While learning about large language models, the issue of vanishing gradients came up. What is a gradient? I attempted to describe it as the difference between where you are and where you want to be (the target), which is given by the loss function. This led to the question of what exactly a loss function is. The video below from IBM Technology explains loss functions: a loss function is an evaluation metric (how well is the model performing) and/or a guide that directs the model’s learning process.
What is a Loss Function? Understanding How AI Models Learn
The primary reason for calculating the loss function is to guide the model’s learning process. It provides a numeric value that indicates how far off the model’s predictions are from the actual results. By analyzing the loss, the model’s parameters can be adjusted (optimization) since the loss function is a feedback mechanism to the model, telling it how well it is performing and where it needs to improve. – What is a Loss Function? Understanding How AI Models Learn
A smaller value of the loss function indicates that the performance of the model has improved.
The gradient of the loss function is useful because it enables algorithms to determine which adjustments (e.g. to weights) will result in a smaller loss. The next video on Gradient descent, how neural networks learn is a helpful introduction to how loss functions are used to guide learning.
Gradient descent, how neural networks learn | DL2
Backpropagation is the algorithm used to compute the gradient. This video from 3Blue1Brown is a helpful explanation of what backpropagation is:
Backpropagation, intuitively | DL3
Two important phenomena in gradient descent are the problems of vanishing and exploding gradients. The Vanishing & Exploding Gradient explained | A problem resulting from backpropagationvideo describes these problems as follows: vanishing gradients mean that updated weights earlier in the network barely change (stuck) which means that the rest of the network cannot really minimize the loss function (i.e. learn). Exploding gradients mean that the earlier weights now increase so much that the optimal value of the loss function will never be achieved because weights become too big too quickly.
Vanishing & Exploding Gradient explained | A problem resulting from backpropagation
I mentioned in my last post (Learning about Large Language Models) that I recently started going through Sebastian Raschka’s Build a Large Language Model from Scratch book. It had been a while since I ran python code on my laptop so I needed to do some cleanup to restore my environment. I cloned the repo and started executing the first cell in Chapter 2:
from importlib.metadata import version
print("torch version:", version("torch"))
print("tiktoken version:", version("tiktoken"))
I got this error: PackageNotFoundError: No package metadata was found for torch".
{
"name": "PackageNotFoundError",
"message": "No package metadata was found for torch",
"stack": "---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
File /opt/homebrew/Cellar/python@3.11/3.11.1/Frameworks/Python.framework/Versions/3.11/lib/python3.11/importlib/metadata/__init__.py:563, in Distribution.from_name(cls, name)
562 try:
--> 563 return next(cls.discover(name=name))
564 except StopIteration:
StopIteration:
During handling of the above exception, another exception occurred:
PackageNotFoundError Traceback (most recent call last)
Cell In[2], line 7
3 print(sys.version)
5 from importlib.metadata import version
----> 7 print(\"torch version:\", version(\"torch\"))
8 print(\"tiktoken version:\", version(\"tiktoken\"))
File /opt/homebrew/Cellar/python@3.11/3.11.1/Frameworks/Python.framework/Versions/3.11/lib/python3.11/importlib/metadata/__init__.py:1008, in version(distribution_name)
1001 def version(distribution_name):
1002 \"\"\"Get the version string for the named package.
1003
1004 :param distribution_name: The name of the distribution package to query.
1005 :return: The version string for the package as defined in the package's
1006 \"Version\" metadata key.
1007 \"\"\"
-> 1008 return distribution(distribution_name).version
File /opt/homebrew/Cellar/python@3.11/3.11.1/Frameworks/Python.framework/Versions/3.11/lib/python3.11/importlib/metadata/__init__.py:981, in distribution(distribution_name)
975 def distribution(distribution_name):
976 \"\"\"Get the ``Distribution`` instance for the named package.
977
978 :param distribution_name: The name of the distribution package as a string.
979 :return: A ``Distribution`` instance (or subclass thereof).
980 \"\"\"
--> 981 return Distribution.from_name(distribution_name)
File /opt/homebrew/Cellar/python@3.11/3.11.1/Frameworks/Python.framework/Versions/3.11/lib/python3.11/importlib/metadata/__init__.py:565, in Distribution.from_name(cls, name)
563 return next(cls.discover(name=name))
564 except StopIteration:
--> 565 raise PackageNotFoundError(name)
PackageNotFoundError: No package metadata was found for torch"
}
How is this showing version 3.10.9 but VS Code is using 3.11 from brew (per the file paths in the error messages? This is how to print the version from a python script as per Printing Python version in output – Stack Overflow
Since I have brew installed, this might be what I need: the comment that “If you brew-install Python, but pip is still not in your path, you might need to re-link, like this brew unlink python && brew link python” at python – How do I install pip on macOS or OS X? – Stack Overflow.
saint@MacBookPro LLMs-from-scratch % brew update
==> Downloading https://ghcr.io/v2/homebrew/portable-ruby/portable-ruby/blobs/sha256:d9faa506c014dedc0b034a68103ba75c9a58242f4d6c67b6ca0f649c39602bcf
######################################################################################################################################################################################################################################### 100.0%
==> Pouring portable-ruby-3.3.7.arm64_big_sur.bottle.tar.gz
==> Homebrew collects anonymous analytics.
Read the analytics documentation (and how to opt-out) here:
https://docs.brew.sh/Analytics
No analytics have been recorded yet (nor will be during this `brew` run).
==> homebrew/core is old and unneeded, untapping to save space...
Untapping homebrew/core...
Untapped 3 commands and 7398 formulae (7,130 files, 1GB).
==> homebrew/cask is old and unneeded, untapping to save space...
Untapping homebrew/cask...
Untapped 7333 casks (4,415 files, 487.2MB).
==> Downloading https://formulae.brew.sh/api/formula_tap_migrations.jws.json
Updated 4 taps (microsoft/git, homebrew/cask-versions, homebrew/core and homebrew/cask).
==> New Formulae
...<hundreds of lines omitted but included python entries below>
python-argcomplete
python-freethreading
python-gdbm@3.12
python-gdbm@3.13
python-matplotlib
python-packaging
python-setuptools
python-tk@3.12
python-tk@3.13
python@3.12
python@3.13
pyupgrade
...
==> Deleted Installed Formulae
icu4c ✘
==> Deleted Installed Casks
git-credential-manager-core ✘ microsoft-openjdk11 ✘
Error: Unexpected method 'appcast' called on Cask adoptopenjdk16.
Follow the instructions here:
https://github.com/Homebrew/homebrew-cask#reporting-bugs
==> Downloading https://formulae.brew.sh/api/cask_tap_migrations.jws.json
==> Outdated Formulae
aom fb303 fribidi gnuplot jasper libheif libtool lua openblas pstoedit sqlite xorgproto
arpack fbthrift gcc graphicsmagick jbig2dec libidn libunistring lz4 openexr pyqt@5 suite-sparse xz
autoconf fig2dev gd harfbuzz jpeg-turbo libidn2 libvmaf maven openjdk python@3.10 sundials zstd
boost fizz gdbm hdf5 jpeg-xl liblqr libx11 mpdecimal openjpeg python@3.11 tcl-tk
brotli flac gettext highway libaec libomp libxau mpfr openssl@1.1 python@3.9 texinfo
ca-certificates fltk ghostscript hwloc libavif libpng libxcb mpg123 openssl@3 qscintilla2 wangle
cairo fmt giflib icu4c@76 libcerf libraw libxdmcp netpbm opus qt@5 watchman
cmake folly git-gui imagemagick libde265 libsndfile libxext ninja pango readline webp
double-conversion fontconfig glib imath libevent libsodium libxrender octave pcre2 shared-mime-info wget
edencommon freetype gmp isl libffi libtiff little-cms2 open-mpi pixman snappy x265
==> Outdated Casks
git-credential-manager microsoft-openjdk microsoft-openjdk@11
You have 113 outdated formulae and 3 outdated casks installed.
You can upgrade them with brew upgrade
or list them with brew outdated.
Error: Unexpected method 'appcast' called on Cask adoptopenjdk16.
Follow the instructions here:
https://github.com/Homebrew/homebrew-cask#reporting-bugs
==> Migrating cask git-credential-manager-core to git-credential-manager
Error: inreplace failed
/opt/homebrew/Caskroom/git-credential-manager/.metadata/2.1.2/20230703191748.675/Casks/git-credential-manager.rb:
expected replacement of /\A\s*cask\s+"git\-credential\-manager\-core"/ with "cask \"git-credential-manager\""
python3 --version is still 3.10.9 after this. I tried running pip but zsh sayd command not found. Unfortunately, linking or unlinking of either python or python3 fails with the errors below (despite ls -l `which python3` showing the same path as before).
saint@MacBookPro LLMs-from-scratch % brew unlink python3
Error: Unexpected method 'appcast' called on Cask adoptopenjdk16.
Follow the instructions here:
https://github.com/Homebrew/homebrew-cask#reporting-bugs
Error: No such keg: /opt/homebrew/Cellar/python3
I decided to install python3 again.
saint@MacBookPro LLMs-from-scratch % brew install python3
==> Downloading https://formulae.brew.sh/api/formula.jws.json
==> Downloading https://formulae.brew.sh/api/cask.jws.json
==> Downloading https://ghcr.io/v2/homebrew/core/python/3.13/manifests/3.13.1
######################################################################################################################################################################################################################################### 100.0%
==> Fetching dependencies for python@3.13: mpdecimal, ca-certificates, openssl@3, readline, sqlite and xz
==> Downloading https://ghcr.io/v2/homebrew/core/mpdecimal/manifests/4.0.0-1
######################################################################################################################################################################################################################################### 100.0%
==> Fetching mpdecimal
==> Downloading https://ghcr.io/v2/homebrew/core/mpdecimal/blobs/sha256:0f5f269bed0e6be2de3edfc4b52867e656f993e5bcff40717f26ee94dd0d2211
######################################################################################################################################################################################################################################### 100.0%
==> Downloading https://ghcr.io/v2/homebrew/core/ca-certificates/manifests/2024-12-31
######################################################################################################################################################################################################################################### 100.0%
==> Fetching ca-certificates
...
<lots of omitted lines>
...
==> Fetching harfbuzz
==> Downloading https://ghcr.io/v2/homebrew/core/harfbuzz/blobs/sha256:2f892566c02b3c8c61aed6f7867b4405e5c814df8500ef4bc4ca91a9e40205a9
######################################################################################################################################################################################################################################### 100.0%
==> Fetching openjdk
==> Downloading https://ghcr.io/v2/homebrew/core/openjdk/blobs/sha256:1285eadf2b5998cda49e4470ee3875e855b0be199765401ad77dc38aea573f49
######################################################################################################################################################################################################################################### 100.0%
Error: can't modify frozen String: "The bottle needs the Xcode Command Line Tools to be installed at /Library/Developer/CommandLineTools.\nDevelopment tools provided by Xcode.app are not sufficient.\n\nYou can install the Xcode Command Line Tools, if desired, with:\n xcode-select --install\n"
This was the new state of affairs is that command (failed):
saint@MacBookPro LLMs-from-scratch % python3 --version
Python 3.13.1
saint@MacBookPro LLMs-from-scratch % which python3
/opt/homebrew/bin/python3
saint@MacBookPro LLMs-from-scratch % ls -l `which python3`
lrwxr-xr-x 1 saint admin 40 Feb 4 17:02 /opt/homebrew/bin/python3 -> ../Cellar/python@3.13/3.13.1/bin/python3
saint@MacBookPro LLMs-from-scratch % which pip
pip not found
Ah, all that agonizing and look at this – did I need to be using pip3 all this time?
saint@MacBookPro LLMs-from-scratch % which pip3
/opt/homebrew/bin/pip3
saint@MacBookPro LLMs-from-scratch % ls -l `which pip3`
lrwxr-xr-x 1 saint admin 37 Feb 4 17:02 /opt/homebrew/bin/pip3 -> ../Cellar/python@3.13/3.13.1/bin/pip3
saint@MacBookPro LLMs-from-scratch %
Interestingly, I still can’t install pytorch using pip3?
saint@MacBookPro LLMs-from-scratch % pip3 install pytorch
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
error: externally-managed-environment
× This environment is externally managed
╰─> To install Python packages system-wide, try brew install
xyz, where xyz is the package you are trying to
install.
If you wish to install a Python library that isn't in Homebrew,
use a virtual environment:
python3 -m venv path/to/venv
source path/to/venv/bin/activate
python3 -m pip install xyz
If you wish to install a Python application that isn't in Homebrew,
it may be easiest to use 'pipx install xyz', which will manage a
virtual environment for you. You can install pipx with
brew install pipx
You may restore the old behavior of pip by passing
the '--break-system-packages' flag to pip, or by adding
'break-system-packages = true' to your pip.conf file. The latter
will permanently disable this error.
If you disable this error, we STRONGLY recommend that you additionally
pass the '--user' flag to pip, or set 'user = true' in your pip.conf
file. Failure to do this can result in a broken Homebrew installation.
Read more about this behavior here: <https://peps.python.org/pep-0668/>
note: If you believe this is a mistake, please contact your Python installation or OS distribution provider. You can override this, at the risk of breaking your Python installation or OS, by passing --break-system-packages.
hint: See PEP 668 for the detailed specification.
saint@MacBookPro LLMs-from-scratch % xcode-select --install
xcode-select: note: install requested for command line developer tools
I installed the command line developer tools when prompted below.
Trying to run the first cell in VS Code with the updated setup now gave this error:
{
"name": "",
"message": "",
"stack": "Running cells with 'Python 3.13.1' requires the ipykernel package.
Run the following command to install 'ipykernel' into the Python environment.
Command: '/opt/homebrew/bin/python3 -m pip install ipykernel -U --user --force-reinstall'"
}
saint@MacBookPro LLMs-from-scratch % /opt/homebrew/bin/python3 -m pip install ipykernel -U --user --force-reinstall
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
error: externally-managed-environment
× This environment is externally managed
╰─> To install Python packages system-wide, try brew install
xyz, where xyz is the package you are trying to
install.
If you wish to install a Python library that isn't in Homebrew,
use a virtual environment:
python3 -m venv path/to/venv
source path/to/venv/bin/activate
python3 -m pip install xyz
If you wish to install a Python application that isn't in Homebrew,
it may be easiest to use 'pipx install xyz', which will manage a
virtual environment for you. You can install pipx with
brew install pipx
You may restore the old behavior of pip by passing
the '--break-system-packages' flag to pip, or by adding
'break-system-packages = true' to your pip.conf file. The latter
will permanently disable this error.
If you disable this error, we STRONGLY recommend that you additionally
pass the '--user' flag to pip, or set 'user = true' in your pip.conf
file. Failure to do this can result in a broken Homebrew installation.
Read more about this behavior here: <https://peps.python.org/pep-0668/>
note: If you believe this is a mistake, please contact your Python installation or OS distribution provider. You can override this, at the risk of breaking your Python installation or OS, by passing --break-system-packages.
hint: See PEP 668 for the detailed specification.
saint@MacBookPro LLMs-from-scratch % brew install ipykernel
==> Downloading https://formulae.brew.sh/api/formula.jws.json
==> Downloading https://formulae.brew.sh/api/cask.jws.json
Warning: No available formula with the name "ipykernel".
==> Searching for similarly named formulae and casks...
Error: No formulae or casks found for ipykernel.
I override the warning using the --break-system-packages flag and the VS Code notebook now runs.
saint@MacBookPro LLMs-from-scratch % python3 -m pip install ipykernel -U --user --force-reinstall --break-system-package
Collecting ipykernel
Downloading ipykernel-6.29.5-py3-none-any.whl.metadata (6.3 kB)
Collecting appnope (from ipykernel)
Downloading appnope-0.1.4-py2.py3-none-any.whl.metadata (908 bytes)
Collecting comm>=0.1.1 (from ipykernel)
Downloading comm-0.2.2-py3-none-any.whl.metadata (3.7 kB)
Collecting debugpy>=1.6.5 (from ipykernel)
Downloading debugpy-1.8.12-cp313-cp313-macosx_14_0_universal2.whl.metadata (1.3 kB)
Collecting ipython>=7.23.1 (from ipykernel)
Downloading ipython-8.32.0-py3-none-any.whl.metadata (5.0 kB)
Collecting jupyter-client>=6.1.12 (from ipykernel)
Downloading jupyter_client-8.6.3-py3-none-any.whl.metadata (8.3 kB)
Collecting jupyter-core!=5.0.*,>=4.12 (from ipykernel)
Downloading jupyter_core-5.7.2-py3-none-any.whl.metadata (3.4 kB)
Collecting matplotlib-inline>=0.1 (from ipykernel)
Downloading matplotlib_inline-0.1.7-py3-none-any.whl.metadata (3.9 kB)
Collecting nest-asyncio (from ipykernel)
Downloading nest_asyncio-1.6.0-py3-none-any.whl.metadata (2.8 kB)
Collecting packaging (from ipykernel)
Downloading packaging-24.2-py3-none-any.whl.metadata (3.2 kB)
Collecting psutil (from ipykernel)
Downloading psutil-6.1.1-cp36-abi3-macosx_11_0_arm64.whl.metadata (22 kB)
Collecting pyzmq>=24 (from ipykernel)
Downloading pyzmq-26.2.1-cp313-cp313-macosx_10_15_universal2.whl.metadata (6.2 kB)
Collecting tornado>=6.1 (from ipykernel)
Downloading tornado-6.4.2-cp38-abi3-macosx_10_9_universal2.whl.metadata (2.5 kB)
Collecting traitlets>=5.4.0 (from ipykernel)
Downloading traitlets-5.14.3-py3-none-any.whl.metadata (10 kB)
Collecting decorator (from ipython>=7.23.1->ipykernel)
Downloading decorator-5.1.1-py3-none-any.whl.metadata (4.0 kB)
Collecting jedi>=0.16 (from ipython>=7.23.1->ipykernel)
Downloading jedi-0.19.2-py2.py3-none-any.whl.metadata (22 kB)
Collecting pexpect>4.3 (from ipython>=7.23.1->ipykernel)
Downloading pexpect-4.9.0-py2.py3-none-any.whl.metadata (2.5 kB)
Collecting prompt_toolkit<3.1.0,>=3.0.41 (from ipython>=7.23.1->ipykernel)
Downloading prompt_toolkit-3.0.50-py3-none-any.whl.metadata (6.6 kB)
Collecting pygments>=2.4.0 (from ipython>=7.23.1->ipykernel)
Downloading pygments-2.19.1-py3-none-any.whl.metadata (2.5 kB)
Collecting stack_data (from ipython>=7.23.1->ipykernel)
Downloading stack_data-0.6.3-py3-none-any.whl.metadata (18 kB)
Collecting python-dateutil>=2.8.2 (from jupyter-client>=6.1.12->ipykernel)
Downloading python_dateutil-2.9.0.post0-py2.py3-none-any.whl.metadata (8.4 kB)
Collecting platformdirs>=2.5 (from jupyter-core!=5.0.*,>=4.12->ipykernel)
Downloading platformdirs-4.3.6-py3-none-any.whl.metadata (11 kB)
Collecting parso<0.9.0,>=0.8.4 (from jedi>=0.16->ipython>=7.23.1->ipykernel)
Downloading parso-0.8.4-py2.py3-none-any.whl.metadata (7.7 kB)
Collecting ptyprocess>=0.5 (from pexpect>4.3->ipython>=7.23.1->ipykernel)
Downloading ptyprocess-0.7.0-py2.py3-none-any.whl.metadata (1.3 kB)
Collecting wcwidth (from prompt_toolkit<3.1.0,>=3.0.41->ipython>=7.23.1->ipykernel)
Downloading wcwidth-0.2.13-py2.py3-none-any.whl.metadata (14 kB)
Collecting six>=1.5 (from python-dateutil>=2.8.2->jupyter-client>=6.1.12->ipykernel)
Downloading six-1.17.0-py2.py3-none-any.whl.metadata (1.7 kB)
Collecting executing>=1.2.0 (from stack_data->ipython>=7.23.1->ipykernel)
Downloading executing-2.2.0-py2.py3-none-any.whl.metadata (8.9 kB)
Collecting asttokens>=2.1.0 (from stack_data->ipython>=7.23.1->ipykernel)
Downloading asttokens-3.0.0-py3-none-any.whl.metadata (4.7 kB)
Collecting pure-eval (from stack_data->ipython>=7.23.1->ipykernel)
Downloading pure_eval-0.2.3-py3-none-any.whl.metadata (6.3 kB)
Downloading ipykernel-6.29.5-py3-none-any.whl (117 kB)
Downloading comm-0.2.2-py3-none-any.whl (7.2 kB)
Downloading debugpy-1.8.12-cp313-cp313-macosx_14_0_universal2.whl (2.5 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 2.5/2.5 MB 36.8 MB/s eta 0:00:00
Downloading ipython-8.32.0-py3-none-any.whl (825 kB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 825.5/825.5 kB 54.9 MB/s eta 0:00:00
Downloading jupyter_client-8.6.3-py3-none-any.whl (106 kB)
Downloading jupyter_core-5.7.2-py3-none-any.whl (28 kB)
Downloading matplotlib_inline-0.1.7-py3-none-any.whl (9.9 kB)
Downloading pyzmq-26.2.1-cp313-cp313-macosx_10_15_universal2.whl (1.3 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1.3/1.3 MB 62.7 MB/s eta 0:00:00
Downloading tornado-6.4.2-cp38-abi3-macosx_10_9_universal2.whl (436 kB)
Downloading traitlets-5.14.3-py3-none-any.whl (85 kB)
Downloading appnope-0.1.4-py2.py3-none-any.whl (4.3 kB)
Downloading nest_asyncio-1.6.0-py3-none-any.whl (5.2 kB)
Downloading packaging-24.2-py3-none-any.whl (65 kB)
Downloading psutil-6.1.1-cp36-abi3-macosx_11_0_arm64.whl (248 kB)
Downloading jedi-0.19.2-py2.py3-none-any.whl (1.6 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1.6/1.6 MB 79.1 MB/s eta 0:00:00
Downloading pexpect-4.9.0-py2.py3-none-any.whl (63 kB)
Downloading platformdirs-4.3.6-py3-none-any.whl (18 kB)
Downloading prompt_toolkit-3.0.50-py3-none-any.whl (387 kB)
Downloading pygments-2.19.1-py3-none-any.whl (1.2 MB)
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Downloading python_dateutil-2.9.0.post0-py2.py3-none-any.whl (229 kB)
Downloading decorator-5.1.1-py3-none-any.whl (9.1 kB)
Downloading stack_data-0.6.3-py3-none-any.whl (24 kB)
Downloading asttokens-3.0.0-py3-none-any.whl (26 kB)
Downloading executing-2.2.0-py2.py3-none-any.whl (26 kB)
Downloading parso-0.8.4-py2.py3-none-any.whl (103 kB)
Downloading ptyprocess-0.7.0-py2.py3-none-any.whl (13 kB)
Downloading six-1.17.0-py2.py3-none-any.whl (11 kB)
Downloading pure_eval-0.2.3-py3-none-any.whl (11 kB)
Downloading wcwidth-0.2.13-py2.py3-none-any.whl (34 kB)
Installing collected packages: wcwidth, pure-eval, ptyprocess, traitlets, tornado, six, pyzmq, pygments, psutil, prompt_toolkit, platformdirs, pexpect, parso, packaging, nest-asyncio, executing, decorator, debugpy, asttokens, appnope, stack_data, python-dateutil, matplotlib-inline, jupyter-core, jedi, comm, jupyter-client, ipython, ipykernel
WARNING: The script pygmentize is installed in '/Users/saint/Library/Python/3.13/bin' which is not on PATH.
Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
WARNING: The script debugpy is installed in '/Users/saint/Library/Python/3.13/bin' which is not on PATH.
Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
WARNING: The scripts jupyter, jupyter-migrate and jupyter-troubleshoot are installed in '/Users/saint/Library/Python/3.13/bin' which is not on PATH.
Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
WARNING: The scripts jupyter-kernel, jupyter-kernelspec and jupyter-run are installed in '/Users/saint/Library/Python/3.13/bin' which is not on PATH.
Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
WARNING: The scripts ipython and ipython3 are installed in '/Users/saint/Library/Python/3.13/bin' which is not on PATH.
Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
Successfully installed appnope-0.1.4 asttokens-3.0.0 comm-0.2.2 debugpy-1.8.12 decorator-5.1.1 executing-2.2.0 ipykernel-6.29.5 ipython-8.32.0 jedi-0.19.2 jupyter-client-8.6.3 jupyter-core-5.7.2 matplotlib-inline-0.1.7 nest-asyncio-1.6.0 packaging-24.2 parso-0.8.4 pexpect-4.9.0 platformdirs-4.3.6 prompt_toolkit-3.0.50 psutil-6.1.1 ptyprocess-0.7.0 pure-eval-0.2.3 pygments-2.19.1 python-dateutil-2.9.0.post0 pyzmq-26.2.1 six-1.17.0 stack_data-0.6.3 tornado-6.4.2 traitlets-5.14.3 wcwidth-0.2.13
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
saint@MacBookPro LLMs-from-scratch %
First cell now fails because the torch package cannot be found:
{
"name": "PackageNotFoundError",
"message": "No package metadata was found for torch",
"stack": "---------------------------------------------------------------------------
StopIteration Traceback (most recent call last)
File /opt/homebrew/Cellar/python@3.13/3.13.1/Frameworks/Python.framework/Versions/3.13/lib/python3.13/importlib/metadata/__init__.py:407, in Distribution.from_name(cls, name)
406 try:
--> 407 return next(iter(cls.discover(name=name)))
408 except StopIteration:
StopIteration:
During handling of the above exception, another exception occurred:
PackageNotFoundError Traceback (most recent call last)
Cell In[1], line 3
1 from importlib.metadata import version
----> 3 print(\"torch version:\", version(\"torch\"))
4 print(\"tiktoken version:\", version(\"tiktoken\"))
File /opt/homebrew/Cellar/python@3.13/3.13.1/Frameworks/Python.framework/Versions/3.13/lib/python3.13/importlib/metadata/__init__.py:987, in version(distribution_name)
980 def version(distribution_name: str) -> str:
981 \"\"\"Get the version string for the named package.
982
983 :param distribution_name: The name of the distribution package to query.
984 :return: The version string for the package as defined in the package's
985 \"Version\" metadata key.
986 \"\"\"
--> 987 return distribution(distribution_name).version
File /opt/homebrew/Cellar/python@3.13/3.13.1/Frameworks/Python.framework/Versions/3.13/lib/python3.13/importlib/metadata/__init__.py:960, in distribution(distribution_name)
954 def distribution(distribution_name: str) -> Distribution:
955 \"\"\"Get the ``Distribution`` instance for the named package.
956
957 :param distribution_name: The name of the distribution package as a string.
958 :return: A ``Distribution`` instance (or subclass thereof).
959 \"\"\"
--> 960 return Distribution.from_name(distribution_name)
File /opt/homebrew/Cellar/python@3.13/3.13.1/Frameworks/Python.framework/Versions/3.13/lib/python3.13/importlib/metadata/__init__.py:409, in Distribution.from_name(cls, name)
407 return next(iter(cls.discover(name=name)))
408 except StopIteration:
--> 409 raise PackageNotFoundError(name)
PackageNotFoundError: No package metadata was found for torch"
}
These are the commands I tried to install pytorch before finding the correct one: pip3 install torch --break-system-packages.
saint@MacBookPro LLMs-from-scratch % brew install torch
==> Downloading https://formulae.brew.sh/api/formula.jws.json
==> Downloading https://formulae.brew.sh/api/cask.jws.json
Warning: No available formula with the name "torch". Did you mean tor, pytorch or orc?
==> Searching for similarly named formulae and casks...
==> Formulae
pytorch ✔ torchvision tor orc
To install pytorch ✔, run:
brew install pytorch ✔
saint@MacBookPro LLMs-from-scratch % brew install pytorch
Warning: pytorch 2.5.1_4 is already installed and up-to-date.
To reinstall 2.5.1_4, run:
brew reinstall pytorch
saint@MacBookPro LLMs-from-scratch % pip3 install torch
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
error: externally-managed-environment
× This environment is externally managed
╰─> To install Python packages system-wide, try brew install
xyz, where xyz is the package you are trying to
install.
If you wish to install a Python library that isn't in Homebrew,
use a virtual environment:
python3 -m venv path/to/venv
source path/to/venv/bin/activate
python3 -m pip install xyz
If you wish to install a Python application that isn't in Homebrew,
it may be easiest to use 'pipx install xyz', which will manage a
virtual environment for you. You can install pipx with
brew install pipx
You may restore the old behavior of pip by passing
the '--break-system-packages' flag to pip, or by adding
'break-system-packages = true' to your pip.conf file. The latter
will permanently disable this error.
If you disable this error, we STRONGLY recommend that you additionally
pass the '--user' flag to pip, or set 'user = true' in your pip.conf
file. Failure to do this can result in a broken Homebrew installation.
Read more about this behavior here: <https://peps.python.org/pep-0668/>
note: If you believe this is a mistake, please contact your Python installation or OS distribution provider. You can override this, at the risk of breaking your Python installation or OS, by passing --break-system-packages.
hint: See PEP 668 for the detailed specification.
saint@MacBookPro LLMs-from-scratch %
saint@MacBookPro LLMs-from-scratch % pip3 install torch --break-system-packages
Collecting torch
Downloading torch-2.6.0-cp313-none-macosx_11_0_arm64.whl.metadata (28 kB)
Collecting filelock (from torch)
Downloading filelock-3.17.0-py3-none-any.whl.metadata (2.9 kB)
Collecting typing-extensions>=4.10.0 (from torch)
Downloading typing_extensions-4.12.2-py3-none-any.whl.metadata (3.0 kB)
Collecting networkx (from torch)
Downloading networkx-3.4.2-py3-none-any.whl.metadata (6.3 kB)
Collecting jinja2 (from torch)
Downloading jinja2-3.1.5-py3-none-any.whl.metadata (2.6 kB)
Collecting fsspec (from torch)
Downloading fsspec-2025.2.0-py3-none-any.whl.metadata (11 kB)
Collecting setuptools (from torch)
Downloading setuptools-75.8.0-py3-none-any.whl.metadata (6.7 kB)
Collecting sympy==1.13.1 (from torch)
Downloading sympy-1.13.1-py3-none-any.whl.metadata (12 kB)
Collecting mpmath<1.4,>=1.1.0 (from sympy==1.13.1->torch)
Downloading mpmath-1.3.0-py3-none-any.whl.metadata (8.6 kB)
Collecting MarkupSafe>=2.0 (from jinja2->torch)
Downloading MarkupSafe-3.0.2-cp313-cp313-macosx_11_0_arm64.whl.metadata (4.0 kB)
Downloading torch-2.6.0-cp313-none-macosx_11_0_arm64.whl (66.5 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 66.5/66.5 MB 74.3 MB/s eta 0:00:00
Downloading sympy-1.13.1-py3-none-any.whl (6.2 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 6.2/6.2 MB 75.0 MB/s eta 0:00:00
Downloading typing_extensions-4.12.2-py3-none-any.whl (37 kB)
Downloading filelock-3.17.0-py3-none-any.whl (16 kB)
Downloading fsspec-2025.2.0-py3-none-any.whl (184 kB)
Downloading jinja2-3.1.5-py3-none-any.whl (134 kB)
Downloading networkx-3.4.2-py3-none-any.whl (1.7 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1.7/1.7 MB 63.7 MB/s eta 0:00:00
Downloading setuptools-75.8.0-py3-none-any.whl (1.2 MB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 1.2/1.2 MB 37.0 MB/s eta 0:00:00
Downloading MarkupSafe-3.0.2-cp313-cp313-macosx_11_0_arm64.whl (12 kB)
Downloading mpmath-1.3.0-py3-none-any.whl (536 kB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 536.2/536.2 kB 27.9 MB/s eta 0:00:00
Installing collected packages: mpmath, typing-extensions, sympy, setuptools, networkx, MarkupSafe, fsspec, filelock, jinja2, torch
Successfully installed MarkupSafe-3.0.2 filelock-3.17.0 fsspec-2025.2.0 jinja2-3.1.5 mpmath-1.3.0 networkx-3.4.2 setuptools-75.8.0 sympy-1.13.1 torch-2.6.0 typing-extensions-4.12.2
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
saint@MacBookPro LLMs-from-scratch %
The pytorch import finally works! The next error is also a PackageNotFoundError: "No package metadata was found for tiktoken" which I addressed with the same installation steps:
saint@MacBookPro LLMs-from-scratch % pip3 install tiktoken
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
error: externally-managed-environment
× This environment is externally managed
╰─> To install Python packages system-wide, try brew install
xyz, where xyz is the package you are trying to
install.
If you wish to install a Python library that isn't in Homebrew,
use a virtual environment:
python3 -m venv path/to/venv
source path/to/venv/bin/activate
python3 -m pip install xyz
If you wish to install a Python application that isn't in Homebrew,
it may be easiest to use 'pipx install xyz', which will manage a
virtual environment for you. You can install pipx with
brew install pipx
You may restore the old behavior of pip by passing
the '--break-system-packages' flag to pip, or by adding
'break-system-packages = true' to your pip.conf file. The latter
will permanently disable this error.
If you disable this error, we STRONGLY recommend that you additionally
pass the '--user' flag to pip, or set 'user = true' in your pip.conf
file. Failure to do this can result in a broken Homebrew installation.
Read more about this behavior here: <https://peps.python.org/pep-0668/>
note: If you believe this is a mistake, please contact your Python installation or OS distribution provider. You can override this, at the risk of breaking your Python installation or OS, by passing --break-system-packages.
hint: See PEP 668 for the detailed specification.
saint@MacBookPro LLMs-from-scratch %
saint@MacBookPro LLMs-from-scratch % pip3 install tiktoken --break-system-packages
Collecting tiktoken
Downloading tiktoken-0.8.0-cp313-cp313-macosx_11_0_arm64.whl.metadata (6.6 kB)
Collecting regex>=2022.1.18 (from tiktoken)
Downloading regex-2024.11.6-cp313-cp313-macosx_11_0_arm64.whl.metadata (40 kB)
Collecting requests>=2.26.0 (from tiktoken)
Downloading requests-2.32.3-py3-none-any.whl.metadata (4.6 kB)
Collecting charset-normalizer<4,>=2 (from requests>=2.26.0->tiktoken)
Downloading charset_normalizer-3.4.1-cp313-cp313-macosx_10_13_universal2.whl.metadata (35 kB)
Collecting idna<4,>=2.5 (from requests>=2.26.0->tiktoken)
Downloading idna-3.10-py3-none-any.whl.metadata (10 kB)
Collecting urllib3<3,>=1.21.1 (from requests>=2.26.0->tiktoken)
Downloading urllib3-2.3.0-py3-none-any.whl.metadata (6.5 kB)
Collecting certifi>=2017.4.17 (from requests>=2.26.0->tiktoken)
Downloading certifi-2025.1.31-py3-none-any.whl.metadata (2.5 kB)
Downloading tiktoken-0.8.0-cp313-cp313-macosx_11_0_arm64.whl (982 kB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 982.8/982.8 kB 24.2 MB/s eta 0:00:00
Downloading regex-2024.11.6-cp313-cp313-macosx_11_0_arm64.whl (284 kB)
Downloading requests-2.32.3-py3-none-any.whl (64 kB)
Downloading certifi-2025.1.31-py3-none-any.whl (166 kB)
Downloading charset_normalizer-3.4.1-cp313-cp313-macosx_10_13_universal2.whl (195 kB)
Downloading idna-3.10-py3-none-any.whl (70 kB)
Downloading urllib3-2.3.0-py3-none-any.whl (128 kB)
Installing collected packages: urllib3, regex, idna, charset-normalizer, certifi, requests, tiktoken
Successfully installed certifi-2025.1.31 charset-normalizer-3.4.1 idna-3.10 regex-2024.11.6 requests-2.32.3 tiktoken-0.8.0 urllib3-2.3.0
[notice] A new release of pip is available: 24.3.1 -> 25.0
[notice] To update, run: python3.13 -m pip install --upgrade pip
saint@MacBookPro LLMs-from-scratch %
Finally, my machine is in a state that can run the code in the Jupyter notebook! This is such a brittle environment. I need to switch to a managed environment to avoid this type of mess.
While digging around in Bugzilla (as is now my usual daily custom), I came across Bug 580468 – JM: Tune Trace JIT Heuristics. It was interesting following the discussion since it was a perfect illustration of the principles being taught in CS470. Therefore, I wrote up this brief summary of the bug discussion to reinforce to myself how practical these issues are: Practical AI.
