#01Oct 27, 2026
cs.LG
GTFormer: A Syntax-Free Graph Network Alternative to Transformers for 8192$\times$ Length Extrapolation in Linear Time
Elisabeth Fink
Self-attention mechanisms have established the Transformer as the dominant backbone across natural language processing, source code intelligence, and automated theorem proving. However, all-to-all pairwise token comparison enforces a quadratic $\mathcal{O}(N^2)$ compute and memory barrier alongside severe softmax attention dilution as sequence length $N$ scales beyond the training horizon. Inspired by recent advances in algebraic graph learning (\textbf{WPNet}), this work introduces \textbf{GTFormer}, a syntax-free hierarchical Graph Neural Network (GNN) that replaces flat self-attention for general long-context sequence modeling. GTFormer organizes raw token streams into a bounded-degree hierarchy combining a balanced binary reduction tree ($\lceil \log_2 N \rceil$ depth), horizontal boundary-bridging shift edges, random expander shortcuts, multi-channel convex highway gating, and a top-down broadcast pass. Across eight long-context code, log, and multi-hop retrieval benchmarks trained exclusively on sequences of length $N \le 512$, GTFormer extrapolates zero-shot to $N = 4{,}194{,}304$ ($8192\times$) on a single commodity GPU in linear $\mathcal{O}(N)$ memory, maintaining near-perfect accuracy where standard and RoPE Transformers suffer from out-of-distribution attention collapse and out-of-memory exhaustion.
#02Oct 27, 2026
cs.LG
MuonGS: Pretraining LLMs with Relaxed Weight-Norm Control
Athanasios Glentis, Dawei Li, Mingyi Hong
Weight decay and explicit weight-norm constraints improve optimizer performance in language model pretraining, yet a unified understanding of why such control helps and how much is needed remains incomplete. We analyze norm control in Muon over the entire training trajectory using the \emph{accumulated effective learning rate}, $C_T=\sum_{t<T}η_t/\|W_t\|_F$, where $η_t$ is the nominal learning rate and $η_t/\|W_t\|_F$ is the effective learning rate relative to the weight norm. For bounded update directions, accumulation over any training interval bounds relative weight displacement. We show that vanilla Muon can accumulate only logarithmically, potentially limiting exploration and helping explain its slower empirical progress, whereas MuonW and MuonH guarantee at least linear accumulation under the stated conditions. Going beyond bounded-norm control, we show that sufficiently slow norm growth guarantees faster accumulation than the logarithmic worst case, opening up less restrictive optimizer designs. Based on this insight, we propose MuonGS, which uses Gram--Schmidt (GS) projection to remove the radial component of each Muon update without fixing the weight norm. With bounded update directions and a constant nominal learning rate, we prove that the weight norm grows at most proportionally to $\sqrt{t}$ after $t$ steps. Consequently, MuonGS guarantees $C_T=Ω(\sqrt{T})$, with accumulation sustained even in later training. Further, for smooth scale-invariant objectives we establish its $O(T^{-1/2})$ stationarity guarantee. In pretraining experiments with 160M- and 400M-parameter dense models as well as a 135M active- and 1B total- parameter MoE model, MuonGS achieves lower validation perplexity than MuonH at long training horizons. In particular, for the dense model it achieves an estimated token-equivalent speedup up to about $15\%$ at matched validation loss to MuonH.
#03Oct 27, 2026
stat.ME
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
Lorenzo Tedesco
In this paper we propose a method for estimating conditional densities from an iid sample using a language-model agent. The agent writes the estimator as a short program that, for each covariate value, returns the estimated conditional distribution of the response. The program is built from a library of probability distributions, so the returned law can be a parametric distribution, a mixture or a multivariate factorization, with parameters given by explicit functions of the covariates. Since the number of operations and constants in the program is limited, the fitted conditional density is a formula that can be inspected and evaluated independently of the agent, while the choice of the model structure and of the fitting procedure is left to the agent. We call this approach agentic distributional regression (ADR). Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under explicit complexity and optimization assumptions, and an oracle inequality for selection using independent validation data. For a stably selected regular structure with sufficiently accurate fitting, we obtain asymptotic normality of the fitted constants. In simulation studies, on twelve real datasets and on a new dataset collected after the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the methods considered.
#04Oct 27, 2026
cs.CV
Zero-Shot Multimodal Event Spotting in Soccer Broadcasts
Sadia Kamal, Mahmudul Hasan, Tony Braskich
Automatic soccer event spotting supports highlight generation, video indexing, and sports analytics, but existing methods depend on large annotated datasets and soccer-specific training. We present a zero-shot framework that detects, classifies, and temporally localizes events in full-length soccer broadcasts without task-specific parameter training. Each match is segmented into overlapping clips represented by a compact visual storyboard and the aligned commentary transcript, which a general-purpose multimodal model processes jointly. On three manually annotated matches containing 130 events, the best configuration achieves 72.0% F1@5s and outperforms SoccerNet-trained CALF and NetVLAD++ in a cross-dataset setting, while the storyboard representation reduces inference cost by 72% compared with individual frames. We further analyze the effects of model family, input representation, and prompt optimization, and introduce an evidence-grounded excitement-scoring stage that ranks detected events with natural-language explanations for highlight selection.
#05Oct 27, 2026
math.ST
Regression Functions as Fields on Covariate Space: Evolution Equations, the Hessian, and Identification
Nobuaki Tanaka
For each time $t$, the regression function $m_t(x)=E[Y_t\mid X_t=x]$ of an outcome on contemporaneous covariates can be regarded as a field on covariate space. We study how this field evolves when the covariates of individual units move as a diffusion and the outcome attached to each unit changes according to its own dynamics. Under mild regularity we show that $m_t$ satisfies a second-order evolution equation whose diffusion term is $\frac12\mathrm{tr}(Σ\nabla^2 m_t)$, the trace of the Hessian of the regression function weighted by the instantaneous covariance $Σ$ of the covariate increments, whose transport term is the drift of the time-reversed covariate process, and whose source term is the conditional mean rate of change of the outcome. The equation is a regression-theoretic reading of a classical transport law, and it yields a Feynman-Kac representation of $m_t$ along reversed covariate paths. We connect the Hessian appearing in the equation to the Hessian estimated by quadratic regression (under Gaussian design the best quadratic approximation has Hessian $E[\nabla^2 m(X)]$ exactly) and to the leading bias of kernel smoothers. For binary outcomes governed by bistable replicator dynamics with imitation among units with similar covariates, the closed equation is of Nagumo type, its planar travelling fronts are exactly logistic in $(x,t)$, and a single logistic regression of the outcome on covariates and time identifies the ratio of diffusion to reaction and the direction of invasion. We discuss identification under panel versus repeated cross-sectional designs and a two-stage estimation strategy, and we illustrate the results with simulations.