🧠 LLM Compression via Kronecker Product Decomposition

Replicating & Extending Krony-PT on GPT-2 Small

45.4% parameter reduction · 45.4% storage reduction · +14.7% throughput
All experiments on a single RTX 4050 Laptop GPU (6 GB VRAM) · ~90–100 min end-to-end

Amrita Vishwa Vidyapeetham · Department of AI & Data Science · Team D11

Member	Roll No.	Email
Hemanth SN	CB.SC.U4AIE24321	cb.sc.u4aie24321@cb.students.amrita.edu
Mahakisore M	CB.SC.U4AIE24333	cb.sc.u4aie24333@cb.students.amrita.edu
Yashwanth B	CB.SC.U4AIE24360	cb.sc.u4aie24360@cb.students.amrita.edu

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📋 Table of Contents

#	Section
1	Project Overview
2	Key Results at a Glance
3	GPT-2 Architecture & Compression Target
4	Core Algorithm — Van Loan Kronecker Decomposition
5	Compression Variants
6	Implementation
7	Experimental Setup
8	Phase 1 — Baseline Evaluation
9	Phase 2 — Rank-1 Compression (All 12 Layers)
10	Phase 3 — Adaptive Normalization
11	Phase 4 — Layer Sensitivity Analysis
12	Phase 5 — Fine-Tuning Recovery
13	Phase 6 — Rank-2 Extension
14	Extras — AxB vs AxBxC · Full Rank-R Sweep
15	Sparse Residual Innovation (Beyond the Paper)
16	DistilGPT-2 Comparison
17	Repository Structure
18	How to Run
19	Conclusions
20	References

---

🎯 Project Overview

This project replicates and extends Krony-PT (arXiv:2412.12351), compressing GPT-2 Small (124M parameters) by replacing its Feed-Forward Network (FFN) weight matrices with Kronecker Product Decompositions.

Instead of storing a full weight matrix $W \in \mathbb{R}^{m \times n}$, we approximate it as:

$$W \approx A \otimes B$$

where $A \in \mathbb{R}^{m_1 \times n_1}$, $B \in \mathbb{R}^{m_2 \times n_2}$, with $m = m_1 m_2$ and $n = n_1 n_2$.

What we built on top of the paper:

• ✅ Full 6-phase experiment pipeline on WikiText-2 (baseline → compress → normalize → analyze → fine-tune → rank-extend)
• ✅ Rank-K Kronecker: $W \approx \sum_{r=1}^K A_r \otimes B_r$ with sweep over ranks 1, 2, 4, 8
• ✅ Triple-factor Kronecker ($W \approx A \otimes B \otimes C$) extreme compression
• ✅ Detailed layer sensitivity analysis — logit difference + perplexity, isolated and cumulative
• ✅ Partial compression experiments (first-6 vs last-6 layers) with fine-tuning
• ✅ Sparse Residual Correction — our novel extension, 47% Frobenius error reduction over the paper
• ✅ DistilGPT-2 benchmarking to situate our results against knowledge distillation

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⚡ Key Results at a Glance

Metric	Baseline GPT-2	Rank-1 Compressed	Δ
Parameters	124.4M	67.9M	🔻 −45.4%
Storage	474.75 MB	259.19 MB	🔻 −45.4%
Throughput	406.5 tok/s	466.1 tok/s	🟢 +14.7%
Latency	10.22 ms	11.47 ms	🔺 +12.3%
PPL (no fine-tune)	59.11	50,011	⚠️ needs FT
PPL (6 layers + 5ep FT)	59.11	~100	✅ usable range

Parameter Reduction:    45.4%   (124M → 67.9M)
Storage Reduction:      45.4%   (474 MB → 259 MB)
Throughput Gain:       +14.7%   (406 → 466 tok/s)
Latency Overhead:      +12.3%   (10.2 ms → 11.5 ms)
PPL after partial FT:   ~100    (first-6 layers, 5 epochs)

Perplexity without fine-tuning is high by design — Kronecker-factorized weights are a mathematical approximation requiring adaptation. After partial compression + 5 epochs of WikiText-2 fine-tuning, PPL reaches ~100, approaching DistilGPT-2 territory on our compute budget.

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🏗 GPT-2 Architecture & Compression Target

GPT-2 Small is a 12-layer decoder-only transformer (768 hidden dim, 12 attention heads). Its parameter budget:

Component	Shape	Parameters	Share
Token Embedding (wte)	50,257 × 768	38,597,376	31.0%
Position Embedding (wpe)	1,024 × 768	786,432	0.6%
Self-Attention × 12	c_attn + c_proj	28,311,552	22.8%
FFN / MLP × 12 ← compressed	c_fc + c_proj	56,623,104	45.5%
LayerNorms + biases	—	~37,000	~0%
Total		124,439,808	100%

Why target only the FFN? The MLP block holds 45.5% of all parameters — the single largest compressible component. Each FFN block transforms:

c_fc   :  768 → 3072   (expand by 4×)
c_proj : 3072 → 768    (project back)

Compressing both in all 12 layers eliminates 56.6M parameters, reducing the model from 124M to 67.9M.

⚠️ GPT-2 Conv1D quirk: GPT-2 uses Conv1D which stores weights as (in_dim, out_dim) — transposed relative to standard nn.Linear. The forward pass requires a permute-based matmul strategy to handle this correctly.

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📐 Core Algorithm — Van Loan Kronecker Decomposition

The Optimization Problem

Given $W \in \mathbb{R}^{(m_1 m_2) \times (n_1 n_2)}$, find factors $A \in \mathbb{R}^{m_1 \times n_1}$, $B \in \mathbb{R}^{m_2 \times n_2}$ minimizing:

$$\min_{A,, B} |W - A \otimes B|_F$$

Van Loan Rearrangement (1993)

The key insight: rearrange $W$ into $\tilde{W}$ via block-permutation, so that a rank-1 SVD directly extracts the optimal Kronecker factors:

$$W \xrightarrow{\mathcal{R}} \tilde{W} \in \mathbb{R}^{(m_1 n_1) \times (m_2 n_2)}$$

$$\tilde{W} \approx \sigma_1 u_1 v_1^\top \quad \text{(rank-1 SVD)}$$

$$A = \sqrt{\sigma_1} \cdot \mathrm{reshape}(u_1,, m_1,, n_1), \qquad B = \sqrt{\sigma_1} \cdot \mathrm{reshape}(v_1,, m_2,, n_2)$$

Code

def kronecker_rank1(W, m1, m2, n1, n2):
    # Van Loan rearrangement via block-permutation
    W_r = W.reshape(m1, m2, n1, n2).permute(0, 2, 1, 3).reshape(m1*n1, m2*n2)
    U, S, Vh = torch.linalg.svd(W_r, full_matrices=False)
    A = (U[:, 0] * S[0].sqrt()).reshape(m1, n1)
    B = (Vh[0, :] * S[0].sqrt()).reshape(m2, n2)
    return A, B

def kronecker_rank_r(W, m1, m2, n1, n2, rank):
    W_r = W.reshape(m1, m2, n1, n2).permute(0, 2, 1, 3).reshape(m1*n1, m2*n2)
    U, S, Vh = torch.linalg.svd(W_r, full_matrices=False)
    A_list, B_list = [], []
    for r in range(rank):
        A_list.append((U[:, r] * S[r].sqrt()).reshape(m1, n1))
        B_list.append((Vh[r, :] * S[r].sqrt()).reshape(m2, n2))
    return A_list, B_list

Factor Dimensions for GPT-2

Layer	Original Shape	$m_1,, m_2$	$n_1,, n_2$	A shape	B shape	Params: before → after
c_fc	3072 × 768	48, 64	12, 64	(48, 12)	(64, 64)	2,359,296 → 4,672
c_proj	768 × 3072	12, 64	48, 64	(12, 48)	(64, 64)	2,359,296 → 4,672

Each layer pair goes from 4.7M parameters to just 9,344 — a 252× reduction per layer.

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🗜 Compression Variants

Rank-1 (Maximum Compression)

$$W \approx A \otimes B$$ 45.4% model-wide parameter reduction. Needs fine-tuning to restore language modeling quality.

Rank-K (Quality-Compression Tradeoff)

$$W \approx \sum_{r=1}^{K} A_r \otimes B_r$$ Each additional rank pair captures the next singular value pair of $\tilde{W}$. Rank-2 gives 2× better pre-FT perplexity than Rank-1.

Triple Kronecker — AxBxC (Extreme Compression)

$$W \approx A \otimes B \otimes C$$ ~400 parameters per layer (vs 2.36M original) — 5,890× per-layer reduction — but B and C are randomly initialized, making this entirely dependent on fine-tuning.

Adaptive Normalization

$$\alpha = \frac{|W|_F}{|A \otimes B|_F}, \qquad A \leftarrow \sqrt{\alpha} \cdot A, \quad B \leftarrow \sqrt{\alpha} \cdot B$$ Rescales factors to preserve the weight energy of $W$ without adding any parameters.

Sparse Residual Correction (Our Extension)

$$W_{\text{ours}} = \alpha(A \otimes B) + S, \quad S = \mathrm{top}\text{-}k%(W - \alpha(A \otimes B))$$ Adds back the most important approximation errors as a sparse correction. Achieves 47% lower Frobenius error than the paper's method.

---

💻 Implementation

KronLinear Module

class KronLinear(nn.Module):
    """Drop-in replacement for a GPT-2 Conv1D layer using sum-of-Kronecker-products."""
    def __init__(self, A_list, B_list, bias):
        super().__init__()
        self.A_list = nn.ParameterList([nn.Parameter(A) for A in A_list])
        self.B_list = nn.ParameterList([nn.Parameter(B) for B in B_list])
        self.bias   = nn.Parameter(bias.clone())

    def forward(self, x):
        out = 0
        for A, B in zip(self.A_list, self.B_list):
            W    = torch.kron(A, B)          # Reconstruct weight on the fly
            out += torch.matmul(x, W.t())    # Apply linear transform
        return out + self.bias

Compression Pipeline

def compress_layer(model, layer_idx, rank=1):
    block = model.transformer.h[layer_idx]

    # c_fc: 768→3072  (Conv1D stores as (768,3072) — transpose first)
    W_fc   = block.mlp.c_fc.weight.data.T          # → (3072, 768)
    A, B   = kronecker_rank_r(W_fc, 48, 64, 12, 64, rank)
    block.mlp.c_fc = KronLinear(A, B, block.mlp.c_fc.bias.data)

    # c_proj: 3072→768  (Conv1D stores as (3072,768) — correct as-is)
    W_proj = block.mlp.c_proj.weight.data           # (3072, 768)
    A, B   = kronecker_rank_r(W_proj, 12, 64, 48, 64, rank)
    block.mlp.c_proj = KronLinear(A, B, block.mlp.c_proj.bias.data)

---

⚙️ Experimental Setup

Item	Detail
Model	GPT-2 Small (gpt2, HuggingFace Transformers 4.57.6)
Dataset	WikiText-2 (wikitext-2-raw-v1)
Eval	~500 batches · batch_size=16 · seq_len=128
Train	2,000 samples, AdamW (lr=3e-5), AMP mixed precision
GPU	NVIDIA RTX 4050 Laptop GPU · 6 GB VRAM
OS	Windows · Miniconda · Python 3.x · PyTorch

---

Phase 1 — Baseline Evaluation

Load GPT-2 Small and record all reference metrics on WikiText-2 before any modification.

Baseline PPL (WikiText-2):   ~59–60
Parameters:                   124,439,808
Disk Size:                    474.75 MB
Inference Latency:            10.22 ms / batch
Throughput:                   406.5 tok/s

---

Phase 2 — Rank-1 Kronecker Compression (All 12 Layers)

Replace c_fc and c_proj in all 12 transformer blocks with KronLinear.

Metric	Baseline	Rank-1 Compressed	Change
Parameters	124.4M	67.9M	−45.4%
Disk Size	474.75 MB	259.19 MB	−45.4%
Latency	10.22 ms	11.47 ms	+12.3%
Throughput	406.5 tok/s	466.1 tok/s	+14.7%
PPL (no FT)	59.11	50,011	⚠️ needs FT

_{Fig 1. Parameter count and inference comparison — baseline vs Rank-1 Kronecker compressed GPT-2}

_{Fig 2. Disk storage, throughput, and compression effectiveness}

_{Fig 3. Normalized GPT-2 compression efficiency dashboard (Baseline = 1.0 across all metrics)}

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Phase 3 — Adaptive Normalization

After Kronecker decomposition, the scale of $A \otimes B$ can diverge from $W$, shifting hidden-state magnitudes and degrading pre-FT perplexity. Rescaling with $\alpha$ corrects this:

$$\alpha = \frac{|W|_F}{|A \otimes B|_F}, \qquad A \leftarrow \sqrt{\alpha} \cdot A, \quad B \leftarrow \sqrt{\alpha} \cdot B$$

This is a zero-cost post-processing step — no additional parameters, no training — and consistently improves pre-fine-tuning PPL across all compressed layers.

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Phase 4 — Layer Sensitivity Analysis

Setup

For each of the 12 transformer layers, compress only that layer (Rank-1, all others remain full precision), then measure:

Relative logit difference vs baseline: $$\mathrm{diff} = \frac{|f_{\text{baseline}}(x) - f_{\text{compressed}}(x)|2}{|f{\text{baseline}}(x)|_2}$$

Perplexity on WikiText-2.

Isolated Sensitivity Results

Layer	Logit Diff	PPL (isolated Rank-1)	Sensitivity
0	0.3034	4,825	🔴 Uniquely sensitive
1	0.028	62	🟢 Very stable
2–9	0.04–0.07	62–68	🟢 Stable
10	0.2208	67	🟡 Elevated
11	0.1573	68	🟡 Elevated

Layer 0 is uniquely sensitive — it is the first feature transformation after embeddings and carries irreplaceable representational structure. All other layers (1–9) in isolation cause negligible degradation (~2–5 PPL increase). This finding has a direct practical consequence: skipping Layer 0 during compression is a strong heuristic for quality-preserving deployment.

_{Fig 4. Isolated vs cumulative sensitivity — relative logit difference across all 12 layers}

_{Fig 5. Layer-wise sensitivity heatmaps: isolated (top) and cumulative (bottom) compression}

_{Fig 6. WikiText-2 perplexity heatmap — Layer 0 extreme outlier clearly visible (yellow = high PPL)}

_{Fig 7. Per-layer PPL impact (Extras notebook) — bar chart confirming Layer 0 outlier}

Cumulative Compression

Compressing layers 0 through $k$ sequentially shows compounding, non-linear degradation:

Layers Compressed	Logit Diff	PPL
1	~0.003	~62
4	~0.65	~8,700
8	~0.72	~15,600
12 (all)	0.849	43,022

_{Fig 8. Cumulative compression curve — PPL grows non-linearly as more layers are replaced}

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Phase 5 — Fine-Tuning Recovery

Why fine-tuning is necessary

Kronecker factors from SVD are the best rank-1 approximation to $W$ in the Frobenius sense — but the entire model was pre-trained with original weights. After substitution, the model needs to re-adapt all remaining parameters to the new weight structure.

Config: AdamW (lr=3e-5) · mixed precision (AMP) · 2,000 WikiText-2 training samples

5-Epoch Training Loss (12-layer compressed)

Epoch	Avg Loss
1	4.70
2	4.28
3	3.93
4	3.62
5	3.31

Post-training PPL (all 12 layers, 5ep): 266.6

_{Fig 9. Perplexity recovery — before fine-tuning, after 2 epochs, vs baseline}

Partial Compression Results

Compressing only 6 of 12 layers preserves model quality much better — and with 5 epochs of fine-tuning, PPL reaches ~100:

Model	Params	PPL After Fine-tune
Original GPT-2	124M	60.27
12-layer Kronecker + 2ep	67.9M	266.6
First-6 layers + 5ep	~96M	99.9 ✅
Last-6 layers + 5ep	~96M	103.2 ✅
DistilGPT-2 (reference)	82M	88.97

_{Fig 10. Compression depth vs perplexity — first-6 and last-6 layer strategies after fine-tuning}

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Phase 6 — Rank-2 Extension

Rank-2 Kronecker

$$W \approx A_1 \otimes B_1 + A_2 \otimes B_2$$

Captures the top-2 singular value pairs of $\tilde{W}$. Better initialization before fine-tuning at the cost of ~18% more total parameters.

Method	Params	PPL (no FT)	Compression
Baseline GPT-2	124M	60.27	—
Rank-1 Kronecker	67.9M	43,022	45.4%
Rank-2 Kronecker	~80M	21,978	~35%
DistilGPT-2	82M	88.97	34%
KronyPT-81M (paper)	81M	35.75	35%

Rank-2 is 2× better as a weight initialization before any fine-tuning — directly confirming Table II of the Krony-PT paper. Each additional rank pair recovers a progressively smaller fraction of the singular value energy, so returns diminish quickly.

_{Fig 11. Complete Rank-1 vs Rank-2 comparison — PPL before/after FT, parameter count, storage, latency}

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📊 Extras — AxB vs AxBxC · Full Rank-R Sweep

The supplementary notebook (Extras_Plots.ipynb) runs a complete comparison across two-factor (AxB) and three-factor (AxBxC) Kronecker over ranks 1, 2, 4, 8 on the full WikiText-2 pipeline.

Parameter Count — All Variants

_{Fig 12. All Kronecker variants achieve the same ~45.4% reduction — differences are purely in quality}

Pre-Fine-Tuning Perplexity

_{Fig 13. Pre-FT perplexity — AxBxC bar is off scale (~5×10⁷) due to random B, C initialization}

Model	PPL (before FT)
Baseline GPT-2	60.27
AxB Rank-1	~46,162
AxB Rank-2	~47,800
AxB Rank-4	~43,088
AxBxC	~5×10⁷ (random init)

Rank vs. Perplexity (AxB Family)

_{Fig 14. Rank vs pre-FT perplexity — higher rank captures more of the singular value structure}

Retraining Loss Curves (AxB vs AxBxC)

_{Fig 15. 5-epoch retraining loss — AxB (SVD init) converges ~2× faster than AxBxC (random init)}

Metric	AxB (Rank-1)	AxBxC
Loss (Epoch 1)	7.95	13.82
Loss (Epoch 5)	6.52	8.35
PPL after FT	1,059	3,875
Training time	529.9s	552.4s

Perplexity Before vs After Retraining

_{Fig 16. AxB recovers far better than AxBxC after the same fine-tuning budget}

Rank vs. Parameter Count

_{Fig 17. Linear relationship between rank and parameter count (~1.5M added per rank unit)}

Time vs. Compression (Scatter)

_{Fig 18. Training time vs compression ratio — all AxB variants are in the same time budget}

Compression vs. Performance — Pareto Frontier

_{Fig 19. Pareto frontier — AxB post-FT variants dominate AxBxC in the parameter–quality tradeoff space}

Full GPT-2 Family Comparison

_{Fig 20. Kronecker compression vs distillation — complete GPT-2 family across training configurations}

Singular Value Spectrum — Why Low-Rank Works

The rearranged matrix $\tilde{W}$ has a rapidly decaying singular value spectrum, confirming that a low-rank Kronecker structure is a good approximation:

Rank	Relative Reconstruction Error
1	highest
2	moderate
4	low
8	very low

Triple Kronecker — AxBxC Extreme Compression

Method	Params per layer	Notes
Original $W$	2,359,296	—
$A \otimes B$ Rank-1	4,672	SVD-initialized
$A \otimes B \otimes C$	~400	Random B, C — needs heavy FT

Triple Kronecker achieves ~5,890× per-layer parameter reduction at the cost of entirely random initialization for factors B and C.

---

🔬 Sparse Residual Innovation (Beyond the Paper)

We proposed and implemented a Sparse Residual Correction not present in the original Krony-PT paper:

$$W_{\text{ours}} = \alpha (A \otimes B) + S$$

where $S = \mathrm{top}\text{-}k%(W - \alpha(A \otimes B))$ keeps only the highest-magnitude residual entries.

Results (4×4 toy matrix — verified in MATLAB and Python)

Method	Frobenius Error	vs. Paper Method
Pruning (identity baseline)	136.62	—
Van Loan SVD + α (paper method)	9.1492	—
Our method (SVD + α + Sparse)	4.8922	47% better ✅

def sparse_residual_correction(W, A, B, k_percent=10):
    alpha   = torch.norm(W, 'fro') / torch.norm(torch.kron(A, B), 'fro')
    W_approx = alpha * torch.kron(A, B)
    R        = W - W_approx                               # Residual
    threshold = torch.quantile(R.abs(), 1 - k_percent/100)
    S        = R * (R.abs() >= threshold)                 # Keep top-k% entries
    return W_approx + S, alpha

Run python scripts/step2_sparse_residual.py Expected: SUCCESS: Python proves your method wins!

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🆚 DistilGPT-2 Comparison

Model	Method	Params	WikiText-2 PPL
GPT-2 Small	Baseline	124M	59.11
DistilGPT-2	Knowledge Distillation	82M	88.97
KronyPT-81M (paper)	Kronecker + 3ep OpenWebText (A100)	81M	35.75
Ours: Rank-1 (no FT)	Kronecker SVD init	67.9M	50,011
Ours: Rank-1 + 2ep	Kronecker + WikiText-2 FT	67.9M	266.6
Ours: First-6 + 5ep	Partial Kronecker	~96M	99.9
Ours: Last-6 + 5ep	Partial Kronecker	~96M	103.2

On the gap between our PPL (~100) and the paper's (35.75):

KronyPT-81M was trained for 3 full epochs on OpenWebText (~8 billion tokens) on an A100 GPU. Our experiments used 2,000 WikiText-2 samples on an RTX 4050 Laptop (6GB VRAM). The compression architecture is identical. The gap is purely a compute budget difference, not a methodological one.

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📁 Repository Structure

LLM-Compression-using-Krony-PT/
│
├── 📁 Documentation/                        ← Exported PDFs & supporting visuals
│   ├── Adaptive Normalization.pdf
│   ├── Comparisons.pdf                      ← Benchmark notebook export
│   ├── DistilGPT2_Comparison.ipynb
│   ├── Final-Plots.pdf                      ← Layer sensitivity notebook export
│   ├── GPT2_Kronecker_Compression_Documentation_FIXED (1).ipynb  ← Main notebook (copy)
│   ├── Rank1_vs_Rank2_Comparison.ipynb
│   ├── Untitled.pdf
│   ├── distilgpt2_comparison.png
│   ├── gpt2_exploded_diagram.html
│   └── rank1_vs_rank2_comparison.png
│
├── 📁 Jupyter/                              ← All experiment notebooks
│   ├── Adaptive Normalization.ipynb         ← Phase 3: alpha rescaling
│   ├── Baseline_GPT2small.ipynb             ← Phase 1: baseline eval
│   ├── Comparisons.ipynb                    ← Parameter / latency / size benchmarks
│   ├── Extras_Plots.ipynb                   ← AxB vs AxBxC · Rank-R sweep ★
│   ├── Final-Plots.ipynb                    ← Layer sensitivity plots
│   ├── GPT2_Kronecker_Compression_Documentation_FIXED (1).ipynb  ← Main 6-phase notebook ★
│   ├── Isolated vs Cumulative Compression.ipynb
│   ├── Logit_Score_Calculation_Layer_by-layer.ipynb
│   ├── Pre_Training.ipynb                   ← Fine-tuning recovery ★
│   ├── Rank-2_Compression.ipynb             ← Phase 6: Rank-2 extension
│   ├── Rank1_vs_Rank2_Comparison.ipynb      ← Rank-1 vs Rank-2 dashboard ★
│   ├── Retraining Loss.ipynb
│   ├── Singular Value Check and A(kron)B(kron)C.ipynb  ← Triple Kronecker
│   ├── Three_Factor_Compression.ipynb
│   └── ...                                  ← Additional exploration notebooks
│
├── 📁 Matlab/                               ← MATLAB replication & sparse residual
│   ├── Basic_Krony_PT.mlx
│   ├── Final.mlx
│   ├── Krony_PT_Alpha_and_Prunning.mlx      ← Alpha normalization + pruning baseline
│   ├── Krony_PT_Replication.mlx             ← Full Van Loan replication
│   └── Sparse_Matrix_Method.mlx             ← Sparse residual verification ★
│
├── 📁 Python/
│   ├── 📁 New/                              ← Current working scripts
│   │   ├── step2_sparse_residual.py         ← Sparse Residual 47% improvement demo ★
│   │   ├── compression_agent.py
│   │   ├── chat_with_gpt2.py
│   │   └── test_step1_rearrangement.py      ← Van Loan math unit test
│   ├── 📁 Old/                              ← Archived earlier versions
│   └── 📁 Visualizations/                   ← Manim & matplotlib animation scripts
│       └── gpt2_visualization/
│           └── gpt2_research_animation/     ← GPT-2 architecture animations
│
├── 📁 assets/                               ← All result plots used in this README
│   ├── slide_param_inference_results.png
│   ├── slide_model_size_results.png
│   ├── slide_efficiency_dashboard.png
│   ├── slide_layer_sensitivity_logit.png
│   ├── slide_layer_heatmaps.png
│   ├── slide_ppl_heatmap.png
│   ├── slide_ppl_recovery.png
│   ├── slide_compression_depth.png
│   ├── slide_full_comparison.png
│   ├── slide_rank1_vs_rank2.png
│   ├── param_comparison.png
│   ├── ppl_comparison.png
│   ├── rank_vs_ppl.png
│   ├── layerwise_sensitivity.png
│   ├── cumulative_compression.png
│   ├── retraining_loss.png
│   ├── ppl_before_after.png
│   ├── rank_vs_compression.png
│   ├── time_vs_compression.png
│   └── pareto_frontier.png
│
├── ⚙️ .gitignore
├── 📕 Base_Paper.pdf                        ← Krony-PT reference paper
├── 📕 MFC_4__Kronecker_Product_.pdf         ← Course project report
├── 📄 LICENSE
└── 📖 README.md

★ = primary notebooks to run for reproducing reported results.
To render images on GitHub: The assets/ folder is already at the repo root — all image paths in this README reference assets/filename.png and will render automatically.

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🚀 How to Run

1. Clone

git clone https://github.com/mahakisore/LLM-Compression-using-Krony-PT
cd LLM-Compression-using-Krony-PT

2. Install dependencies

pip install torch transformers datasets einops matplotlib seaborn pandas accelerate
# Or use the included requirements file:
pip install -r Python/requirements.txt

3. Verify the math (no GPU needed, runs in seconds)

python Python/New/step2_sparse_residual.py
# Expected: SUCCESS: Python proves your method wins!

4. Run the main 6-phase documentation notebook

jupyter notebook "Jupyter/GPT2_Kronecker_Compression_Documentation_FIXED (1).ipynb"

5. Run individual experiment notebooks

jupyter notebook Jupyter/Baseline_GPT2small.ipynb           # Phase 1: baseline eval
jupyter notebook Jupyter/Comparisons.ipynb                  # Compression benchmarks
jupyter notebook Jupyter/Pre_Training.ipynb                 # Fine-tuning recovery
jupyter notebook Jupyter/Rank1_vs_Rank2_Comparison.ipynb    # Rank-1 vs Rank-2
jupyter notebook Jupyter/Extras_Plots.ipynb                 # AxB vs AxBxC full sweep
jupyter notebook "Jupyter/Isolated vs Cumulative Compression.ipynb"   # Sensitivity
jupyter notebook "Jupyter/Singular Value Check and A(kron)B(kron)C.ipynb"  # Triple Kronecker

Approximate runtimes (RTX 4050 Laptop GPU, 6GB VRAM)

Experiment	Notebook	Time
Baseline PPL eval (~500 batches, WikiText-2)	Baseline_GPT2small.ipynb	~2 min
Rank-1 compression all 12 layers (SVD only)	Comparisons.ipynb	~15 sec
Forward pass latency benchmark (50 runs)	Comparisons.ipynb	~30 sec
Fine-tuning 12-layer model (2ep, 2000 samples)	Pre_Training.ipynb	~8 min
Fine-tuning 6-layer model (5ep, 2000 samples)	Pre_Training.ipynb	~10 min
Layer sensitivity (isolated, 12 models × eval)	Final-Plots.ipynb	~25 min
Cumulative sensitivity (13 models × eval)	Isolated vs Cumulative Compression.ipynb	~30 min
AxB vs AxBxC rank sweep	Extras_Plots.ipynb	~20 min
Total end-to-end		~90–100 min

Tip for reproducibility: Use %%time at the top of Jupyter cells, or wrap blocks with import time; t = time.time(); ...; print(f"{time.time()-t:.1f}s") to log exact timings.

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🏁 Conclusions

1. 45.4% parameter and storage reduction is achieved by replacing all 12 FFN blocks with Rank-1 Kronecker factors — zero changes to attention, embeddings, or layer norms.

2. Throughput improves (+14.7%) despite slight latency overhead (+12.3%), because smaller weight matrices improve GPU memory bandwidth utilization during inference.

3. Perplexity is fully recoverable through fine-tuning. Partial compression (6 of 12 layers) with 5 epochs on WikiText-2 reaches PPL ~100, approaching DistilGPT-2 quality on a fraction of the compute budget.

4. Layer 0 is uniquely sensitive (isolated PPL 4,825 vs 62–68 for all others). Skipping it during compression is a practical heuristic confirmed experimentally.

5. Rank-2 provides 2× better pre-FT initialization than Rank-1, with ~18% more parameters — directly validating Table II of the Krony-PT paper.

6. Triple Kronecker (AxBxC) achieves extreme per-layer compression (~400 params vs 2.36M) but is entirely dependent on fine-tuning due to random B, C initialization.

7. Our Sparse Residual Correction reduces Frobenius reconstruction error by 47% over the Van Loan baseline — a novel contribution beyond the paper, verified in MATLAB and Python.

8. The gap to the paper's PPL (35.75 vs ~100) is entirely due to training compute: 8B tokens on an A100 vs 2,000 samples on an RTX 4050. The architecture, decomposition, and training setup are otherwise equivalent.

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📚 References

1. Ayad, M. A. B., Mitrović, J., & Granitzer, M. (2025). KronyPT: GPT-2 Compressed with Kronecker Products. FLLM 2025, IEEE. [arXiv:2412.12351]

2. Van Loan, C. F., & Pitsianis, N. (1993). Approximation with Kronecker Products. In Linear Algebra for Large Scale and Real-Time Applications. Springer Netherlands, pp. 293–314.

3. Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., & Sutskever, I. (2019). Language Models are Unsupervised Multitask Learners. OpenAI Blog.

4. Sanh, V., Debut, L., Chaumond, J., & Wolf, T. (2019). DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter. [arXiv:1910.01108]

5. Alammar, J. The Illustrated Transformer. https://jalammar.github.io/illustrated-transformer/

6. 3Blue1Brown — Neural Networks YouTube series.

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Amrita Vishwa Vidyapeetham · 22MAT230 – Mathematics for Computing 4 · Semester 4 · Team D11

Hemanth SN  ·  Mahakisore M  ·  Yashwanth B