Industry
SpaceX secures option to buy AI startup Cursor for 60bn or partner for 10bn
Elon Musk speaks at the SpaceX Hyperloop Pod Competition II in Hawthorne, California, in 2017. Elon Musk speaks at the SpaceX Hyperloop Pod Competition II in Hawthorne, California, in 2017. Cursor is a Silicon Valley startup using AI to automate coding as Elon Musk's firm seeks foothold in the AI market SpaceX said it has secured an option to either acquire code-generation startup Cursor for $60bn later this year, or pay $10bn for their new partnership, as it pushes deeper into the lucrative market for AI developer tools. Along with OpenAI and Anthropic, Cursor is one of several Silicon Valley startups that has drawn waves of developers by using artificial intelligence to automate coding, a business where AI companies have found early commercial traction. The deal could give xAI, the Grok chatbot maker that SpaceX merged with in February, a stronger foothold in the AI coding market where it has so far lagged rivals.
Brains on Beats
Umut Güçlü, Jordy Thielen, Michael Hanke, Marcel van Gerven, Marcel A. J. van Gerven
We developed task-optimized deep neural networks (DNNs) that achieved state-ofthe-art performance in different evaluation scenarios for automatic music tagging. These DNNs were subsequently used to probe the neural representations of music. Representational similarity analysis revealed the existence of a representational gradient across the superior temporal gyrus (STG). Anterior STG was shown to be more sensitive to low-level stimulus features encoded in shallow DNN layers whereas posterior STG was shown to be more sensitive to high-level stimulus features encoded in deep DNN layers.
Heterogeneity-Aware Personalized Federated Learning for Industrial Predictive Analytics
Federated prognostics enable clients (e.g., companies, factories, and production lines) to collaboratively develop a failure time prediction model while keeping each client's data local and confidential. However, traditional federated models often assume homogeneity in the degradation processes across clients, an assumption that may not hold in many industrial settings. To overcome this, this paper proposes a personalized federated prognostic model designed to accommodate clients with heterogeneous degradation processes, allowing them to build tailored prognostic models. The prognostic model iteratively facilitates the underlying pairwise collaborations between clients with similar degradation patterns, which enhances the performance of personalized federated learning. To estimate parameters jointly using decentralized datasets, we develop a federated parameter estimation algorithm based on proximal gradient descent. The proposed approach addresses the limitations of existing federated prognostic models by simultaneously achieving model personalization, preserving data privacy, and providing comprehensive failure time distributions. The superiority of the proposed model is validated through extensive simulation studies and a case study using the turbofan engine degradation dataset from the NASA repository.
Last-Iterate Guarantees for Learning in Co-coercive Games
Chandak, Siddharth, Tamizholi, Ramanan, Bambos, Nicholas
We establish finite-time last-iterate guarantees for vanilla stochastic gradient descent in co-coercive games under noisy feedback. This is a broad class of games that is more general than strongly monotone games, allows for multiple Nash equilibria, and includes examples such as quadratic games with negative semidefinite interaction matrices and potential games with smooth concave potentials. Prior work in this setting has relied on relative noise models, where the noise vanishes as iterates approach equilibrium, an assumption that is often unrealistic in practice. We work instead under a substantially more general noise model in which the second moment of the noise is allowed to scale affinely with the squared norm of the iterates, an assumption natural in learning with unbounded action spaces. Under this model, we prove a last-iterate bound of order $O(\log(t)/t^{1/3})$, the first such bound for co-coercive games under non-vanishing noise. We additionally establish almost sure convergence of the iterates to the set of Nash equilibria and derive time-average convergence guarantees.
Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
Skifstad, Julian, Yang, Xinyue Annie, Chou, Glen
Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering
Beyond Bellman: High-Order Generator Regression for Continuous-Time Policy Evaluation
Zheng, Yaowei, Zhang, Richong, Wu, Shenxi, Bian, Shirui, Zhang, Haosong, Zeng, Li, Ma, Xingjian, Zhang, Yichi
We study finite-horizon continuous-time policy evaluation from discrete closed-loop trajectories under time-inhomogeneous dynamics. The target value surface solves a backward parabolic equation, but the Bellman baseline obtained from one-step recursion is only first-order in the grid width. We estimate the time-dependent generator from multi-step transitions using moment-matching coefficients that cancel lower-order truncation terms, and combine the resulting surrogate with backward regression. The main theory gives an end-to-end decomposition into generator misspecification, projection error, pooling bias, finite-sample error, and start-up error, together with a decision-frequency regime map explaining when higher-order gains should be visible. Across calibration studies, four-scale benchmarks, feature and start-up ablations, and gain-mismatch stress tests, the second-order estimator consistently improves on the Bellman baseline and remains stable in the regime where the theory predicts visible gains. These results position high-order generator regression as an interpretable continuous-time policy-evaluation method with a clear operating region.
SpaceX and Cursor strike partnership that might end in a 60 billion acquisition
The X and xAI owner is now working closely together with the maker of the AI coding tool. The xAI and SpaceX logos appear on a smartphone screen placed on a reflective surface onto which an abstract black and blue illustration is projected. SpaceX and AI company Cursor have struck a new partnership that could see the owner of X buy the AI company for $60 billion later this year. SpaceXAI and @cursor_ai are now working closely together to create the world's best coding and knowledge work AI, SpaceX wrote in a post on X. SpaceXAI and @cursor_ai are now working closely together to create the world's best coding and knowledge work AI. According to SpaceX, the deal allows for it to either invest $10 billion into the company known for its AI coding tool, or acquire it entirely later this year for $60 billion.
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