High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression

Wenqing Su; Yihan Zhao; Ying Yang

REVIEW 3 major objections 4 minor 37 references

High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Exact risk formula for continual ridge regression in high dimensions

desk verdict A genuine first result on exact asymptotic risk for continual ridge regression, with one load-bearing caveat (equal-distribution of θ) that the abstract over-sells and some unverified imported RMT machinery. read the letter →

arxiv 2508.15494 v1 pith:KFXOOKRA submitted 2025-08-21 stat.ME cs.LG

Yihan Zhao , Wenqing Su , Ying Yang This is my paper

classification stat.MEcs.LG MSC 62J0760B2062H12

keywords continuallearningridgeregressionhigh-dimensionalasymptoticsrandommatrixtheorypredictionriskcatastrophicforgettingbackwardtransferforward

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Continual learning models must keep predicting old tasks while adapting to new ones, and the paper asks when this trade-off can be quantified. It studies the simplest continual learner—ridge regression updated sequentially without replaying past data—and proves that in high dimensions its prediction risk on every task converges almost surely to an explicit formula. The formula depends only on the task covariances, ridge penalties, noise level, and the ratio of parameter dimension to sample size, and it yields exact limits for average risk, backward transfer, and forward transfer. This makes catastrophic forgetting and positive transfer quantitative rather than qualitative, and it allows the authors to draw risk curves showing how tuning and task similarity shape the learning dynamics.

What carries the argument

The load-bearing object is the resolvent of the regularized sample covariance matrix, (Σ̂_t + λ_t I)^{-1}, together with its deterministic equivalent. The proof shows that normalized traces of products of these resolvents concentrate, and that the joint empirical spectral distribution of the task covariance matrices fixes the scalar recursion coefficients appearing in the final risk formula. The entire high-dimensional matrix problem is thereby reduced to a low-dimensional recursion: transfer matrices B_t = λ_t(Σ̂_t + λ_t I)^{-1} propagate past estimates forward, and their averaged traces satisfy deterministic fixed-point equations whose solution enters directly into the asymptotic predictio

What would settle it

Simulate a two-task sequence with shared diagonal covariance matrices and a fixed coefficient vector concentrated on a single eigenvector, letting p and n grow with p/n_t → φ. If the observed prediction risk converges to the value predicted by Equation (9), the equal-distribution condition is unnecessary; if the risk fluctuates or converges elsewhere, the boundary is real and the formula does not apply to that coefficient structure.

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Extended reading notes

Core claim

The paper claims that in the proportional-limit regime—where each task sample size n_t and parameter dimension p grow together with p/n_t tending to a positive constant—the prediction risk of the continual ridge estimator converges almost surely to an explicit deterministic expression. The expression, given as Equation (9), is built from deterministic equivalents of resolvent matrices and the limiting spectral measure of the task covariances, and it captures how past estimators are compounded through products of transfer matrices. From this single formula the paper derives almost-sure limits for the three standard continual-learning evaluation metrics: weighted average risk, backward transfe

Load-bearing premise

The central proof assumes that when task covariance matrices are not isotropic, the true regression coefficients are equally distributed across their common eigenvectors (or are random with isotropic covariance); the paper itself notes that for fixed, unevenly structured θ the limiting risk may not exist.

Editorial extensions

If this is right

For any task sequence satisfying the assumptions, the asymptotic performance of continual ridge regression is fully determined by the tuple (Σ_t, λ_t, σ², p/n_t), so algorithms can be compared by closed-form risk rather than by simulation.
The almost-sure limits for average risk, backward transfer, and forward transfer mean that forgetting and transfer become deterministic quantities in the proportional-limit regime, with their signs and magnitudes readable from the risk curves.
With well-chosen regularization, average risk decreases nearly monotonically with task count and forward transfer eventually dominates; under-regularization delays forward transfer and inflates average risk.
The greedy per-step choice of ridge parameter—minimizing the current average risk—gives a computable tuning rule for continual learning when future tasks are unknown.
The theoretical risk curves for random versus increasing covariance shifts predict qualitatively different dynamics, including risk that rises to a peak and then declines when task covariances drift in a trended way.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The equal-distribution requirement on θ is the real boundary of the result: for a fixed coefficient vector concentrated on a few eigenvectors, the paper itself notes that the limiting risk may fail to exist, so the formula should be read as an averaged or random-θ prediction rather than a guarantee for every true coefficient vector.
Because the limit depends on task geometry only through the joint spectral distribution of covariances, task similarity here means similarity of eigenstructure; tasks that differ by a rotation of the feature basis would need a separate analysis.
The closed-form risk makes it possible to compute the regret of the greedy tuning rule against the offline oracle that knows all future tasks, a comparison the paper does not carry out.
The same resolvent-recursion mechanism should apply to any continual estimator with quadratic regularizers, such as elastic-net or EWC-style penalties, so the framework may extend before nonlinear models become tractable.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The headline: this is a real result, not a repackaging. It gives the first exact high-dimensional asymptotic prediction risk for continual ridge regression, and from it closed-form limits for average risk, backward transfer, and forward transfer. The proof structure in the appendix is genuine derivation—resolvent equations, concentration via Markov and Borel–Cantelli, deterministic equivalents—not fitted curves. The related-work placement is honest: Li et al. is fixed-design two-task bounds, Zhao et al. covers estimation error only, Evron et al. uses cyclic orderings. The novelty claim holds.

The soft spots are real but mostly at the edges. The one that matters is the equal-distribution condition on θ for non-isotropic covariances. The authors disclose it after Eq. (11) in Section 3, but the abstract's 'exact expressions' claim is materially broader than the theorem's actual domain. For a fixed, structured θ such as e_1, the limit need not exist and formula (9) does not apply. That restriction should be in the abstract or at least the introduction. It doesn't undercut the theorem as stated—under the stated assumptions the math is consistent—but the paper should stop advertising unqualified exactness.

Two other things. The experimental 'phenomena' come from an oracle/greedy regularization rule that minimizes the risk being plotted. That is fine for illustration, but the paper should label it more clearly as illustrative, not as evidence about practical continual learning. And I could not verify the provenance of the imported RMT results (Theorem 11, Corollary 12, Lemmas 13–15) from the received text; the equation rendering is badly garbled in places. That is a verification gap, not a demonstrated flaw, but the authors need to supply exact references and a clean version.

The citation pattern is not a problem. Self-citation to Zhao et al. 2024 is appropriate because that work covers estimation error only; this paper goes further.

Verdict: yes, send it to peer review. It deserves a serious referee. The referee will need to check the imported lemmas and the equal-distribution condition carefully, but the central derivation is substantial and the main limitation is disclosed in the body, even if the abstract overreaches.

Referee Report

3 major / 4 minor

Summary. The paper studies continual ridge regression in a high-dimensional linear model where p is proportional to the sample size of each task. The estimator is updated sequentially by ridge-regularizing the loss around the previous estimator. The main result, Theorem 3, claims an almost-sure closed-form limit for the out-of-sample prediction risk under proportional-limit asymptotics, expressed through deterministic equivalents and the limiting spectral measures of the task covariance matrices. From this limit the authors derive asymptotic expressions for three continual-learning metrics: average risk, backward transfer, and forward transfer. Three covariance structures (identical isotropic, isotropic with different scales, and diagonal block-structured) are worked out and supported by simulations. The paper also discusses a greedy regularization-parameter selection rule.

Significance. If the main theorem is correct, the paper provides a substantial advance: exact asymptotic risk formulas for continual ridge regression, extending the literature beyond two-task bounds and worst-case analyses, and making the dependence on task covariance spectra, ridge parameters, and dimension-to-sample ratios explicit. The derivation is principled in that the risk expressions are consequences of resolvent equations under stated assumptions rather than fitted curves, and the simulations appear to validate the formulas for the examples shown. The main value is as a benchmark and analytical tool for continual linear regression, provided the domain of applicability is stated precisely.

major comments (3)

[Section 3, paragraph after Eq. (11); Theorem 3] The abstract and introduction claim 'exact expressions of the asymptotic prediction risk' without qualification, but the paragraph after Eq. (11) concedes that for non-isotropic task covariances the limiting risk may not exist for all θ satisfying Assumption 3. Convergence is guaranteed only if the components of θ are equally distributed along the common eigenvectors of the Σ_t, or if θ is random with isotropic covariance. This is a condition on the unknown target θ, not on the method or on the feature distribution. A fixed structured θ such as θ = e_1 is outside the theorem even though it satisfies ordinary bounded-coordinate conditions. If Assumption 3 already includes the equal-distribution condition, the theorem is internally consistent but this must be stated explicitly and the abstract must be qualified; if not, Theorem 3 is overbroad. This is the load-bearing domain question for t
[Assumptions for Theorem 3; Section 3.2] The theorem and examples assume that the task covariance matrices share a common eigenbasis (they are simultaneously diagonalizable). The contribution statement says task similarity is characterized by the joint empirical spectral distribution of the task covariances, but that is only true in the common-eigenvector case. If the Σ_t have different eigenbases, the limiting risk can depend on the rotation of θ relative to the task covariances and is not determined by the spectra alone. The simultaneous-diagonalizability restriction should be stated explicitly in the theorem and its scope discussed, rather than appearing only implicitly in the remark after Eq. (11) and in the diagonal examples.
[Appendix B.3] The proof of Theorem 3 is a proof skeleton: the bias and variance terms are reduced to Theorem 11 and Corollary 12, but the verification of all hypotheses of those deterministic-equivalent results for the continual-ridge products (e.g., bounded operator norms, convergence of the relevant empirical spectral distributions, and the equal-distribution control of θ) is not carried out in detail. Since these deterministic-equivalent results are the foundation of Eq. (9), the paper should either provide their full statements and proofs or give precise references and explicitly check the assumptions in the continual setting. This is needed for the main theorem to be considered rigorously established rather than plausibly derived.

minor comments (4)

[Section 4.1, Eq. (12)] The phrase 'oracle optimal regularization parameter' is potentially misleading. The rule in Eq. (12) is a greedy rule that minimizes the current average risk, not an oracle rule that minimizes the final average risk. The authors acknowledge this in the same paragraph, but the terminology should be changed to avoid confusion.
[Section 4, Figures 1–3] The simulation figures compare theoretical curves to simulated points, but the text does not report the finite values of p and n, the number of independent repetitions, or error bars. Given that the claim is almost-sure convergence, reporting Monte Carlo standard errors across repetitions would substantially strengthen the visual validation.
[Throughout] The paper uses 'exact' and 'asymptotic' interchangeably. Since the results are almost-sure limits in a proportional asymptotic regime, the word 'exact' should be reserved for the limit expressions and not appear in contexts that might suggest finite-sample exactness.
[Section 4, first paragraph] There is an apparent typo: 'continual risk regression' should be 'continual ridge regression'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: risk expressions are derived from resolvent identities and stated assumptions, not fitted or imported as the conclusion.

full rationale

The central claim (Theorem 3) is a limit theorem: under proportional-limit asymptotics and Assumptions 3-5, prediction risk converges a.s. to a closed-form expression built from deterministic equivalents and the limiting spectral measure. Risk curves for average risk, backward transfer, forward transfer are evaluated from the theorem and compared to simulations; they are not fitted constants. The recursion (3) and bias-variance decomposition (Lemma 1) are algebraic identities, and subsequent RMT arguments are technical lemmas with proofs in the appendix. No equation makes the target quantity equal to its inputs by definition, and no fitted parameter is renamed as a prediction. The paper explicitly acknowledges a scope limitation (Section 3, after Eq. 11, p.13): for non-isotropic covariance matrices with common eigenvectors, the limiting risk may not exist for arbitrary fixed theta; convergence is guaranteed only when theta coordinates are equally distributed along eigenvectors or theta is random with isotropic covariance. This is a condition on the unknown truth, not a circular use of the conclusion. Reliance on the authors' prior framework is not load-bearing circularity because the technical content is reproved in this paper's appendix. Hence no significant circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical or statistical entities are invented. The load-bearing inputs are the regularization sequence (chosen oracle in experiments), the assumed joint convergence of task covariances, and the equal-distribution condition on θ. These determine the applicability of the risk formulas; noise variance σ² and the dimension ratio p/n are treated as given inputs.

free parameters (2)

ridge regularization sequence λ_t = Oracle greedy minimizer of the current average risk in experiments, Eq. (12); arbitrary input in the theory
Tuning input of the estimator, not fitted in the derivation; in Sections 4.1-4.3 it is chosen to minimize the very risk being plotted, which conditions the reported phenomena on the oracle choice.
average-risk weights w_i = n_i / Σ_j n_j by default
User-chosen evaluation weights in the definition of average risk; a standard default that does not affect the theorem.

assumptions (5)

standard math Deterministic equivalents for resolvents of sample covariances with general Σ_t (Theorem 11, Corollary 12) and trace concentration bounds (Lemmas 13-15)
Bedrock of the proof of Theorem 3; the conditions on feature moments are assumed via Assumptions 3-5 and the moment conditions in Lemma 13. The provenance of these results is not fully visible in the provided text.
domain assumption Joint empirical spectral distribution of Σ_1,...,Σ_T converges (Assumption 3), with task covariance matrices co-diagonalizable in the examples
The limiting object Q_s and the risk-curve expressions exist only when the covariances' ESDs converge jointly; in the block example the paper states 'we assume that the covariance matrices are all diagonal' (page 13).
domain assumption True coefficient vector θ equally distributed along the eigenvectors, or random θ with Cov(θ) = σ_θ² I
Required so that Q_s converges weakly and the limiting risk exists for non-isotropic covariances (page 13); without it, the limits in Theorem 3 need not exist.
domain assumption Shared fixed coefficient vector θ across tasks, zero-mean features, additive i.i.d. noise with variance σ²
The linear model (1) in Section 2; the entire analysis is conditional on this generative model.
domain assumption Sufficient moments for feature entries and bounded operator norm of covariances (Assumptions 4-5, Lemma 13 moment conditions)
Needed for the concentration and deterministic equivalent steps, e.g., 'if the entries of X has 2k-th moment' in the proof around Lemma 14.

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Pith. "Pith review of High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression." pith.science (2026). https://pith.science/paper/KFXOOKRA

@misc{pith2026250815494,
  author       = {Pith},
  title        = {Pith review of: High-dimensional Asymptotics of Generalization Performance in Continual Ridge Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KFXOOKRA}},
  note         = {Machine review of arXiv:2508.15494}
}

read the original abstract

Continual learning is motivated by the need to adapt to real-world dynamics in tasks and data distribution while mitigating catastrophic forgetting. Despite significant advances in continual learning techniques, the theoretical understanding of their generalization performance lags behind. This paper examines the theoretical properties of continual ridge regression in high-dimensional linear models, where the dimension is proportional to the sample size in each task. Using random matrix theory, we derive exact expressions of the asymptotic prediction risk, thereby enabling the characterization of three evaluation metrics of generalization performance in continual learning: average risk, backward transfer, and forward transfer. Furthermore, we present the theoretical risk curves to illustrate the trends in these evaluation metrics throughout the continual learning process. Our analysis reveals several intriguing phenomena in the risk curves, demonstrating how model specifications influence the generalization performance. Simulation studies are conducted to validate our theoretical findings.

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Works this paper leans on

37 extracted references · 36 canonical work pages

[1]

Bai and J

Z. Bai and J. Silverstein. Spectral Analysis of Large Dimensional Random Matrices, Second Edition. Springer, New York, 2010

work page 2010
[2]

Buzzega, M

P. Buzzega, M. Boschini, A. Porrello, and S. Calderara. Rethinking experience replay: a bag of tricks for continual learning. In International Conference on Pattern Recognition, pages 2180--2187, 2021

work page 2021
[3]

Couillet and Z

R. Couillet and Z. Liao. Random Matrix Methods for Machine Learning. Cambridge University Press, Cambridge, 2022

work page 2022
[4]

Couillet, M

R. Couillet, M. Debbah, and J. W. Silverstein. A deterministic equivalent for the analysis of correlated MIMO multiple access channels. IEEE Transactions on Information Theory, 57 0 (6): 0 3493--3514, 2011

work page 2011
[5]

De Lange, R

M. De Lange, R. Aljundi, M. Masana, S. Parisot, X. Jia, A. Leonardis, G. Slabaugh, and T. Tuytelaars. A continual learning survey: Defying forgetting in classification tasks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44 0 (7): 0 3366--3385, 2022

work page 2022
[6]

L. H. Dicker and M. A. Erdogdu. Flexible results for quadratic forms with applications to variance components estimation . The Annals of Statistics, 45 0 (1): 0 386--414, 2017

work page 2017
[7]

Dobriban and Y

E. Dobriban and Y. Sheng. WONDER : Weighted one-shot distributed ridge regression in high dimensions. Journal of Machine Learning Research, 21 0 (66): 0 1--52, 2020

work page 2020
[8]

Dobriban and Y

E. Dobriban and Y. Sheng. Distributed linear regression by averaging . The Annals of Statistics, 49 0 (2): 0 918--943, 2021

work page 2021

Show all 37 references

[9]

Dobriban and S

E. Dobriban and S. Wager. High-dimensional asymptotics of prediction: Ridge regression and classification . The Annals of Statistics, 46 0 (1): 0 247--279, 2018

2018
[10]

Evron, E

I. Evron, E. Moroshko, R. Ward, N. Srebro, and D. Soudry. How catastrophic can catastrophic forgetting be in linear regression? In Conference on Learning Theory, pages 4028--4079, 2022

2022
[11]

E. Fini, V. G. T. da Costa, X. Alameda-Pineda, E. Ricci, K. Alahari, and J. Mairal. Self-supervised models are continual learners. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 9611--9620, 2022

2022
[12]

Goldfarb and P

D. Goldfarb and P. Hand. Analysis of overparameterization in continual learning under a linear model. arXiv preprint arXiv:2502.10442, 2025

2025 arXiv
[13]

M. B. Gurbuz and C. Dovrolis. NISPA : Neuro-inspired stability-plasticity adaptation for continual learning in sparse networks. In International Conference on Machine Learning, pages 8157--8174, 2022

2022
[14]

Hachem, P

W. Hachem, P. Loubaton, and J. Najim. Deterministic equivalents for certain functionals of large random matrices . The Annals of Applied Probability, 17 0 (3): 0 875--930, 2007

2007
[15]

Hastie, A

T. Hastie, A. Montanari, S. Rosset, and R. J. Tibshirani. Surprises in high-dimensional ridgeless least squares interpolation . The Annals of Statistics, 50 0 (2): 0 949--986, 2022

2022
[16]

S. C. Hoi, D. Sahoo, J. Lu, and P. Zhao. Online learning: A comprehensive survey. Neurocomputing, 459: 0 249--289, 2021

2021
[17]

X. Jin, A. Sadhu, J. Du, and X. Ren. Gradient-based editing of memory examples for online task-free continual learning. In Advances in Neural Information Processing Systems, pages 29193--29205, 2021

2021
[18]

S. Jung, H. Ahn, S. Cha, and T. Moon. Continual learning with node-importance based adaptive group sparse regularization. In Advances in Neural Information Processing Systems, pages 3647--3658, 2020

2020
[19]

Kirkpatrick, R

J. Kirkpatrick, R. Pascanu, N. Rabinowitz, J. Veness, G. Desjardins, A. A. Rusu, K. Milan, J. Quan, T. Ramalho, A. Grabska-Barwinska, D. Hassabis, C. Clopath, D. Kumaran, and R. Hadsell. Overcoming catastrophic forgetting in neural networks. Proceedings of the National Academy...

2017
[20]

S. Lee, S. Goldt, and A. Saxe. Continual learning in the teacher-student setup: Impact of task similarity. In International Conference on Machine Learning, pages 6109--6119, 2021

2021
[21]

H. Li, J. Wu, and V. Braverman. Fixed design analysis of regularization-based continual learning. In Proceedings of The 2nd Conference on Lifelong Learning Agents, pages 513--533, 2023

2023
[22]

Y. Li, M. Li, M. S. Asif, and S. Oymak. Provable and efficient continual representation learning. arXiv preprint arXiv:2203.02026, 2022

2022 arXiv
[23]

Li and D

Z. Li and D. Hoiem. Learning without forgetting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40 0 (12): 0 2935--2947, 2018

2018
[24]

Lopez-Paz and M

D. Lopez-Paz and M. Ranzato. Gradient episodic memory for continual learning. In Advances in Neural Information Processing Systems, page 6470–6479, 2017

2017
[25]

V. A. Mar c enko and L. A. Pastur. Distribution of eigenvalues for some sets of random matrices. Mathematics of The Ussr-sbornik, 1 0 (4): 0 457--483, 1967

1967
[26]

J. L. McClelland, B. L. McNaughton, and R. CO’Reilly. Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory. Psychological Rewiew, 102 0 (3): 0 419--457, 1995

1995
[27]

McCloskey and N

M. McCloskey and N. J. Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. In Psychology of learning and motivation, volume 24, pages 109--165. 1989

1989
[28]

Ramesh and P

R. Ramesh and P. Chaudhari. Model zoo: A growing brain that learns continually. In International Conference on Learning Representations, 2022

2022
[29]

Rebuffi, A

S.-A. Rebuffi, A. Kolesnikov, G. Sperl, and C. H. Lampert. iCaRL : Incremental classifier and representation learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 5533--5542, 2017

2017
[30]

Riemer, I

M. Riemer, I. Cases, R. Ajemian, M. Liu, I. Rish, Y. Tu, and G. Tesauro. Learning to learn without forgetting by maximizing transfer and minimizing interference. In International Conference on Learning Representations, 2019

2019
[31]

Ritter, A

H. Ritter, A. Botev, and D. Barber. Online structured laplace approximations for overcoming catastrophic forgetting. In Advances in Neural Information Processing Systems, pages 3742--3752, 2018

2018
[32]

Silverstein and Z

J. Silverstein and Z. Bai. On the empirical distribution of eigenvalues of a class of large dimensional random matrices. Journal of Multivariate Analysis, 54 0 (2): 0 175--192, 1995

1995
[33]

L. Wang, X. Zhang, H. Su, and J. Zhu. A comprehensive survey of continual learning: Theory, method and application. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46 0 (8): 0 5362--5383, 2024

2024
[34]

Y. Wen, Z. Tan, K. Zheng, C. Xie, and W. Huang. Provable contrastive continual learning. In International Conference on Machine Learning, pages 52819--52838, 2024

2024
[35]

C. Yang, M. Tiomoko, and Z. Wang. Optimizing spca-based continual learning: A theoretical approach. In International Conference on Learning Representations, 2023

2023
[36]

J. Yao, S. Zheng, and Z. Bai. Large Sample Covariance Matrices and High-Dimensional Data Analysis. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2015

2015
[37]

X. Zhao, H. Wang, W. Huang, and W. Lin. A statistical theory of regularization-based continual learning. In International Conference on Machine Learning, pages 61021--61039, 2024

2024

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Bai and J

Z. Bai and J. Silverstein. Spectral Analysis of Large Dimensional Random Matrices, Second Edition. Springer, New York, 2010

work page 2010

[2] [2]

Buzzega, M

P. Buzzega, M. Boschini, A. Porrello, and S. Calderara. Rethinking experience replay: a bag of tricks for continual learning. In International Conference on Pattern Recognition, pages 2180--2187, 2021

work page 2021

[3] [3]

Couillet and Z

R. Couillet and Z. Liao. Random Matrix Methods for Machine Learning. Cambridge University Press, Cambridge, 2022

work page 2022

[4] [4]

Couillet, M

R. Couillet, M. Debbah, and J. W. Silverstein. A deterministic equivalent for the analysis of correlated MIMO multiple access channels. IEEE Transactions on Information Theory, 57 0 (6): 0 3493--3514, 2011

work page 2011

[5] [5]

De Lange, R

M. De Lange, R. Aljundi, M. Masana, S. Parisot, X. Jia, A. Leonardis, G. Slabaugh, and T. Tuytelaars. A continual learning survey: Defying forgetting in classification tasks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44 0 (7): 0 3366--3385, 2022

work page 2022

[6] [6]

L. H. Dicker and M. A. Erdogdu. Flexible results for quadratic forms with applications to variance components estimation . The Annals of Statistics, 45 0 (1): 0 386--414, 2017

work page 2017

[7] [7]

Dobriban and Y

E. Dobriban and Y. Sheng. WONDER : Weighted one-shot distributed ridge regression in high dimensions. Journal of Machine Learning Research, 21 0 (66): 0 1--52, 2020

work page 2020

[8] [8]

Dobriban and Y

E. Dobriban and Y. Sheng. Distributed linear regression by averaging . The Annals of Statistics, 49 0 (2): 0 918--943, 2021

work page 2021