FlashOptim can reduce the memory footprint of training LLMs for simulating tissue mechanics.

FlashOptim (a memory-efficient optimizer variant leveraging fused kernel operations and reduced-precision state storage) reduces peak GPU memory consumption during training of Large Language Models (LLMs) fine-tuned or pre-trained for tissue mechanics simulation tasks by at least 20% compared to standard AdamW baseline, without degrading simulation accuracy (measured by relative L2 error on stress-strain predictions) by more than 5% relative.

Minimum Viable Test (MVT): Fine-tune a 7B-parameter LLM (e.g., LLaMA-2-7B or Mistral-7B) on a tissue mechanics simulation dataset using three optimizer configurations — (A) standard AdamW FP32 states, (B) 8-bit Adam (bitsandbytes baseline), and (C) FlashOptim — measuring peak GPU memory, training throughput, and downstream simulation accuracy. Run 3 random seeds per configuration. Total MVT scope: 9 training runs.

Full Validation: Extend to 1B, 7B, and 13B model sizes; include ablations over sequence length (512, 2048, 8192), batch size (8, 32, 128), and tissue type (hyperelastic, viscoelastic, poroelastic). Add statistical significance testing and Pareto frontier analysis of memory vs. accuracy tradeoff.

# FlashOptim EVP Implementation Sketch
# =====================================

import torch
import torch.nn as nn
from transformers import AutoModelForCausalLM, AutoTokenizer
from torch.cuda import memory_stats
import triton
import triton.language as tl

# --- 1. FlashOptim Optimizer (Sketch) ---
class FlashOptim(torch.optim.Optimizer):
    """
    FlashOptim: Fused 8-bit optimizer with Triton kernels.
    Stores optimizer states (m, v) in INT8 with per-block scaling.
    """
    def __init__(self, params, lr=1e-4, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0.01, block_size=2048):
        defaults = dict(lr=lr, betas=betas, eps=eps,
                       weight_decay=weight_decay, block_size=block_size)
        super().__init__(params, defaults)
        self.block_size = block_size

    @torch.no_grad()
    def step(self, closure=None):
        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                state = self.state[p]

                # Initialize quantized states
                if len(state) == 0:
                    state['step'] = 0
                    # Store in INT8 instead of FP32 → 4x memory reduction
                    state['exp_avg'] = torch.zeros_like(
                        p.data, dtype=torch.int8)
                    state['exp_avg_sq'] = torch.zeros_like(
                        p.data, dtype=torch.int8)
                    state['scale_m'] = torch.ones(
                        p.data.numel() // self.block_size + 1)
                    state['scale_v'] = torch.ones(
                        p.data.numel() // self.block_size + 1)

                state['step'] += 1
                beta1, beta2 = group['betas']

                # Dequantize → update → requantize (fused Triton kernel)
                _flash_optim_update_kernel(
                    p.data, grad,
                    state['exp_avg'], state['exp_avg_sq'],
                    state['scale_m'], state['scale_v'],
                    beta1, beta2, group['lr'], group['eps'],
                    group['weight_decay'], state['step'],
                    self.block_size
                )

@triton.jit
def _flash_optim_update_kernel(
    param_ptr, grad_ptr, m_ptr, v_ptr,
    scale_m_ptr, scale_v_ptr,
    beta1, beta2, lr, eps, wd, step, block_size,
    BLOCK_SIZE: tl.constexpr
):
    """Fused dequant → Adam update → requant in single kernel pass."""
    pid = tl.program_id(0)
    offsets = pid * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)

    # Load INT8 states and scales
    m_int8 = tl.load(m_ptr + offsets)
    v_int8 = tl.load(v_ptr + offsets)
    scale_m = tl.load(scale_m_ptr + pid)
    scale_v = tl.load(scale_v_ptr + pid)

    # Dequantize
    m = m_int8.to(tl.float32) * scale_m / 127.0
    v = v_int8.to(tl.float32) * scale_v / 127.0

    # Load grad and param
    grad = tl.load(grad_ptr + offsets).to(tl.float32)
    param = tl.load(param_ptr + offsets).to(tl.float32)

    # Adam update
    m = beta1 * m + (1 - beta1) * grad
    v = beta2 * v + (1 - beta2) * grad * grad
    m_hat = m / (1 - beta1 ** step)
    v_hat = v / (1 - beta2 ** step)
    param = param - lr * (m_hat / (tl.sqrt(v_hat) + eps) + wd * param)

    # Requantize with new scales
    new_scale_m = tl.max(tl.abs(m)) / 127.0 + 1e-8
    new_scale_v = tl.max(tl.abs(v)) / 127.0 + 1e-8
    m_int8_new = (m / new_scale_m).to(tl.int8)
    v_int8_new = (v / new_scale_v).to(tl.int8)

    # Store results
    tl.store(param_ptr + offsets, param.to(tl.bfloat16))
    tl.store(m_ptr + offsets, m_int8_new)
    tl.store(v_ptr + offsets, v_int8_new)
    tl.store(scale_m_ptr + pid, new_scale_m)
    tl.store(scale_v_ptr + pid, new_scale_v)


# --- 2. Tissue Mechanics Dataset ---
class TissueMechanicsDataset(torch.utils.data.Dataset):
    """
    Tokenized FEM simulation data.
    Input: boundary conditions (forces, displacements) as token sequences.
    Output: stress/strain field tokens.
    """
    def __init__(self, data_path, tokenizer, max_length=2048):
        self.data = torch.load(data_path)  # List of (BC, stress, strain) tuples
        self.tokenizer = tokenizer
        self.max_length = max_length

    def __len__(self):
        return len(self.data)

    def __getitem__(self, idx):
        bc, stress, strain = self.data[idx]
        # Tokenize: "BC: [values] -> STRESS: [values] STRAIN: [values]"
        text = f"BC: {bc.tolist()} -> STRESS: {stress.tolist()}"
        tokens = self.tokenizer(text, max_length=self.max_length,
                               truncation=True, return_tensors='pt')
        return tokens


# --- 3. Memory Profiling Harness ---
class MemoryProfiler:
    def __init__(self):
        self.snapshots = []

    def record(self, label):
        torch.cuda.synchronize()
        stats = torch.cuda.memory_stats()
        self.snapshots.append({
            'label': label,
            'peak_allocated_gb': stats['allocated_bytes.all.peak'] / 1e9,
            'current_allocated_gb': stats['allocated_bytes.all.current'] / 1e9,
            'reserved_gb': stats['reserved_bytes.all.current'] / 1e9
        })

    def report(self):
        return {s['label']: s['peak_allocated_gb'] for s in self.snapshots}


# --- 4. Main Experiment Loop ---
def run_experiment(optimizer_name, model_name, dataset_path,
                   batch_size=32, seq_len=2048, n_steps=1000, seed=42):
    torch.manual_seed(seed)
    torch.cuda.reset_peak_memory_stats()

    # Load model
    model = AutoModelForCausalLM.from_pretrained(
        model_name, torch_dtype=torch.bfloat16).cuda()
    tokenizer = AutoTokenizer.from_pretrained(model_name)

    # Select optimizer
    if optimizer_name == 'adamw':
        optimizer = torch.optim.AdamW(model.parameters(), lr=2e-5,
                                      weight_decay=0.01)
    elif optimizer_name == 'adam8bit':
        import bitsandbytes as bnb
        optimizer = bnb.optim.Adam8bit(model.parameters(), lr=2e-5)
    elif optimizer_name == 'flashoptim':
        optimizer = FlashOptim(model.parameters(), lr=2e-5,
                               block_size=2048)

    # Dataset
    dataset = TissueMechanicsDataset(dataset_path, tokenizer, seq_len)
    loader = torch.utils.data.DataLoader(dataset, batch_size=batch_size)

    profiler = MemoryProfiler()
    profiler.record('pre_training')

    losses = []
    for step, batch in enumerate(loader):
        if step >= n_steps:
            break
        batch = {k: v.cuda() for k, v in batch.items()}
        outputs = model(**batch, labels=batch['input_ids'])
        loss = outputs.loss
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()
        losses.append(loss.item())

        if step % 100 == 0:
            profiler.record(f'step_{step}')

    profiler.record('post_training')

    return {
        'optimizer': optimizer_name,
        'model': model_name,
        'memory_profile': profiler.report(),
        'peak_memory_gb': torch.cuda.max_memory_allocated() / 1e9,
        'final_loss': losses[-1],
        'loss_curve': losses
    }


# --- 5. Accuracy Evaluation ---
def evaluate_tissue_accuracy(model, test_loader, device='cuda'):
    """Compute relative L2 error on stress/strain predictions."""
    model.eval()
    total_l2_error = 0.0
    total_norm = 0.0

    with torch.no_grad():
        for batch in test_loader:
            inputs = batch['input_ids'].to(device)
            targets = batch['stress_targets'].to(device)  # Ground truth FEM
            predictions = model.generate(inputs, max_new_tokens=256)
            pred_stress = decode_stress_tokens(predictions)  # Domain decoder
            l2_error = torch.norm(pred_stress - targets)
            total_l2_error += l2_error.item()
            total_norm += torch.norm(targets).item()

    return total_l2_error / total_norm  # Relative L2 error


# --- 6. Comparison Runner ---
def run_full_comparison():
    results = {}
    configs = [
        ('adamw', 'meta-llama/Llama-2-7b-hf'),
        ('adam8bit', 'meta-llama/Llama-2-7b-hf'),
        ('flashoptim', 'meta-llama/Llama-2-7b-hf'),
    ]
    for opt_name, model_name in configs:
        seed_results = []
        for seed in [42, 123, 777]:
            r = run_experiment(opt_name, model_name,
                              'data/tissue_mechanics_train.pt',
                              seed=seed)
            seed_results.append(r)
        results[opt_name] = seed_results

    # Compute memory reduction
    adamw_mem = np.mean([r['peak_memory_gb'] for r in results['adamw']])
    flashoptim_mem = np.mean([r['peak_memory_gb']
                              for r in results['flashoptim']])
    reduction_pct = (adamw_mem - flashoptim_mem) / adamw_mem * 100

    print(f"AdamW peak memory: {adamw_mem:.2f} GB")
    print(f"FlashOptim peak memory: {flashoptim_mem:.2f} GB")
    print(f"Memory reduction: {reduction_pct:.1f}%")

    # Statistical test
    from scipy.stats import wilcoxon
    adamw_mems = [r['peak_memory_gb'] for r in results['adamw']]
    fo_mems = [r['peak_memory_gb'] for r in results['flashoptim']]
    stat, p_val = wilcoxon(adamw_mems, fo_mems)
    print(f"Wilcoxon p-value: {p_val:.4f}")

    return results, reduction_pct, p_val


if __name__ == '__main__':
    results, reduction, p = run_full_comparison()
    print(f"SUCCESS: {reduction >= 20.0 and p < 0.05}")