We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our end-to-end formal infrastructure implement the missing contents in latest Lean 4 Mathlib library, including a complete development of Gaussian Lipschitz concentration, the first formalization of Dudley’s entropy integral theorem for sub-Gaussian processes, and an application to least-squares (sparse) regression with a sharp rate. The project was carried out using a human-AI collaborative workflow, in which humans design proof strategies […]

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SpyderBot is a cutting-edge LLM analytics platform that reveals exactly how AI models like ChatGPT, Grok, and Gemini see your brand and your competitors. Using a network of over 20,000 distributed LLM-bots, SpyderBot tracks real-time Share of Voice, competitor visibility scores, sentiment analysis, and LLM crawler activity on your website — insights that traditional analytics tools completely miss. For brands and agencies, it answers critical questions: → Where do we rank in AI answers? → Which competitors are […]

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arXiv:2601.08842v1 Announce Type: new Abstract: Safety architectures for language models increasingly rely on external monitors to detect errors and inject corrective signals at inference time. For such systems to function in interactive settings, models must be able to incorporate externally provided confidence information into their verbal responses. In this work, we test whether instruction-tuned language models preserve this controllability across different interaction modes. Using Llama-3.2-3B on GSM8K, we perform a causal intervention study in which explicit external confidence […]

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arXiv:2601.21043v1 Announce Type: new Abstract: Touch data from mobile devices are collected at scale but reveal little about the interactions that produce them. While biomechanical simulations can illuminate motor control processes, they have not yet been developed for touch interactions. To close this gap, we propose a novel computational problem: synthesizing plausible motion directly from logs. Our key insight is a reinforcement learning-driven musculoskeletal forward simulation that generates biomechanically plausible motion sequences consistent with events recorded in touch […]

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arXiv:2601.11744v2 Announce Type: replace-cross Abstract: We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the corresponding central-limit-theorem-based confidence intervals by a factor depending on the square root of the propensity score. We show that this performance gap can be closed, designing nonasymptotic confidence intervals that have the same effective sample size as their asymptotic counterparts. Our approach involves […]

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The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. Given a set of cities and the distances between them, the task is to find the shortest possible route that visits each city exactly once and returns to the starting point. Despite its simple formulation, TSP is NP-hard,and understanding how algorithms search for optimal solutions can be difficult for students encountering the problem for the first time. To make this process more tangible, […]

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arXiv:2601.04214v1 Announce Type: new Abstract: Human decision-making heavily relies on active sensing, a well-documented cognitive behaviour for evidence gathering to accommodate ever-changing environments. However, its operational mechanism in the real world remains non-trivial. Currently, an in-laboratory paradigm, called evidence accumulation modelling (EAM), points out that human decision-making involves transforming external evidence into internal mental beliefs. However, the gap in evidence affordance between real-world contexts and laboratory settings hinders the effective application of EAM. Here we generalize EAM to […]

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Table of Links Abstract and Introduction Definitions Literature Review Argument Development The AI Model’s Potential for Feeling During Inference Conclusion and References 4 Argument Development In this section, we develop a comprehensive argument examining the potential sentience of the OpenAI-o1 model, integrating insights from neuroscience, philosophy of mind, and AI research. Central to this analysis is the adoption of functionalism, a philosophical framework that posits mental states are defined by their functional roles rather than their physical substrates […]

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