Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregressive process and adapting existing coupling techniques, we prove the geometric-moment contraction of high-dimensional SGD for constant learning rates, thereby establishing asymptotic stationarity of the iterates. Building on this, we derive the q-th moment convergence of SGD and ASGD for any q 2 in general ℓs-norms, and, in particular, the ℓ -norm that is frequently adopted in high-dimensional sparse or structured models. Furthermore, we provide sharp high-probability concentration analysis which entails the probabilistic bound of high-dimensional ASGD. Beyond closing a critical gap in SGD theory, our proposed framework offers a novel toolkit for analyzing a broad class of high-dimensional learning algorithms.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in MLLM post-training for perception policy learning. While promising, our initial experiments reveal that incorporating a thinking process through RL does not consistently lead to performance gains across all visual perception tasks. This leads us to delve into the essential role of RL in the context of visual perception. In this work, we return to the fundamentals and explore the effects of RL on different perception tasks. We observe that the perceptual perplexity is a major factor in determining the effectiveness of RL. We also observe that reward design plays a crucial role in further approaching the upper limit of model perception. To leverage these findings, we propose Perception-R1, a scalable RL framework using GRPO during MLLM post-training.

Federated Learning (FL) confronts a significant challenge known as data heterogeneity, which impairs model performance and convergence. Existing methods have made notable progress in addressing this issue. However, improving performance in certain heterogeneity scenarios remains an overlooked question: How robust are these methods to deploy under diverse heterogeneity scenarios? To answer this, we conduct comprehensive evaluations across varied heterogeneity scenarios, showing that most existing methods exhibit limited robustness. Meanwhile, insights from these experiments highlight that sharing statistical information can mitigate heterogeneity by enabling clients to update with a global perspective. Motivated by this, we propose FedGPS (Federated Goal-Path Synergy), a novel framework that seamlessly integrates statistical distribution and gradient information from others. Specifically, FedGPS statically modifies each client's learning objective to implicitly model the global data distribution using surrogate information, while dynamically adjusting local update directions with gradient information from other clients at each round. Extensive experiments show that FedGPS outperforms state-of-the-art methods across diverse heterogeneity scenarios, validating its effectiveness and robustness.

Try One of macOS 27's Best Features Right Now Apple's fall macOS release will let you build Shortcuts by typing what you want to happen. But Claude Code and Codex users don't have to wait. Buried deep inside everything announced at WWDC this year was something I, an Apple Shortcuts enthusiast, can't wait to try: the ability to make Apple Shortcuts using generative artificial intelligence. In macOS 27, you'll be able to just type what you want a shortcut to do, and the app will build it. Anyone who builds shortcuts regularly knows the process of doing so can be tedious, even if the end results save you a lot of time.

Pump.Fun's Bounties Platform Is a Black Hole of Circular Grifting The crypto platform claims you can "pay anyone to do anything," from quitting a job on camera to getting a memecoin-themed tattoo. But it mostly seems like people trying to scam each other. Would you run into a crowded university lecture hall, fart into a megaphone, and bellow "fartcoin" at the top of your lungs? If so--and should you have the means to document this stunt on video, preferably capturing the audience's reaction--you may claim a reward of approximately $1,000 . The money, of course, will be dispensed in fartcoin, a meme cryptocurrency trading at a little over 10 cents at time of publication, with a total market capitalization hovering around $130 million. Such is the promise of Pump.Fun GO, a new feature on Pump.Fun, one of the fastest-growing crypto businesses of the past few years.

When you purchase through links in our articles, we may earn a small commission. I can't stop using this website that lets me drive through cities around the world Drive and Listen combines street-level video with live local radio for a surprisingly immersive experience--even if it's only from your desktop. Drive and Listen might not sound like it, but it's strangely relaxing once you try it. The site provides exactly the experience the name suggests: Pick a city anywhere in the world, press play, and sit back as you ride along through the streets listening to local radio stations. The site was created during the pandemic by a student in Turkey who missed traveling and wanted a way to reconnect with places beyond his own neighborhood.

Large language models (LLMs) have demonstrated exceptional performance in reasoning tasks such as mathematics and coding, matching or surpassing human capabilities. However, these impressive reasoning abilities face significant challenges in specialized domains. Taking Go as an example, although AlphaGo has established the high performance ceiling of AI systems in Go, mainstream LLMs still struggle to reach even beginner-level proficiency, let alone perform natural language reasoning. This performance gap between general-purpose LLMs and domain experts is significantly limiting the application of LLMs on a wider range of domain-specific tasks. In this work, we aim to bridge the divide between LLMs' general reasoning capabilities and expert knowledge in domain-specific tasks. We perform mixed fine-tuning with structured Go expertise and general long Chain-ofThought (CoT) reasoning data as a cold start, followed by reinforcement learning to integrate expert knowledge in Go with general reasoning capabilities. Through this methodology, we present LoGos, a powerful LLM that not only maintains outstanding general reasoning abilities, but also conducts Go gameplay in natural language, demonstrating effective strategic reasoning and accurate next-move prediction. LoGos achieves performance comparable to human professional players, substantially surpassing all existing LLMs. Through this work, we aim to contribute insights on applying general LLM reasoning capabilities to specialized domains.

Tactile sensing is crucial for achieving human-level robotic capabilities in ma-nipulation tasks [ 54].

Recently, large vision-language models (LVLMs) have rapidly gained popularity for their strong generation and reasoning capabilities given diverse multimodal inputs. However, these models incur significant computational and memory overhead during inference, which greatly hinders the efficient deployment in practical scenarios. The extensive key-value (KV) cache, necessitated by the lengthy input and output sequences, notably contributes to the high inference cost. Based on this, recent works have investigated ways to reduce the KV cache size for higher efficiency. Although effective, they generally overlook the distinct importance distributions of KV vectors across layers and maintain the same cache size for each layer during the next token prediction.

While recent multimodal large language models (MLLMs) have advanced automated ECG interpretation, they still face two key limitations: (1) insufficient multimodal synergy between ECG time series and ECG images, and (2) limited explainability in linking diagnoses to granular waveform evidence. We introduce GEM, the first MLLM unifying ECG time series, 12-lead ECG images and text for grounded and clinician-aligned ECG interpretation. GEM enables feature-grounded analysis, evidence-driven reasoning, and a clinician-like diagnostic process through three core innovations: a dual-encoder framework extracting complementary time series and image features, cross-modal alignment for effective multimodal understanding, and knowledge-guided instruction data generation for generating high-granularity grounding data (ECG-Grounding) linking diagnoses to measurable parameters (e.g., QRS/PR Intervals). Additionally, we propose the Grounded ECGUnderstanding task, a clinically motivated benchmark designed to comprehensively assess the MLLM's capability in grounded ECG understanding. Experimental results on both existing and our proposed benchmarks show GEM significantly improves predictive performance (CSN 7.4%), explainability (22.7%), and grounding (25.3%), making it a promising approach for real-world clinical applications.