{"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/polynomial-regression-as-a-task-for","title":"Polynomial Regression as a Task for Understanding In-context Learning Through Finetuning and Alignment","arxiv_id":"2407.19346","date":"2024-07-27","proceeding":null,"authors":["Max Wilcoxson","Morten Svendgård","Ria Doshi","Dylan Davis","Reya Vir","Anant Sahai"],"abstract":"Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or multi-layer-perceptrons lack the structure required to explore things like prompting and alignment within models capable of in-context-learning. We propose univariate polynomial regression as a function class that is just rich enough to study prompting and alignment, while allowing us to visualize and understand what is going on clearly.","url_abs":"https://arxiv.org/abs/2407.19346v1","url_pdf":"https://arxiv.org/pdf/2407.19346v1.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":"polynomial-regression-as-a-task-for","repo_url":"https://github.com/MSNetrom/in-context-poly-playground","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"in-context-learning","task_name":"In-Context Learning"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2407.19346","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2407.19346"}},"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":"deterministic:regex_extraction","url":"https://github.com/in-context-learning-2024/in-context","reach":null},{"provenance":"deterministic:regex_extraction","url":"https://github.com/dtsip/in-context-learning","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/MSNetrom/in-context-poly-playground","reach":null}],"summary":{"ran":6,"ran_honours":1,"unverified":5},"by_repo_kind":{"official":{"samples":3,"ran":2,"repositories":1},"found_in_text":{"samples":9,"ran":5,"repositories":2}},"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":7,"samples":[{"code_sha256_prefix":"3eb106cd7a7e9cc1","entry":"LinearRegression","repo":"MSNetrom/in-context-poly-playground","repo_kind":"official","path":"src/function_classes/linear.py","file_url":"https://github.com/MSNetrom/in-context-poly-playground/blob/HEAD/src/function_classes/linear.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3eb106cd7a7e9cc1"}},{"code_sha256_prefix":"926e7dbb8fa5faf9","entry":"LinearRegression","repo":"dtsip/in-context-learning","repo_kind":"found_in_text","path":"src/tasks.py","file_url":"https://github.com/dtsip/in-context-learning/blob/HEAD/src/tasks.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"926e7dbb8fa5faf9"}},{"code_sha256_prefix":"d368898a33daca4b","entry":"QuadraticRegression","repo":"MSNetrom/in-context-poly-playground","repo_kind":"official","path":"src/function_classes/linear.py","file_url":"https://github.com/MSNetrom/in-context-poly-playground/blob/HEAD/src/function_classes/linear.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d368898a33daca4b"}},{"code_sha256_prefix":"0aee68a20552f9dd","entry":"QuadraticRegression","repo":"dtsip/in-context-learning","repo_kind":"found_in_text","path":"src/tasks.py","file_url":"https://github.com/dtsip/in-context-learning/blob/HEAD/src/tasks.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0aee68a20552f9dd"}},{"code_sha256_prefix":"e2972d7794b7ddbc","entry":"generate_chebyshev_coefficients","repo":"in-context-learning-2024/in-context","repo_kind":"found_in_text","path":"src/function_classes/chebyshev.py","file_url":"https://github.com/in-context-learning-2024/in-context/blob/HEAD/src/function_classes/chebyshev.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e2972d7794b7ddbc"}},{"code_sha256_prefix":"fc94f27a0973e093","entry":"mean_squared_error","repo":"dtsip/in-context-learning","repo_kind":"found_in_text","path":"src/tasks.py","file_url":"https://github.com/dtsip/in-context-learning/blob/HEAD/src/tasks.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fc94f27a0973e093"}},{"code_sha256_prefix":"348d63a78eb4cb94","entry":"squared_error","repo":"dtsip/in-context-learning","repo_kind":"found_in_text","path":"src/tasks.py","file_url":"https://github.com/dtsip/in-context-learning/blob/HEAD/src/tasks.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"348d63a78eb4cb94"}},{"code_sha256_prefix":"160b660cf85ae216","entry":"AbstractionError","repo":"in-context-learning-2024/in-context","repo_kind":"found_in_text","path":"src/function_classes/chebyshev.py","file_url":"https://github.com/in-context-learning-2024/in-context/blob/HEAD/src/function_classes/chebyshev.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"160b660cf85ae216"}},{"code_sha256_prefix":"f0b437535684e5a1","entry":"ChebyshevKernelLinearRegression","repo":"in-context-learning-2024/in-context","repo_kind":"found_in_text","path":"src/function_classes/chebyshev.py","file_url":"https://github.com/in-context-learning-2024/in-context/blob/HEAD/src/function_classes/chebyshev.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f0b437535684e5a1"}},{"code_sha256_prefix":"5896b81a520fc291","entry":"FunctionClass","repo":"MSNetrom/in-context-poly-playground","repo_kind":"official","path":"src/function_classes/linear.py","file_url":"https://github.com/MSNetrom/in-context-poly-playground/blob/HEAD/src/function_classes/linear.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5896b81a520fc291"}},{"code_sha256_prefix":"38900f51ceeb94d5","entry":"FunctionClass","repo":"in-context-learning-2024/in-context","repo_kind":"found_in_text","path":"src/function_classes/chebyshev.py","file_url":"https://github.com/in-context-learning-2024/in-context/blob/HEAD/src/function_classes/chebyshev.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"38900f51ceeb94d5"}},{"code_sha256_prefix":"3e016983bf585f29","entry":"Task","repo":"dtsip/in-context-learning","repo_kind":"found_in_text","path":"src/tasks.py","file_url":"https://github.com/dtsip/in-context-learning/blob/HEAD/src/tasks.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3e016983bf585f29"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}