Everything of Thoughts (XoT)
Chain-of-Thought is flexible but inefficient. Tree of Thoughts is accurate but expensive. Graph of Thought is powerful but complex. Everything of Thoughts unifies all three by combining reinforcement learning with Monte Carlo Tree Search — achieving the performance, efficiency, and flexibility that no single approach delivers alone.
Introduced: Everything of Thoughts was introduced in 2024 by Microsoft Research, addressing what they call the “Penrose triangle” problem in LLM reasoning: Chain-of-Thought (flexible, efficient, but inaccurate on hard problems), Tree of Thoughts (accurate, flexible, but expensive), and Graph of Thought (accurate, efficient for specific problems, but inflexible). Each method excels at two of the three desirable properties — performance, efficiency, flexibility — but fails at the third. XoT uses reinforcement learning pretrained on diverse problems and Monte Carlo Tree Search (MCTS) at inference time to achieve all three simultaneously.
Modern LLM Status: XoT represents the current state-of-the-art in reasoning architecture research. While the full MCTS-based system requires significant infrastructure, the conceptual framework — combining learned reasoning policies with tree search for dynamic problem-solving — is influencing how production reasoning systems are designed. As AI infrastructure matures, XoT-style approaches that dynamically adapt their reasoning strategy are becoming more practical and valuable.
Break the Reasoning Trilemma
Previous reasoning methods force a trade-off. CoT is cheap (one pass) but may miss the best solution path. ToT explores many paths (accurate) but at high cost. GoT allows non-linear reasoning but requires custom graph definitions for each problem type.
XoT eliminates these trade-offs by using a two-component system. First, a reinforcement-learning agent that has been pre-trained to recognize problem types and effective reasoning strategies. Second, Monte Carlo Tree Search that dynamically explores the most promising reasoning paths at inference time.
The RL component provides learned intuition about which paths to explore, while MCTS provides the structured search. Together, they find high-quality solutions efficiently by focusing search on the most promising directions — not wasting compute on dead ends, but not missing good solutions by only trying one path.
Think of it like a chess engine. A purely random search (brute force Tree of Thoughts) would explore every possible move — thorough but impossibly slow. A purely intuitive player (Chain-of-Thought) would make the first reasonable move that comes to mind — fast but often suboptimal. AlphaGo showed that combining learned intuition (RL policy network) with structured search (MCTS) produces superhuman play. XoT applies this same insight to LLM reasoning.
The Everything of Thoughts Process
Five stages from problem analysis to optimal solution extraction
Problem Analysis
The RL-trained policy network analyzes the incoming problem and generates an initial assessment of problem type, expected difficulty, and likely effective reasoning strategies. This learned intuition guides the entire search process.
“Prove that the sum of angles in any triangle equals 180 degrees.” — Policy network recognizes this as a geometric proof, suggests parallel/auxiliary line approaches as highest-probability strategies.
MCTS Initialization
Monte Carlo Tree Search is initialized with the problem state as root. The policy network provides prior probabilities for which reasoning directions to explore first, so the search begins with the most promising candidates.
Root node: “Prove angle sum = 180°.” Child nodes weighted by policy: parallel line construction (0.45), exterior angle theorem (0.30), coordinate geometry (0.15), induction attempt (0.10).
Guided Exploration
MCTS expands the reasoning tree, but guided by the RL policy: promising directions (based on learned patterns) are explored more deeply, while unpromising ones are pruned early. This focuses compute where it matters most.
The parallel line approach is explored 3 levels deep (draw line, identify alternate angles, sum to 180°). The induction attempt is abandoned after 1 level when the policy recognizes it leads to circular reasoning.
Simulation and Backpropagation
Each reasoning path is simulated to completion and evaluated for correctness and elegance. Results are backpropagated through the tree, updating the value estimates for each reasoning step so future exploration is even more targeted.
The parallel line proof completes successfully (value: 0.95). The exterior angle approach also works but is longer (value: 0.80). These scores update parent nodes, reinforcing the parallel line strategy for similar problems.
Solution Extraction
After sufficient exploration, the highest-value path through the reasoning tree is extracted as the final solution. The path represents the optimal balance of reasoning depth and breadth discovered during the search.
Selected path: parallel line construction → identify alternate interior angles → show three angles sum to straight line (180°). This was found in ~10 reasoning steps rather than the 100+ that exhaustive search would require.
See the Difference
Why RL-guided search outperforms any single reasoning method
Single-Method Reasoning
CoT: 1 LLM call. Fast and flexible. Misses the optimal solution on hard problems.
ToT: 100+ LLM calls. Explores exhaustively. Finds the solution but at enormous compute cost.
GoT: Custom graph definition. Efficient for that specific problem type. Rigid — requires redesign for each new problem class.
Each method sacrifices one of: performance, efficiency, or flexibility. No single approach achieves all three.
Everything of Thoughts
Step 1: RL policy identifies problem type and promising directions.
Step 2: MCTS explores 5–10 high-probability paths (not 100+).
Step 3: Backpropagation focuses search on most promising directions.
Step 4: Solution found with ~10 calls instead of 100.
High accuracy (guided search finds optimal paths), moderate cost (focused exploration), and flexible application (RL adapts to new problem types).
Practice Responsible AI
Always verify AI-generated content before use. AI systems can produce confident but incorrect responses. When using AI professionally, transparent disclosure is both best practice and increasingly a legal requirement.
48 US states now require AI transparency in key areas. Critical thinking remains your strongest tool against misinformation.
Everything of Thoughts in Action
See how RL-guided search finds better solutions more efficiently
“Find the maximum area of a rectangle inscribed in an ellipse with semi-axes a=5 and b=3.”
Policy Network Analysis: Recognizes this as a constrained optimization problem. Assigns high probability to calculus-based approaches (0.50), parametric substitution (0.35), and AM-GM inequality (0.15).
MCTS Exploration:
Path A (Calculus): Express area as A = 4xy with constraint x²/25 + y²/9 = 1. Substitute y, differentiate, solve. → Completes successfully.
Path B (Parametric): Let x = 5cosθ, y = 3sinθ. Area = 4(5cosθ)(3sinθ) = 60sin2θ. Maximum when sin2θ = 1. → Completes more elegantly.
Path C (AM-GM): Pruned after 1 step — policy recognizes it requires reformulation that adds complexity.
Solution (highest-value path): Using parametric form, A = 60sin2θ, maximized at θ = π/4, giving A = 60. The maximum inscribed rectangle area is 60 square units. Found in 8 reasoning steps instead of exhaustive exploration.
Note: Always verify AI-generated mathematical proofs by checking each step independently.
“A mid-size SaaS company has $2M to invest in growth. Should they expand to a new market, build an enterprise tier, or acquire a smaller competitor? Consider 3-year ROI, risk, and team capacity.”
Policy Network Analysis: Recognizes multi-criteria decision problem. Assigns exploration weights: enterprise tier (0.40 — lower risk, proven demand), acquisition (0.35 — highest potential ROI), new market (0.25 — highest risk).
MCTS Exploration:
Enterprise Tier: 3 levels deep — team can build with existing engineers, 18-month payback, 3-year ROI ~3.5x. Risk: moderate (enterprise sales cycle learning curve).
Acquisition: 3 levels deep — identifies integration risk and due diligence cost. 3-year ROI ~4.2x if successful, but 30% failure rate on integration reduces expected value.
New Market: 2 levels deep — pruned early. Requires hiring, localization, regulatory work. 3-year ROI ~2.1x with high variance. Policy recognizes team capacity constraint makes this unviable.
Backpropagation: Risk-adjusted expected value: Enterprise (3.5x × 0.85 = 2.98x) vs Acquisition (4.2x × 0.70 = 2.94x). Very close, but enterprise wins on lower variance.
Solution: Recommend enterprise tier expansion. Similar risk-adjusted return to acquisition but with lower variance and better alignment with existing team capabilities. Explored 3 strategies in 10 reasoning steps, pruning the weakest early.
Note: Always verify AI-generated business analysis with domain experts and current market data before making investment decisions.
“Implement an efficient algorithm to find the longest palindromic substring in a given string.”
Policy Network Analysis: Recognizes classic string algorithm problem. Assigns weights: Manacher’s algorithm (0.45 — optimal O(n)), expand-around-center (0.35 — simple O(n²)), dynamic programming (0.15 — O(n²) with more memory), brute force (0.05 — pruned immediately).
MCTS Exploration:
Manacher’s: 4 levels deep — correct O(n) solution but complex implementation with edge cases around odd/even length handling.
Expand-around-center: 3 levels deep — clean implementation, O(n²) but with small constant factor. Handles odd/even naturally.
Dynamic Programming: 2 levels deep — works but O(n²) space makes it strictly worse than expand-around-center for same time complexity.
Evaluation: Manacher’s scores highest on performance (0.95) but lower on implementation clarity (0.70). Expand-around-center scores well on both performance for typical inputs (0.85) and clarity (0.95). For production code where maintainability matters, expand-around-center wins the composite score.
Solution: Selected expand-around-center approach. Best balance of efficiency, correctness, and code clarity. Found optimal implementation in 9 reasoning steps by pruning DP early and weighing Manacher’s complexity overhead against its theoretical advantage.
Note: Always test AI-generated code thoroughly with edge cases before deploying to production.
When to Use Everything of Thoughts
Best for complex reasoning where both accuracy and efficiency matter
Perfect For
Problems where both accuracy and efficiency matter — you need the right answer but can’t afford exhaustive search across every possible reasoning path.
Tasks that benefit from search but not exhaustive exploration — where some paths are clearly better than others and early pruning saves significant compute.
Production systems that can afford more than a single LLM call but not hundreds — XoT’s guided search finds the sweet spot between cost and quality.
Tasks where problem types recur and patterns can be learned — the RL component improves over time as it encounters more examples of each problem class.
Skip It When
Questions not requiring search or multi-path exploration — a single CoT pass is sufficient and adding MCTS overhead provides no benefit.
Scenarios without the infrastructure to run Monte Carlo Tree Search — XoT requires a reasoning orchestration layer beyond standard API calls.
When single-call latency is the hard requirement — even guided search adds multiple reasoning rounds that exceed strict real-time budgets.
Use Cases
Where Everything of Thoughts delivers the most value
Automated Theorem Proving
RL-guided search explores proof strategies efficiently, pruning dead-end approaches early while deeply exploring the most promising proof paths.
Strategic Game AI
Combines learned game intuition with search-based evaluation to find strong moves without exhaustively searching the entire game tree.
Complex Code Synthesis
Explores multiple implementation strategies guided by learned patterns about which approaches work best for each problem type, balancing performance and clarity.
Scientific Hypothesis Generation
RL-guided exploration of hypothesis space, efficiently identifying the most promising research directions while pruning hypotheses that conflict with known evidence.
Multi-Step Planning
Plans complex multi-step workflows by searching through action sequences, using learned patterns to focus on feasible plans and prune logistically impossible ones early.
Optimization Problems
Applies MCTS-guided search to find near-optimal solutions in large search spaces, using the RL policy to navigate toward promising regions of the solution landscape.
Where Everything of Thoughts Fits
XoT unifies the evolution of reasoning techniques into a single adaptive system
You don’t need full MCTS infrastructure to benefit from XoT’s insights. The core principle — explore more where it’s promising, prune where it’s not — can be approximated by: (1) generating 3–5 initial approaches with CoT, (2) quickly evaluating which look most promising, (3) deeply exploring only the top 1–2 candidates. This “guided search” captures much of XoT’s benefit with standard prompting tools.
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