Daren Wang

Daren Wang, Hong Xu, Jiawen Xian

This paper introduces PolyGnosis 2.0, a pioneering multi-agent architecture designed to extract predictive intelligence by synthesizing Polymarket anomaly signals with global Open Source Intelligence (OSINT) streams, specifically Global Database of Events, Language, and Tone (GDELT). We define and target "Perspective Mismatches", the narrative divergence between Polymarket sentiment and global media flows, as high-alpha trading signals. Moving beyond generic agentic superiority, we rigorously quantify the efficacy of "Harness Engineering" techniques, including reflection loops, tool-calling, divide-and-conquer partitioning (D&C), and chain-of-thought (CoT), within high-noise financial domains. Our empirical evaluation against human-expert benchmarks reveals that while structural partitioning is mandatory for multi-dimensional alignment, unconstrained terminal reflection actively induces logical drift. Furthermore, we identify a pervasive "consensus bias" across all agent configurations during narrative reasoning, necessitating deterministic validation. Ultimately, we isolate a Pareto-optimal configuration that achieves professional-grade analytical precision while minimizing latency and token overhead, providing a robust blueprint for autonomous intelligence in prediction markets.

Daren Wang

This project reproduces and extends the recently proposed ``Recursive Language Models'' (RLMs) framework by Zhang et al. (2026). This framework enables Large Language Models (LLMs) to process near-infinite contexts by offloading the prompt into an external REPL environment. While the original paper relies on a default recursion depth of 1 and suggests deeper recursion as a future direction, this study specifically investigates the impact of scaling the recursion depth. Using state-of-the-art open-source agentic models (DeepSeek v3.2 and Kimi K2), I evaluated pure LLM, RLM (depth=1), and RLM (depth=2) on the S-NIAH and OOLONG benchmarks. The findings reveal a compelling phenomenon: Deeper recursion causes models to ``overthink''. While depth-1 RLMs effectively boost accuracy on complex reasoning tasks, applying deeper recursion (depth=2) or using RLMs on simple retrieval tasks paradoxically degrades performance and exponentially inflates execution time (e.g., from 3.6s to 344.5s) and token costs. Code and data are available at: https://github.com/drbillwang/rlm-reproduction

Shivam Kumar, Haotian Xu, Carlos Misael Madrid Padilla et al.

We study denoising of a third-order tensor when the ground-truth tensor is not necessarily Tucker low-rank. Specifically, we observe $$ Y=X^\ast+Z\in \mathbb{R}^{p_{1} \times p_{2} \times p_{3}}, $$ where $X^\ast$ is the ground-truth tensor, and $Z$ is the noise tensor. We propose a simple variant of the higher-order tensor SVD estimator $\widetilde{X}$. We show that uniformly over all user-specified Tucker ranks $(r_{1},r_{2},r_{3})$, $$ \| \widetilde{X} - X^* \|_{ \mathrm{F}}^2 = O \Big( κ^2 \Big\{ r_{1}r_{2}r_{3}+\sum_{k=1}^{3} p_{k} r_{k} \Big\} \; + \; ξ_{(r_{1},r_{2},r_{3})}^2\Big) \quad \text{ with high probability.} $$ Here, the bias term $ξ_{(r_1,r_2,r_3)}$ corresponds to the best achievable approximation error of $X^\ast$ over the class of tensors with Tucker ranks $(r_1,r_2,r_3)$; $κ^2$ quantifies the noise level; and the variance term $κ^2 \{r_{1}r_{2}r_{3}+\sum_{k=1}^{3} p_{k} r_{k}\}$ scales with the effective number of free parameters in the estimator $\widetilde{X}$. Our analysis achieves a clean rank-adaptive bias--variance tradeoff: as we increase the ranks of estimator $\widetilde{X}$, the bias $ξ(r_{1},r_{2},r_{3})$ decreases and the variance increases. As a byproduct we also obtain a convenient bias-variance decomposition for the vanilla low-rank SVD matrix estimators.

Carlos Misael Madrid Padilla, Zhi Zhang, Xiaokai Luo et al.

In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements. By accounting for dependencies across time and space, our models better reflect the complexities of real-world data, enhancing both predictive performance and theoretical robustness. We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data. We broaden existing theoretical findings of temporal-spatial analysis by applying them to neural networks in more general contexts and demonstrate that our proof techniques are effective for models with short-range dependence. Our empirical simulations across various synthetic response functions underscore the superior performance of our method, outperforming established approaches in the existing literature. These findings provide valuable insights into the strong capabilities of dense neural networks (Dense NN) for temporal-spatial modeling across a broad range of function classes.

Yifan Peng, Yuehaw Khoo, Daren Wang

Multivariate density estimation is of great interest in various scientific and engineering disciplines. In this work, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariate density functions with a reduced curse of dimensionality. Our VRS framework conceptualizes multivariate functions as infinite-size matrices/tensors, and facilitates a new sketching technique motivated by the numerical linear algebra literature to reduce the variance in density estimation problems. We demonstrate the robust numerical performance of VRS through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network density estimators and classical kernel methods in numerous distribution models. Additionally, we offer theoretical justifications for VRS to support its ability to deliver density estimation with a reduced curse of dimensionality.

Yi Yu, Oscar Hernan Madrid Padilla, Daren Wang et al.

We study the problem of online network change point detection. In this setting, a collection of independent Bernoulli networks is collected sequentially, and the underlying distributions change when a change point occurs. The goal is to detect the change point as quickly as possible, if it exists, subject to a constraint on the number or probability of false alarms. In this paper, on the detection delay, we establish a minimax lower bound and two upper bounds based on NP-hard algorithms and polynomial-time algorithms, i.e., \[ \mbox{detection delay} \begin{cases} \gtrsim \log(1/α) \frac{\max\{r^2/n, \, 1\}}{κ_0^2 n ρ},\\ \lesssim \log(Δ/α) \frac{\max\{r^2/n, \, \log(r)\}}{κ_0^2 n ρ}, & \mbox{with NP-hard algorithms},\\ \lesssim \log(Δ/α) \frac{r}{κ_0^2 n ρ}, & \mbox{with polynomial-time algorithms}, \end{cases} \] where $κ_0, n, ρ, r$ and $α$ are the normalised jump size, network size, entrywise sparsity, rank sparsity and the overall Type-I error upper bound. All the model parameters are allowed to vary as $Δ$, the location of the change point, diverges. The polynomial-time algorithms are novel procedures that we propose in this paper, designed for quick detection under two different forms of Type-I error control. The first is based on controlling the overall probability of a false alarm when there are no change points, and the second is based on specifying a lower bound on the expected time of the first false alarm. Extensive experiments show that, under different scenarios and the aforementioned forms of Type-I error control, our proposed approaches outperform state-of-the-art methods.

Yen-Chi Chen, Daren Wang, Alessandro Rinaldo et al.

Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence diagrams. How do we summarize them, average them or cluster them? One approach -- the persistence intensity function -- was introduced informally by Edelsbrunner, Ivanov, and Karasev (2012). Here we provide a modification and formalization of this approach. Using the persistence intensity function, we can visualize multiple diagrams, perform clustering and conduct two-sample tests.