MLX Apple Silicon Skill

"Unified memory means no GPU↔CPU transfers - arrays live in shared memory."

Trit: +1 (PLUS - generative) Color: Warm (optimistic/fast)

Overview

MLX is Apple's ML framework for Apple Silicon:

• Unified Memory: No GPU↔CPU data transfers
• Lazy Evaluation: Compute only what's needed
• Metal Backend: Native GPU acceleration
• 4-bit Quantization: 75% smaller models

MLX-LM provides high-level LLM APIs.

Quick Start

# Install (macOS Apple Silicon)
pip install mlx mlx-lm

# Install (Linux CUDA - v0.28+)
pip install "mlx[cuda]"

# Generate text
mlx_lm.generate --model mlx-community/Mistral-7B-Instruct-v0.3-4bit \
  --prompt "Hello" --max-tokens 100

# Interactive chat
mlx_lm.chat --model mlx-community/Mistral-7B-Instruct-v0.3-4bit

# Vision/Multimodal (mlx-vlm)
pip install mlx-vlm
mlx_vlm.chat --model mlx-community/Qwen2.5-VL-7B-Instruct-4bit

Python API

Basic Generation

from mlx_lm import load, generate

# Load 4-bit quantized model
model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

# Generate
messages = [{"role": "user", "content": "Write a haiku"}]
prompt = tokenizer.apply_chat_template(messages, add_generation_prompt=True)
text = generate(model, tokenizer, prompt=prompt, max_tokens=100)
print(text)

Streaming Generation

from mlx_lm import load, stream_generate

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

for response in stream_generate(model, tokenizer, prompt="Hello", max_tokens=100):
    print(response.text, end="", flush=True)
    # response.token, response.logprobs, response.generation_tps available

Batch Generation

from mlx_lm import load, batch_generate

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

prompts = ["Story about AI", "Explain ML", "Write a poem"]
result = batch_generate(model, tokenizer, prompts, max_tokens=100)

for text in result.texts:
    print(text)

Sampling Control

from mlx_lm import load, generate
from mlx_lm.sample_utils import make_sampler

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

sampler = make_sampler(
    temp=0.7,              # Temperature
    top_p=0.9,             # Nucleus sampling
    top_k=50,              # Top-k sampling
    min_p=0.05,            # Min probability threshold
    repetition_penalty=1.1
)

text = generate(model, tokenizer, prompt="Tell me a joke", sampler=sampler)

Prompt Caching (Multi-turn)

from mlx_lm import load, stream_generate
from mlx_lm.models.cache import make_prompt_cache, save_prompt_cache, load_prompt_cache

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

# Create cache for system prompt + context
system = "You are an expert. " + long_context
cache = make_prompt_cache(model)

# Prime the cache
for r in stream_generate(model, tokenizer, system, prompt_cache=cache, max_tokens=1):
    break

# Save for reuse
save_prompt_cache("my_cache.safetensors", cache)

# Later: reuse with different queries
cache = load_prompt_cache("my_cache.safetensors")
for r in stream_generate(model, tokenizer, "What is 2+2?", prompt_cache=cache, max_tokens=50):
    print(r.text, end="", flush=True)

KV Cache Rotation (Long Sequences)

from mlx_lm import load, generate

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")

# Limit KV cache to 512 tokens (bounded memory for long sequences)
text = generate(
    model, tokenizer,
    prompt="Very long context...",
    max_kv_size=512,
    max_tokens=1000
)

Speculative Decoding

from mlx_lm import load, stream_generate

# Main model
model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")
# Faster draft model
draft_model, _ = load("mlx-community/Mistral-3B-Instruct-4bit")

for r in stream_generate(
    model, tokenizer,
    prompt="Tell me about ML",
    draft_model=draft_model,
    num_draft_tokens=3,
    max_tokens=512
):
    print(r.text, end="", flush=True)

Model Conversion & Quantization

from mlx_lm import convert

# Download, quantize, and optionally upload
convert(
    hf_path="mistralai/Mistral-7B-Instruct-v0.3",
    mlx_path="./my-mistral-4bit",
    quantize=True,
    q_bits=4,           # 4-bit, 8-bit, or MXFP4/NVFP4
    q_group_size=64,
    dtype="float16",
    upload_repo="mlx-community/my-mistral-4bit"  # Optional
)

# CLI conversion
mlx_lm.convert --hf-path mistralai/Mistral-7B-Instruct-v0.3 \
  -q --upload-repo mlx-community/my-mistral-4bit

LoRA/QLoRA Fine-Tuning

LoRALinear Adapter

import mlx.core as mx
import mlx.nn as nn

class LoRALinear(nn.Module):
    """Low-Rank Adaptation: W' = W + scale * (A @ B)"""
    def __init__(self, input_dims, output_dims, r=8, scale=20.0, dropout=0.0):
        self.linear = nn.Linear(input_dims, output_dims)
        self.dropout = nn.Dropout(p=dropout)
        self.scale = scale
        # A: (input, r), B: (r, output) - B zero-init for stable start
        self.lora_a = mx.random.uniform(low=-1/mx.sqrt(input_dims), 
                                         high=1/mx.sqrt(input_dims), 
                                         shape=(input_dims, r))
        self.lora_b = mx.zeros((r, output_dims))
    
    def __call__(self, x):
        y = self.linear(x)
        z = (self.dropout(x) @ self.lora_a) @ self.lora_b
        return y + (self.scale * z).astype(x.dtype)

Training Loop with Gradient Accumulation

from functools import partial
import mlx.optimizers as optim

# Freeze base, unfreeze LoRA layers
model.freeze()
for l in model.model.layers[-16:]:  # Last 16 layers
    l.self_attn.q_proj = LoRALinear.from_linear(l.self_attn.q_proj)
    l.self_attn.v_proj = LoRALinear.from_linear(l.self_attn.v_proj)

optimizer = optim.Adam(learning_rate=1e-5)

def loss_fn(model, inputs, targets, lengths):
    logits = model(inputs)
    mask = build_mask(lengths)
    ce = nn.losses.cross_entropy(logits, targets) * mask
    return ce.sum() / mask.sum()

loss_and_grad = nn.value_and_grad(model, loss_fn)

# Compiled step with gradient accumulation
@partial(mx.compile, inputs=model.state, outputs=model.state)
def step(batch, accumulated_grad, do_update, accum_steps):
    loss, grad = loss_and_grad(model, *batch)
    if accumulated_grad:
        grad = tree_map(lambda a, b: a + b, grad, accumulated_grad)
    if do_update:
        grad = tree_map(lambda g: g / accum_steps, grad)
        optimizer.update(model, grad)
        grad = None
    return loss, grad

# Gradient checkpointing for memory
mx.checkpoint(layer.__call__)  # Recompute activations in backward

CLI Fine-Tuning

mlx_lm.lora --model mlx-community/Mistral-7B-Instruct-v0.3-4bit \
  --data ./train.jsonl --iters 1000 --batch-size 4 \
  --lora-layers 16 --lora-rank 8 --learning-rate 1e-5 \
  --adapter-path ./adapters

Sampling Strategies

from mlx_lm.sample_utils import make_sampler

# Temperature: higher = more random
# Top-K: keep top K tokens only
# Top-P (nucleus): keep tokens until cumsum(prob) > p
# Min-P: keep tokens with prob > top_prob * min_p
# Repetition penalty: discourage repeated tokens

sampler = make_sampler(
    temp=0.7,
    top_p=0.9,
    top_k=50,
    min_p=0.05,
    repetition_penalty=1.1,
    repetition_context_size=100
)

# Sampler internals:
# 1. Apply repetition penalty to seen tokens
# 2. Apply top-k filter (argpartition)
# 3. Apply min-p filter (relative to top logprob)
# 4. Apply top-p filter (cumulative threshold)
# 5. Sample with temperature: categorical(logits / temp)

Generation Loop Internals

# Prefill: process prompt in chunks
for i in range(0, len(prompt), prefill_step_size):
    chunk = prompt[i:i+prefill_step_size]
    _ = model(chunk, cache=cache)

# Decode: async token generation
stream = mx.new_stream(mx.default_device())
with mx.stream(stream):
    for _ in range(max_tokens):
        logits = model(tokens[None], cache=cache)[:, -1, :]
        logprobs = logits - mx.logsumexp(logits, keepdims=True)
        token = sampler(logprobs)
        mx.async_eval(token)
        yield token

Speculative Decoding

from mlx_lm import load, stream_generate

# Main model + faster draft model
model, tok = load("mlx-community/Mistral-7B-4bit")
draft, _ = load("mlx-community/Mistral-1B-4bit")

for r in stream_generate(
    model, tok, prompt="...",
    draft_model=draft,
    num_draft_tokens=4,  # Draft generates 4, main verifies
):
    print(r.text, end="")
# Pattern: draft → verify → accept prefix → rewind cache

Supported Models

Text Models (mlx-lm)

• Llama (2, 3, 3.2, 3.3)
• Mistral (v0.1-v0.3, Nemo)
• Phi (3, 3.5, 4)
• Gemma (2, 3)
• Qwen (2, 2.5, 3, Coder)
• DeepSeek (v2, v3, R1)
• Mixtral (MoE 8x7B, 8x22B)
• 100+ more on mlx-community

Vision/Multimodal (mlx-vlm)

• Qwen-VL (2, 2.5, 3)
• LLaVA (1.5, 1.6, NeXT, Interleave)
• PaliGemma (2)
• Pixtral (12B)
• Molmo (7B, 72B)
• DeepSeek-VL (v2)
• Phi-3-Vision, Florence2, Idefics3

# Vision example
from mlx_vlm import load, generate
model, processor = load("mlx-community/Qwen2.5-VL-7B-Instruct-4bit")
output = generate(model, processor, "image.jpg", "Describe this image")

Core MLX Concepts

Unified Memory

import mlx.core as mx

# Arrays live in shared memory - no GPU↔CPU transfers
a = mx.random.normal((1000, 1000))
b = mx.random.normal((1000, 1000))
c = mx.matmul(a, b)  # Automatic device selection, no data copy

Lazy Evaluation

import mlx.core as mx

a = mx.ones((1000, 1000))
b = mx.ones((1000, 1000))
c = mx.matmul(a, b)  # Not computed yet

mx.eval(c)  # Now computed

Composable Transforms

import mlx.core as mx

def loss_fn(w, x, y):
    return mx.mean((mx.matmul(x, w) - y) ** 2)

# Automatic differentiation
grad_fn = mx.grad(loss_fn)

# Vectorization
vmap_fn = mx.vmap(loss_fn)

Performance

GF(3) Triads

mlx-apple-silicon (+1) ⊗ unworld (0) ⊗ segal-types (-1) = 0 ✓
mlx-apple-silicon (+1) ⊗ gay-mcp (0) ⊗ temporal-coalgebra (-1) = 0 ✓
mlx-apple-silicon (+1) ⊗ rama-gay-clojure (0) ⊗ bisimulation-game (-1) = 0 ✓

Commands

# Generate
mlx_lm.generate --model MODEL --prompt "..." --max-tokens N

# Chat
mlx_lm.chat --model MODEL

# Convert
mlx_lm.convert --hf-path HF_MODEL -q --mlx-path ./local

# Cache prompt
mlx_lm.cache_prompt --model MODEL --prompt "..." --prompt-cache-file cache.safetensors

# LoRA fine-tune
mlx_lm.lora --model MODEL --data ./data --output ./lora-adapters

Integration with Gay.jl Coloring

from mlx_lm import load, stream_generate

# Each generation step can be colored by trit
GOLDEN = 0x9E3779B97F4A7C15

def splitmix64(x):
    z = (x + GOLDEN) & 0xFFFFFFFFFFFFFFFF
    z = ((z ^ (z >> 30)) * 0xBF58476D1CE4E5B9) & 0xFFFFFFFFFFFFFFFF
    z = ((z ^ (z >> 27)) * 0x94D049BB133111EB) & 0xFFFFFFFFFFFFFFFF
    return (z ^ (z >> 31)) & 0xFFFFFFFFFFFFFFFF

def token_to_trit(token_id, seed):
    h = splitmix64(seed ^ token_id)
    return (h % 3) - 1  # {-1, 0, +1}

model, tokenizer = load("mlx-community/Mistral-7B-Instruct-v0.3-4bit")
seed = 0x42D

for i, r in enumerate(stream_generate(model, tokenizer, prompt="Hello", max_tokens=10)):
    trit = token_to_trit(r.token, seed + i)
    print(f"{r.text} [trit={trit:+d}]", end=" ")

Model Architecture Internals (LLaMA)

Attention with Grouped Query Attention (GQA)

class Attention(nn.Module):
    def __init__(self, args):
        self.n_heads = args.num_attention_heads      # e.g., 32
        self.n_kv_heads = args.num_key_value_heads   # e.g., 8 (GQA compression)
        self.head_dim = args.hidden_size // self.n_heads
        self.scale = self.head_dim ** -0.5
        
        self.q_proj = nn.Linear(dim, self.n_heads * self.head_dim)
        self.k_proj = nn.Linear(dim, self.n_kv_heads * self.head_dim)
        self.v_proj = nn.Linear(dim, self.n_kv_heads * self.head_dim)
        self.o_proj = nn.Linear(self.n_heads * self.head_dim, dim)
        self.rope = initialize_rope(...)
    
    def __call__(self, x, mask=None, cache=None):
        B, L, D = x.shape
        q = self.q_proj(x).reshape(B, L, self.n_heads, -1).transpose(0, 2, 1, 3)
        k = self.k_proj(x).reshape(B, L, self.n_kv_heads, -1).transpose(0, 2, 1, 3)
        v = self.v_proj(x).reshape(B, L, self.n_kv_heads, -1).transpose(0, 2, 1, 3)
        
        # RoPE: Rotary Position Embeddings (θ_i = base^(-2i/d))
        q, k = self.rope(q, offset=cache.offset if cache else 0), self.rope(k, offset=cache.offset if cache else 0)
        
        if cache:
            k, v = cache.update_and_fetch(k, v)
        
        out = mx.fast.scaled_dot_product_attention(q, k, v, scale=self.scale, mask=mask)
        return self.o_proj(out.transpose(0, 2, 1, 3).reshape(B, L, -1))

SwiGLU MLP

class MLP(nn.Module):
    def __call__(self, x):
        # SwiGLU: Down(SiLU(Gate(x)) ⊙ Up(x))
        return self.down_proj(nn.silu(self.gate_proj(x)) * self.up_proj(x))

TransformerBlock (Pre-Norm)

class TransformerBlock(nn.Module):
    def __call__(self, x, mask=None, cache=None):
        h = x + self.self_attn(self.input_layernorm(x), mask, cache)
        return h + self.mlp(self.post_attention_layernorm(h))

Automatic Differentiation

import mlx.core as mx
import mlx.nn as nn
import mlx.optimizers as optim

def loss_fn(model, x, y):
    logits = model(x)
    return mx.mean(nn.losses.cross_entropy(logits, y))

# Value and gradient in one pass
loss_and_grad_fn = nn.value_and_grad(model, loss_fn)
loss, grads = loss_and_grad_fn(model, inputs, targets)

# Gradient clipping + optimizer step
grads = optim.clip_grad_norm(grads, max_norm=1.0)
optimizer.update(model, grads)
mx.eval(model.parameters(), optimizer.state)

Gradient Flow Through Attention

∂L/∂values ← softmax_backward(attention_weights, ∂L/∂output)
∂L/∂scores ← attention_weights^T @ ∂L/∂output
∂L/∂keys   ← queries^T @ ∂L/∂scores  
∂L/∂queries ← ∂L/∂scores @ keys
# All fused in mx.fast.scaled_dot_product_attention backward

RoPE Variants

KV Cache Strategies

# Standard incremental cache
cache = KVCache()  # Pre-allocates in 256-token chunks

# Rotating cache for sliding window attention (Mistral, LLaMA 3.2)
cache = RotatingKVCache(max_size=4096, keep=4)  # keep=N attention sinks

# Prompt caching (reuse system prompt)
from mlx_lm.models.cache import make_prompt_cache, save_prompt_cache
cache = make_prompt_cache(model)
save_prompt_cache("system.safetensors", cache)

Latent Space Topology

Extracting Hidden States

# Hook into transformer layers for latent analysis
def extract_activations(model, inputs):
    activations = []
    h = model.model.embed_tokens(inputs)
    for layer in model.model.layers:
        h = layer(h, mask=None, cache=None)
        activations.append(h.copy())  # Snapshot each layer
    return activations

# Analyze residual stream
residual_norms = [mx.linalg.norm(a, axis=-1).mean() for a in activations]

Hyperbolic Distance (Beyond Euclid)

def poincare_distance(u, v, eps=1e-5):
    """Hyperbolic distance in Poincaré ball model"""
    diff = u - v
    norm_u = mx.linalg.norm(u, axis=-1, keepdims=True)
    norm_v = mx.linalg.norm(v, axis=-1, keepdims=True)
    norm_diff = mx.linalg.norm(diff, axis=-1, keepdims=True)
    
    denom = (1 - norm_u**2) * (1 - norm_v**2) + eps
    return mx.arccosh(1 + 2 * norm_diff**2 / denom)

# For attention patterns: heads form hyperbolic tree structures
# Low curvature → flat Euclidean, High curvature → hierarchical

Active Inference Integration

def free_energy(model, x, prior_mean, prior_var):
    """Variational free energy for active inference"""
    # Prediction: forward pass gives expected sensory input
    pred = model(x)
    
    # Prediction error (likelihood)
    pred_error = mx.mean((pred - x) ** 2)
    
    # Complexity (KL divergence from prior)
    posterior = model.model.layers[-1].self_attn.rope  # Use RoPE as approximate posterior
    kl = 0.5 * mx.sum(posterior / prior_var + mx.log(prior_var) - 1)
    
    return pred_error + kl  # Minimize to update beliefs

References

• ml-explore/mlx (23K★)
• ml-explore/mlx-lm (3.1K★)
• mlx-community on HuggingFace
• MLX Documentation
• LLaMA model implementation

Skill Name: mlx-apple-silicon Type: LLM Inference / Apple Silicon / Autodiff Trit: +1 (PLUS - generative) GF(3): Generates tokens deterministically Platform: macOS with Apple Silicon Active Inference: Supports latent space extraction + free energy minimization

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Autodiff

• jax [○] via bicomodule
  • Automatic differentiation

Bibliography References

• general: 734 citations in bib.duckdb

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 5. Evaluation

Concepts: eval, apply, interpreter, environment

GF(3) Balanced Triad

mlx-apple-silicon (−) + SDF.Ch5 (−) + [balancer] (−) = 0

Skill Trit: -1 (MINUS - verification)

Secondary Chapters

• Ch3: Variations on an Arithmetic Theme
• Ch4: Pattern Matching
• Ch6: Layering
• Ch10: Adventure Game Example
• Ch1: Flexibility through Abstraction

Connection Pattern

Evaluation interprets expressions. This skill processes or generates evaluable forms.

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.