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tp4-feature-learning Use this skill when working with infinite-width neural networks for feature learning, replicating Word2Vec or MAML experiments from the Tensor Programs series (TP4), or implementing infinite-width limits (GP, NTK, muP) for meta-learning and word embedding tasks.
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article_references.md 129 B name tp4-feature-learning description Use this skill when working with infinite-width neural networks for feature learning, replicating Word2Vec or MAML experiments from the Tensor Programs series (TP4), or implementing infinite-width limits (GP, NTK, muP) for meta-learning and word embedding tasks.
TP4: Feature Learning in Infinite-Width Neural Networks
When to Use
Implementing infinite-width neural network experiments (GP, NTK, muP/feature learning limits)
Replicating Word2Vec experiments with infinite-width models
Running MAML (Model-Agnostic Meta-Learning) with infinite-width networks on Omniglot
Studying the Tensor Programs series of papers empirically
Comparing finite vs. infinite-width neural network behavior
Keywords: infinite-width, feature learning, NTK, GP, muP, MAML, Word2Vec, Tensor Programs, meta-learning
Quick Reference
Installation / Setup
Prerequisites
Python 3.x
C compiler (for Word2Vec C source)
PyTorch
MAML Experiment Setup
cd TP4MAML
pip install -r requirements.txt
cd meta
pip install -r requirements.txt
Word2Vec Experiment Setup
cd Word2Vec
make
bash scripts/create-text8-data.sh
bash scripts/create-fil9-data.sh
Core Features
InfGP1LP: Infinite-width Gaussian Process limit for a 1-hidden-layer perceptronFinGP1LP: Finite-width GP baseline for comparisonInfNTK1LP: Infinite-width NTK limit for a 1-hidden-layer perceptronInfSGD: Custom SGD optimizer for infinite-width networks with proper scalingInfMultiStepLR: Learning rate scheduler compatible with InfSGDInfMAML: Infinite-width MAML metalearner for Omniglot few-shot classificationCachedOmniglot: Efficient cached Omniglot dataset loaderWord2Vec C implementation: Modified word2vec supporting infinite-width training modes
Usage Examples
Running All MAML Experiments
cd TP4MAML
bash train_all.sh
Training MAML (finite width)
cd TP4MAML/meta
python train.py --dataset omniglot --num-ways 5 --num-shots 1
Training Infinite-Width MAML
cd TP4MAML/meta
python train.py --dataset omniglot --num-ways 5 --num-shots 1 --inf
Word2Vec Training (text8, standard)
cd Word2Vec
bash scripts/train-text8.sh
Word2Vec Training (text8, infinite-width)
cd Word2Vec
bash scripts/train-text8-inf.sh
Word2Vec Evaluation
cd Word2Vec
bash scripts/evaluate.sh
Key APIs / Models
TP4MAML/inf/inf1lp.py
InfGP1LP — Infinite GP limit 1-layer perceptronFinGP1LP — Finite GP baselineInfNTK1LP — Infinite NTK limit 1-layer perceptron
TP4MAML/inf/optim.py
InfSGD(params, lr, ...) — SGD optimizer scaled for infinite-width networksInfMultiStepLR(optimizer, milestones, gamma) — LR scheduler for InfSGD
TP4MAML/inf/utils.py
safe_sqrt(arr, eps) — Numerically stable square rootsafe_acos(arr, eps) — Numerically stable arccosF00ReLU(c, v, v2) — ReLU kernel function used in GP/NTK computationsMyLinear — Custom linear layer with infinite-width scaling
TP4MAML/meta/maml/metalearners/infmaml.py
InfMAML — Meta-learner implementing MAML for infinite-width networks
TP4MAML/meta/maml/metalearners/maml.py
MAML — Standard MAML meta-learner
TP4MAML/meta/cached_omniglot.py
CachedOmniglot — Omniglot dataset with cachingOmniglotClassDataset — Per-class Omniglot datasetOmniglot — Base Omniglot loader
TP4MAML/inf/dynamicarray.py
DynArr — Dynamic array for storing activations during infinite-width forward passesCycArr — Cyclic array variant
Common Patterns & Best Practices
Use --inf flag in train.py to switch between finite and infinite-width MAML
The infinite-width models do not store explicit weights; instead they accumulate kernel computations
For Word2Vec, the train-*-inf.sh scripts set hyperparameters appropriate for infinite-width training
Always build the C binaries before running Word2Vec experiments (make in Word2Vec/)
The train_all.sh script in TP4MAML/ runs all configurations sequentially for full replication
Demo Scripts
scripts/inf_network_demo.py
"""
TP4 Feature Learning - Infinite-Width Network Demo
Demonstrates usage of the TP4MAML inf module:
- InfGP1LP, InfNTK1LP for infinite-width 1-hidden-layer perceptrons
- InfSGD optimizer
- Utility functions (safe_sqrt, safe_acos, F00ReLU)
Requires: torch, numpy
Run from the repo root: python scripts/inf_network_demo.py
"""
import sys
import os
sys.path.insert(0 , os.path.join(os.path.dirname(__file__), '..' , 'TP4MAML' ))
import torch
import torch.nn as nn
import numpy as np
def demo_utils ():
"""Demonstrate utility functions from TP4MAML/inf/utils.py"""
try :
from inf.utils import safe_sqrt, safe_acos, F00ReLU, MyLinear
print ("=== Utility Functions ===" )
arr = torch.tensor([-1e-10 , 0.0 , 1.0 , 4.0 ])
result = safe_sqrt(arr, eps=1e-6 )
print (f"safe_sqrt({arr.tolist()} ) = {result.tolist()} " )
arr2 = torch.tensor([-1.0 - 1e-10 , -1.0 , 0.0 , 1.0 , 1.0 + 1e-10 ])
result2 = safe_acos(arr2, eps=1e-6 )
print (f"safe_acos(clipped) = )
scripts/maml_training_demo.py
"""
TP4 MAML Training Demo
Shows how to invoke MAML training programmatically (mirroring train.py usage).
Demonstrates the dataset loading and metalearner API.
Requires: torch, torchmeta (see TP4MAML/meta/requirements.txt)
Run from TP4MAML/meta/: python ../../scripts/maml_training_demo.py
"""
import sys
import os
import argparse
MAML_META_PATH = os.path.join(os.path.dirname(__file__), '..' , 'TP4MAML' , 'meta' )
MAML_INF_PATH = os.path.join(os.path.dirname(__file__), '..' , 'TP4MAML' )
sys.path.insert(0 , MAML_META_PATH)
sys.path.insert(0 , MAML_INF_PATH)
def build_omniglot_dataset (data_folder: str , num_ways: int = 5 , num_shots: int = 1 ,
num_shots_test: int = 15 ):
"""
Build Omniglot meta-learning dataset using CachedOmniglot.
Args:
data_folder: Path to Omniglot data directory.
num_ways: Number of classes per episode (N-way).
num_shots: Number of support examples per class (K-shot).
num_shots_test: Number of query examples per class.
Returns:
Tuple of (meta_train_dataset, meta_val_dataset, meta_test_dataset)
"""
try :
from cached_omniglot import CachedOmniglot
import torchmeta
from torchmeta.transforms import ClassSplitter, Categorical
from torchvision.transforms import Compose, Resize, ToTensor
transform = Compose([Resize(28 ), ToTensor()])
meta_train = CachedOmniglot(
data_folder,
num_classes_per_task=num_ways,
transform=transform,
target_transform=Categorical(num_ways),
class_augmentations=[torchmeta.transforms.Rotation([{result2.tolist()}
0.5
1.0
1.0
print
f"F00ReLU(c=0.5, v=1, v2=1) = {k.item():.4 f} "
10
5
3
10
print
f"MyLinear(10->5) output shape: {out.shape} "
except
as
print
f"Could not import inf.utils (run from repo root with TP4MAML in path): {e} "
def
demo_dynamic_arrays
"""Demonstrate DynArr and CycArr from TP4MAML/inf/dynamicarray.py"""
try
from
import
print
"\n=== Dynamic Arrays ==="
for
in
range
5
3
4
print
f"DynArr length after 5 appends: {len (darr)} "
3
for
in
range
6
float
print
f"CycArr (capacity=3) last 3 values: {[carr[i].item() for i in range (len (carr))]} "
except
as
print
f"Could not import inf.dynamicarray: {e} "
def
demo_inf_models
"""Demonstrate InfGP1LP, FinGP1LP, InfNTK1LP from TP4MAML/inf/inf1lp.py"""
try
from
import
print
"\n=== Infinite-Width 1-Layer Perceptron Models ==="
16
5
8
0
4
print
"Building InfGP1LP..."
print
f" InfGP1LP created: {type (gp_model).__name__} "
print
"Building InfNTK1LP..."
print
f" InfNTK1LP created: {type (ntk_model).__name__} "
print
"Building FinGP1LP..."
256
print
f" FinGP1LP created: {type (fin_model).__name__} "
print
f" FinGP1LP forward output shape: {logits.shape} "
except
as
print
f"Could not import inf.inf1lp: {e} "
except
as
print
f"Error in inf model demo: {e} "
def
demo_inf_sgd
"""Demonstrate InfSGD optimizer from TP4MAML/inf/optim.py"""
try
from
import
print
"\n=== InfSGD Optimizer ==="
10
5
0.01
0.9
print
f"InfSGD created with lr=0.01, momentum=0.9"
10
20
0.1
print
f"InfMultiStepLR created with milestones=[10, 20], gamma=0.1"
4
10
0
5
4
for
in
range
3
print
f" Step {step+1 } : loss={loss.item():.4 f} , lr={scheduler.get_last_lr()} "
except
as
print
f"Could not import inf.optim: {e} "
except
as
print
f"Error in InfSGD demo: {e} "
def
demo_maml_structure
"""Show the MAML metalearner interface (TP4MAML/meta/maml/metalearners/)"""
try
0
'..'
'TP4MAML'
'meta'
from
import
print
"\n=== MAML Metalearner ==="
print
f"MAML class imported: {MAML} "
print
" MAML implements standard Model-Agnostic Meta-Learning."
print
" Use train.py --inf flag to switch to InfMAML."
except
as
print
f"\nCould not import MAML metalearner: {e} "
if
"__main__"
print
"TP4 Feature Learning in Infinite-Width Neural Networks - Demo\n"
print
"\nDemo complete."
90
180
270
True
True
print
f"CachedOmniglot meta-train: {len (meta_train)} tasks"
return
except
as
print
f"Could not build Omniglot dataset (missing torchmeta or data): {e} "
return
None
except
as
print
f"Dataset error: {e} "
return
None
def
demonstrate_metalearner_api
"""
Show the API surface of MAML and InfMAML metalearners.
"""
print
"=== MAML / InfMAML API ===\n"
try
from
import
print
f"MAML class: {MAML.__module__} .{MAML.__name__} "
print
f" __init__ signature: see references/api_reference.md"
print
f" Key methods: train(), evaluate(), get_outer_loss()"
except
as
print
f"MAML import failed: {e} "
try
from
import
print
f"\nInfMAML class: {InfMAML.__module__} .{InfMAML.__name__} "
print
f" Extends MAML for infinite-width networks using InfGP1LP/InfNTK1LP"
except
as
print
f"InfMAML import failed: {e} "
try
from
import
print
f"\nMetaSGD class: {MetaSGD.__module__} .{MetaSGD.__name__} "
print
f" Meta-SGD variant with per-parameter learned learning rates"
except
as
print
f"MetaSGD import failed: {e} "
def
show_training_command_equivalents
"""
Print the equivalent train.py CLI commands for common configurations.
"""
print
"\n=== Equivalent train.py Commands ===\n"
"description"
"5-way 1-shot Omniglot, finite MAML"
"cmd"
"python train.py --dataset omniglot --num-ways 5 --num-shots 1 --num-steps 5"
"description"
"5-way 1-shot Omniglot, infinite-width MAML (GP limit)"
"cmd"
"python train.py --dataset omniglot --num-ways 5 --num-shots 1 --num-steps 5 --inf --use-gp"
"description"
"5-way 5-shot Omniglot, infinite-width MAML (NTK limit)"
"cmd"
"python train.py --dataset omniglot --num-ways 5 --num-shots 5 --num-steps 5 --inf"
"description"
"Run all experiments (uses train_all.sh)"
"cmd"
"cd TP4MAML && bash train_all.sh"
for
in
print
f"# {cfg['description' ]} "
print
f" {cfg['cmd' ]} \n"
def
show_word2vec_commands
"""
Show Word2Vec experiment commands.
"""
print
"=== Word2Vec Experiment Commands ===\n"
"Build C binaries"
"cd Word2Vec && make"
"Prepare text8 data"
"bash Word2Vec/scripts/create-text8-data.sh"
"Prepare fil9 data"
"bash Word2Vec/scripts/create-fil9-data.sh"
"Train text8 (finite)"
"bash Word2Vec/scripts/train-text8.sh"
"Train text8 (infinite)"
"bash Word2Vec/scripts/train-text8-inf.sh"
"Train fil9 (finite)"
"bash Word2Vec/scripts/train-fil9.sh"
"Train fil9 (infinite)"
"bash Word2Vec/scripts/train-fil9-inf.sh"
"Evaluate embeddings"
"bash Word2Vec/scripts/evaluate.sh"
for
in
print
f"# {name} "
print
f" {cmd} \n"
if
"__main__"
print
"TP4 MAML Training Demo\n"
if
len
1
1
print
f"\n=== Building Omniglot Dataset from {data_folder} ==="
5
1
if
is
not
None
print
"Dataset built successfully."
else
print
"\nTip: Pass a data folder path as argument to test dataset loading."
print
" python maml_training_demo.py /path/to/omniglot/data"
