Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework
Authors: Mustafa Hajij, Lennart Bastian, Sarah Osentoski, Hardik Kabaria, John Davenport, Dawood, Balaji Cherukuri, Joseph Kocheemoolayil, Nastaran Shahmansouri, Adrian Lew, Theodore Papamarkou, Tolga Birdal
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results establish CTNNs as a principled multi-scale foundation for the next generation of deep learning architectures. ... We conduct experiments on synthetic and real data in numerous settings to support the generality of our framework. These include learning physical dynamics, graph classification in homophillic and heterophilic cases and classifying higher-order complexes. |
| Researcher Affiliation | Collaboration | Mustafa Hajij1,2 Lennart Bastian3,7 Sarah Osentoski1 Hardik Kabaria1 John L. Davenport1 Sheik Dawood1 Balaji Cherukuri1 Joseph G. Kocheemoolayil1 Nastaran Shahmansouri1 Adrian Lew4 Theodore Papamarkou5 Tolga Birdal6 1Vinci4D 2University of San Francisco 3Technical University of Munich 4Stanford University 5Poly Shape 6Imperial College London 7MCML |
| Pseudocode | Yes | In Algorithm 1, we provide the pseudocode for our generic copresheaf-based transformer layer. This algorithm outlines the layer-wise update rule combining self-attention within cells of equal rank and cross-attention between different ranks, using learned copresheaf morphisms to transfer features between stalks. ... Algorithm 2 shows the pseudocode for the Copresheaf Conv used in our experiments. |
| Open Source Code | Yes | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: We will also release our code and data publicly upon publication. |
| Open Datasets | Yes | Data. MUTAG dataset, a nitroaromatic compound classification benchmark consisting of 188 molecular graphs... The UCI airfoil dataset (1 503 rows)... The TREC dataset consists of questions labeled with one of 6 coarse categories. |
| Dataset Splits | Yes | For heat and advection, the dataset is split into 500:100 train/test samples. For the unsteady Stokes data, the dataset is split into 160:40 train/test samples. ... The dataset is split into 80% train and 20% test samples. ... Our synthetic dataset comprises 200 training and 50 test CCs ... The dataset consists of 480:160 train/test samples, balanced across the four classes. ... We train on the TREC training set (5452 samples) ... The test set (500 samples) is used for evaluation. |
| Hardware Specification | No | Justification: Compute is not explicitly discussed; however, timings are not presented as part of the argument about the proposed approach and are not needed for a to replicate the results. Compute resources are modest (single GPU runs); details are not essential to reproducing results. |
| Software Dependencies | No | We train our networks using Adam W wiht a learning rate of 10 3, cosine LR scheduling, and batch size of two. ... All models are trained using Adam with a learning rate of 0.01, and a batch size of 16. ... Models are trained for four epochs using Adam with a learning rate of 10 3 and a batch size of 8, minimizing cross-entropy loss. |
| Experiment Setup | Yes | Model and training. For heat and advection, we use two transformer layers (positional encoding, four heads, stalk dimension equal to 16), followed by a mean pooling and linear head yielding 64D token embeddings. We train our networks using Adam W wiht a learning rate of 10 3, cosine LR scheduling, and batch size of two. We use 50 epochs for the heat dataset and 80 for the advection dataset, and report the results over three seeds. For the unsteady Stokes data, we test a compact convolution-transformer U-Net consisting of a convolutional encoder with two input and 32 output channels, followed by two transformer layers (four heads, hidden dimension equal to 32, and stalk dimension 8), and a convolutional decoder mapping back to two output channels. We train it for 300 epochs using Adam W with a batch size of four. |