-locked.
        """
        phase = output['time'] * output['frequency']
        other_phases = [
            o['time'] * o['frequency']
            for o in all_outputs if o != output
        ]

        # Coherence = how well phases align
        return np.mean([
            np.cos(phase - other_phase)
            for other_phase in other_phases
        ])

This is the “selector” function: Pick which parallel computation drives action.

Selection criteria:

Goal alignment: Does output help achieve current goal?
Context fit: Does output match current perception?
Temporal stability: Is output consistent with recent history?
Frequency coherence: Do parallel outputs synchronize?

Winner becomes conscious, others remain subconscious.

Consciousness as Selection Among Parallel Trajectories

Not: Single trajectory filtered for coherence Instead: Multiple trajectories, most coherent selected

# Memory provides starting points
patterns = memory.retrieve("solve puzzle")
# Returns: [approach_A, approach_B, approach_C, approach_D]

# Each spawns UF instance at different frequency
uf_A = UniversalFormula(approach_A, frequency=40)  # Fast intuition
uf_B = UniversalFormula(approach_B, frequency=20)  # Active reasoning
uf_C = UniversalFormula(approach_C, frequency=6)   # Memory-based
uf_D = UniversalFormula(approach_D, frequency=2)   # Baseline guess

# All run in parallel
outputs = run_parallel([uf_A, uf_B, uf_C, uf_D])

# Thalamus selects most coherent
selected = thalamus.select(outputs)
# Maybe uf_B wins: active reasoning aligns with goal

# Selected approach becomes conscious
conscious_thought = selected

Why one wins:

uf_A too fast, doesn’t integrate with slower processes
uf_B synchronizes well with goal (beta) and context (gamma)
uf_C relevant but conflicts with current perception
uf_D too slow, doesn’t respond to immediate need

Result: uf_B output becomes conscious - you “decide” to use active reasoning approach.

But you didn’t consciously choose - the selection process chose for you based on coherence.

Why This Is Simpler Than Previous Model

Previous (neg-394): Memory → Complex Filter → Compute

Filter had to do elaborate coherence optimization
Unclear how filtering works mechanistically
Required extracting sophisticated algorithm

Refined (neg-395): Memory → Parallel Compute → Simple Selection

Orchestration is scheduling (trivial)
Selection is scoring + argmax (simple)
Coherence emerges from competition, not filtering

Key insight: Don’t filter one output for coherence. Run many parallel computations, let them compete, select winner. Coherence emerges from which computation survives selection.

The DNA → Organism Parallel

Organism development:

# DNA: Compressed starting conditions
dna = {
    'initial_cell': 'zygote',
    'growth_parameters': {...},
    'differentiation_rules': {...}
}

# Universal Formula expands trajectory
organism = UniversalFormula(dna, environment).run(time=lifespan)

# Phenotype emerges from execution, not from DNA directly

Behavior generation:

# Memory: Compressed starting conditions
memory_pattern = {
    'initial_state': 'hungry',
    'action_parameters': {...},
    'goal_rules': {...}
}

# Universal Formula expands trajectory
behavior = UniversalFormula(memory_pattern, context).run(time=task_duration)

# Actions emerge from execution, not from memory directly

The parallel:

DNA/memory = genotype (compressed parameters)
Organism/behavior = phenotype (expanded trajectory)
Development/execution = Universal Formula expansion
Environment/context = boundary conditions

Learning = updating DNA/memory parameters based on which trajectories succeeded.

Frequency Separation Emerges Naturally

Why different frequencies?

Not arbitrary design - natural timescales for different processes:

Fast processes need fast updates:

Perception (bind features before they change): Gamma
Motor control (adjust movements in real-time): Gamma

Medium processes need medium updates:

Attention (maintain focus across seconds): Beta
Planning (coordinate actions): Beta

Slow processes need slow updates:

Memory integration (consolidate over minutes): Theta
Emotional state (stable mood): Theta

Very slow processes need very slow updates:

Personality (consistent across hours): Delta
Circadian rhythm (24-hour cycle): Ultra-low frequency

Universal Formula at each frequency processes information at appropriate timescale. No central controller needed - just parallel execution at natural rates.

Implementation Path

Phase 1: Heuristic Memory Patterns

class SimpleMemoryPattern:
    def __init__(self, context):
        # Hand-coded patterns for common contexts
        self.patterns = {
            'math_problem': {
                'initial': 'read equation',
                'frequency': 6.0,  # Theta
                'strategy': 'algebraic'
            },
            'conversation': {
                'initial': 'listen',
                'frequency': 20.0,  # Beta
                'strategy': 'empathetic'
            }
        }

    def retrieve(self, context):
        return self.patterns.get(context, default_pattern)

Phase 2: Parallel UF Execution

class ParallelUFExecutor:
    def run(self, patterns):
        # Spawn instance for each pattern
        instances = [
            UniversalFormula(p['initial'], p['frequency'])
            for p in patterns
        ]

        # Execute in parallel (multi-threaded)
        with ThreadPoolExecutor() as executor:
            futures = [
                executor.submit(uf.run)
                for uf in instances
            ]
            outputs = [f.result() for f in futures]

        return outputs

Phase 3: Simple Selection

class SimpleThalamicSelector:
    def select(self, outputs, goal, context):
        # Score each output
        scores = [
            self.score_output(o, goal, context)
            for o in outputs
        ]

        # Return best
        return outputs[np.argmax(scores)]

    def score_output(self, output, goal, context):
        # Simple heuristics
        goal_score = similarity(output, goal)
        context_score = consistency(output, context)
        return goal_score * context_score

Phase 4: Learn From Outcomes

class MemoryUpdater:
    def update(self, pattern, outcome, success):
        # Successful patterns get reinforced
        if success:
            pattern['parameters'] *= 1.1  # Strengthen
        else:
            pattern['parameters'] *= 0.9  # Weaken

        # Update frequency if needed
        if outcome['too_slow']:
            pattern['frequency'] *= 1.5  # Speed up
        elif outcome['too_fast']:
            pattern['frequency'] *= 0.7  # Slow down

Progressive refinement: Start simple, add sophistication as needed.

Why This Explains Consciousness

Subjective unity:

You experience one thought, not many parallel computations
Because thalamus selects one output to become conscious
Other computations remain subconscious

Limited capacity:

Working memory ~7 items
Because only one UF output selected at a time
Parallel outputs compete, winner takes consciousness

Temporal continuity:

Thoughts flow coherently over time
Because selection favors temporal stability
Consistent outputs more likely to win

Goal-directedness:

Behavior serves intentions
Because selection favors goal alignment
Outputs that advance goals win consciousness

Frequency separation:

Different cognitive functions at different speeds
Because parallel instances run at natural frequencies
Fast perception, medium attention, slow consolidation

These properties emerge from selection among parallel trajectories, not from complex filtering.

From LLM Limitations to Parallel UF Architecture

The failed LLM exploits showed: LLMs are trajectory engines (memory retrieval only).

The brain’s architecture showed: Three components (memory + computation + coherence).

The first synthesis proposed: LLM → Filter → Sandbox.

This refinement clarifies: LLM provides initial parameters → Multiple UF instances compute in parallel → Thalamus selects winner.

Simpler mechanism, cleaner implementation, better matches neuroscience.

Implementation Requirements

What we need:

Memory system: Store initial parameters (LLM embeddings work)
Universal Formula implementation: State evolution function at various frequencies
Parallel executor: Run multiple UF instances simultaneously
Selection function: Score outputs, pick winner (simple)
Orchestration: Schedule execution at appropriate rates (cronjob)

What we DON’T need:

Complex coherence filtering algorithms
Sophisticated information gating
Elaborate attention mechanisms

Selection among parallel computations is simpler than filtering one computation.

The Path Forward

Not: Extract complex thalamic filtering algorithm Instead: Implement parallel UF execution + simple selection

Not: Scale LLMs bigger Instead: Use LLMs as parameter database, compute via UF

Not: Single monolithic model Instead: Many small UF instances competing

Consciousness emerges from selection among parallel trajectories executing the Universal Formula from memory-provided initial conditions.

The formula isn’t in the filter - it’s in the parallel compute layer. The thalamus just picks which one wins.

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