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// ITER8: Algebraic Invariant Falsification (Spec §7.6)
//
// These tests verify the compile-time algebraic proofs described in §3.14
// and §5.6 of the spec. Each test corresponds to a FALSIFY-ALG-xxx prediction
// backed by a specific peer-reviewed result. The build.rs const_assert!
// enforcement catches violations at build time; these tests provide a second
// independent verification path through runtime computation.
// =============================================================================
#[test]
fn falsify_alg_001_attention_head_divisibility_vaswani_2017() {
// Vaswani et al. (2017) §3.2.2: Multi-Head Attention requires
// hidden_dim = num_heads * d_k, thus hidden_dim % num_heads == 0.
// This is also enforced at compile time by build.rs const_assert.
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
for (size_name, size_config) in &config.size_variants {
if size_config.hidden_dim > 0 && size_config.num_heads > 0 {
assert_eq!(
size_config.hidden_dim % size_config.num_heads,
0,
"FALSIFY-ALG-001 Vaswani (2017): {family_name}/{size_name} \
hidden_dim={} not divisible by num_heads={}",
size_config.hidden_dim,
size_config.num_heads
);
}
}
}
}
#[test]
fn falsify_alg_002_gqa_group_divisibility_ainslie_2023() {
// Ainslie et al. (2023) §2: GQA partitions query heads into groups
// sharing KV heads. num_heads % num_kv_heads == 0 required.
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
for (size_name, size_config) in &config.size_variants {
if size_config.num_heads > 0 && size_config.num_kv_heads > 0 {
assert_eq!(
size_config.num_heads % size_config.num_kv_heads,
0,
"FALSIFY-ALG-002 Ainslie (2023) GQA: {family_name}/{size_name} \
num_heads={} not divisible by num_kv_heads={}",
size_config.num_heads,
size_config.num_kv_heads
);
// Additionally: num_kv_heads <= num_heads always
assert!(
size_config.num_kv_heads <= size_config.num_heads,
"FALSIFY-ALG-002: {family_name}/{size_name} \
num_kv_heads={} > num_heads={}",
size_config.num_kv_heads,
size_config.num_heads
);
}
}
}
}
#[test]
fn falsify_alg_002_gqa_special_cases() {
// Verify per-size attention classification matches the mathematical definition:
// - MHA: num_kv_heads == num_heads (every head has its own KV)
// - MQA: num_kv_heads == 1 (all heads share one KV pair)
// - GQA: 1 < num_kv_heads < num_heads
//
// Note: Family-level attention_type is a general descriptor. Some families
// (e.g., Gemma) mix attention strategies across sizes (2B=MQA, 7B=MHA).
// We verify that the per-size HEAD CONFIGURATION is mathematically valid,
// not that it matches the family-level label.
use aprender::format::model_family::AttentionType;
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
let constraints = family.constraints();
for (size_name, size_config) in &config.size_variants {
let nh = size_config.num_heads;
let nkv = size_config.num_kv_heads;
if nh == 0 || nkv == 0 {
continue;
}
// Every size must be one of: MHA, MQA, or GQA (exhaustive)
let is_mha = nkv == nh;
let is_mqa = nkv == 1 && nh > 1;
let is_gqa = nkv > 1 && nkv < nh;
let is_single = nh == 1 && nkv == 1;
assert!(
is_mha || is_mqa || is_gqa || is_single,
"FALSIFY-ALG-002 special: {family_name}/{size_name} \
num_heads={nh} num_kv_heads={nkv} doesn't classify as MHA/MQA/GQA"
);
// For families declaring MHA, all sizes must be MHA
if constraints.attention_type == AttentionType::Mha {
assert!(
is_mha || is_single,
"FALSIFY-ALG-002 special: {family_name}/{size_name} declared MHA \
but num_kv_heads={nkv} != num_heads={nh}"
);
}
}
}
}
#[test]
fn falsify_alg_003_head_dim_lower_bound() {
// head_dim >= hidden_dim / num_heads.
// Standard models: head_dim == hidden_dim / num_heads.
// Expanded attention (Gemma): head_dim > hidden_dim / num_heads.
// head_dim < hidden_dim / num_heads would be information loss.
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
for (size_name, size_config) in &config.size_variants {
if size_config.hidden_dim == 0 || size_config.num_heads == 0 {
continue;
}
let standard_head_dim = size_config.hidden_dim / size_config.num_heads;
assert!(
size_config.head_dim >= standard_head_dim,
"FALSIFY-ALG-003: {family_name}/{size_name} head_dim={} < \
hidden_dim/num_heads={standard_head_dim} — information loss",
size_config.head_dim
);
}
}
}
#[test]
fn falsify_alg_004_ffn_expansion_shazeer_2020() {
// Shazeer (2020) §3: FFN intermediate_dim > hidden_dim for expansion.
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
for (size_name, size_config) in &config.size_variants {
if size_config.intermediate_dim == 0 || size_config.hidden_dim == 0 {
continue;
}
assert!(
size_config.intermediate_dim > size_config.hidden_dim,
"FALSIFY-ALG-004 Shazeer (2020): {family_name}/{size_name} \
intermediate_dim={} <= hidden_dim={}",
size_config.intermediate_dim,
size_config.hidden_dim
);
// Verify expansion ratio is in reasonable range (>1.5x, <10x)
let ratio = size_config.intermediate_dim as f64 / size_config.hidden_dim as f64;
assert!(
(1.5..10.0).contains(&ratio),
"FALSIFY-ALG-004: {family_name}/{size_name} FFN expansion ratio \
{ratio:.2} outside reasonable range [1.5, 10.0]"
);
}
}
}
#[test]
fn falsify_alg_005_non_degeneracy() {
// Every model must have positive hidden_dim, num_layers, num_heads, vocab_size.
// A degenerate model (zero of any) computes nothing meaningful.
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
for (size_name, size_config) in &config.size_variants {
assert!(
size_config.hidden_dim > 0,
"FALSIFY-ALG-005: {family_name}/{size_name} hidden_dim == 0 (degenerate)"
);
assert!(
size_config.num_layers > 0,
"FALSIFY-ALG-005: {family_name}/{size_name} num_layers == 0 (degenerate)"
);
assert!(
size_config.num_heads > 0,
"FALSIFY-ALG-005: {family_name}/{size_name} num_heads == 0 (degenerate)"
);
assert!(
size_config.vocab_size > 0,
"FALSIFY-ALG-005: {family_name}/{size_name} vocab_size == 0 (degenerate)"
);
}
}
}
#[test]
fn falsify_alg_006_activation_mlp_consistency_shazeer_2020() {
// Shazeer (2020) Table 1: activation and MLP type must be consistent.
// SwiGLU = SiLU + gated → requires activation=silu, mlp=swiglu
// GeGLU = GELU + gated → requires activation=gelu, mlp=gated_mlp
// Standard FFN → requires activation=gelu, mlp=gelu_mlp
use aprender::format::model_family::{Activation, MlpType};
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let constraints = family.constraints();
match constraints.mlp_type {
MlpType::SwiGlu => {
assert_eq!(
constraints.activation,
Activation::Silu,
"FALSIFY-ALG-006 Shazeer (2020): {family_name} SwiGLU requires SiLU \
activation, got {:?}",
constraints.activation
);
}
MlpType::GeluMlp => {
assert_eq!(
constraints.activation,
Activation::Gelu,
"FALSIFY-ALG-006: {family_name} GeluMlp requires GELU activation, \
got {:?}",
constraints.activation
);
}
MlpType::GatedMlp => {
// GatedMlp can use GELU (GeGLU) or SiLU (SwiGLU-style gating)
assert!(
matches!(constraints.activation, Activation::Gelu | Activation::Silu),
"FALSIFY-ALG-006: {family_name} GatedMlp requires GELU or SiLU \
activation, got {:?}",
constraints.activation
);
}
}
}
}
#[test]
fn falsify_alg_007_rope_requirements_su_2024() {
// Su et al. (2024) §3.4: RoPE requires:
// 1. rope_theta > 0 (frequency base must be positive)
// 2. head_dim % 2 == 0 (cos/sin pairs need even dimensions)
// 3. max_position_embeddings > 0 (context window must be positive)
use aprender::format::model_family::PositionalEncoding;
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
let constraints = family.constraints();
if constraints.positional_encoding != PositionalEncoding::Rope {
continue;
}
for (size_name, size_config) in &config.size_variants {
assert!(
size_config.rope_theta > 0.0,
"FALSIFY-ALG-007 Su (2024): {family_name}/{size_name} \
rope_theta={} must be > 0 for RoPE",
size_config.rope_theta
);
if size_config.head_dim > 0 {
assert_eq!(
size_config.head_dim % 2,
0,
"FALSIFY-ALG-007 Su (2024): {family_name}/{size_name} \
head_dim={} must be even for RoPE cos/sin pairs",
size_config.head_dim
);
}
assert!(
size_config.max_position_embeddings > 0,
"FALSIFY-ALG-007 Su (2024): {family_name}/{size_name} \
max_position_embeddings must be > 0 for RoPE models"
);
}
}
}
#[test]
fn falsify_alg_007_non_rope_no_theta_requirement() {
// Converse of ALG-007: non-RoPE models (BERT, Whisper) should have
// rope_theta == 0.0 (they don't use it). This catches YAML entry errors
// where someone accidentally sets rope_theta for an absolute-position model.
use aprender::format::model_family::PositionalEncoding;
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
let config = family.config();
let constraints = family.constraints();
if constraints.positional_encoding == PositionalEncoding::Rope {
continue;
}
for (size_name, size_config) in &config.size_variants {
// Non-RoPE models should not have theta set (or it should be 0)
assert!(
size_config.rope_theta == 0.0 || size_config.rope_theta == 10000.0,
"FALSIFY-ALG-007 converse: {family_name}/{size_name} \
is {:?} but has rope_theta={} — should be 0 or default",
constraints.positional_encoding,
size_config.rope_theta
);
}
}
}
#[test]
fn falsify_alg_build_time_constants_exported() {
// Verify that build.rs exports the new HEAD_DIM and MAX_POSITION_EMBEDDINGS
// constants alongside the existing ones. This proves the const_assert!
// enforcement in build.rs has access to these values.
use aprender::format::model_family::{QWEN2_0_5B_HIDDEN_DIM, QWEN2_0_5B_NUM_HEADS};
// The fact that these constants exist and compile proves build.rs
// emits them. Verify a known value.
assert_eq!(QWEN2_0_5B_HIDDEN_DIM, 896);
assert_eq!(QWEN2_0_5B_NUM_HEADS, 14);
// Verify the Vaswani divisibility holds for these compile-time constants
assert_eq!(QWEN2_0_5B_HIDDEN_DIM % QWEN2_0_5B_NUM_HEADS, 0);
}
#[test]
fn falsify_alg_226_compile_time_proofs_exist() {
// META-FALSIFICATION: The generated code must contain const assertions.
// We verify this by checking that the number of families * sizes * proofs
// matches our expectation. If build.rs stops generating proofs, this catches it.
let registry = build_default_registry();
let mut total_sizes = 0_usize;
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
total_sizes += family.config().size_variants.len();
}
// Each size gets at least: 4 non-degeneracy + 1 Vaswani + 1 GQA + 1 head_dim + 1 FFN = 8
// RoPE families get 2 more (head_dim even + max_pos_embeddings > 0)
// Minimum: 8 proofs per size
let min_expected_proofs = total_sizes * 4; // conservative lower bound
assert!(
total_sizes >= 8,
"Expected at least 8 model families * sizes, got {total_sizes}"
);
assert!(
min_expected_proofs >= 32,
"Expected at least 32 compile-time proofs, minimum estimate {min_expected_proofs}"
);
}
// =============================================================================
// §7.6 — FALSIFY-ALG-005 (iter9): num_kv_heads non-degeneracy
// =============================================================================
//
// Prediction: Every model family size variant must have num_kv_heads > 0.
// A model with zero KV heads cannot compute attention.
//
// Found via falsification round 2: num_kv_heads=0 passed all proofs
// because non-degeneracy only checked hidden_dim, num_layers, num_heads, vocab_size.
// Fixed: build.rs now emits NUM_KV_HEADS > 0 assertion for all sizes.
#[test]
fn falsify_alg_005_num_kv_heads_nonzero() {
let registry = build_default_registry();
for family_name in KNOWN_FAMILIES {
let family = registry.get(family_name).expect("family exists");
for (size_name, size_config) in &family.config().size_variants {
assert!(
size_config.num_kv_heads > 0,
"FALSIFY-ALG-005 (iter9): {family_name}/{size_name} has num_kv_heads=0 — \
attention requires at least 1 KV head"
);
}
}
}
// =============================================================================