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| 1 |
+
---
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| 2 |
+
license: apache-2.0
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| 3 |
+
language:
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| 4 |
+
- en
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| 5 |
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tags:
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+
- diffusion
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| 7 |
+
- speculative-decoding
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| 8 |
+
- rectified-flow
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| 9 |
+
- dit
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| 10 |
+
- qwen
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| 11 |
+
- math-reasoning
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| 12 |
+
datasets:
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| 13 |
+
- AI-MO/NuminaMath-CoT
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| 14 |
+
base_model:
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| 15 |
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- Qwen/Qwen3.5-9B
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| 16 |
+
---
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| 17 |
+
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| 18 |
+
# Continuous Latent Speculative Decoding (CLSD)
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| 19 |
+
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| 20 |
+
**Architecture**: ~4.0B Hybrid Causal DiT (Rectified Flow) + 9B Frozen Verifier
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| 21 |
+
**Target**: SOTA mathematical reasoning via continuous latent speculative decoding
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| 22 |
+
**Key Innovation**: First hybrid DeltaNet/Attention causal diffusion transformer
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| 23 |
+
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| 24 |
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---
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| 25 |
+
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| 26 |
+
## Thesis
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| 27 |
+
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Autoregressive language models are bottlenecked by sequential generation. CLSD deploys a
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| 29 |
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hybrid causal Diffusion Transformer (DiT) — a strided 12-layer slice of Qwen3.5-9B —
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| 30 |
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operating in the continuous embedding space of the same frozen Qwen3.5-9B verifier.
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| 31 |
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Both models share the exact same 4096-dimensional manifold, the same tokenizer,
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| 32 |
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and the same attention geometry. No projection bridges, no dimensional translation loss.
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| 33 |
+
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| 34 |
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Qwen3.5-9B uses a hybrid architecture: 24 Gated DeltaNet (linear attention) layers + 8
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standard quadratic attention layers in a repeating [3xDeltaNet, 1xAttention] pattern.
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| 36 |
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The DiT preserves this hybrid structure and keeps **causal masking** -- DeltaNet linear
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| 37 |
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recurrence is strictly causal by design and cannot be flipped to bidirectional.
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| 38 |
+
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| 39 |
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The DiT drafts 32 candidate 128-token embedding sequences simultaneously in 2 Euler steps.
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| 40 |
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The verifier evaluates them in a single batched forward pass. The DiT is aligned via
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| 41 |
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Cross-Entropy backpropagation through the frozen verifier.
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| 42 |
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> **Why causal diffusion works**: The conditioning vector C is injected via adaLN into
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| 44 |
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> every position simultaneously, providing global context regardless of attention mask.
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| 45 |
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> Token 1 does not need to see token 128 -- C already carries the full prompt context.
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> The causal constraint actually forces the DiT to learn autoregressive-like internal
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> logic, which mirrors the frozen verifier expectations.
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| 48 |
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---
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| 50 |
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| 51 |
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## Architecture
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| 52 |
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### Models
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| 54 |
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| 55 |
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| Role | Model | Params | Dim | Layers | Attn Heads | KV Heads |
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| 56 |
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|------|-------|--------|-----|--------|-----------|----------|
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| 57 |
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| **Generator (DiT)** | Qwen3.5-9B -> strided 12-layer slice | ~4.0B | 4096 | 12 | 16 | 4 |
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| 58 |
+
| **Verifier (frozen)** | Qwen3.5-9B (text tower) | 9B | 4096 | 32 | 16 | 4 |
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| 59 |
+
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| 60 |
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### The Strided Graft
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| 61 |
+
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| 62 |
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```
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| 63 |
+
Source layers: [0, 3, 6, 9, 12, 15, 18, 21, 24, 26, 28, 31]
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| 64 |
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Layer types: [D, A, D, D, D, A, D, D, D, D, D, A ]
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| 65 |
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DiT indices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
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| 66 |
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| 67 |
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D = DeltaNet (linear_attention), A = full_attention
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| 68 |
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Result: 9 DeltaNet + 3 full_attention layers
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| 69 |
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```
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| 70 |
+
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| 71 |
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### Modifications to Grafted Layers
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| 72 |
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| 73 |
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1. **Strip the LM head** -- the DiT outputs continuous embeddings, not logits
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| 74 |
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2. **Keep causal masking** -- preserves 100% of pre-trained weight integrity
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| 75 |
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3. **Inject adaLN-Zero modulators** -- one per block, nn.Linear(4096, 24576)
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| 76 |
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4. **Zero-initialize** -- at step 0 the network acts as identity
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| 77 |
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5. **Timestep conditioning** -- sinusoidal embedding + conditioning vector C
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| 78 |
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6. **Learned local positional embedding** -- nn.Parameter(zeros(1, 128, 4096))
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| 80 |
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---
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| 81 |
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## Training Pipeline
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| 84 |
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### Pre-Flight: Embedding Extraction
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Target embeddings pre-computed from **AI-MO/NuminaMath-CoT** (mathematical chain-of-thought reasoning):
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| 87 |
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- Tokenize reasoning paths with Qwen tokenizer
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| 88 |
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- Lookup embeddings via Qwen3.5-9B frozen embedding matrix E (248320 x 4096)
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- Chunk into fixed 128-token windows
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- Save as [64, 128, 4096] safetensors shards
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| 92 |
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**Result**: 2,294 shard files x 64 chunks = **146,790 total chunks** (~144 GB)
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| 94 |
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### Stage A: Rectified Flow (Velocity Regression)
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| 96 |
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Teach the DiT the straight-line velocity field from noise to embeddings using Rectified Flow:
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x_t = (1 - t) * x_0 + t * x_1, t in [0, 1]
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L_RF = ||v_theta(x_t, t, C) - (x_1 - x_0)||^2
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| 102 |
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| Property | DDPM + LCM (old) | Rectified Flow (this work) |
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| 103 |
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|----------|-------------------|---------------------------|
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| 104 |
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| Training objective | Noise prediction | Velocity prediction (v) |
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| 105 |
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| Trajectory shape | Curved (needs 1000 steps) | **Straight line** |
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| Distillation required? | Yes | **No** |
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| Native inference steps | 2 (after distillation) | **1-2 Euler steps natively** |
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| 108 |
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| 109 |
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**This release**: Stage A trained on 1x NVIDIA B200 for 50,000 steps:
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| 111 |
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| Parameter | Value |
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| 112 |
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|-----------|-------|
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| 113 |
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| Optimizer | AdamW (lr=1e-4, warmup 100 steps, cosine decay) |
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| 114 |
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| Batch size | 32 |
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| 115 |
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| Steps | 50,000 |
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| 116 |
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| Wall-clock | 154.8 minutes |
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| 117 |
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| Final MSE loss | ~0.013 (converged by step 5K) |
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| 118 |
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| Checkpoints included | 5K, 10K, 20K, 30K, 40K, final |
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| 119 |
+
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| 120 |
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### Stage C: CE Alignment (Next)
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| 121 |
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| 122 |
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Shift the DiT from outputs that look like embeddings to outputs that make
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| 123 |
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the 9B verifier produce correct tokens:
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| 124 |
+
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| 125 |
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```
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| 126 |
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z ~ N(0,I) -> DiT(z, C) -> [2 Euler steps] -> X (128x4096)
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| 127 |
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-> Qwen_frozen(X, past_kv) -> logits (128x248320)
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| 128 |
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```
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| 129 |
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| 130 |
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L_total = alpha * CE(logits, targets) + beta * MSE(X, E(targets))
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| 131 |
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| 132 |
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- alpha = 1.0 (CE drives alignment)
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| 133 |
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- beta = 0.1 -> 0 over training (MSE regularizer anneals)
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| 134 |
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| 135 |
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---
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| 136 |
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| 137 |
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## Live Inference (Target)
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| 138 |
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| 139 |
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1. User submits a reasoning prompt
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| 140 |
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2. 9B Verifier runs forward pass -> extracts C (4096-d) + KV cache
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| 141 |
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3. DiT samples 32 noise vectors, generates 32 candidate 128-token branches in **2 Euler steps**
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| 142 |
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4. 9B Verifier evaluates all 32 branches in one batched forward pass
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| 143 |
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5. **Causal Guillotine**: Scan Top-1 draft left-to-right, truncate at first position where log-prob drops below threshold
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| 144 |
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6. Qwen samples the correct token, new C generated, loop repeats
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| 145 |
+
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| 146 |
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**Target latency**: <500ms per 128-token block
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+
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| 148 |
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---
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| 149 |
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| 150 |
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## Repository Contents
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| 151 |
+
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| 152 |
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```
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| 153 |
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embeddings/ # Pre-computed NuminaMath-CoT embeddings (146K chunks)
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| 154 |
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batch_0000.safetensors # Each: [64, 128, 4096]
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| 155 |
+
...
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| 156 |
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checkpoints/
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| 157 |
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dit_stage_a_step_5000.pt
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| 158 |
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dit_stage_a_step_10000.pt
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| 159 |
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dit_stage_a_step_20000.pt
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| 160 |
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dit_stage_a_step_30000.pt
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| 161 |
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dit_stage_a_step_40000.pt
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| 162 |
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dit_stage_a_final.pt # 50K steps, converged
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| 163 |
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```
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| 164 |
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| 165 |
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### Loading a Checkpoint
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| 166 |
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| 167 |
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```python
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| 168 |
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from clsd.grafted_dit import graft_dit_from_qwen, STRIDE_INDICES
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| 169 |
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from transformers import AutoModelForCausalLM
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| 170 |
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import torch
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| 171 |
+
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| 172 |
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# Build the DiT architecture
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| 173 |
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qwen = AutoModelForCausalLM.from_pretrained("Qwen/Qwen3.5-9B", dtype=torch.bfloat16)
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| 174 |
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dit, embed_tokens = graft_dit_from_qwen(qwen, slice_indices=STRIDE_INDICES)
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| 175 |
+
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| 176 |
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# Load trained weights
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| 177 |
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state_dict = torch.load("checkpoints/dit_stage_a_final.pt", weights_only=True)
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| 178 |
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dit.load_state_dict(state_dict)
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| 179 |
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```
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| 180 |
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---
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| 182 |
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| 183 |
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## Key Architectural Decisions
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| 184 |
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| 185 |
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1. **Shared 4096-d space**: Generator and verifier operate in the same embedding geometry natively. No projection layers, no information bottlenecks.
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| 186 |
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2. **Strided layer slice**: DiT inherits geometric knowledge from early, middle, and late layers of the 9B.
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| 187 |
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3. **Rectified Flow over DDPM**: Linear trajectories -> no distillation stage -> native 2-step generation.
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| 188 |
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4. **Instruct/Instruct architecture**: Both drafter and verifier sliced from the same model. Zero distributional gap at initialization.
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| 189 |
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5. **Monte Carlo parallel search**: 32 branches x 128 tokens = 4,096 candidate tokens per inference step.
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| 190 |
+
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| 191 |
+
---
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| 192 |
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| 193 |
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## Citation
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| 194 |
+
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| 195 |
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```bibtex
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| 196 |
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@misc{clsd2026,
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| 197 |
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title={Continuous Latent Speculative Decoding: A Hybrid Causal DiT for Parallel Reasoning},
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year={2026},
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| 199 |
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url={https://huggingface.co/datasysdev/clsd}
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| 200 |
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}
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| 201 |
+
```
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| 202 |
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## License
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| 204 |
+
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Apache 2.0
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