From Overthinking to Evolution: Why AI's Best Breakthroughs Happen Outside the Black Box

AlphaEvolve and Darwin Gödel Machine (DGM) shine an LRM path towards orchestration with Tools & Algorithms

Everything is Computer

Large Reasoning Models: Trends, Capabilities, and Future Directions

Quick High-Level Overview

I’ve been thinking about various trends with Large Reasoning Models (LRMs), related Reinforcement Learning (RL) techniques, the debate on their reasoning capabilities, and the successes of systems like AlphaEvolve and Darwin Gödel Machine (DGM).

The following documents refer, and are worth going through:

1. The Illusion of Thinking

2. A Statistical Physics of Language Model Reasoning

3. Stop Anthropomorphizing Intermediate Tokens as Reasoning/Thinking Traces!

4. (How) Do Reasoning Models Reason?

5. RL in Name Only? Analyzing the Structural Assumptions in RL post-training for LLMs

6. Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens

7. Deepmind’s AlphaEvolve

8. The Darwin Gödel Machine: AI that improves itself by rewriting its own code (DGM)

The AI Reasoning Paradox: What's Really Happening Under the Hood

For a few years now, I guess, a bit more prominently since 2022, large AI models have stunned researchers and the public alike with their ability to generate essays, solve equations, write code, and even pass law exams. At first glance, these feats seem to suggest that machines are learning to reason like us—following logical steps, adjusting to context, and solving novel problems.

But look closer, and a stranger picture emerges.

Some models excel at basic puzzles… only to completely fail as complexity increases.

Others generate flawless logic chains that don't correspond to any real understanding.

And a few, orchestrated the right way, generate new algorithms or scientific discoveries—seemingly out of nowhere.

So what's going on?

The Core Reality: Is It All Just Pattern Matching?

What if I said - Every modern AI system—from GPT-4 to Claude to the latest reasoning models—operates on the same fundamental mechanism: statistical pattern matching. They don't reason like humans, manipulate symbols like traditional AI, or follow programmed logic trees. Instead, they identify patterns in vast amounts of text and generate responses that statistically resemble what might come next.

Hang on. Let’s rewind that back again…….it sounds a little too simplistic? Are things really that simple?

Maybe it’s a bit more nuanced than all that?

✅ What’s True

1. Statistical Pattern Matching
   ✔️ Yes, modern large language models (LLMs) like GPT-4 and Claude are fundamentally trained to predict the next token in a sequence based on patterns in massive datasets. This process is driven by probabilistic modeling, not logical deduction.

2. No Symbolic Manipulation (in the classic sense)
   ✔️ They do not natively manipulate symbols in the way traditional symbolic AI systems (like Prolog or expert systems) do. Instead of applying hand-coded rules or symbolic logic trees, LLMs learn associations implicitly through training.

3. No Human-Like Reasoning
   ✔️ They do not "reason" like humans with intent, understanding, or true beliefs. Their reasoning is emergent and statistical, not deliberative in the cognitive sense.

---

⚠️ What’s Oversimplified or Misleading

1. "Only" Statistical Pattern Matching
   ⚠️ While technically correct, this framing underplays the complexity and capabilities that emerge from this statistical foundation. Modern LLMs can perform surprisingly sophisticated reasoning, abstraction, and generalization—even if these are not done symbolically or consciously.

2. Emergent Behaviors
   ❗ Recent studies (e.g. on "grokking" or "tool use" in LLMs) show that models can simulate logic, perform arithmetic, and even chain steps in reasoning—not because they are explicitly trained to do so, but because these behaviors emerge from optimization across large-scale data and compute.

3. Architectural Nuances
   🔍 Newer models (like OpenAI's reasoning-focused models, or Anthropic’s Claude 3 series) may include mechanisms to scaffold reasoning, such as internal scratchpads or self-reflection. These are still built on transformer foundations, but they attempt to guide the model toward more structured thinking.

---

🧠 So let me do a Summary Rewrite (more precisely):

Every modern AI system—like GPT-4, Claude, and other large reasoning models—relies on predicting patterns in data using probabilistic modeling. While they do not reason like humans or manipulate explicit symbols like traditional AI, they can simulate reasoning through complex pattern recognition. Their responses are generated based on statistical likelihoods learned from vast text corpora, leading to behaviors that may appear intelligent without being grounded in programmed logic or conscious understanding.

But let’s keep this simple: Predicting patterns in data using probabilistic modelling….responses generated based on statistical likelihoods => Statistical Pattern Matching

This is the unchanging foundation.

But here's where it gets interesting: depending on the contextual factors surrounding this core mechanism, we get dramatically different outcomes.

The Contextual Multipliers

Four key factors shape how pattern matching translates into performance:

🎯 Training Data: What patterns were available to learn from? What Modalities?

🏗️ Model Architecture: How is the pattern matching structured and scaled?

⚡ Post-Training Methods: How is the model refined after initial training?

📊 Task Complexity: How many interconnected patterns need to be matched simultaneously?

The magic—and the confusion—happens in how these factors interact with the core pattern-matching engine.

---

Four Views of “The Same Elephant”?

In a way, as I see it, researchers looking at AI reasoning have developed four distinct perspectives. Each focuses on different aspects of how contextual factors shape pattern-matching outcomes:

Is It Reasoning or Just A Blue Elephant?

🔻 The Collapse View: When Complexity Breaks Pattern Matching - The Illusion of Thinking

Focus: Task Complexity as the limiting factor

The Discovery: When researchers tested models on carefully controlled puzzles (Tower of Hanoi, logic problems), they found a predictable pattern:

• Simple tasks: Basic models often outperform "reasoning" models

• Medium complexity: Reasoning models show clear advantages

• High complexity: Both types completely collapse

The Twist: As problems get harder, models actually reduce their reasoning effort, even with computational budget to spare. It's like a student giving up and writing one-sentence answers when the test gets difficult.

What This Reveals: Pattern matching works until the required patterns become too complex to reliably match. There's a hard ceiling on compositional reasoning that no amount of "thinking tokens" can overcome. Let’s just call it “limitations of the context window”.

---

🔁 The Dynamical View: Pattern Matching as State Navigation - A Statistical Physics of Language Model Reasoning

Focus: Model Architecture and how it shapes internal dynamics

The Insight: Instead of step-by-step logic, AI "reasoning" looks more like movement through a landscape of possible mental states—some productive, some confused, some confidently wrong.

The Method: By modeling AI reasoning as a dynamical system, researchers can map these state trajectories and predict when a model is about to fail—before it gives a wrong answer.

What This Reveals: The model architecture creates a hidden landscape where certain paths naturally lead to better outcomes. "Reasoning" is really navigation through this space, guided by pattern recognition rather than logical rules.

---

🧍‍♂️ The Illusion View: When Training Data Creates False Patterns - (How) Do Reasoning Models Reason?

Focus: Training Data and Post-Training Methods creating misleading signals

The Uncomfortable Truth: Models trained on wrong or random reasoning chains sometimes perform just as well as those trained on perfect logic. The intermediate "thinking" steps often have little correlation with answer accuracy.

The Training Effect: Longer, more elaborate reasoning might just be a side effect of reward systems that accidentally incentivize verbosity over validity.

What This Reveals: What looks like reasoning may be "compiled retrieval"—the training process encodes checking and verification directly into pattern matching, creating reasoning-like outputs without reasoning-like processes.

---

🧬 The Orchestration View: When System Architecture Amplifies Pattern Matching - AlphaEvolve & DGM

Focus: How external frameworks can dramatically enhance core capabilities

The Breakthrough: Systems like AlphaEvolve don't just use pattern matching—they orchestrate it within evolutionary loops:

• Generate variations using language models (Gemini 2.5 Flash for breadth of ideas; Gemini 2.5 Pro for depth of ideas)

• Test automatically against real benchmarks

• Keep winners, evolve losers

• Repeat with validation at every step

The Results: New algorithms that outperform human solutions, including 50+ year breakthroughs in mathematics and computer science.

What This Reveals: The most impressive capabilities emerge when pattern matching is embedded in systems with proper feedback loops, external validation, and iterative improvement.

---

The Unified Picture

These four perspectives aren't contradictory—they're actually complementary views of how the same underlying mechanism (statistical pattern matching) produces vastly different outcomes depending on context:

DeepMind's Extraordinary Breakthroughs

• Core Mechanism: Statistical pattern matching

• Key Contextual Factors: Vast specialized datasets + optimized architectures + targeted applications

• Outcome: Verifiable breakthroughs in narrow, well-defined domains

Consumer Chat Models (GPT, Claude, etc.)

• Core Mechanism: Statistical pattern matching

• Key Contextual Factors: Diverse training data + RLHF post-training + broad task exposure

• Outcome: Impressive general capabilities but inconsistent reliability

The Critical Research Findings

• Core Mechanism: Statistical pattern matching

• Key Contextual Factors: Controlled environments + systematic complexity scaling

• Outcome: Clear limitations and failure modes that traditional benchmarks miss

Visually captured this way:

The Matrix is not the Blue or Red Pill - The Matrix is the Green Pill!

Emergence and Trends of Large Reasoning Models (LRMs) since 2024

Indeed Large Language Models (LLMs) have evolved to include specialized variants designed for reasoning tasks, referred to as Large Reasoning Models (LRMs). Especially since the releases in 2024 of OpenAI’s o1 Model, and early 2025 with Deepseek’s R1.

These models are characterized by their "thinking" mechanisms, such as long Chain-of-Thought (CoT) with self-reflection. At least that is how these models have been trained - to give us semblance of thought & self-reflection. Examples today include OpenAI's o3, DeepSeek-R1, Claude 3.7 Sonnet Thinking, and Gemini Thinking. This emergence suggests a potential paradigm shift in how AI systems approach complex reasoning and problem-solving.

But not all reasoning-related capabilities are created equal. We’ve all seen those “chains of thought”, but their performances can differ based on the complexities of problems being solved, and say - the effort or difficulty required. Below are very rough estimates of how good the Large Reasoning Model Core Capabilities are:

As many have seen, and definitely with how things are being done, the overall trend in AI development is one of unprecedented acceleration. AI systems are increasingly moving beyond basic conversational interfaces to become agents capable of performing multi-step tasks and "doing work." This shift towards autonomy is a defining trend of new reasoning products. The scope of ambition for these models is much higher, aiming for models that can work autonomously for extended periods and exhibit traits like skill, calibration, strategy, and abstraction. Whether we like to admit or not, AI is being integrated across various industries and is a top priority for major tech companies. No one really wants to be left behind, as I see it. Let’s try the experiment - because it really is just that interesting!

RL Techniques and Reinforcement Learning with Verifiable Rewards (RLVR)

Reinforcement Learning (RL) has turned out to be a key technique in training these next-generation reasoning models. A specific paradigm driving this progress is Reinforcement Learning with Verifiable Rewards (RLVR). This involves training language models by providing rewards or penalties based on verifiable outcomes in specific environments. Examples of environments that provide these ground truth rewards include:

• Math verifiers for mathematical problem-solving

• LLM-as-a-judge for factual checks

• Code sandboxes for executing and testing generated code

• More complex environments for diverse reasoning tasks

RLVR is seen as essential for pushing the boundaries of what models can achieve autonomously. It is currently the most popular method for achieving inference-time scaling, allowing models to generate longer Chain-of-Thought sequences or perform multi-turn actions while improving performance. Training compute allocation is shifting, with post-training efforts, including RL, potentially becoming a larger proportion of the total compute budget. Scaling RL has just begun. RL is promising and exciting for improving reasoning abilities, both independently and in tandem with inference-time scaling.

The Debate: Do LRMs Truly Reason or Just Exhibit Pattern Matching - will never end….

As reflected above, I note the ongoing debate about whether LRMs are capable of generalizable reasoning or primarily leveraging complex patterns matching forms. And I will add further to the quick notes given above:

Arguments Supporting Reasoning/Thinking Capabilities

Chain-of-Thought Processing: LRMs generate detailed thinking processes (Chain-of-Thought) before providing answers, which has been shown to improve performance on reasoning benchmarks.

Statistical Physics Framework: A statistical physics framework models sentence-level hidden state trajectories in LMs as a stochastic dynamical system. This framework identifies distinct latent semantic regimes with unique drift/variance profiles, which can be interpreted as different reasoning phases, such as systematic decomposition or answer synthesis.

Switching Linear Dynamical System (SLDS): The SLDS model, inspired by this framework, captures transitions between these regimes. This includes modeling shifts into "misaligned states" where the model deviates from factual reasoning. This perspective views LLMs not just as static function approximators but as dynamical systems capable of rapid shifts in semantic representation under contextual influence.

Arguments Challenging "True" Reasoning

Generalization Failures: Despite sophisticated mechanisms like self-reflection learned through RL, LRMs fail to develop generalizable problem-solving capabilities. In controlled puzzle environments where complexity can be systematically varied, accuracy collapses to zero beyond a certain threshold.

Inconsistent Performance: Performance is inconsistent across different puzzle types, even when they require a similar number of sequential steps (compositional depth). Models that perform well on one type of puzzle might struggle with another of comparable theoretical difficulty.

Computational Limitations: LRMs show limitations in performing exact computation. Providing the explicit solution algorithm for a complex task like the Tower of Hanoi does not significantly improve performance or prevent accuracy collapse. This suggests limitations not just in finding solutions but also in executing prescribed logical steps and verifying them.

Overthinking Phenomenon: Analysis of reasoning traces reveals "overthinking" on simpler problems, where models explore incorrect solutions even after finding the correct one, leading to computational waste.

Reduced Effort at High Complexity: At high complexity, models counterintuitively reduce their reasoning effort (measured by thinking tokens) despite facing more difficult problems and having available token budget. This suggests a fundamental scaling limitation in LRM thinking capabilities relative to problem complexity.

Inconsistent Failure Patterns: Failure patterns can be inconsistent; models may fail earlier in the solution sequence for higher complexity problems despite requiring longer overall solutions, contradicting expectations of consistent algorithmic planning.

This debate highlights the challenge of understanding the internal mechanisms of these black-box models and the need for controlled evaluation environments to probe their fundamental capabilities.

And yet, a reminder - Many Successes with Specialized RL Systems and Agents

Recent work combining LLMs within larger search or evolutionary frameworks has shown significant success.

AlphaEvolve

AlphaEvolve is an evolutionary coding agent that orchestrates an autonomous pipeline of LLMs. Its task is to improve algorithms by making direct changes to code, using an evolutionary approach and receiving feedback from evaluators. AlphaEvolve iteratively improves algorithms, leading to new scientific and practical discoveries.

Key Features and Successes:

• Comprehensive Code Evolution: Evolving entire code files (hundreds of lines of code) in any language, unlike predecessors that focused on single functions or limited lines

• Extended Evaluation: Using longer evaluation times (hours, in parallel)

• Advanced Integration: Benefiting from state-of-the-art LLMs and rich context in prompts

• Multi-objective Optimization: Simultaneously optimizing multiple metrics

• Infrastructure Impact: Optimizing critical components of Google's computational infrastructure, such as developing a more efficient data center scheduling algorithm, simplifying hardware accelerator circuit design, and accelerating LLM training

• Mathematical Breakthroughs: Discovering novel, provably correct algorithms that surpass state-of-the-art solutions in mathematics and computer science. This includes finding a procedure to multiply two 4x4 complex-valued matrices using 48 scalar multiplications, offering the first improvement over Strassen's algorithm in 56 years for this setting

• Open Problem Solutions: Matching or surpassing best-known constructions on a large number of open mathematical problems, including improving bounds on the Minimum Overlap Problem set by Erdős and the Kissing Numbers problem

• Versatile Performance: Demonstrating versatility and speed by evolving heuristic search programs

Darwin Gödel Machine (DGM)

The Darwin Gödel Machine (DGM) is a self-referential, self-improving AI that writes and modifies its own code to become a better coding agent. It addresses the theoretical Gödel Machine's impractical requirement of formal proof by using empirical validation via coding benchmarks to test if a self-modification is beneficial.

Key Aspects and Successes:

• Self-Modification: Iteratively modifying its own codebase, thereby improving its ability to modify code

• Evolutionary Archive: Maintaining an archive of generated coding agents, inspired by biological evolution and open-endedness

• Iterative Improvement: Sampling from the archive, self-modifying, evaluating on a coding benchmark, and adding the valid new agent to the archive

• Benchmark Performance: Achieving performance increases on coding benchmarks: SWE-bench from 20.0% to 50.0%, and Polyglot from 14.2% to 30.7%

• Component Enhancement: Automatically improving components like code editing tools, long-context window management, and peer-review mechanisms

• Baseline Superiority: Outperforming baselines without self-improvement or open-ended exploration, showing that both components are essential for sustained progress

• Model Generalization: Demonstrating improvements that can generalize across different underlying Large Language Models

• Human-Competitive Performance: Achieving performance comparable to or outperforming handcrafted, human-designed agents on benchmarks

Relationship Between Specialized RL Systems and Underlying LRMs

Systems like AlphaEvolve and DGM highlight the power of combining state-of-the-art LLMs (including LRMs) with sophisticated search and evolutionary frameworks. The LLMs within these systems act as powerful components, such as creative generators, code modifiers, or agents capable of reading, writing, and executing code.

AlphaEvolve leverages the Gemini 2.5 Flash and Gemini 2.5 Pro LLMs' ability to generate, critique, and evolve a pool of algorithms, with the process grounded by code execution and automatic evaluation.

DGM uses foundation models (like Claude 3.7 Sonnet) to power its coding agents, which use tools and modify their own code based on analysis of evaluation logs.

These successes demonstrate that while current LRMs, when evaluated in isolation on complex reasoning tasks, show limitations like collapse or inconsistent behavior (as seen in the "Illusion of Thinking" study), they can be extraordinarily effective when integrated into a larger system that provides structure, iterative validation, and search. The power often comes from the orchestration of the LLM's capabilities within a guided search or evolutionary process, rather than solely from the LRM's intrinsic, standalone reasoning ability.

Techniques and Strategies to Improve LRM Reasoning/Thinking

Drawing from the limitations of LRM’s identified and the successes of orchestrated systems, several techniques and strategies are relevant for improving the underlying LRMs themselves:

Further Development of RL Techniques

• Enhanced RLVR: Continued research into RL with verifiable rewards (RLVR)

• Data Bootstrapping: Bootstrapping training data specifically for complex planning and strategic thinking

• Credit Assignment: Refining credit assignment in RL for long reasoning chains

• Random RL Tricks: Exploring random RL tricks for performance gains, such as overlong filtering, two-sided clipping, and resetting reference models

• Sequence Optimization: Developing RL to improve sequence length and performance simultaneously

Improving Core Reasoning Traits

Calibration: Teaching models to understand problem difficulty and adjust reasoning effort accordingly, avoiding both overthinking on simple tasks and insufficient effort on complex ones. This needs to become model-native.

Strategy: Improving the model's ability to choose the correct high-level plan before diving into details. This is crucial for avoiding getting trapped in unproductive paths.

Abstraction: Enhancing the model's capability to break down complex tasks and plans into smaller, solvable chunks.

Memory Management: Developing better internal mechanisms for managing context and information over long reasoning processes.

Error Handling: Training models to avoid repeating mistakes and to handle unexpected outcomes or constraints more effectively.

Addressing Limitations Highlighted by Controlled Studies

• Robustness Enhancement: Improving robustness and generalizability to increasing complexity across diverse problem domains

• Computational Precision: Enhancing the capacity for precise, exact computation and adherence to logical rules, even when an algorithm is provided

• Overthinking Reduction: Reducing the "overthinking" phenomenon on simple problems

• Consistency Improvement: Improving the consistency and reliability of reasoning processes, potentially by reducing the variance in failure patterns

Learning from Orchestrated Systems

• Feedback Integration: Exploring how the iterative feedback loops and empirical validation used in AlphaEvolve and DGM could be integrated or distilled into the training of the underlying LLMs themselves

• Solution Archiving: Leveraging techniques like maintaining an archive of diverse, interesting solutions discovered by systems like DGM to inform future model training

• Structured Modification: Integrating structured approaches to code modification (like diffs) into training data or model architecture

Modeling Reasoning Dynamics

Using frameworks like the Statistical Physics model (SLDS) can provide insights into how models transition between states, potentially helping to predict and mitigate slips into misaligned or failure states.

The Way (I See) Evolutionary Timelines Possibly Go….Specialized → Generalized Easily Within the next 18 months

Note: The dates/timelines specificity is completely unimportant & irrelevant!

More importantly, is that we will eventually see a convergence of specialized/generalized paths as algorithms/systems/tools integrations and model performances improve.

A Framework (of sorts)

AI Problem-Solving: A Summary Formula

The underlying commonality across all current AI models (Large Language Models, Large Reasoning Models, and specialized AI systems) is their fundamental Statistical Mechanism. However, their Performance—what they can accomplish—varies significantly based on several Contextual Factors.

Core Principle: AI_Mechanism = Statistical_Pattern_Matching

Performance Spectrum: AI_Performance = AI_Mechanism + (Training_Data + Model_Architecture + Post-Training_Methods + Task_Complexity)

Interpreting the Outcomes (Flow -> from Shared Mechanism & Varying Factors):

1. Kambhampati's Perspective: Statistical_Pattern_Matching + (Impressive_Outputs) -> Not_True_Human_Reasoning

   • This reflects that even high performance from the statistical mechanism does not equate to genuine human-like thought or understanding, explaining his warnings against anthropomorphism.

2. DeepMind's Successes (e.g., AlphaEvolve, AlphaFold): Statistical_Pattern_Matching + (Vast_Data + Optimized_Architectures + Targeted_Applications) -> Extraordinary_Verifiable_Breakthroughs

   • This illustrates how the same statistical mechanism, when pushed to its limits with immense data and specific design, can yield truly groundbreaking, concrete results, justifying their achievements.

3. Chat Models (e.g., Claude, DeepSeek, OpenAI o-series): Statistical_Pattern_Matching + (Varied_Training_Data + Diverse_Tasks + RLVR) -> In-Between_Reliability_Spectrum

   • This shows that for general-purpose chat models, performance falls on a spectrum, influenced by the quality and specificity of their training, the nature of the task, and the effectiveness of post-training methods like Reinforcement Learning with Verifiable Rewards (RLVR).

In essence: All current AI systems share the same fundamental statistical engine. What makes their "intelligence" appear so different—from Kambhampati's warnings to DeepMind's breakthroughs and the varied reliability of chat models—is how powerfully and precisely that engine is applied and optimized for specific tasks and contexts.

What This Means for the Future

Understanding AI reasoning as "contextually-shaped pattern matching" rather than human-like cognition has profound implications:

For Developers

Don't rely on reasoning appearance: Impressive logical chains might be meaningless without external validation.

Design for orchestration: The biggest breakthroughs come from systems that organize multiple AI components with proper feedback loops.

Expect complexity walls: Individual models will hit hard limits where they suddenly fail, regardless of apparent reasoning ability.

For Researchers

Focus on contextual factors: The interesting questions aren't about the core mechanism (it's pattern matching) but about how different contexts shape its expression.

Build validation into evaluation: Apparent reasoning without external verification may be largely meaningless.

Study system-level properties: The most important capabilities emerge from architectures, not individual models.

For Society

Prepare for inconsistency: AI systems will continue to show remarkable capabilities in some areas while failing catastrophically in others.

Value human judgment: As AI becomes more sophisticated at pattern matching, human oversight and validation becomes more—not less—critical.

Expect surprises: The interaction between pattern matching and contextual factors will continue producing unexpected capabilities and limitations.

The Bottom Line

The AI reasoning paradox resolves when we stop asking "Do these models really think?" and start asking "How can we design contexts that make pattern matching produce the outcomes we want?"

The future belongs not to better individual reasoning engines, but to better orchestration of the powerful pattern-matching engines we already have.

And maybe that's the more interesting challenge anyway.

It is how I see things…..

Have a great weekend, all.