The Abstraction and Reasoning Corpus: Conclusion & References

This paper is available on arxiv under CC 4.0 license. Authors: (1) Mattia Atzeni, EPFL, Switzerland and mattia.atzeni@outlook.it; (2) Mrinmaya Sachan, ETH Zurich, Switzerland; (3) Andreas Loukas, Prescient Design, Switzerland. Table of Links Abstract & Introduction Formalizing the Group-Action Learning Problem Attention Masks for Core Geometry Priors The LATFORMER Architecture Experiments Related Work Conclusion & References A. Additional Details on the Model B. Additional Experiments and Details on the Experimental Setup C. Limitations and Future Work D. Deferred Proofs 7. Conclusion Motivated by the long-term ambitious goal of infusing core knowledge priors in neural networks, this paper focused on how to help deep learning models to learn geometric transformations efficiently. Specifically, we proposed to incorporate lattice symmetry biases into attention mechanisms by modulating the attention weights using learned soft masks. We have shown that attention masks implementing the actions of the symmetry group of a hypercubic lattice exist, and we provided a way to represent these masks. This motivated us to introduce LATFORMER, a model that generates attention masks corresponding to lattice symmetry priors using a CNN. Our results on synthetic tasks show that our model can generalize better than the same attention modules without masking and Transformers. Moreover, the performance of our method on a subset of ARC provides the first evidence that deep learning can be used on this dataset, which is widely considered as an important open challenge for research on artificial intelligence. References Acquaviva, S., Pu, Y., Kryven, M., Wong, C., Ecanow, G. E., Nye, M. I., Sechopoulos, T., Tessler, M. H., and Tenenbaum, J. B. Communicating natural programs to humans and machines. CoRR, abs/2106.07824, 2021. URL https://arxiv.org/abs/2106.07824. Andreoli, J.-M. Convolution, attention and structure embedding. arXiv preprint arXiv:1905.01289, 2019. Atzeni, M. and Atzori, M. What is the cube root of 27? question answering over codeontology. In Vrandecic, D., Bontcheva, K., Suarez-Figueroa, M. C., Presutti, V., ´ Celino, I., Sabou, M., Kaffee, L., and Simperl, E. (eds.), The Semantic Web - ISWC 2018 - 17th International Semantic Web Conference, Monterey, CA, USA, October 8-12, 2018, Proceedings, Part I, volume 11136 of Lecture Notes in Computer Science, pp. 285–300. Springer, 2018. doi: 10.1007/978-3-030-00671-6\ 17. URL https:// doi.org/10.1007/978-3-030-00671-6_17. Atzeni, M., Bogojeska, J., and Loukas, A. SQALER: scaling question answering by decoupling multi-hop and logical reasoning. In Ranzato, M., Beygelzimer, A., Dauphin, Y. N., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pp. 12587– 12599, 2021. URL https://proceedings. neurips.cc/paper/2021/hash/ 68bd22864919297c8c8a8c32378e89b4-Abstract. html. Bahdanau, D., Murty, S., Noukhovitch, M., Nguyen, T. H., de Vries, H., and Courville, A. C. Systematic generalization: What is required and can it be learned? In ICLR 2019, 2019. Battaglia, P. W., Hamrick, J. B., Bapst, V., SanchezGonzalez, A., Zambaldi, V. F., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., Gul¨ c¸ehre, C¸ ., Song, F., Ballard, A. J., Gilmer, J., Dahl, G. E., Vaswani, A., Allen, K., Nash, C., Langston, V., Dyer, C., Heess, N., Wierstra, D., Kohli, P., Botvinick, M., Vinyals, O., Li, Y., and Pascanu, R. Relational inductive biases, deep learning, and graph networks. CoRR, abs/1806.01261, 2018. Bengio, Y. The consciousness prior. CoRR, abs/1709.08568, 2017. Bronstein, M. M., Bruna, J., Cohen, T., and Velickovi ˇ c,´ P. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges. arXiv preprint arXiv:2104.13478, 2021. Chollet, F. On the measure of intelligence. CoRR, abs/1911.01547, 2019. URL http://arxiv.org/ abs/1911.01547. Cordonnier, J.-B., Loukas, A., and Jaggi, M. On the relationship between self-attention and convolutional layers. In Eighth International Conference on Learning Representations-ICLR 2020, number CONF, 2020. Cordonnier, J.-B., Loukas, A., and Jaggi, M. On the relationship between self-attention and convolutional layers. In Eighth International Conference on Learning Representations-ICLR 2020, number CONF, 2020. Goyal, Y., Khot, T., Summers-Stay, D., Batra, D., and Parikh, D. Making the V in VQA matter: Elevating the role of image understanding in visual question answering. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pp. 6325–6334. IEEE Computer Society, 2017. doi: 10.1109/CVPR.2017.670. URL https://doi.org/10.1109/CVPR.2017.670. Graves, A., Wayne, G., and Danihelka, I. Neural turing machines. arXiv preprint arXiv:1410.5401, 2014. Graves, A., Wayne, G., Reynolds, M., Harley, T., Danihelka, I., Grabska-Barwinska, A., Colmenarejo, S. G., Grefenstette, E., Ramalho, T., Agapiou, J. P., Badia, A. P., Hermann, K. M., Zwols, Y., Ostrovski, G., Cain, A., King, H., Summerfield, C., Blunsom, P., Kavukcuoglu, K., and Hassabis, D. Hybrid computing using a neural network with dynamic external memory. Nat., 538 (7626):471–476, 2016. doi: 10.1038/nature20101. URL https://doi.org/10.1038/nature20101. Gul, M. S. K., Batz, M., and Keinert, J. Pixel-wise ¨ confidences for stereo disparities using recurrent neural networks. 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In Wallach, H. M., Larochelle, H., Beygelzimer, A., d’Alche-Buc, F., Fox, E. B., and ´ Garnett, R. (eds.), Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pp. 5901–5914, 2019. Jiang, W., Trulls, E., Hosang, J., Tagliasacchi, A., and Yi, K. M. COTR: correspondence transformer for matching across images. In 2021 IEEE/CVF International Conference on Computer Vision, ICCV 2021, Montreal, QC, Canada, October 10-17, 2021, pp. 6187–6197. IEEE, 2021. doi: 10.1109/ICCV48922.2021.00615. URL https://doi.org/10.1109/ICCV48922. 2021.00615. Johnson, J., Hariharan, B., van der Maaten, L., Fei-Fei, L., Zitnick, C. L., and Girshick, R. B. CLEVR: A diagnostic dataset for compositional language and elementary visual reasoning. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pp. 1988–1997. 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This paper is available on arxiv under CC 4.0 license. Authors: (1) Mattia Atzeni, EPFL, Switzerland and mattia.atzeni@outlook.it; (2) Mrinmaya Sachan, ETH Zurich, Switzerland; (3) Andreas Loukas, Prescient Design, Switzerland. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Mattia Atzeni, EPFL, Switzerland and mattia.atzeni@outlook.it; (2) Mrinmaya Sachan, ETH Zurich, Switzerland; (3) Andreas Loukas, Prescient Design, Switzerland. Table of Links Abstract & Introduction Formalizing the Group-Action Learning Problem Attention Masks for Core Geometry Priors The LATFORMER Architecture Experiments Related Work Conclusion & References A. Additional Details on the Model B. Additional Experiments and Details on the Experimental Setup C. Limitations and Future Work D. Deferred Proofs Abstract & Introduction Abstract & Introduction Formalizing the Group-Action Learning Problem Formalizing the Group-Action Learning Problem Attention Masks for Core Geometry Priors Attention Masks for Core Geometry Priors The LATFORMER Architecture The LATFORMER Architecture Experiments Experiments Related Work Related Work Conclusion & References Conclusion & References A. Additional Details on the Model A. Additional Details on the Model B. Additional Experiments and Details on the Experimental Setup B. Additional Experiments and Details on the Experimental Setup C. Limitations and Future Work C. Limitations and Future Work D. Deferred Proofs D. Deferred Proofs 7. Conclusion Motivated by the long-term ambitious goal of infusing core knowledge priors in neural networks, this paper focused on how to help deep learning models to learn geometric transformations efficiently. Specifically, we proposed to incorporate lattice symmetry biases into attention mechanisms by modulating the attention weights using learned soft masks. We have shown that attention masks implementing the actions of the symmetry group of a hypercubic lattice exist, and we provided a way to represent these masks. This motivated us to introduce LATFORMER, a model that generates attention masks corresponding to lattice symmetry priors using a CNN. Our results on synthetic tasks show that our model can generalize better than the same attention modules without masking and Transformers. Moreover, the performance of our method on a subset of ARC provides the first evidence that deep learning can be used on this dataset, which is widely considered as an important open challenge for research on artificial intelligence. References Acquaviva, S., Pu, Y., Kryven, M., Wong, C., Ecanow, G. E., Nye, M. I., Sechopoulos, T., Tessler, M. H., and Tenenbaum, J. B. Communicating natural programs to humans and machines. CoRR, abs/2106.07824, 2021. URL https://arxiv.org/abs/2106.07824. Andreoli, J.-M. Convolution, attention and structure embedding. arXiv preprint arXiv:1905.01289, 2019. Atzeni, M. and Atzori, M. What is the cube root of 27? question answering over codeontology. In Vrandecic, D., Bontcheva, K., Suarez-Figueroa, M. C., Presutti, V., ´ Celino, I., Sabou, M., Kaffee, L., and Simperl, E. (eds.), The Semantic Web - ISWC 2018 - 17th International Semantic Web Conference, Monterey, CA, USA, October 8-12, 2018, Proceedings, Part I, volume 11136 of Lecture Notes in Computer Science, pp. 285–300. Springer, 2018. doi: 10.1007/978-3-030-00671-6\ 17. URL https:// doi.org/10.1007/978-3-030-00671-6_17. Atzeni, M., Bogojeska, J., and Loukas, A. SQALER: scaling question answering by decoupling multi-hop and logical reasoning. In Ranzato, M., Beygelzimer, A., Dauphin, Y. N., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pp. 12587– 12599, 2021. URL https://proceedings. neurips.cc/paper/2021/hash/ 68bd22864919297c8c8a8c32378e89b4-Abstract. html. Bahdanau, D., Murty, S., Noukhovitch, M., Nguyen, T. H., de Vries, H., and Courville, A. C. Systematic generalization: What is required and can it be learned? In ICLR 2019, 2019. Battaglia, P. W., Hamrick, J. B., Bapst, V., SanchezGonzalez, A., Zambaldi, V. F., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., Gul¨ c¸ehre, C¸ ., Song, F., Ballard, A. J., Gilmer, J., Dahl, G. E., Vaswani, A., Allen, K., Nash, C., Langston, V., Dyer, C., Heess, N., Wierstra, D., Kohli, P., Botvinick, M., Vinyals, O., Li, Y., and Pascanu, R. Relational inductive biases, deep learning, and graph networks. CoRR, abs/1806.01261, 2018. Bengio, Y. The consciousness prior. CoRR, abs/1709.08568, 2017. Bronstein, M. M., Bruna, J., Cohen, T., and Velickovi ˇ c,´ P. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges. arXiv preprint arXiv:2104.13478, 2021. Chollet, F. On the measure of intelligence. CoRR, abs/1911.01547, 2019. URL http://arxiv.org/ abs/1911.01547. Cordonnier, J.-B., Loukas, A., and Jaggi, M. On the relationship between self-attention and convolutional layers. In Eighth International Conference on Learning Representations-ICLR 2020, number CONF, 2020. Cordonnier, J.-B., Loukas, A., and Jaggi, M. On the relationship between self-attention and convolutional layers. In Eighth International Conference on Learning Representations-ICLR 2020, number CONF, 2020. Goyal, Y., Khot, T., Summers-Stay, D., Batra, D., and Parikh, D. Making the V in VQA matter: Elevating the role of image understanding in visual question answering. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017, pp. 6325–6334. IEEE Computer Society, 2017. doi: 10.1109/CVPR.2017.670. URL https://doi.org/10.1109/CVPR.2017.670. Graves, A., Wayne, G., and Danihelka, I. Neural turing machines. arXiv preprint arXiv:1410.5401, 2014. Graves, A., Wayne, G., Reynolds, M., Harley, T., Danihelka, I., Grabska-Barwinska, A., Colmenarejo, S. G., Grefenstette, E., Ramalho, T., Agapiou, J. P., Badia, A. P., Hermann, K. M., Zwols, Y., Ostrovski, G., Cain, A., King, H., Summerfield, C., Blunsom, P., Kavukcuoglu, K., and Hassabis, D. Hybrid computing using a neural network with dynamic external memory. Nat., 538 (7626):471–476, 2016. doi: 10.1038/nature20101. URL https://doi.org/10.1038/nature20101. Gul, M. S. K., Batz, M., and Keinert, J. Pixel-wise ¨ confidences for stereo disparities using recurrent neural networks. 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IEEE Computer Society, 2017a. doi: 10.1109/CVPR.2017.215. URL https://doi.org/10.1109/CVPR.2017.215. Johnson, J., Hariharan, B., van der Maaten, L., Hoffman, J., Fei-Fei, L., Zitnick, C. L., and Girshick, R. B. Inferring and executing programs for visual reasoning. In IEEE International Conference on Computer Vision, ICCV 2017, Venice, Italy, October 22-29, 2017, pp. 3008–3017. IEEE Computer Society, 2017b. doi: 10.1109/ICCV.2017.325. URL https://doi.org/10.1109/ICCV.2017. 325. Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Zˇ´ıdek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. Nature, 596(7873):583–589, 2021. Kolev, V., Georgiev, B., and Penkov, S. Neural abstract reasoner. CoRR, abs/2011.09860, 2020. URL https: //arxiv.org/abs/2011.09860. Lake, B. M. and Baroni, M. Generalization without systematicity: On the compositional skills of sequence-tosequence recurrent networks. 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