Research Discussion: Multi-Domain Extensions for Creative Problem Solving #33
Description
Research Discussion: Multi-Domain Extensions for Creative Problem Solving
Note: I should mention upfront that I used AI assistance to help articulate these ideas. While the core insights and direction come from my own thinking, I wouldn't have been able to express the technical details clearly without that help. I believe the underlying concepts are worth discussing despite this assistance in presentation.
I've been thinking about how HRM might work beyond the current puzzle domains and wanted to share some ideas that could be useful for the community - particularly building on the interest in Issue #3 for general usage examples.
The Pattern I'm Seeing
HRM's hierarchical convergence approach seems to remind me of how I solve problems when coding. There's this pattern where you have high-level strategic thinking ("I need to refactor this API") combined with detailed tactical work ("check each function call, update the tests"), and sometimes you realize mid-way through that your initial approach was wrong and you need to restart with a different strategy.
This same pattern shows up in lots of domains:
- Code refactoring: Figuring out the best place to add new functionality without breaking existing systems
- System design: Where to put caching layers, service boundaries, monitoring points
- Mathematical proofs: When to focus on specific constraints vs when to step back and try a completely different approach
- Resource allocation: Balancing immediate tactical needs against longer-term strategic positioning
What strikes me as interesting is that these all seem to involve finding optimal "intervention points" in complex systems - which appears to be similar to what HRM's architecture is designed for.
Technical Ideas
1. Multi-Domain Input Support
From what I can tell, HRM currently focuses on grid-based problems. But it seems like the core reasoning approach could potentially work for other input types:
class UniversalInputEncoder(nn.Module):
def __init__(self, config):
self.grid_encoder = GridEncoder(config) # existing
self.sequence_encoder = SequenceEncoder(config) # new
self.graph_encoder = GraphEncoder(config) # new
self.input_type_classifier = nn.Linear(config.input_dim, 3)
def forward(self, input_data, input_type=None):
if input_type is None:
input_type = self.classify_input_type(input_data)
if input_type == 'grid':
return self.grid_encoder(input_data)
elif input_type == 'sequence':
return self.sequence_encoder(input_data)
elif input_type == 'graph':
return self.graph_encoder(input_data)This would potentially allow training on code ASTs, system architecture diagrams, logical formulas, etc.
2. Environment Boundary Detection
The thing about "change placement" problems is that you need to understand the boundaries and constraints of your environment. A boundary detection module could identify intervention points and predict ripple effects:
class BoundaryDetectionModule(nn.Module):
"""Detect intervention points and boundaries in problem space"""
def __init__(self, config):
self.boundary_encoder = TransformerEncoder(
d_model=config.hidden_dim,
nhead=config.num_heads,
num_layers=config.boundary_layers
)
# Predict different types of boundaries
self.boundary_classifier = nn.Linear(config.hidden_dim, config.num_boundary_types)
# Integration with existing modules
self.h_integration = nn.Linear(config.hidden_dim * 2, config.hidden_dim)
def forward(self, problem_state, environment_state=None):
# Combine problem and environment info
if environment_state is not None:
combined_state = torch.cat([problem_state, environment_state], dim=-1)
else:
combined_state = problem_state
# Detect boundaries
boundary_features = self.boundary_encoder(combined_state)
boundary_types = self.boundary_classifier(boundary_features)
return boundary_features, boundary_types
def integrate_with_h_module(self, h_state, boundary_features):
"""Integrate boundary information into H-module planning"""
combined = torch.cat([h_state, boundary_features], dim=-1)
return self.h_integration(combined)3. Cross-Domain Pattern Matching
One thing that seems missing is the ability to learn patterns that transfer between different types of problems. Like recognizing that "caching frequently accessed data" applies whether you're optimizing web requests or mathematical computations:
class AnalogyModule(nn.Module):
def __init__(self, config):
# Pattern extraction is just an encoder
self.pattern_encoder = TransformerEncoder(config.pattern_layers)
# Pattern matching is just attention/similarity
self.pattern_matcher = nn.MultiheadAttention(config.hidden_dim, config.num_heads)
# Memory bank is just learned embeddings
self.pattern_memory = nn.Embedding(config.memory_size, config.hidden_dim)
def analogical_reasoning(self, current_problem, memory_bank):
"""Find patterns from different domains"""
# Abstract current problem to general patterns
abstract_pattern = self.extract_pattern(current_problem)
# Search across domains for similar patterns
analogous_solutions = self.pattern_match_across_domains(
abstract_pattern,
memory_bank
)
# Adapt solutions from other domains
adapted_solutions = []
for solution in analogous_solutions:
adapted = self.adapt_solution(solution, current_problem)
adapted_solutions.append(adapted)
return adapted_solutions4. Problem Reframing Capability
Sometimes the biggest insight is realizing you're solving the wrong problem entirely. A reframing module could generate alternative ways to think about the same situation:
class ReframingModule(nn.Module):
def __init__(self, config):
# Generate alternative problem encodings
self.reframe_generator = TransformerDecoder(config.reframe_layers)
# Score which reframing is best
self.reframe_scorer = nn.Linear(config.hidden_dim, 1)
def reframe_problem(self, problem_representation, context):
"""Change the problem representation entirely"""
# Generate alternative problem framings
alternative_frames = []
# Constraint relaxation: "What if we don't need to solve X?"
relaxed_constraints = self.relax_constraints(problem_representation)
alternative_frames.extend(relaxed_constraints)
# Level shift: "What if this is really a Y problem, not an X problem?"
level_shifts = self.shift_abstraction_level(problem_representation)
alternative_frames.extend(level_shifts)
# Domain transfer: "What if we treat this as a Z-type problem?"
domain_transfers = self.transfer_domains(problem_representation)
alternative_frames.extend(domain_transfers)
return self.evaluate_framings(alternative_frames)Enhanced Architecture
Putting it all together, you'd have something like:
class CreativeHRM:
def __init__(self):
# Core reasoning (original HRM)
self.H_strategic = HighLevelModule() # Strategic planning
self.L_tactical = LowLevelModule() # Detailed execution
# New creative reasoning modules
self.B_boundary = BoundaryModule() # Environment scanning
self.A_analogy = AnalogyModule() # Cross-domain pattern matching
self.R_reframe = ReframingModule() # Problem representation change
def creative_hierarchical_reasoning(self, problem):
"""Extended HRM with creative modules"""
# Initialize all modules
z_H = self.init_strategic_state()
z_L = self.init_tactical_state()
z_B = self.init_boundary_state()
z_A = self.init_analogy_state()
z_R = self.init_reframe_state()
for meta_cycle in range(max_meta_cycles):
# CREATIVE PHASE (slowest timescale)
if meta_cycle % reframe_interval == 0:
# Reframe the problem entirely
new_framings = self.R_reframe(problem, z_H, z_L)
if self.should_adopt_reframing(new_framings):
problem = self.adopt_new_framing(new_framings[0])
z_H, z_L = self.reset_with_new_framing(problem)
# ANALOGICAL PHASE (medium-slow timescale)
if meta_cycle % analogy_interval == 0:
# Search for cross-domain solutions
analogical_insights = self.A_analogy(problem, self.memory_bank)
z_H = self.integrate_analogical_insights(z_H, analogical_insights)
# BOUNDARY SCANNING PHASE (medium timescale)
if meta_cycle % boundary_interval == 0:
# Scan for optimal intervention points
boundary_analysis = self.B_boundary(problem, environment)
z_H = self.update_strategy_with_boundaries(z_H, boundary_analysis)
# STANDARD HRM PHASE (fast timescale)
for cycle in range(standard_cycles):
# Original HRM hierarchical convergence
for step in range(T):
z_L = self.L_tactical(z_L, z_H, problem)
z_H = self.H_strategic(z_H, z_L)
# Check if solution found at this level
if self.solution_found(z_H):
return self.extract_solution(z_H)
return self.extract_best_solution(z_H)Memory Architecture for Learning
To make cross-domain transfer work, you'd need a way to store and retrieve solution patterns:
class CreativeMemoryBank:
def __init__(self):
# Organize memory by abstraction patterns, not just domains
self.pattern_memory = {
'boundary_patterns': {}, # Successful intervention strategies
'analogy_patterns': {}, # Cross-domain solution mappings
'reframing_patterns': {}, # Successful problem reframings
'failure_patterns': {} # What didn't work and why
}
def store_creative_solution(self, problem, solution_path, outcome):
"""Store not just the solution, but the creative process"""
# Extract the creative insights that led to success
creative_insights = {
'boundary_choices': solution_path.boundary_decisions,
'analogies_used': solution_path.analogical_leaps,
'reframings_tried': solution_path.problem_reframings,
'intervention_points': solution_path.change_locations
}
# Abstract to patterns for future use
abstract_patterns = self.extract_transferable_patterns(
problem, creative_insights, outcome
)
self.update_pattern_memory(abstract_patterns)Why This Could Work
HRM's design already appears to have most of the pieces you'd need:
- Hierarchical convergence seems to prevent getting stuck in local optima - the H-module appears able to restart the L-module with a completely different approach
- Multi-timescale processing appears to match how creative insights actually work - fast tactical thinking plus slower strategic realization
- Adaptive computation time already lets the model "think longer" for harder problems
- One-step gradients may mean you can train deep reasoning without the usual instability issues
The extensions would add:
- Environmental awareness through boundary detection
- Cross-domain learning through pattern memory
- Input flexibility through universal encoders
- Problem reframing through alternative representation generation
Possible Implementation Path
For anyone who wants to explore this:
Phase 1: Multi-Domain Foundation (4-6 weeks)
- Universal input encoder for different problem types
- Environment state tracking infrastructure
- Basic cross-domain training pipeline
- Solution quality metrics beyond just accuracy
Phase 2: Boundary-Aware Reasoning (6-8 weeks)
- Boundary detection module implementation
- Integration with existing H/L modules
- Code refactoring dataset with labeled "optimal placements"
- Evaluation framework for change placement quality
Phase 3: Analogical Transfer (8-12 weeks)
- Pattern memory architecture
- Cross-domain training methodology
- Evaluation benchmarks for analogical reasoning
- Integration testing with boundary detection
Phase 4: Problem Reframing (6-8 weeks)
- Alternative representation generation
- Reframing quality assessment
- End-to-end creative problem solving pipeline
- Performance comparison with Chain-of-Thought approaches
Connection to Existing Work
This builds directly on:
- Issue General Usage Example? #3: Concrete approach for applying HRM beyond puzzles
- Issue Add Reasoning-Gym Experiments #5: Architecture that could handle Reasoning-Gym's diverse task types
- Issue Reproducibility results of Sudoku-Extreme and ARC-AGI 1 #12: Solution quality metrics might help with reproducibility debugging
The core insight is that HRM's hierarchical reasoning approach seems naturally suited for "creative" problem solving - you just need to give it the right environmental awareness and memory structures.
Open Questions
Some things I'm curious about:
- Can boundary detection actually be learned from code repositories without explicit labels?
- Do solution patterns really transfer between domains, or is that just wishful thinking?
- How would this approach compare to retrieval-augmented generation methods?
- When do problems need creative reframing vs just systematic optimization?
Note: I don't have the bandwidth to work on implementing this myself, but wanted to share these ideas in case they're useful for anyone else exploring multi-domain reasoning. The HRM architecture seems uniquely well-positioned for this kind of extension given its brain-inspired design.
Would be curious to hear thoughts from the @sapientinc team and anyone else interested in extending reasoning capabilities!