Tootfinder

"When every student in a class processes information through the same language model, they are learning to reason through the same system. This introduces a new threat vector on the developing mind.
The model's statistical biases become the student's default framing. The model's reasoning structure becomes the student's reasoning structure. LLMs homogenize not just language but also perspective and reasoning strategies. "

Adults Lose Skills to AI. Children Never Build Them.
Discussions of cognitive offloading often miss a critical distinction: What AI does to a 45-year-old's brain is categorically different from what it does to a 14-year-old's.

🔊 #NowPlaying on #BBCRadio3:
#ClassicalLive
- Tchaikovsky's Polish Symphony from the BBC Symphony Orchestra
Elizabeth Alker introduces an afternoon of specially made recordings including a performance of Tchaikovsky's Symphony No. 3 from the BBC Symphony Orchestra.
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https://www.bbc.co.uk/programmes/m002q5qb

Statistical Query Lower Bounds for Smoothed Agnostic Learning
Ilias Diakonikolas, Daniel M. Kane
https://arxiv.org/abs/2602.21191 https://arxiv.org/pdf/2602.21191 https://arxiv.org/html/2602.21191
arXiv:2602.21191v1 Announce Type: new
Abstract: We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus on the prototypical task of agnostically learning halfspaces under subgaussian distributions in the smoothed model. The best known upper bound for this problem relies on $L_1$-polynomial regression and has complexity $d^{\tilde{O}(1/\sigma^2) \log(1/\epsilon)}$, where $\sigma$ is the smoothing parameter and $\epsilon$ is the excess error. Our main result is a Statistical Query (SQ) lower bound providing formal evidence that this upper bound is close to best possible. In more detail, we show that (even for Gaussian marginals) any SQ algorithm for smoothed agnostic learning of halfspaces requires complexity $d^{\Omega(1/\sigma^{2} \log(1/\epsilon))}$. This is the first non-trivial lower bound on the complexity of this task and nearly matches the known upper bound. Roughly speaking, we show that applying $L_1$-polynomial regression to a smoothed version of the function is essentially best possible. Our techniques involve finding a moment-matching hard distribution by way of linear programming duality. This dual program corresponds exactly to finding a low-degree approximating polynomial to the smoothed version of the target function (which turns out to be the same condition required for the $L_1$-polynomial regression to work). Our explicit SQ lower bound then comes from proving lower bounds on this approximation degree for the class of halfspaces.
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🔊 #NowPlaying on #BBCRadio3:
#ClassicalLive
- Tchaikovsky's Symphony No. 5 from the BBC Symphony Orchestra
Elizabeth Alker introduces an afternoon of specially made recordings including a performance of Tchaikovsky's Symphony No. 5 from the BBC Symphony Orchestra.
Relisten now 👇
https://www.bbc.co.uk/programmes/m002q52l

Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior sampling
Jonathan Spence, Tob\'ias I. Liaudat, Konstantinos Zygalakis, Marcelo Pereyra
https://arxiv.org/abs/2602.20758 https://arxiv.org/pdf/2602.20758 https://arxiv.org/html/2602.20758
arXiv:2602.20758v1 Announce Type: new
Abstract: Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs), variational auto-encoders and normalising flows offer a computationally efficient alternative for posterior sampling. However, push-forward models are opaque as they lack the modularity of Bayes Theorem, leading to poor generalisation with respect to changes in the likelihood function. In this work, we introduce a novel approach to GAN architecture design by applying deep unfolding to Langevin MCMC algorithms. This paradigm maps fixed-step iterative algorithms onto modular neural networks, yielding architectures that are both flexible and amenable to interpretation. Crucially, our design allows key model parameters to be specified at inference time, offering robustness to changes in the likelihood parameters. We train these unfolded samplers end-to-end using a supervised regularized Wasserstein GAN framework for posterior sampling. Through extensive Bayesian imaging experiments, we demonstrate that our proposed approach achieves high sampling accuracy and excellent computational efficiency, while retaining the physics consistency, adaptability and interpretability of classical MCMC strategies.
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🔊 #NowPlaying on #BBCRadio3:
#ClassicalLive
- Respighi's Roman Festivals
Elizabeth Alker introduces an afternoon of specially made recordings including a performance of Respighi's Roman Festivals performed by the Luxembourg Philharmonic Orchestra
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https://www.bbc.co.uk/programmes/m002rhgq

High-Dimensional Robust Mean Estimation with Untrusted Batches
Maryam Aliakbarpour, Vladimir Braverman, Yuhan Liu, Junze Yin
https://arxiv.org/abs/2602.20698 https://arxiv.org/pdf/2602.20698 https://arxiv.org/html/2602.20698
arXiv:2602.20698v1 Announce Type: new
Abstract: We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection of sources that are both statistically heterogeneous and potentially malicious. We formalize this challenge through a double corruption landscape: an $\varepsilon$-fraction of users are entirely adversarial, while the remaining ``good'' users provide data from distributions that are related to $P$, but deviate by a proximity parameter $\alpha$.
Unlike existing work on the untrusted batch model, which typically measures this deviation via total variation distance in discrete settings, we address the continuous, high-dimensional regime under two natural variants for deviation: (1) good batches are drawn from distributions with a mean-shift of $\sqrt{\alpha}$, or (2) an $\alpha$-fraction of samples within each good batch are adversarially corrupted. In particular, the second model presents significant new challenges: in high dimensions, unlike discrete settings, even a small fraction of sample-level corruption can shift empirical means and covariances arbitrarily.
We provide two Sum-of-Squares (SoS) based algorithms to navigate this tiered corruption. Our algorithms achieve the minimax-optimal error rate $O(\sqrt{\varepsilon/n} \sqrt{d/nN} \sqrt{\alpha})$, demonstrating that while heterogeneity $\alpha$ represents an inherent statistical difficulty, the influence of adversarial users is suppressed by a factor of $1/\sqrt{n}$ due to the internal averaging afforded by the batch structure.
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Understanding the Role of Rehearsal Scale in Continual Learning under Varying Model Capacities
JinLi He, Liang Bai, Xian Yang
https://arxiv.org/abs/2602.20791 https://arxiv.org/pdf/2602.20791 https://arxiv.org/html/2602.20791
arXiv:2602.20791v1 Announce Type: new
Abstract: Rehearsal is one of the key techniques for mitigating catastrophic forgetting and has been widely adopted in continual learning algorithms due to its simplicity and practicality. However, the theoretical understanding of how rehearsal scale influences learning dynamics remains limited. To address this gap, we formulate rehearsal-based continual learning as a multidimensional effectiveness-driven iterative optimization problem, providing a unified characterization across diverse performance metrics. Within this framework, we derive a closed-form analysis of adaptability, memorability, and generalization from the perspective of rehearsal scale. Our results uncover several intriguing and counterintuitive findings. First, rehearsal can impair model's adaptability, in sharp contrast to its traditionally recognized benefits. Second, increasing the rehearsal scale does not necessarily improve memory retention. When tasks are similar and noise levels are low, the memory error exhibits a diminishing lower bound. Finally, we validate these insights through numerical simulations and extended analyses on deep neural networks across multiple real-world datasets, revealing statistical patterns of rehearsal mechanisms in continual learning.
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🔊 #NowPlaying on #BBCRadio3:
#ClassicalLive
- Sibelius' Second Symphony
Elizabeth Alker introduces an afternoon of specially made recordings including Sibelius' Symphony No. 2 from the BBC Philharmonic Orchestra and music from R3 New Generation Artists
Relisten now 👇
https://www.bbc.co.uk/programmes/m002rfjy