Title: Generalization vs Specialization under Concept Shift
Venue: NeurIPS 2025
Accepted: yes
Keywords: concept shift

distribution shift

ridge regression

thermodynamic limit

high-dimensional learning

solvable model

out-of-distribution generalization
Abstract: Machine learning models are often brittle under distribution shift, i.e., when data distributions at test time differ from those during training. Understanding this failure mode is central to identifying and mitigating safety risks of mass adoption of machine learning. Here we analyze ridge regression under concept shift—a form of distribution shift in which the input-label relationship changes at test time. We derive an exact expression for prediction risk in the thermodynamic limit. Our results reveal nontrivial effects of concept shift on generalization performance, including a phase transition between weak and strong concept shift regimes and nonmonotonic data dependence of test performance even when double descent is absent. Our theoretical results are in good agreement with experiments based on transformers pretrained to solve linear regression; under concept shift, too long context length can be detrimental to generalization performance of next token prediction. Finally, experiments on MNIST and FashionMNIST further validate our theoretical predictions, suggesting these phenomena represent a fundamental aspect of learning under distribution shift.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies regression/classification performance with ridge regression under concept shift and show that concept shift can change the qualitative behavior of generalization behavior. Authors report experimental results for regression tasks using pretrained transformers to solve linear regression and for classification tasks using well known MNIST and FashionMNIST datasets. Empirical investigations show that ridge regression fails to generalize even with infinite data under a strong enough concept shift. They also demonstrate that too much data can harm generalization when dealing with anisotropy in features.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- The topic addressed by this paper is of great significance since concept shift remains an active challenge for many ML systems in practice.\n- The theoretical aspect of the paper is solid and it provides a rigorous understanding of model performance under concept shift. The studied setting, i.e. concept shift, is well defined.\n- Experimental results shed light into less explored aspect of generalization performance under the studied settings e.g. empirical studies of how anisotropic features can cause more data hurting generalization performance.\n\n**Weaknesses**\n- Authors study concept shift's impact on ridge regression, an inherently linear model, which may make the observed model behavior specific to this oversimplified settings.\n- The impact of concept shift on generalization performance is not well studied for classification tasks since the studied datasets for classification are rather simple and do not pose real world concept shift challenges.\n- The paper is not easy to read. e.g. instead of using intuitive and easy to understand X and Y axis titles, authors have decided to use mathematical statements. e.g. Figure captions do not highlight the main observations/takeaways.\n- Limitations of the work are not clearly and comprehensively listed by the authors.\n\nQUESTIONS:\n- How can researchers and machine learning practitioners leverage the learning from this work in their work? In particular, detecting or predicting concept shift in test data under real world settings can be hard or impossible which makes it challenging whether or not to consider that takeaways from this work at training stage.\n\nLIMITATIONS:\n- Please refer to the first two bullets under the **weaknesses** section of this review.\n- The high-dimensional limit assumption made in the paper does not necessarily match the practical settings.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper develops an exact theory of concept shift scenario in which the relationship between inputs and labels changes at test time, and studies how this shift alters the generalization behaviour of learning algorithms. They verify the analytic predictions with experiments, finding close quantitative and qualitative agreement. The paper provides a detailed theoretical and experimental characterization of how concept shift affects generalization.\n\nSTRENGTHS AND WEAKNESSES:\n## Srengths:\n1.\tThe paper delves deep into the issue of machine learning models under concept shift, centering on ridge regression to derive exact expressions. The methodology is rigorous.\n2.\tThe paper is well-structured and logically coherent. It starts with the problem of distribution shift, narrows down to concept shift, and elaborates on the research background and significance. It then proceeds to theoretically analyze ridge regression under concept shift. The experimental section follows naturally.\n3.\tUnderstanding the generalization of machine learning models under distribution shift is crucial for developing safe and robust techniques. This paper focuses on the relatively less-studied concept shift, offering valuable insights.\n## Weaknesses\n1.\tWhile the paper provides a detailed analysis of concept shift under ridge regression, the scope of its research is relatively limited.\n2.\tSome mathematical derivations and notations in the paper are quite complex, which may pose challenges for readers without a strong mathematical background.\n3.\tThe practical applicability of the findings remains to be further demonstrated.\n\nQUESTIONS:\n1.\tThe paper focuses on ridge regression. How do the findings extend to other machine learning models?\n2.\tThe experiments are limited to MNIST and FashionMNIST. Could more diverse datasets be used to validate the findings? How do the results vary across different types of data distributions and problem domains?\n3.\tWhat advantages does this work offer over previous solutions?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a theoretical study of how concept shift—a change in the input-label relationship—affects generalization in ridge regression. The authors provide exact expressions for prediction risk in the high-dimensional limit and identify a sharp phase transition: when concept shift is strong, adding more training data can actually worsen test performance. Experiments using in-context learning with transformers and classification on MNIST/FashionMNIST support the theory.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper identifies a clear and interesting phenomenon: more training data can hurt generalization under strong concept shift. \n2. The theoretical analysis is rigorous and based on a solvable model, offering precise characterizations. \n3. Experimental results on transformers and classification tasks are generally consistent with the theoretical predictions.\n\nWeaknesses:\n1. The theoretical results rely heavily on idealized settings: linear models, Gaussian features, and optimally tuned ridge regression. These are useful for analysis but may not reflect practical machine learning scenarios. Would similar effects appear with nonlinear models, neural networks, or non-Gaussian data? \n2. The shift is modeled only as scaling or rotating the regression coefficients. In real-world problems, concept shift is often more complex, involving sparse, structured, or gradual changes. Discuss how realistic this modeling is, and whether the findings generalize to more practical types of shift. \n3. While the paper highlights its novelty, it does not sufficiently compare with prior theoretical work on concept drift, streaming learning, or temporal domain generalization. \n4. The transformer experiments focus only on simple synthetic tasks (linear regression) and PCA-modified MNIST. These setups are still far from real-world settings.\n\nQUESTIONS:\nSee the Strengths And Weaknesses section.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper analyzes the mean-field behavior of generalization under **concept shift** in ridge regression, where the input–label mapping changes at test time. The authors derive a closed-form expression for the test error and study its properties on simple data models under *optimal* in-distribution regularization. They uncover a phase transition that separates a **generalization phase** (more data helps) from a **specialization phase** (more data hurts). These insights are then applied to in-context learning (ICL) and classification tasks, and validated in realistic experiments.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n1. The paper is well written and easy to follow; the problem setting and theoretical results are presented clearly.\n2. Asymptotics of regression under concept shift are not well studied; the authors make a solid contribution by providing an intuitive mathematical exposition.\n3. They identify a novel “double-descent” behavior that interestingly appears only at test time.\n4. The theory is applied to ICL and shown to hold in non-trivial experimental settings.\n\n### Weaknesses\n\nThe theory focuses on *optimal* ridge regression to isolate generalization behavior under concept shift. With sub-optimal ridge, in-distribution generalization always degrades, but it is unclear whether the same holds for the OOD case. Optimal ridge may overspecialize the predictor to the training task and thus potentially contribute to poorer OOD performance. Couldn't there be an alternative ridge parameter which marginally worsens ID risk yet substantially improve OOD risk?\n\nAlso, the previous literature mainly considered optimizing ridge parameter with respect to OOD generalization (ref.\\[30,43]). How would that change the story? If optimally tuned ridge regression for ID yields an increasing OOD test risk, would tuning to optimal OOD ridge parameter have a similar effect on ID generalization?\n\nBelow are a few comments/suggestions\n\n1. **Line 85.** The risk need not approach to zero, but rather to an irreducible error (see ref. \\[43]) for generic feature maps. Likewise, the statement in line 88 is confusing; it would make more sense to me if $\\tilde\\beta_1 = \\beta_1$ and $\\tilde\\beta_{i>1} = 0$. It is just a technicality, but it confused me the first time I read it.\n2. **Line 117.** *nonrobut* → *non-robust*.\n3. Please clarify how your results differ from those of **Yue et al. (2023)** ([https://openreview.net/forum?id=Jw3ck7FWZh](https://openreview.net/forum?id=Jw3ck7FWZh)).\n4. What is the nature of the weak-to-strong concept-shift phase transition? Does it constitute a genuine phase transition in the strict statistical-mechanics sense—for example, does the risk exhibit a non-analyticity in κ cos θ—or is it merely a sharp crossover? A brief discussion would help readers interpret the result.\n\nQUESTIONS:\nSee above\n\nLIMITATIONS:\nThe study is limited to simple Gaussian data.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}