{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/explicit-and-data-efficient-encoding-via","title":"Explicit and data-Efficient Encoding via Gradient Flow","arxiv_id":"2412.00864","date":"2024-12-01","proceeding":null,"authors":["Kyriakos Flouris","Anna Volokitin","Gustav Bredell","Ender Konukoglu"],"abstract":"The autoencoder model typically uses an encoder to map data to a lower dimensional latent space and a decoder to reconstruct it. However, relying on an encoder for inversion can lead to suboptimal representations, particularly limiting in physical sciences where precision is key. We introduce a decoder-only method using gradient flow to directly encode data into the latent space, defined by ordinary differential equations (ODEs). This approach eliminates the need for approximate encoder inversion. We train the decoder via the adjoint method and show that costly integrals can be avoided with minimal accuracy loss. Additionally, we propose a $2^{nd}$ order ODE variant, approximating Nesterov's accelerated gradient descent for faster convergence. To handle stiff ODEs, we use an adaptive solver that prioritizes loss minimization, improving robustness. Compared to traditional autoencoders, our method demonstrates explicit encoding and superior data efficiency, which is crucial for data-scarce scenarios in the physical sciences. Furthermore, this work paves the way for integrating machine learning into scientific workflows, where precise and efficient encoding is critical. \\footnote{The code for this work is available at \\url{https://github.com/k-flouris/gfe}.}","url_abs":"https://arxiv.org/abs/2412.00864v2","url_pdf":"https://arxiv.org/pdf/2412.00864v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"explicit-and-data-efficient-encoding-via","repo_url":"https://github.com/k-flouris/gfe","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2412.00864","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2412.00864"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/k-flouris/gfe","reach":null}],"summary":{"ran_violates":1,"ran_honours":1},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":2,"samples":[{"code_sha256_prefix":"3ec0684ac41e99b4","entry":"step_size_func","repo":"k-flouris/gfe","repo_kind":"official","path":"gflow.py","file_url":"https://github.com/k-flouris/gfe/blob/HEAD/gflow.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3ec0684ac41e99b4"}},{"code_sha256_prefix":"5920d47c32997c4a","entry":"time_steps_func","repo":"k-flouris/gfe","repo_kind":"official","path":"gflow.py","file_url":"https://github.com/k-flouris/gfe/blob/HEAD/gflow.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5920d47c32997c4a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}