Notes on fastai Book Ch. 6

Chapter 6 covers multi-label classification and image regression.

This post is part of the following series:

• Deep Learning for Coders with fastai & PyTorch

• Multi-Label Classification
• Regression
• References

Multi-Label Classification

• the problem of identifying the categories of objects in images that may not contain exactly one type of object
  • there may be more than one kind of object or none at all that belong to the target classes
• single-label classifiers cannot properly handle input that either does not contain an object of a target class or contains multiple objects of a different target classes
  • a single-label classifier trained to recognize cats and dogs could not handle an image that contains both cats and dogs
• models deployed in production are more likely to encounter input with zero matches or more than one match

The Data

from fastai.vision.all import *

The PASCAL Visual Object Classes Challenge 2007 Dataset

• http://host.robots.ox.ac.uk/pascal/VOC/voc2007/
• contains twenty classes
• multiple classes may be present in the same image
• classification labels are stored in a CSV file

---

path = untar_data(URLs.PASCAL_2007)
path

Path('/home/innom-dt/.fastai/data/pascal_2007')

---

path.ls()

(#8) [Path('/home/innom-dt/.fastai/data/pascal_2007/segmentation'),Path('/home/innom-dt/.fastai/data/pascal_2007/test'),Path('/home/innom-dt/.fastai/data/pascal_2007/train.csv'),Path('/home/innom-dt/.fastai/data/pascal_2007/valid.json'),Path('/home/innom-dt/.fastai/data/pascal_2007/train'),Path('/home/innom-dt/.fastai/data/pascal_2007/train.json'),Path('/home/innom-dt/.fastai/data/pascal_2007/test.csv'),Path('/home/innom-dt/.fastai/data/pascal_2007/test.json')]

---

df = pd.read_csv(path/'train.csv')
df.head()

	fname	labels	is_valid
0	000005.jpg	chair	True
1	000007.jpg	car	True
2	000009.jpg	horse person	True
3	000012.jpg	car	False
4	000016.jpg	bicycle	True

Class lables are stored in a space-delimited string

Pandas and DataFrames

• https://pandas.pydata.org/docs/index.html
• https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html

---

# Access rows and columns using the `iloc` property 
df.iloc[:,0]

0       000005.jpg
1       000007.jpg
2       000009.jpg
3       000012.jpg
4       000016.jpg
           ...    
5006    009954.jpg
5007    009955.jpg
5008    009958.jpg
5009    009959.jpg
5010    009961.jpg
Name: fname, Length: 5011, dtype: object

---

df.iloc[0,:]
# Trailing :s are always optional (in numpy, pytorch, pandas, etc.),
#   so this is equivalent:
df.iloc[0]

fname       000005.jpg
labels           chair
is_valid          True
Name: 0, dtype: object

---

# Get a column by name
df['fname']

0       000005.jpg
1       000007.jpg
2       000009.jpg
3       000012.jpg
4       000016.jpg
           ...    
5006    009954.jpg
5007    009955.jpg
5008    009958.jpg
5009    009959.jpg
5010    009961.jpg
Name: fname, Length: 5011, dtype: object

---

# Initialize a new data frame using a dictionary
tmp_df = pd.DataFrame({'a':[1,2], 'b':[3,4]})
tmp_df

	a	b
0	1	3
1	2	4

---

# Perform calculations using columns
tmp_df['c'] = tmp_df['a']+tmp_df['b']
tmp_df

	a	b	c
0	1	3	4
1	2	4	6

Constructing a DataBlock

• Dataset: a collection that returns a tuple of your independent and dependent variable for a single item
• DataLoader: An iterator that provides a stream of mini-batches, where each mini-batch is a tuple of a batch of independent variables and a batch of dependent variables
• Datasets: an iterator that contains a training Dataset and a validation Dataset
• DataLoaders: an object that contains a training DataLoader and a validation DataLoader
• By default, a DataBlock assumes we have an input and a target

Python Lambda Functions

• great for quickly iterating
• not compatible with serialization
• How to Use Python Lambda Functions

One-hot encoding: using a vector of 0s, with a 1 in each location that is represented in the data

---

# Start with a data block created with no parameters
dblock = DataBlock()

---

# Add a Datasets object using the DataFrame
dsets = dblock.datasets(df)

---

len(dsets.train),len(dsets.valid)

(4009, 1002)

---

# Grabs the same thing twice
# Need to specify an input and a target
x,y = dsets.train[0]
x,y

(fname       008663.jpg
 labels      car person
 is_valid         False
 Name: 4346, dtype: object,
 fname       008663.jpg
 labels      car person
 is_valid         False
 Name: 4346, dtype: object)

---

x['fname']

'008663.jpg'

---

# Tell the DataBlock how to extract the input and target from the DataFrame
# Using lamda functions
dblock = DataBlock(get_x = lambda r: r['fname'], get_y = lambda r: r['labels'])
dsets = dblock.datasets(df)
dsets.train[0]

('005620.jpg', 'aeroplane')

Note: Do not use lambda functions if you need to export the Learner

---

# Tell the DataBlock how to extract the input and target from the DataFrame
# Using standard functions
def get_x(r): return r['fname']
def get_y(r): return r['labels']
dblock = DataBlock(get_x = get_x, get_y = get_y)
dsets = dblock.datasets(df)
dsets.train[0]

('002549.jpg', 'tvmonitor')

Note: Need the full file path for the dependent variable and need to split the dependent variables on the space character

---

def get_x(r): return path/'train'/r['fname']
def get_y(r): return r['labels'].split(' ')
dblock = DataBlock(get_x = get_x, get_y = get_y)
dsets = dblock.datasets(df)
dsets.train[0]

(Path('/home/innom-dt/.fastai/data/pascal_2007/train/002844.jpg'), ['train'])

ImageBlock

• https://docs.fast.ai/vision.data.html#ImageBlock
• A TransformBlock for images

MultiCategoryBlock

• https://docs.fast.ai/data.block.html#MultiCategoryBlock
• A TransformBlock for multi-label categorical targets
• Uses One-hot encoding
• Expects to receive a list of strings

---

ImageBlock

<function fastai.vision.data.ImageBlock(cls=<class 'fastai.vision.core.PILImage'>)>

---

MultiCategoryBlock

<function fastai.data.block.MultiCategoryBlock(encoded=False, vocab=None, add_na=False)>

---

dblock = DataBlock(blocks=(ImageBlock, MultiCategoryBlock),
                   get_x = get_x, get_y = get_y)
dsets = dblock.datasets(df)
dsets.train[0]

(PILImage mode=RGB size=500x375,
 TensorMultiCategory([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.]))

---

# Check which object class is represented by the above one-hot encoding
idxs = torch.where(dsets.train[0][1]==1.)[0]
dsets.train.vocab[idxs]

(#1) ['dog']

---

# Define a function to split the dataset based on the is_valid column
def splitter(df):
    train = df.index[~df['is_valid']].tolist()
    valid = df.index[df['is_valid']].tolist()
    return train,valid

dblock = DataBlock(blocks=(ImageBlock, MultiCategoryBlock),
                   splitter=splitter,
                   get_x=get_x, 
                   get_y=get_y)

dsets = dblock.datasets(df)
dsets.train[0]

(PILImage mode=RGB size=500x333,
 TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))

---

dblock = DataBlock(blocks=(ImageBlock, MultiCategoryBlock),
                   splitter=splitter,
                   get_x=get_x, 
                   get_y=get_y,
                   item_tfms = RandomResizedCrop(128, min_scale=0.35))
dls = dblock.dataloaders(df)

---

dls.show_batch(nrows=1, ncols=3)

---

dblock.summary(df)

Setting-up type transforms pipelines
Collecting items from            fname          labels  is_valid
0     000005.jpg           chair      True
1     000007.jpg             car      True
2     000009.jpg    horse person      True
3     000012.jpg             car     False
4     000016.jpg         bicycle      True
...          ...             ...       ...
5006  009954.jpg    horse person      True
5007  009955.jpg            boat      True
5008  009958.jpg  person bicycle      True
5009  009959.jpg             car     False
5010  009961.jpg             dog     False

[5011 rows x 3 columns]
Found 5011 items
2 datasets of sizes 2501,2510
Setting up Pipeline: get_x -> PILBase.create
Setting up Pipeline: get_y -> MultiCategorize -- {'vocab': None, 'sort': True, 'add_na': False} -> OneHotEncode -- {'c': None}

Building one sample
  Pipeline: get_x -> PILBase.create
    starting from
      fname       000012.jpg
labels             car
is_valid         False
Name: 3, dtype: object
    applying get_x gives
      /home/innom-dt/.fastai/data/pascal_2007/train/000012.jpg
    applying PILBase.create gives
      PILImage mode=RGB size=500x333
  Pipeline: get_y -> MultiCategorize -- {'vocab': None, 'sort': True, 'add_na': False} -> OneHotEncode -- {'c': None}
    starting from
      fname       000012.jpg
labels             car
is_valid         False
Name: 3, dtype: object
    applying get_y gives
      [car]
    applying MultiCategorize -- {'vocab': None, 'sort': True, 'add_na': False} gives
      TensorMultiCategory([6])
    applying OneHotEncode -- {'c': None} gives
      TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])

Final sample: (PILImage mode=RGB size=500x333, TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))

Collecting items from            fname          labels  is_valid
0     000005.jpg           chair      True
1     000007.jpg             car      True
2     000009.jpg    horse person      True
3     000012.jpg             car     False
4     000016.jpg         bicycle      True
...          ...             ...       ...
5006  009954.jpg    horse person      True
5007  009955.jpg            boat      True
5008  009958.jpg  person bicycle      True
5009  009959.jpg             car     False
5010  009961.jpg             dog     False

[5011 rows x 3 columns]
Found 5011 items
2 datasets of sizes 2501,2510
Setting up Pipeline: get_x -> PILBase.create
Setting up Pipeline: get_y -> MultiCategorize -- {'vocab': None, 'sort': True, 'add_na': False} -> OneHotEncode -- {'c': None}
Setting up after_item: Pipeline: RandomResizedCrop -- {'size': (128, 128), 'min_scale': 0.35, 'ratio': (0.75, 1.3333333333333333), 'resamples': (2, 0), 'val_xtra': 0.14, 'max_scale': 1.0, 'p': 1.0} -> ToTensor
Setting up before_batch: Pipeline: 
Setting up after_batch: Pipeline: IntToFloatTensor -- {'div': 255.0, 'div_mask': 1}

Building one batch
Applying item_tfms to the first sample:
  Pipeline: RandomResizedCrop -- {'size': (128, 128), 'min_scale': 0.35, 'ratio': (0.75, 1.3333333333333333), 'resamples': (2, 0), 'val_xtra': 0.14, 'max_scale': 1.0, 'p': 1.0} -> ToTensor
    starting from
      (PILImage mode=RGB size=500x333, TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))
    applying RandomResizedCrop -- {'size': (128, 128), 'min_scale': 0.35, 'ratio': (0.75, 1.3333333333333333), 'resamples': (2, 0), 'val_xtra': 0.14, 'max_scale': 1.0, 'p': 1.0} gives
      (PILImage mode=RGB size=128x128, TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))
    applying ToTensor gives
      (TensorImage of size 3x128x128, TensorMultiCategory([0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]))

Adding the next 3 samples

No before_batch transform to apply

Collating items in a batch

Applying batch_tfms to the batch built
  Pipeline: IntToFloatTensor -- {'div': 255.0, 'div_mask': 1}
    starting from
      (TensorImage of size 4x3x128x128, TensorMultiCategory of size 4x20)
    applying IntToFloatTensor -- {'div': 255.0, 'div_mask': 1} gives
      (TensorImage of size 4x3x128x128, TensorMultiCategory of size 4x20)

Binary Cross-Entropy

• Getting Model Activations
  • it is important to know how to manually get a mini-batch, pass it into a model, and look at the activations
• Can’t directly use nll_loss or softmax for a one-hot-encoded dependent variable
  • softmax requires all predictions sum to 1 and tends to push one activation to be much larger than all the other
    • not desirable when there may be multiple objects or none at all in a single image
  • nll_loss returns the value of just one activation
• binary cross-entropy combines mnist_loss with log

---

learn = cnn_learner(dls, resnet18)

to_cpu(b)

• https://docs.fast.ai/torch_core.html#to_cpu
• Recursively map lists of tensors in b to the cpu.

---

to_cpu

<function fastai.torch_core.to_cpu(b)>

---

x,y = to_cpu(dls.train.one_batch())
activs = learn.model(x)
activs.shape

torch.Size([64, 20])

---

activs[0]

TensorBase([ 0.5674, -1.2013,  4.5409, -1.5284, -0.6600,  0.0999, -2.4757, -0.8773, -0.2934, -1.4746, -0.1738,  2.1763, -3.4473, -1.1407,  0.1783, -1.6922, -2.3396,  0.7602, -1.4213, -0.4334],
       grad_fn=<AliasBackward0>)

Note: The raw model activations are not scaled between [0,1]

---

def binary_cross_entropy(inputs, targets):
    inputs = inputs.sigmoid()
    return -torch.where(targets==1, inputs, 1-inputs).log().mean()

---

binary_cross_entropy(activs, y)

TensorMultiCategory(1.0367, grad_fn=<AliasBackward0>)

nn.BCELoss

• https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html#torch.nn.BCELoss
• measures the binary cross entropy between the predictions and target

nn.BCEWithLogitsLoss

• https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html#torch.nn.BCEWithLogitsLoss
• combines a sigmoid layer and the BCELoss in a single class

---

nn.BCEWithLogitsLoss

torch.nn.modules.loss.BCEWithLogitsLoss

---

loss_func = nn.BCEWithLogitsLoss()
loss = loss_func(activs, y)
loss

TensorMultiCategory(1.0367, grad_fn=<AliasBackward0>)

Python Partial Functions

• https://docs.python.org/3/library/functools.html#functools.partial
• return a new partial object that will behave like a function with the positional and keyword arguments
• allows us to bind a function with some arguments or keyword arguments

---

partial

functools.partial

---

def say_hello(name, say_what="Hello"): return f"{say_what} {name}."
say_hello('Jeremy'),say_hello('Jeremy', 'Ahoy!')

('Hello Jeremy.', 'Ahoy! Jeremy.')

---

f = partial(say_hello, say_what="Bonjour")
f("Jeremy"),f("Sylvain")

('Bonjour Jeremy.', 'Bonjour Sylvain.')

accuracy_multi

• https://docs.fast.ai/metrics.html#accuracy_multi
• compute accuracy using a threshold value

---

accuracy_multi

<function fastai.metrics.accuracy_multi(inp, targ, thresh=0.5, sigmoid=True)>

---

learn = cnn_learner(dls, resnet50, metrics=partial(accuracy_multi, thresh=0.2))
learn.fine_tune(3, base_lr=3e-3, freeze_epochs=4)

epoch	train_loss	valid_loss	accuracy_multi	time
0	0.942860	0.704590	0.234223	00:06
1	0.821557	0.550972	0.293825	00:06
2	0.604402	0.202164	0.813645	00:06
3	0.359336	0.122809	0.943466	00:06

epoch	train_loss	valid_loss	accuracy_multi	time
0	0.135016	0.122502	0.944601	00:07
1	0.118378	0.107208	0.950478	00:07
2	0.098511	0.103568	0.951613	00:07

---

learn.metrics = partial(accuracy_multi, thresh=0.1)
learn.validate()

(#2) [0.10356765240430832,0.9294222593307495]

---

learn.metrics = partial(accuracy_multi, thresh=0.99)
learn.validate()

(#2) [0.10356765240430832,0.9427291750907898]

---

preds,targs = learn.get_preds()

---

accuracy_multi(preds, targs, thresh=0.9, sigmoid=False)

TensorBase(0.9566)

---

# Try a few different threshold values to see which works best
xs = torch.linspace(0.05,0.95,29)
accs = [accuracy_multi(preds, targs, thresh=i, sigmoid=False) for i in xs]
plt.plot(xs,accs);

Regression

• a model is defined by it independent and dependent variables, along with its loss function
• image regression: the independent variable is an image and the dependent variable is one or more floating point numbers
• key point model:
  • a key point refers to a specific location represented in an image

Assemble the Data

BIWI Kinect Head Pose Database

• https://icu.ee.ethz.ch/research/datsets.html
• over 15k images of 20 people recorded with a Kinect while turning their heads around freely
• Depth and rgb images are provided for each frame
• ground in the form of the 3D location of the head and its rotation angles
• contains 24 directories numbered from 01 to 24 which correspond to the different people photographed
  • each directory has a corresponding .obj file
  • each directory contains .cal files containing the calibration data for the depth and color cameras
  • each image has a corresponding _pose.txt file containing the location of center of the head in 3D and the head rotation encoded as 3D rotation matrix

---

path = untar_data(URLs.BIWI_HEAD_POSE)
path

Path('/home/innom-dt/.fastai/data/biwi_head_pose')

---

path.ls().sorted()

(#50) [Path('/home/innom-dt/.fastai/data/biwi_head_pose/01'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01.obj'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/02'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/02.obj'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/03'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/03.obj'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/04'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/04.obj'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/05'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/05.obj')...]

---

(path/'01').ls().sorted()

(#1000) [Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/depth.cal'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00003_pose.txt'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00003_rgb.jpg'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00004_pose.txt'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00004_rgb.jpg'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00005_pose.txt'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00005_rgb.jpg'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00006_pose.txt'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00006_rgb.jpg'),Path('/home/innom-dt/.fastai/data/biwi_head_pose/01/frame_00007_pose.txt')...]

---

# recursivley get all images in the 24 subdirectories
img_files = get_image_files(path)
# get the file names for the corresponding pose.txt files
def img2pose(x): return Path(f'{str(x)[:-7]}pose.txt')
pose_file = img2pose(img_files[0])
pose_file

Path('/home/innom-dt/.fastai/data/biwi_head_pose/22/frame_00304_pose.txt')

---

!cat $pose_file

0.999485 -0.00797222 -0.031067 
-0.00416483 0.928156 -0.372168 
0.031802 0.372106 0.927645 

62.3638 96.2159 979.839 

---

im = PILImage.create(img_files[0])
im.shape

(480, 640)

---

im.to_thumb(160)

np.genfromtxt

• https://numpy.org/doc/stable/reference/generated/numpy.genfromtxt.html
• Load data from a text file

---

np.genfromtxt

<function numpy.genfromtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, skip_header=0, skip_footer=0, converters=None, missing_values=None, filling_values=None, usecols=None, names=None, excludelist=None, deletechars=" !#$%&'()*+,-./:;<=>?@[\\]^{|}~", replace_space='_', autostrip=False, case_sensitive=True, defaultfmt='f%i', unpack=None, usemask=False, loose=True, invalid_raise=True, max_rows=None, encoding='bytes', *, like=None)>

---

# Contains the calibration values for this folder's rgb camera
# Skip the last six lines in the file 
cal = np.genfromtxt(path/'01'/'rgb.cal', skip_footer=6)
cal

array([[517.679,   0.   , 320.   ],
       [  0.   , 517.679, 240.5  ],
       [  0.   ,   0.   ,   1.   ]])

---

# Extract the 2D coordinates for the center of a head
# Serves as the get_y function for a DataBlock
def get_ctr(f):
    # Skip the last 3 lines in the file
    ctr = np.genfromtxt(img2pose(f), skip_header=3)
    c1 = ctr[0] * cal[0][0]/ctr[2] + cal[0][2]
    c2 = ctr[1] * cal[1][1]/ctr[2] + cal[1][2]
    return tensor([c1,c2])

---

np.genfromtxt(img2pose(img_files[0]), skip_header=3)

array([ 62.3638,  96.2159, 979.839 ])

---

get_ctr(img_files[0])

tensor([352.9487, 291.3338])

PointBlock

• Documentation: https://docs.fast.ai/vision.data.html#PointBlock
• Source Code: https://github.com/fastai/fastai/blob/d84b426e2afe17b3af09b33f49c77bd692625f0d/fastai/vision/data.py#L74
• A TransfromBlock for points in an image
• Lets fastai know to perform the same data augmentation steps to the key point values as to the images

---

PointBlock

<fastai.data.block.TransformBlock at 0x7fb65aaf5490>

---

# Construct custom DataBlock
biwi = DataBlock(
    blocks=(ImageBlock, PointBlock),
    get_items=get_image_files,
    get_y=get_ctr,
    # Have the validation set contain images for a single person
    splitter=FuncSplitter(lambda o: o.parent.name=='13'),
    batch_tfms=[*aug_transforms(size=(240,320)), 
                Normalize.from_stats(*imagenet_stats)]
)

---

dls = biwi.dataloaders(path)
dls.show_batch(max_n=9, figsize=(8,6))

---

xb,yb = dls.one_batch()
xb.shape,yb.shape

(torch.Size([64, 3, 240, 320]), torch.Size([64, 1, 2]))

---

yb[0]

TensorPoint([[-0.1246,  0.0960]], device='cuda:0')

Training a Model

# Set range of coordinate values for the model output to [-1,1]
learn = cnn_learner(dls, resnet18, y_range=(-1,1))

---

def sigmoid_range(x, lo, hi): return torch.sigmoid(x) * (hi-lo) + lo

---

plot_function(partial(sigmoid_range,lo=-1,hi=1), min=-4, max=4)

---

dls.loss_func

FlattenedLoss of MSELoss()

---

min_lr, steep_lr, valley = learn.lr_find(suggest_funcs=(minimum, steep, valley))

---

min_lr

0.006918309628963471

---

steep_lr

2.0892961401841603e-05

---

valley

0.0010000000474974513

---

lr = 1e-2
learn.fine_tune(3, lr)

epoch	train_loss	valid_loss	time
0	0.048689	0.026659	00:36

epoch	train_loss	valid_loss	time
0	0.007270	0.002140	00:47
1	0.002966	0.000160	00:47
2	0.001556	0.000042	00:47

---

# Calculate the Root Mean Squared Error
math.sqrt(0.000042)

0.00648074069840786

---

learn.show_results(ds_idx=1, nrows=3, figsize=(6,8))

References

• Deep Learning for Coders with fastai & PyTorch
• The fastai book GitHub Repository

Previous: Notes on fastai Book Ch. 5

Next: Notes on fastai Book Ch. 7

---

About Me:

I’m Christian Mills, a deep learning consultant specializing in practical AI implementations. I help clients leverage cutting-edge AI technologies to solve real-world problems.

Interested in working together? Fill out my Quick AI Project Assessment form or learn more about me.