arXiv subjects

Jinqi Tang

Publications and source records attributed to Jinqi Tang.

3 recordsLinked to original sources

arXiv2026

Breaking the One-Player Extension Barrier: History-Aware Repair for Multiplayer Approximate Nash Equilibria

Computation of Nash equilibria is a central problem in algorithmic game theory, yet exact equilibrium computation is $\mathsf{PPAD}$-complete even for two-player games. This hardness motivates the study of polynomial-time algorithms for approximate Nash equilibria. While substantial progress has been made for two-player and three-player games, existing algorithms for general $m$-player games have largely relied on repeatedly applying one-player extension starting from improved fixed-player algorithms. Such improvements can at best strengthen the classical $1-1/m$ guarantee to $1-1/(m-c)$, for some constant $c$ independent of $m$. We break this long-standing barrier by developing an iterative algorithm that directly tackles general $m$-player games and achieves a $(1-(σ_{\star}-ε)/m)$-approximation for fixed $ε> 0$ and sufficiently large $m$, where $σ_\star\approx1.5867$ is the unique root in $(1,2)$ of $σ_\star^3-19σ_\star^2+27σ_\star+1=0$. Our approach rests on a novel iterative descent-and-repair framework that allows multiple rounds of repair. At the heart of our analysis is a new potential function inspired by continuous-time dynamics, which certifies progress across iterations and ensures polynomial-time termination. Our results highlight the power of history-aware, iterative repair in breaking approximation barriers for multiplayer games.

cs.GT↗

arXiv2026

Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries

The theoretical understanding of multi-layer neural networks is largely confined to overparameterized settings, which obscure parameter identifiability and incur high sample complexity. Neural tangent kernel (NTK) provides a general theory for wide networks, but does not offer efficient sample-complexity guarantees. Recent feature-learning results go beyond kernel methods for single-neuron, multi-index, and hierarchical targets. However, the analysis is often restricted to shallow or specific architectures and to the overparameterized regime. We break this paradigm to achieve parameter-level recovery of deep target networks, albeit by using active data queries. Specifically, we study $L$-layer polynomial networks with even degree-$k$ monomial activations and nonnegative higher-layer weights. This structure makes the target network input-convex, while the optimization landscape remains highly nonconvex with respect to the parameters. Leveraging input convexity and active queries, we propose \textbf{ASPIRE} (\textbf{A}ctive \textbf{S}am\textbf{P}ling for \textbf{I}terative \textbf{R}ecovery via \textbf{E}igendirections), a layerwise sampling-based diagonalization algorithm that recovers all network parameters to $δ$-accuracy with sample complexity $ \widetilde O_{k,L}\left(d^{L^2+O(L)}δ^{-2e}\right) $ in polynomial time. To our knowledge, this is the \emph{first} parameter-recovery guarantee for deep target networks whose exponent grows only polynomially with depth, as well as the \emph{first} justification for the effectiveness of using high-quality data in neural network training, with a remarkably \emph{exponential} separation.

cs.LG↗

arXiv2026

From Prefix Cache to Fusion RAG Cache: Accelerating LLM Inference in Retrieval-Augmented Generation

Retrieval-Augmented Generation enhances Large Language Models by integrating external knowledge, which reduces hallucinations but increases prompt length. This increase leads to higher computational costs and longer Time to First Token (TTFT). To mitigate this issue, existing solutions aim to reuse the preprocessed KV cache of each retrieved chunk to accelerate RAG. However, the lack of cross-chunk contextual information leads to a significant drop in generation quality, leaving the potential benefits of KV cache reuse largely unfulfilled. The challenge lies in how to reuse the precomputed KV cache of chunks while preserving generation quality. We propose FusionRAG, a novel inference framework that optimizes both the preprocessing and reprocessing stages of RAG. In the offline preprocessing stage, we embed information from other related text chunks into each chunk, while in the online reprocessing stage, we recompute the KV cache for tokens that the model focuses on. As a result, we achieve a better trade-off between generation quality and efficiency. According to our experiments, FusionRAG significantly improves generation quality at the same recomputation ratio compared to previous state-of-the-art solutions. By recomputing fewer than 15% of the tokens, FusionRAG achieves up to 70% higher normalized F1 scores than baselines and reduces TTFT by 2.66x-9.39x compared to Full Attention.

cs.CL↗