DeepSeek-R1: The MoE Fallacy and the True Source of Emergent Reasoning

A Mathematical and Empirical Dissection of Why DeepSeek-R1 Has Nothing to Do with MoE

In my previous article, How DeepSeek-R1 Pushed the Frontiers of Reasoning, I provided a detailed breakdown of R1’s training process. This latest piece directly addresses the false claim that DeepSeek-R1’s reasoning abilities come from its MoE base. That notion is a complete misunderstanding of how reasoning emerges in large language models.

1. Addressing a Deeply Flawed Assumption

DeepSeek-R1 has set a new standard for reasoning-intensive large language models (LLMs), demonstrating emergent Chain-of-Thought (CoT) capabilities, self-reflection, long-horizon reasoning skills, and multi-step problem-solving. Unlike traditional LLMs that rely on brute-force parameter scaling, DeepSeek-R1 is explicitly designed to prioritize reasoning depth over raw fluency.

However, a fundamental misconception exists:

Since DeepSeek-R1 was trained on DeepSeek-V3, which employed Mixture of Experts (MoE), some claim that DeepSeek-R1’s emergent reasoning capabilities are dependent on MoE mechanisms, such as expert routing, sparse activation, and modular parameter sharing.

This assumption is entirely incorrect. DeepSeek-R1 is a fully dense model and it does not rely on MoE-style expert gating or selective activation of subsets of parameters at all. Yet, it exhibits superior reasoning ability compared to previous MoE-based models, proving that MoE is neither a necessary nor a sufficient condition for emergent reasoning capabilities.

The only reason DeepSeek-R1’s underlying architecture was categorized as MoE , mentioned just once in a table in the entire research paper, was because the researchers were referencing the 671B parameter DeepSeek-R1 prior to distillation for comparison. This classification was purely for context and had no bearing on DeepSeek-R1’s actual design or functionality. That’s all there is to it.

One empirical fact alone disproves the MoE dependency hypothesis:

DeepSeek-R1-Distill-Qwen-32B is not an MoE model and yet it retains all reasoning properties of DeepSeek-R1.

If MoE were essential to DeepSeek-R1’s emergent reasoning, then distilling the model into a fully dense architecture should have eliminated its ability to perform deep, structured reasoning. But it did not.

This paper presents a mathematically complete analysis establishing that:

1. DeepSeek-R1’s reasoning emergence is independent of MoE, arising instead from reinforcement learning (RL) reward alignment.
2. Chain-of-Thought (CoT) reasoning follows a probabilistic inference framework that is orthogonal to model architecture.
3. A non-MoE model trained identically would yield the same reasoning emergence, proving MoE is irrelevant to the process.
4. Reinforcement learning constructs structured reasoning pathways in a way that does not depend on MoE-based sparsity.
5. DeepSeek-R1-Distill-Qwen-32B retains all reasoning properties despite having no MoE, which is decisive empirical proof.

In this paper, I will dissect these claims mathematically and theoretically, using:

• Probabilistic inference formulations of CoT.
• Policy gradient and Bellman convergence proofs for reasoning emergence.
• Computational complexity arguments proving MoE provides no reasoning advantage.
• Empirical validation through DeepSeek-R1-Distill-Qwen-32B and benchmark results.

2. The Fundamental Divide: MoE vs. Fully Dense Models

2.1 Mixture of Experts (MoE): Sparse Activation and Conditional Computation

A Mixture of Experts (MoE) model is designed to conditionally activate a sparse subset of parameters for each input, reducing computational load per forward pass. The formal MoE function is:

where:

• f_i(x) is the i-th expert function
• g_i(x) is a gating function satisfying ∑ g_i(x) = 1, which determines which subset of experts is active
• Only k-out-of-N experts are activated per input

The gating function follows a softmax:

This ensures that only certain experts are engaged in each pass, minimizing computation while maintaining parameter efficiency. However, it has no direct influence on reasoning depth.

For more details, I had written about MoE architectures in depth on Aug 28th, 2016 here : Committee of Intelligent Machines

2.2 Why DeepSeek-R1 is Fully Dense and MoE-Free

DeepSeek-R1 follows a fully dense transformer model without MoE-style sparse activation:

where:

• All parameters contribute uniformly to every inference step. No gating, no selective activation.
• Every token influences the full network, unlike MoE where only a subset of experts process a given input.

Since DeepSeek-R1-Distill-Qwen-32B has no MoE and retains its reasoning abilities, this is direct empirical proof that MoE is not responsible for emergent reasoning.

3. Chain-of-Thought (CoT) is Model-Agnostic

3.1 Probabilistic Inference Formulation of CoT

Chain-of-Thought (CoT) is not an architectural feature but an emergent inference process governed by hierarchical probabilistic reasoning. Given an input sequence X, the reasoning trajectory is formulated as a latent variable model:

where:

• Z represents latent reasoning steps
• P(Y ∣ Z, X) represents the final answer conditioned on intermediate reasoning

Using variational inference, the ELBO (Evidence Lower Bound) formulation proves that CoT emerges as an optimization constraint:

This equation explicitly shows that CoT reasoning chains form as a consequence of optimization constraints, not due to MoE architecture.

3.2 Recursive Reasoning as a Markov Decision Process

CoT reasoning follows a recursive Markov decision process (MDP) formulation:

Since this probability factorization holds for any autoregressive model, CoT reasoning is independent of whether the base model is MoE or dense.

4. Reinforcement Learning, Not MoE, Induces Structured Reasoning

4.1 Group Relative Policy Optimization (GRPO) and Reward Alignment

DeepSeek-R1’s Group Relative Policy Optimization (GRPO) framework reinforces structured reasoning depth without MoE-based sparsity. The GRPO loss is:

where:

• A_i​ is the advantage estimation of response o_i​
• D_KL is the divergence regularization to prevent policy collapse

Since GRPO updates reasoning policy solely based on reward functions, not architecture, reasoning capability is induced by RL alone.

Here is a more detailed policy optimization flow in section 2.2.1 of the R1 paper:

click on image to enlarge

4.2 Bellman Convergence and the Recursive Structure of Reasoning

To formalize this, we frame reasoning as a Markov Decision Process (MDP), where:

• States (s) correspond to intermediate reasoning steps.
• Actions (a) represent logical transformations applied to context.
• Rewards (r) are assigned based on structured CoT correctness.
• Policy (π) represents the learned reasoning trajectory.

Using Bellman’s recursive formulation, the expected reasoning value function follows:

where:

• V^π(s) is the expected reasoning quality at step s.
• γ is the discount factor, controlling dependency on future reasoning steps.
• P(s’ | s, a) is the transition probability, modeling logical step dependencies.

Since DeepSeek-R1 optimizes policy gradients over reasoning trajectories, its structured reasoning depth is dictated by Bellman convergence to an optimal reasoning policy, not by MoE parameter sparsity.

Applying policy gradient updates, we obtain:

where:

• J(θ) is the cumulative reasoning objective.
• τ denotes a sampled reasoning trajectory.
• A_t​ is the advantage estimate, aligning reasoning with reward-based optimization.

This directly refutes the claim that MoE is required for reasoning emergence. Reasoning depth is driven entirely by policy gradient optimization over structured trajectories, irrespective of architectural sparsity.

5. Empirical Proof: DeepSeek-R1-Distill-Qwen-32B

Finally, If reasoning depended on MoE, then distilling DeepSeek-R1 into a fully dense model should eliminate reasoning. But DeepSeek-R1-Distill-Qwen-32B retains all reasoning properties, proving that:

By the Universal Approximation Theorem, a non-MoE model can replicate reasoning capabilities perfectly.

5.1 The Smoking Gun

The strongest empirical refutation of the claim that DeepSeek-R1’s reasoning abilities require MoE lies in the very nature of DeepSeek-R1-Distill-Qwen-32B, a model that maintains all of DeepSeek-R1’s reasoning capabilities despite being fully dense.

This is not a theoretical argument. It is a smoking gun proof that DeepSeek-R1’s emergent reasoning behaviors are model agnostic and stem purely from reinforcement learning, structured optimization, and Chain-of-Thought training, not from architectural sparsity or expert gating.

Qwen-32B: Fully Dense, Yet Retaining R1’s Reasoning Power

Unlike the QwenMoE series, which employs sparse activation and expert routing, Qwen-32B is a fully dense transformer model with:

• Rotary Positional Embedding (RoPE) enhancing positional representation for long-context comprehension
• SwiGLU Activation Function improving efficiency and model convergence
• RMSNorm a stability mechanism crucial for deep transformers
• Attention QKV Bias refining attention computations for improved token representations

The model is not MoE based. It activates all parameters in every forward pass rather than conditionally routing inputs through a subset of expert networks. Its architecture consists of 64 layers, utilizing grouped query attention with 40 attention heads for queries and 8 for keys and values, enabling it to handle 131,072 token contexts efficiently.

Here are the distilled model benchmarks.

The Empirical Breakpoint

If DeepSeek-R1’s reasoning depended on MoE, then distilling it into a fully dense model should have degraded its ability to execute multi-step logical inference, self-consistency, and Chain-of-Thought reasoning. However, it did not.

Instead, DeepSeek-R1-Distill-Qwen-32B retains all the core reasoning capabilities of its parent model, demonstrating that:

1. MoE is neither a necessary nor a sufficient condition for emergent reasoning
2. Reasoning is an optimization-driven phenomenon, not an architectural byproduct
3. A fully dense model, when trained under the same reinforcement learning and Chain-of-Thought paradigms, can achieve identical reasoning capacity

This is not just an argument from theory. It is direct experimental evidence that DeepSeek-R1’s intelligence does not stem from MoE, but from structured reasoning incentives in its training process.

A true smoking gun.

Personal Provocation

The argument that DeepSeek-V3’s MoE foundation is responsible for R1’s reasoning is one of those lazy takes that falls apart under the slightest scrutiny. At best, MoE provided computational efficiency by activating only a subset of parameters per forward pass. But efficiency has nothing to do with reasoning. Similar computational advantages exist in non-MoE architectures that use dynamic sparsity like Sparse Transformers, low-rank approximations like ALBERT or LoRA, or structured pruning methods. These approaches reduce active computation while retaining the ability to model complex patterns. Computational savings are not exclusive to MoE architectures.

Take any of these dense, non-MoE models, apply R1’s training pipeline, and you get the same computational efficiency, scalability and emergent reasoning. The only difference is that people would stop peddling the false idea that MoE had anything to do with R1’s emergent reasoning. The real source of R1’s intelligence is not found in selective parameter activation. It is found in its reinforcement learning framework, structured optimization, and Chain-of-Thought training.

Addendum on Qwen Architecture

The Qwen family has evolved quite a bit, so it can be confusing to keep track! Here’s a breakdown of the main architectures and where DeepSeek-R1-Distill-Qwen-32B fits in:

1. Qwen (The Original Series):

• Architecture: Primarily dense models (all parameters active).
• Sizes: 0.5B, 1.8B, 4B, 7B, 14B, 32B, 72B
• Focus: General purpose language model, good at text generation and understanding.
• Examples: Qwen-7B, Qwen-32B

2. Qwen2MoE:

• Architecture: Mixture-of-Experts (MoE), where different parts of the model specialize in different tasks.
• Sizes: Various, often upcycled from dense models (e.g., Qwen1.5-MoE-A2.7B is upcycled from Qwen-1.8B).
• Focus: Efficiency and improved performance by activating only necessary parts of the model.
• Examples: Qwen1.5-MoE-A2.7B

3. Qwen2:

• Architecture: Includes both dense and MoE models.
• Sizes: 0.5B, 1.5B, 7B, 57B (MoE), 72B
• Focus: Improved performance, especially in chat applications.
• Examples: Qwen2–7B, Qwen2–57B-A14B (MoE)

4. Qwen2.5:

• Architecture: Dense and MoE. Notably includes the largest Qwen model yet.
• Sizes: 0.5B, 1.5B, 3B, 7B, 14B, 32B, 72B, Qwen2.5-Max (MoE)
• Focus: Further performance improvements, scaling up model size.
• Examples: Qwen2.5–7B, Qwen2.5-Max

5. Specialized Qwen Models:

• Qwen-VL: Vision-language model for understanding images and text together.
• Qwen-Audio: Processes and understands audio input.
• Qwen-Coder: Assists with coding tasks.
• Qwen-Math: Focuses on mathematical problem-solving.

Where does DeepSeek-R1-Distill-Qwen-32B belong?

It belongs to the Qwen (Original Series) family. It’s built upon the Qwen-32B dense model as its foundation.

Keep in mind that this is a simplified overview. The Qwen family is constantly evolving with new models and architectures being developed!