Qwen3.5-9B-C3SM-SDM-Agentic-Coder

1. Mathematical Abstract & Ontological Foundation

Let $\mathcal{M} \subset \mathbb{R}^{d_{\text{in}} \times d_{\text{out}}}$ denote the smooth finite-dimensional Riemannian parameter manifold of autoregressive causal language model projections, equipped with the metric induced by the Fisher information operator:

$$g_{\theta}(u, v) = \mathbb{E}{x \sim \mathcal{D}} \left[ \langle \nabla\theta \log p_\theta(x), u \rangle \langle \nabla_\theta \log p_\theta(x), v \rangle \right]$$

Traditional parameter fusion methodologies—such as linear spherical interpolation ($\operatorname{SLERP}$), coordinate-wise task arithmetic ($\tau$-scaling), and unregularized weight summation—implicitly presume local Euclidean flatness ($\operatorname{Riem}(\mathcal{M}) \equiv 0$). When aggregating multiple distinct fine-tuned vector fields across overparameterized manifolds ($d \approx 9.2 \times 10^9$), this assumption collapses, causing non-linear geodesic divergence, destructive interference in non-commuting projection bases, and high-frequency spectral noise within trailing singular modes.

The Curvature-Calibrated Spectral Consensus with Sinusoidal Depth Modulation ($\operatorname{C3SM-SDM}$) framework is an operator-theoretic merging protocol designed to construct an optimal agentic coding and multi-turn tool-calling parameterization $W^*$. It operates via continuous harmonic depth modulation, Bernoulli-rescaled stochastic coordinate sparsification, directional majority sign election, randomized low-rank subspace orthogonalization, and geodesic Frobenius norm retraction.

       [Base: MiMo-V2.6-Distill]
                   │
                   ▼ (W_0)
        [Task Delta Extraction] ─────── Δ_k = W_k - W_0
                   │
                   ▼
     [Harmonic DARE Sparsification] ── p(z) = p_max - Δp · sin(πz)
                   │
                   ▼
     [Harmonic TIES Polar Consensus] ── S(z) = sgn( Σ λ_k(z) Δ̃_k )
                   │
                   ▼
     [Randomized SVD Denoising] ───── Π_r(z) = U_r Σ_r V_r^T
                   │
                   ▼
     [Harmonic Task Amplitude] ────── α(z) = α_min + Δα · sin²(πz)
                   │
                   ▼
     [Frobenius Manifold Retraction] ── W* = (W_0 + α Δ_spectral) · [ ρ_target / ||W||_F ]

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2. Morphological Base and Constituent Donors

The parameterization is anchored upon a distilled reasoning foundation $W_0$, synthesized across four domain-specialized tangent perturbations ${\Delta_k}_{k=1}^4$:

$$\mathcal{H} = \left{ W_0, \Delta_{\text{Ornith}}, \Delta_{\text{Qwopus}}, \Delta_{\text{OxCoder}}, \Delta_{\text{Qwen3.8}} \right}$$

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3. Mathematical Formulation of the C3SM-SDM Operator

Let $L = 32$ denote the total cardinality of discrete decoder blocks within the causal transformer backbone. We define the normalized depth coordinate function $\zeta: {0, \dots, L-1} \to [0, 1]$ as:

$$\zeta(l) \triangleq \frac{l}{L - 1}, \quad l \in [0, 31]$$

Boundary elements $\mathcal{B} = {W_{\text{embed}}, W_{\text{head}}, W_{\text{norm}}}$ are assigned gauge coordinates $\zeta(W_{\text{embed}}) = 0.0$ and $\zeta(W_{\text{head}}) = \zeta(W_{\text{norm}}) = 1.0$.

Depth Metric:  z = 0.0 ────────────────────── z = 0.5 ────────────────────── z = 1.0
Task Scale:    α(z) = 0.20 ────────────────── α(z) = 0.85 ────────────────── α(z) = 0.20
DARE Drop:     p(z) = 0.50 ────────────────── p(z) = 0.30 ────────────────── p(z) = 0.50
SVD Rank:      r(z) = 32 ──────────────────── r(z) = 96 ──────────────────── r(z) = 32
Focus:         [Token Syntax]            [Core Algorithmic Reasoning]    [Logit Calibration]

3.1. Continuous Harmonic Task-Vector Amplitude Modulation

To resolve the trade-off between semantic capacity injection and vocabulary logit collapse, the scalar task-multiplier $\alpha: [0, 1] \to \mathbb{R}^+$ is parameterized as a non-linear half-period power wave:

$$\alpha(z) \triangleq \alpha_{\min} + \left(\alpha_{\max} - \alpha_{\min}\right) \sin^2\left(\pi z\right)$$

Where empirical operational bounds are constrained by $\alpha_{\min} = 0.20$ and $\alpha_{\max} = 0.85$.

$$\lim_{z \to 0^+} \alpha(z) = 0.20, \quad \alpha(0.5) = 0.85, \quad \lim_{z \to 1^-} \alpha(z) = 0.20$$

This distribution stabilizes shallow token-level parsing ($l \in [0, 5]$) and deep probability distributions ($l \in [27, 31]$) while maximizing task-vector transfer within the intermediate reasoning blocks ($l \in [10, 22]$).

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3.2. Harmonic Drop-and-Rescale (DARE) Stochastic Sparsification

Let $\Delta_k \in \mathbb{R}^{d_1 \times d_2}$ define the task perturbation matrix for donor $k \in {1, 2, 3, 4}$. Extreme fine-tuning induces high-entropy, low-magnitude perturbations across arbitrary parameter directions. We apply an inverted harmonic Bernoulli mask:

$$p(z) \triangleq p_{\max} - \left(p_{\max} - p_{\min}\right) \sin\left(\pi z\right)$$

With $p_{\min} = 0.30$ and $p_{\max} = 0.50$. For each coordinate $(i, j) \in [1, d_1] \times [1, d_2]$, the stochastic sparsification operator $\mathfrak{D}_p: \mathbb{R} \to \mathbb{R}$ is defined as:

$$\tilde{\Delta}{k, (i, j)} \triangleq \frac{1}{1 - p(z)} \cdot M{k, (i, j)} \cdot \Delta_{k, (i, j)}, \quad M_{k, (i, j)} \sim \operatorname{Bernoulli}\left(1 - p(z)\right)$$

Expectation and Variance Invariance Proof:

$$\mathbb{E}{M}\left[\tilde{\Delta}{k, (i, j)}\right] = \frac{1}{1 - p(z)} \mathbb{E}\left[M_{k, (i, j)}\right] \Delta_{k, (i, j)} = \frac{1 - p(z)}{1 - p(z)} \Delta_{k, (i, j)} = \Delta_{k, (i, j)}$$

$$\operatorname{Var}{M}\left(\tilde{\Delta}{k, (i, j)}\right) = \left(\frac{\Delta_{k, (i, j)}}{1 - p(z)}\right)^2 \operatorname{Var}\left(M_{k, (i, j)}\right) = \frac{p(z)}{1 - p(z)} \left(\Delta_{k, (i, j)}\right)^2$$

This formulation preserves the unbiased first moment while attenuating destructive baseline interference by up to $50%$ at the structural network boundaries.

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3.3. Phase-Shifted Harmonic Domain Allocation

Let $\Omega = {\text{attn}, \text{mlp}, \text{recurrent}, \text{head}, \text{norm}}$ denote the partition of parameter modules. The unnormalized constituent mixing coefficients $w_k(z)$ are modulated via continuous harmonic phase shifts:

$$w_k(z) \triangleq \bar{w}_k^{(\Omega)} \cdot \left[ 1.0 + A_k \cdot \sin\left(\pi z + \phi_k\right) \right]$$

The dynamic barycentric coordinate projection $\lambda_k: [0, 1] \to \Delta^3$ guarantees unit measure:

$$\lambda_k(z) \triangleq \frac{w_k(z)}{\sum_{m=1}^4 w_m(z)}, \quad \sum_{k=1}^4 \lambda_k(z) \equiv 1, \quad \forall z \in [0, 1]$$

Harmonic Domain Phase Distribution:
  λ_1 (Ornith)   [φ = -0.20π]: Peaks at z ≈ 0.35  (Deductive Logic & Context)
  λ_2 (Qwopus)   [φ =  0.00π]: Peaks at z ≈ 0.50  (Tool Execution & Syntax)
  λ_3 (OxCoder)  [φ = +0.25π]: Peaks at z ≈ 0.65  (Algorithmic Code Synthesis)
  λ_4 (Qwen3.8)  [φ = +0.05π]: Stabilizing Field  (General World Knowledge)

$$\begin{aligned} \phi &= \begin{bmatrix} -0.20\pi, & 0.00\pi, & +0.25\pi, & +0.05\pi \end{bmatrix}^T \ A &= \begin{bmatrix} 0.35, & 0.45, & 0.50, & 0.20 \end{bmatrix}^T \end{aligned}$$

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3.4. Truncated Incoherent Sign Consensus (TIES)

To eliminate gradient collision where donors exert opposing forces on identical parameter coordinates, we define the coordinate-wise directional consensus vector $S \in {-1, 0, 1}^{d_1 \times d_2}$:

$$S_{(i, j)}(z) \triangleq \operatorname{sgn}\left( \sum_{k=1}^4 \lambda_k(z) \cdot \tilde{\Delta}_{k, (i, j)} \right)$$

The directional projection operator $\mathcal{T}: \mathbb{R}^{d_1 \times d_2} \to \mathbb{R}^{d_1 \times d_2}$ zeros out conflicting gradients:

$$\hat{\Delta}{k, (i, j)} \triangleq \begin{cases} \tilde{\Delta}{k, (i, j)} & \text{if } \operatorname{sgn}\left(\tilde{\Delta}{k, (i, j)}\right) = S{(i, j)}(z) \ 0 & \text{otherwise} \end{cases}$$

The accumulated raw consensus tensor is derived as:

$$\Delta_{\text{consensus}}(z) = \sum_{k=1}^4 \lambda_k(z) \cdot \hat{\Delta}_k$$

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3.5. Truncated SVD Spectral Subspace Projection

For all 2D linear transformations $W \in \mathbb{R}^{d_1 \times d_2}$ (where $\min(d_1, d_2) > r(z)$), the high-rank singular spectrum of $\Delta_{\text{consensus}}$ exhibits high noise entropy. We formulate a depth-varying rank truncation function $r: [0, 1] \to \mathbb{N}$:

$$r(z) \triangleq \left\lfloor r_{\min} + \left(r_{\max} - r_{\min}\right) \cdot \sin\left(\pi z\right) \right\rceil, \quad r_{\min} = 32, ; r_{\max} = 96$$

We compute the optimal rank-$r(z)$ spectral projection via the Eckart-Young-Mirsky theorem:

$$\Pi_{r(z)}\left(\Delta_{\text{consensus}}\right) \triangleq \arg\min_{\operatorname{rank}(X) \le r(z)} \left| \Delta_{\text{consensus}} - X \right|_F$$

Using randomized singular value decomposition ($\operatorname{rSVD}$):

$$\Delta_{\text{consensus}} \approx U_{r(z)} \Sigma_{r(z)} V_{r(z)}^T = \sum_{i=1}^{r(z)} \sigma_i \cdot u_i \otimes v_i$$

Where $U_{r(z)} \in \mathbb{R}^{d_1 \times r(z)}$, $\Sigma_{r(z)} \in \mathbb{R}^{r(z) \times r(z)}$, and $V_{r(z)} \in \mathbb{R}^{d_2 \times r(z)}$. This transformation removes incoherent non-principal spectral components:

$$\Delta_{\text{spectral}}(z) = \begin{cases} \Pi_{r(z)}\left(\Delta_{\text{consensus}}\right) & \text{if } \operatorname{dim}(W) = 2 \wedge \text{Submodule} \in {\text{attn}, \text{mlp}} \ \Delta_{\text{consensus}} & \text{otherwise} \end{cases}$$

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3.6. Frobenius Gauge Invariance & Manifold Retraction

Direct task-vector addition $W_0 + \alpha(z) \Delta_{\text{spectral}}$ causes norm inflation, leading to activation saturation in root-mean-square normalization layers ($\operatorname{RMSNorm}$). We introduce a continuous geodesic norm retraction:

$$\rho_{\text{target}}(z) \triangleq (1 - \beta) \left| W_0 \right|F + \beta \left( \sum{k=1}^4 \lambda_k(z) \left| W_k \right|_F \right), \quad \beta = 0.50$$

$$W_{\text{intermediate}} = W_0 + \alpha(z) \cdot \Delta_{\text{spectral}}(z)$$

The final parameterization $W^*$ is mapped onto the calibrated target hypersphere:

$$W^* \triangleq W_{\text{intermediate}} \cdot \left( \frac{\rho_{\text{target}}(z)}{\left| W_{\text{intermediate}} \right|_F + \epsilon} \right)$$

Where $\epsilon = 10^{-8}$ guarantees numerical stability against vanishing gradients.

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4. Manifold Pruning: Multi-Modal & Speculative Annihilation

To allow conversion to the standard causal GGUF binary specification via llama.cpp, non-causal multimodal projections and draft speculative layers were pruned.

Let $\mathcal{W}{\text{Total}}$ represent the parameter space of XiaomiMiMo/MiMo-V2.6-Distill-Qwen-9B. The projection operator $\mathcal{P}{\text{Causal}}: \mathcal{W}{\text{Total}} \to \mathcal{W}{\text{Causal}}$ eliminates:

1. Multimodal Encoders & Projectors: $$\forall \theta \in \left{ W \mid \operatorname{Match}\left(\text{regex}, \text{"visual."}\right) \vee \operatorname{Match}\left(\text{regex}, \text{"multi_modal_projector."}\right) \right} \implies \theta \to \emptyset$$
2. Multi-Token Prediction (MTP) Heads: $$\forall \theta \in \left{ W \mid \operatorname{Match}\left(\text{regex}, \text{"mtp."}\right) \vee \operatorname{Match}\left(\text{regex}, \text{"shared_head."}\right) \right} \implies \theta \to \emptyset$$
3. Speculative Decoding Transformer Layers: $$\forall l \ge 32 \implies \text{DecoderBlock}(l) \to \emptyset$$
4. Structural Config Flattening: $$\operatorname{Schema}\left(\mathcal{C}{\text{base}}\right): \left{ \text{"text_config"}: \Phi \right} \implies \mathcal{C}{\text{flattened}} = \Phi \cup \left{ \text{"architectures"}: [\text{"Qwen2ForCausalLM"}] \right}$$ $$\text{with } \operatorname{Purge}\left( \text{"mtp_num_hidden_layers"}, \text{"vision_config"}, \text{"image_token_id"} \right)$$

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5. Architectural Tensor Specification

========================================================================================================
Block Index (l)      Module Path                           Tensor Dimensions        Submodule Class
========================================================================================================
[Input]              model.embed_tokens.weight             [248320, 4096]           Head / Categorical
--------------------------------------------------------------------------------------------------------
0 <= l < 32          model.layers.{l}.input_layernorm       [4096]                   RMSNorm (1D)
0 <= l < 32          model.layers.{l}.self_attn.q_proj      [4096, 4096]             Attention (GQA)
0 <= l < 32          model.layers.{l}.self_attn.k_proj      [1024, 4096]             Attention (GQA)
0 <= l < 32          model.layers.{l}.self_attn.v_proj      [1024, 4096]             Attention (GQA)
0 <= l < 32          model.layers.{l}.self_attn.o_proj      [4096, 4096]             Attention (GQA)
0 <= l < 32          model.layers.{l}.self_attn.conv1d      [4096, 1, 4]             DeltaNet (3D Conv)
0 <= l < 32          model.layers.{l}.post_attention_norm  [4096]                   RMSNorm (1D)
0 <= l < 32          model.layers.{l}.mlp.gate_proj         [18944, 4096]            SwiGLU FFN
0 <= l < 32          model.layers.{l}.mlp.up_proj           [18944, 4096]            SwiGLU FFN
0 <= l < 32          model.layers.{l}.mlp.down_proj         [4096, 18944]            SwiGLU FFN
--------------------------------------------------------------------------------------------------------
[Final]              model.norm.weight                     [4096]                   RMSNorm (1D)
[Output]             lm_head.weight                        [248320, 4096]           Head / Categorical
========================================================================================================

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6. Prompt Formalization & Agentic Chat Template

The integration utilizes Olivia Rossi’s Improved Chat Template for Qwen 3.x, framing conversations as deterministic state transitions across system, user, tool execution, and chain-of-thought scratchpad environments.

6.1. Operational State Automaton

$$\mathcal{S}_{\text{prompt}} = \langle \text{System} \rangle \to \langle \text{Thought (CoT)} \rangle \to \langle \text{Tool Call} \rangle \to \langle \text{Tool Result} \rangle \to \langle \text{Response} \rangle$$

<|im_start|>system
You are a state-of-the-art autonomous coding agent equipped with multi-turn tool capabilities.
# Tools Available:
[{"type": "function", "function": {"name": "execute_bash", "description": "Execute arbitrary shell commands in an isolated container.", "parameters": {"type": "object", "properties": {"command": {"type": "string"}}, "required": ["command"]}}}]<|im_end|>
<|im_start|>user
Locate all recursive memory leaks in the `/src/engine` directory and write a patch.<|im_end|>
<|im_start|>thought
1. Formal Goal: Traverse directory tree and inspect C/C++ translation units.
2. Strategy: Issue find command via `execute_bash`.
3. Synthesizing tool call payload in JSON schema format.<|im_end|>
<|im_start|>call:execute_bash{"command": "grep -rnE 'malloc\(|new ' /src/engine"}<|im_end|>
<|im_start|>tool
/src/engine/allocator.cpp:42: void* ptr = malloc(sz);
/src/engine/allocator.cpp:98: char* buf = new char[1024];<|im_end|>
<|im_start|>thought
Identified missing free/delete handlers in `/src/engine/allocator.cpp`. Writing corrective RAII wrappers.<|im_end|>
<|im_start|>assistant
I have identified two unbounded allocations in `/src/engine/allocator.cpp`. Here is the proposed patch using modern C++ RAII semantics:
...
<|im_end|>

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7. Inference Runtime & Generation Hyperparameters

The model's probability distribution is optimized under the following configuration:

$$\mathcal{P}(y_t \mid y_{<t}, x) = \operatorname{Softmax}\left( \frac{\operatorname{Logits}(y_t)}{\tau} \right)$$

generation_config = {
    "temperature": 0.45,                 # Low entropy avoids exploratory syntax divergence
    "top_p": 0.90,                       # Nucleus sampling truncates non-viable probability tails
    "min_p": 0.05,                       # Drops tokens with probability < 5% of max token
    "repetition_penalty": 1.05,          # Prevents deterministic recursive looping in AST generation
    "max_new_tokens": 8192,              # Extended sequence horizon for complete file synthesis
    "do_sample": True,
    "pad_token_id": 151643,
    "eos_token_id": [151643, 151645]     # Standard EOS (<|endoftext|>, <|im_end|>)
}

---

8. Quantitative Evaluation

Evaluation was conducted under greedy decoding ($\tau \to 0$) across multi-turn programming and agentic evaluation benchmarks:

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9. Downstream Quantization Protocol (GGUF)

The sanitization steps guarantee conversion using the official llama.cpp pipeline without missing-weight exceptions:

# Step 1: Clone and prepare llama.cpp runtime
git clone https://github.com/ggerganov/llama.cpp
cd llama.cpp && cmake -B build && cmake --build build --config Release -j

# Step 2: Convert pure HF weights to 16-bit GGUF binary
python3 convert_hf_to_gguf.py \
    --outfile qwen3.5-9b-c3sm-sdm-f16.gguf \
    --outtype f16 \
    /path/to/merged_model_directory

# Step 3: Compute optimal dynamic k-quants (Recommended: Q4_K_M or Q5_K_M)
./build/bin/llama-quantize qwen3.5-9b-c3sm-sdm-f16.gguf qwen3.5-9b-c3sm-sdm-Q4_K_M.gguf Q4_K_M
./build/bin/llama-quantize qwen3.5-9b-c3sm-sdm-f16.gguf qwen3.5-9b-c3sm-sdm-Q5_K_M.gguf Q5_K_M
./build/bin/llama-quantize qwen3.5-9b-c3sm-sdm-f16.gguf qwen3.5-9b-c3sm-sdm-Q8_0.gguf Q8_0

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10. Citation & Theoretical Attribution

@article{c3sm_sdm_2026,
  title   = {Curvature-Calibrated Spectral Consensus with Harmonic Sinusoidal Depth Modulation for Causal LM Fusion},
  author  = {Rossi, Olivia and Merging & Optimization Research Initiative},
  year    = {2026}
}