The CLRS Algorithmic Reasoning Benchmark

Learning representations of algorithms is an emerging area of machine learning, seeking to bridge concepts from neural networks with classical algorithms. The CLRS Algorithmic Reasoning Benchmark (CLRS) consolidates and extends previous work torward evaluation algorithmic reasoning by providing a suite of implementations of classical algorithms. These algorithms have been selected from the third edition of the standard Introduction to Algorithms by Cormen, Leiserson, Rivest and Stein.

Installation

The CLRS Algorithmic Reasoning Benchmark can be installed with pip directly from GitHub, with the following command:

pip install git+git://github.com/deepmind/clrs.git

Getting started

To set up a Python virtual environment with the required dependencies, run:

python3 -m venv clrs_env
source clrs_env/bin/activate
python setup.py install

and to run our example baseline model:

python -m clrs.examples.run

Algorithms as graphs

CLRS implements the selected algorithms in an idiomatic way, which aligns as closely as possible to the original CLRS 3ed pseudocode. By controlling the input data distribution to conform to the preconditions we are able to automatically generate input/output pairs. We additionally provide trajectories of "hints" that expose the internal state of each algorithm, to both optionally simplify the learning challenge and to distinguish between different algorithms that solve the same overall task (e.g. sorting).

In the most generic sense, algorithms can be seen as manipulating sets of objects, along with any relations between them (which can themselves be decomposed into binary relations). Accordingly, we study all of the algorithms in this benchmark using a graph representation. In the event that objects obey a more strict ordered structure (e.g. arrays or rooted trees), we impose this ordering through inclusion of predecessor links.

How it works

For each algorithm, we provide a canonical set of train, eval and test trajectories for benchmarking out-of-distribution generalization.

where "problem size" refers to e.g. the length of an array or number of nodes in a graph, depending on the algorithm. These trajectories can be used like so:

train_ds, spec = clrs.clrs21_train("bfs")

for step in range(num_train_steps):
  feedback = train_sampler.next(batch_size)
  model.train(feedback.features)

Here, feedback is a namedtuple with the following structure:

Feedback = collections.namedtuple('Feedback', ['features', 'outputs'])
Features = collections.namedtuple('Features', ['inputs', 'hints', 'lengths'])

where the content of Features can be used for training and outputs is reserved for evaluation. Each field of the tuple is an ndarray with a leading batch dimension. Because hints are provided for the full algorithm trajectory, these contain an additional time dimension padded up to the maximum length max(T) of any trajectory within the dataset. The lengths field specifies the true length t <= max(T) for each trajectory, which can be used e.g. for loss masking.

Please see the examples directory for full working Graph Neural Network (GNN) examples using JAX and the DeepMind JAX Ecosystem of libraries.

What we provide

Algorithms

Our initial CLRS-21 benchmark includes the following 21 algorithms. More algorithms will be supported in the near future.

• Divide and conquer
  • Maximum subarray (Kadane)
• Dynamic programming
  • Matrix chain order
  • Optimal binary search tree
• Graphs
  • Depth-first search
  • Breadth-first search
  • Topological sort
  • Minimum spanning tree (Prim)
  • Single-source shortest-path (Bellman Ford)
  • Single-source shortest-path (Dijsktra)
  • DAG shortest paths
  • All-pairs shortest-path (Floyd Warshall)
• Greedy
  • Task scheduling
• Searching
  • Minimum
  • Binary search
  • Quickselect
• Sorting
  • Insertion sort
  • Bubble sort
  • Heapsort
  • Quicksort
• Strings
  • String matcher (naive)
  • String matcher (KMP)

Baselines

We additionally provide JAX implementations of the following GNN baselines:

• Graph Attention Networks (Velickovic et al., ICLR 2018)
• Message-Passing Neural Networks (Gilmer et al., ICML 2017)

Citation

To cite the CLRS Algorithmic Reasoning Benchmark:

@article{deepmind2021clrs,
  author = {Petar Veli\v{c}kovi\'{c} and Adri\`{a} Puigdom\`{e}nech Badia and
    David Budden and Razvan Pascanu and Andrea Banino and Misha Dashevskiy and
    Raia Hadsell and Charles Blundell},
  title = {The CLRS Algorithmic Reasoning Benchmark},
  year = {2021},
}