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Tight Sample Complexity of Transformers

arXiv:2606.09731v1 Announce Type: new Abstract: We tightly characterize the VC dimension of depth-$L$ Transformers with a total of $W$ parameters, mapping an input sequence of length $T$ to a single output, establishing an upper bound of $O(L W \log (T W))$ and a nearly matching lower bound of $\Omega(L W \log (T W / L))$. We further tightly characterize the sample complexity of chain-of-thought learning using such a Transformer, showing teacher forcing (i.e. selecting a predictor consistent...

arXiv CS 1d ago

Learning to Bet for Horizon-Aware Anytime-Valid Testing

Announce Type: replace-cross Abstract: We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state space $(t, \log W_t)$, where $t$ is the time and $W_t$ is the test martingale value. We first show that in certain interior regions of the state space, policies that deviate significantly from Kelly betting are...

arXiv CS 7d ago

Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures

arXiv:2411.12438v2 Announce Type: replace Abstract: We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the...

arXiv CS 8d ago

If you don't fall for these extortionists' calls, they'll show up with USB sticks

If they don't get you online, they'll try in person. A data-theft and extortion gang has targeted “dozens” of banks, law firms, and other professional services companies in the US from January through May, using fake help desk calls and other social-engineering techniques to gain access to corporate IT environments, according to Google’s Mandiant incident response team. And when those remote-deception methods don’t work, the criminals sometimes show up at victims’ physical offices, posing as...

The Register 4d ago

The anti-lexicographic SUS-anchor: a near-optimal k=1 sampling scheme

arXiv:2606.01190v2 Announce Type: replace Abstract: In recent years, there has been a renewed interest in the search for low density minimizer schemes. These schemes take a window of $w$ consecutive $k$-mers, and sample one of them: the smallest under some specific order. Schemes such as the mod-minimizer provide a low density (fraction of sampled $k$-mers) when $k \gg w$, while schemes such as the greedy minimizer work well for explicit small parameters roughly in the regime $k \leq 2w$,...

arXiv CS 7d ago

The anti-lexicographic SUS-anchor: a near-optimal k=1 sampling scheme

Announce Type: new Abstract: In recent years, there has been a renewed interest in the search for low density minimizer schemes. These schemes take a window of $w$ consecutive $k$-mers, and sample one of them: the smallest under some specific order. Schemes such as the mod-minimizer provide a low density (fraction of sampled $k$-mers) when $k \gg w$, while schemes such as the greedy minimizer work well for explicit small parameters roughly in the regime $k \leq 2w$, for $k$ and $w$ up to...

arXiv CS 8d ago

Counting Distinct (Non-)Crossing Substrings in Optimal Time

Announce Type: replace Abstract: Let $w$ be a string of length $n$. The problem of counting factors crossing a position -- Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Lecroq, and Rytter, 2021] -- asks to count the number $\mathcal{C}(w,k)$ (resp. $\mathcal{N}(w,k)$) of distinct substrings in $w$ that have occurrences containing (resp.

arXiv CS 5d ago

A Matter Wi-Fi Light Bulb in Rust on the Raspberry Pi Pico 2 W

This repository contains examples for the Raspberry Pi Pico 2 (RP2350) board, written in Rust using the Embassy async framework. cargo generate --git https://github.com/ImplFerris/pico2-template.git --name rust-rpico2-embassy-examples Board: Raspberry Pi Pico 2 - MCU: RP2350 (Dual-core Arm Cortex-M33 and RISC-V cores) - On-board peripherals: - LED on GPIO25 - I2C pins: - I2C0 SDA: GPIO4 - I2C0 SCL: GPIO5 - I2C1 SDA: GPIO2 - I2C1 SCL: GPIO3 - UART pins: - UART0 TX: GPIO0, UART0 RX: GPIO1 -...

Hacker News 2d ago

Hard labels sampled from sparse targets mislead rotation invariant algorithms

Announce Type: replace-cross Abstract: One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic regression, the feedback can be either soft labels, corresponding to the true conditional probability of the data (as in distillation), or sampled hard labels (taking values $\pm 1$).

arXiv CS 2d ago