Experiments & Analysis

A comprehensive guide to validation protocols, practical libraries, and analytical metrics for evaluating optimization algorithms across various domains.

Computer Vision

Image Classification

Classification remains the primary testbed for verifying the convergence speed and generalization capability of new optimizers.

Standard Benchmarks

  • CIFAR-10/100: For initial debugging and small-scale verification.
  • ImageNet-1k: The gold standard for large-scale regime verification.

Backbone Models

ResNet-50 ViT-Base/Large ConvNeXt

Generative Models

Evaluating stability and sample quality in generative tasks, which often involve complex loss landscapes.

Tasks & Models

  • Diffusion: DDPM, Stable Diffusion (Latent Diffusion).
  • DiT: Diffusion Transformers (Sora, Stable Diffusion 3).
  • GANs: StyleGAN (legacy comparisons).

Key Metrics

FID (Fréchet Inception Distance) IS (Inception Score) CLIP Score

Object Detection & Segmentation

Verifying optimization in multi-task settings (classification + localization) with complex loss functions.

Standard Benchmarks

  • COCO: Common Objects in Context.
  • LVIS: Large Vocabulary Instance Segmentation.

Metrics

mAP (box) mAP (mask)

Large Language Models (LLM)

Pre-training & Fine-tuning

Validating optimizers on LLMs requires handling massive scale, distributed training stability, and long-horizon convergence.

Datasets

C4 (Colossal Clean Crawled Corpus), The Pile, RedPajama.

Architectures

GPT-2/3 (Decoder-only), LLaMA, OPT, BERT (Encoder-only).

Training Schemes

Full Pre-training, LoRA/QLoRA (Parameter-Efficient Fine-Tuning), Instruction Tuning.

Evaluation Metrics

  • Perplexity (PPL) Lower is better
  • Downstream Accuracy MMLU, HellaSwag, GSM8K
  • Training Stability Loss spikes, divergence checks

Advanced Analysis

  • Scaling Laws Fit power laws \( L(N) \approx C N^{-\alpha} \) to predict performance at scale.
  • Instruction Tuning & RLHF Verify optimizer effectiveness in alignment stages (SFT, DPO, PPO).

Multimodal LLMs (MLLM)

Validating optimization in multimodal settings involves ensuring alignment between different modalities (e.g., Vision and Language) without catastrophic forgetting of individual capabilities.

Common Models

LLaVA, CLIP, BLIP-2, Flamingo

Tasks

Visual Question Answering (VQA), Image Captioning, Text-to-Image Retrieval

Metrics

VQA Accuracy, CIDEr (Captioning), Recall@K (Retrieval)

Reinforcement Learning (RL)

RL optimization presents unique challenges like non-stationary data distributions, high variance in gradient estimates, and the need for exploration-exploitation balance.

On-Policy Methods

Optimization must be stable as data is generated by the current policy.

PPO GRPO GSPO

Off-Policy / Offline

Learning directly from preference datasets without reward modeling.

DPO SimPO KTO

Practical Libraries for Experimentation

Analysis Methods & Metrics

Convergence Rate

Measure how quickly the training loss decreases. Analyze iterations to reach specific loss thresholds.

Metric: Iterations to \(\epsilon\)-accuracy

Generalization Gap

The difference between Training and Test Accuracy. Smaller gap indicates better generalization (flatter minima).

Metric: \( Acc_{train} - Acc_{test} \)

Hyperparam Sensitivity

Robustness to learning rate, weight decay, and momentum. Visualize the "sweet spot" size.

Visualization: 2D Heatmaps

Computational Efficiency

Wall-clock time per iteration and peak memory usage. Throughput translates directly to training cost.

Metric: Tokens/sec or Images/sec

Hessian Spectrum

Analyze top eigenvalues (\(\lambda_{max}\)). Lower \(\lambda_{max}\) typically correlates with better generalization.

Tool: PyHessian

Rep. Similarity (CKA)

Centered Kernel Alignment measures similarity between learned features layer-by-layer.

Metric: CKA Score \([0, 1]\)