Existing distribution compression methods, like Kernel Herding (KH), were originally developed for unlabelled data.

These are the hottest Prime Day TV deals on our favorite screens and streaming devices. Ready to upgrade your television? This is an excellent time to buy a new TV or streaming device. Running from June 23 through June 26, the Prime Day TV deals are phenomenal--especially on art televisions like the Samsung Frame Pro and Amazon's new Ember Artline . Salivating over that new QLED or just need an entry-level TV for the kitchen?

Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting the one with the best empirical performance. However, running each algorithm on every training instance is computationally expensive, making scalability a central challenge. In practice, a common workaround is to evaluate algorithms on smaller proxy instances derived from the original inputs. However, this practice has remained largely ad hoc and lacked theoretical grounding. We provide the first theoretical foundations for this practice by formalizing the notion of size generalization: predicting an algorithm's performance on a large instance by evaluating it on a smaller, representative instance, subsampled from the original instance. We provide size generalization guarantees for three widely used clustering algorithms (single-linkage, k-means++, and Gonzalez's k-centers heuristic) and two canonical max-cut algorithms (Goemans-Williamson and Greedy). We characterize the subsample size sufficient to ensure that performance on the subsample reflects performance on the full instance, and our experiments support these findings.

We've gone from A to Z to find Amazon's best Prime Day deals on the gear worth owning. Amazon Prime Day is here once again. Amazon's annual Prime Day deals aims to entice us with an endless scroll of "discounts (some real, many fake), hammering away with red slashes, big percentages off, and coupons you can only see after adding to cart. While Prime Day deals aren't what they once were--its success has inspired a massive number of fake deals and attracted obscure brands--there are still some very significant discounts to be found. For the next four days, the WIRED Reviews team will be pooling our hundreds of years of collective expertise to find actual savings on products we have personally tested and approved. Let us absorb the neon signage and "buy now" buttons on your behalf and share the deals worth sharing. We'll keep this list updated frequently for the duration of the sale, which runs from June 23 to June 26. This is our very favorite MagSafe power bank . Wireless and MagSafe charging aren't always the fastest or most efficient, but despite its bulk, this large-capacity bank can top off modern phones once (or maybe a little more than that) without overheating or taking forever. One of the best budget wireless chargers is even more affordable thanks to Prime Day. You can buy fancier, faster wireless chargers, but if you just want a simple option that'll top off your phone, this is worth checking out. It can deliver up to 10 watts, though you'll need to supply your own wall adapter. Want something that can fast charge your phone, juice up your tablet, and even refill your laptop? This generous 25,000-mAh capacity can do it all, but stops shy of the carry-on air travel limit. The maximum output is 165 watts for two devices, but 100 watts for a single device. It has lovely rounded edges, a retractable, flat, 2.3-foot USB-C cable on the top, and a snazzy, durable, braided 1-foot USB-C cable that doubles as a carry loop. This remains one of my favorite Windows laptops, despite the recent price increases. But now, it's unexpectedly dropped to $835 for Prime Day, making it the best laptop Prime Day deal I've found so far. Price aside, though, my favorite feature is the 3:2 aspect ratio screen, which also has a faster 120-Hz refresh rate. It's absolutely gorgeous, and all the extra vertical screen space gives more room to work with. A new version just got announced with a more powerful Snapdragon X2 chip inside, but it's considerably more expensive . Unlike so many Windows laptops around $500, the OmniBook 3 has excellent performance and battery life. And while the touchpad isn't the best, the specs alone make it the very best cheap laptop you can buy.

Membership inference attacks (MIAs) are used to test practical privacy of machine learning models. MIAs complement formal guarantees from differential privacy (DP) under a more realistic adversary model. We analyze MIA vulnerability of fine-tuned neural networks both empirically and theoretically, the latter using a simplified model of fine-tuning. We show that the vulnerability of non-DP models when measured as the attacker advantage at a fixed false positive rate reduces according to a simple power law as the number of examples per class increases. A similar power-law applies even for the most vulnerable points, but the dataset size needed for adequate protection of the most vulnerable points is very large.

As major progress in LLM-based long-form text generation enables paradigms such as retrieval-augmented generation (RAG) and inference-time scaling, safely incorporating private information into the generation remains a critical open question.

We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each graph in an equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention.

While large language models (LLMs) demonstrate impressive capabilities across numerous applications, their robustness remains a critical concern. This paper is motivated by a specific vulnerability: the order sensitivity of LLMs. This vulnerability manifests itself as the order bias observed when LLMs decide between possible options (for example, a preference for the first option) and the tendency of LLMs to provide different answers when options are reordered. The use cases for this scenario extend beyond the classical case of multiple-choice question answering to the use of LLMs for multidocument tasks and as automated evaluators in AI pipelines. We introduce Set-LLM, a novel architectural adaptation for pretrained LLMs that enables the processing of mixed set-text inputs with permutation invariance guarantees. The adaptations involve a new attention mask and new positional encodings specifically designed for sets. We provide a theoretical proof of invariance and demonstrate through experiments that Set-LLM can be trained effectively, achieving comparable or improved performance and maintaining the runtime of the original model, while altogether eliminating order sensitivity.

We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.

In this paper, we address the challenges associated with merging low-rank adaptations of large neural networks. With the rise of parameter-efficient adaptation techniques, such as Low-Rank Adaptation (LoRA), model fine-tuning has become more accessible. While fine-tuning models with LoRA is highly efficient, existing merging methods often sacrifice this efficiency by merging fully-sized weight matrices. We propose the Core Space merging framework, which enables the merging of LoRA-adapted models within a common alignment basis, thereby preserving the efficiency of low-rank adaptation while substantially improving accuracy across tasks. We further provide a formal proof that projection into Core Space ensures no loss of information and provide a complexity analysis showing the efficiency gains. Extensive empirical results demonstrate that Core Space significantly improves existing merging techniques and achieves state-of-the-art results on both vision and language tasks while utilizing a fraction of the computational resources.