#01Oct 20, 2026
cs.AI
Evolving Semantic Indexes for Generative Retrieval
Jinming Nian, Jyun-Yu Jiang, Henry Tsai and 2 more
Generative retrieval (GR) casts search and recommendation as autoregressive generation of discrete semantic identifiers (SIDs). SID design largely determines GR quality, but its discrete, interdependent components (SID construction, collision handling, decoding, and training) cannot be optimized end-to-end with gradients and remain largely hand-designed. We introduce a framework that improves these components through LLM-driven evolutionary program search, to our knowledge the first application of this approach to GR. A locally served, open-weight 31B model mutates executable GR components, so no proprietary LLM API is used, and a 1M-parameter proxy decoder provides fast feedback in place of repeatedly training the 1B target generator. Across 21 SID programs on NQ320K, proxy and target Recall@100 show strong rank correlation (Spearman $ρ= 0.90$). Guided by this proxy, evolution improves the seed GR on NQ320K, MSMARCO300K, and a multilingual e-commerce dataset under a fixed training recipe. On NQ320K, jointly evolving SID construction and collision handling improves Recall@1 from 55.8% to 59.3% and Recall@100 from 85.8% to 90.6%. A component study shows that proxy reliability depends on what is evolved: improvements transfer reliably for the semantic index but not for the generator's training objective or the full pipeline. LLM-driven evolutionary search is thus a practical tool for GR design, provided proxy reliability is established for the chosen search space.
#02Oct 20, 2026
cs.LG
Convergence of stochastic gradient descent for learning linear neural networks
Gabin Maxime Nguegnang, Bubacarr Bah, Holger Rauhut and 1 more
Stochastic gradient descent (SGD) is the cornerstone of modern deep learning, yet its theoretical convergence properties remain poorly understood in non-convex settings. To address this gap, we study SGD dynamics in deep linear neural networks - simplified models that retain key non-convex characteristics while remaining analytically tractable. Building on recent results for gradient descent, we extend convergence guarantees to SGD under regularized squared loss. We establish almost sure boundedness of SGD iterates. Using the framework of asymptotic pseudotrajectories from stochastic approximation theory, our analysis establishes then, for both deterministic and adaptive step-size choices, convergence of SGD to the set of critical points under mild conditions (without relying on Lipschitz properties or whitened data). To our knowledge, this is the first work providing almost sure convergence guarantees for SGD in deep linear networks, bridging the gap between theoretical optimization and practical stochastic training.
#03Oct 20, 2026
cs.CC
Two $\operatorname{ReLU}$ Layers is All You Need
Florestan Brunck, Christoph Hertrich, Kilian Ruess and 2 more
We prove that every $\operatorname{ReLU}$ network can be exactly simulated by a $\operatorname{ReLU}$ network with two hidden layers. We present two proofs: one that is based on fillings in homological algebra and a direct combinatorial proof.
#04Oct 20, 2026
cs.LG
Efficient Edge-aware Attention Network for Graph Generation
Vincent Jung, Alba Carballo-Castro, Yiming Qin and 2 more
Graph generative models commonly use graph-specific Transformer architectures to jointly update node and edge features. However, these architectures do not directly benefit from recent hardware-aware attention implementations, limiting their scalability. The adaptation is, however, non-trivial: edge and graph-level features must be injected into pairwise attention scores, graph masks must be respected, and dynamic edge updates remain a major source of quadratic memory usage. We propose an edge-aware attention layer for graph generation that incorporates structural information through head-wise score modulation, while updating edge representations with a lightweight residual mechanism that retains attention-score dependent edge updates. This layer can be effectively implemented using PyTorch's FlexAttention. We achieve similar generation quality to our baseline while reducing peak GPU memory by around 65% and substantially improving training and sampling throughput. These results suggest that the proposed architecture is a practical step toward scalable graph foundation models.
#05Oct 20, 2026
cs.LG
GraphCast-Mamba: Learning Non-Markovian Corrections for Weather Forecasting
Ilya Vilkoviskiy, Liang-Hong Mo, Suozhi Huang and 1 more
Unresolved atmospheric processes can introduce history dependence beyond the short input windows used by many weather forecasting models. We introduce GraphCast--Mamba, which augments a frozen, pretrained $1^\circ$ GraphCast backbone with a trainable Mamba correction branch combining graph message passing and Mamba layers. The branch retains a temporal memory state across successive six-hour forecast steps, learning corrections informed by temporal context beyond GraphCast's two-frame input. Training is confined to the correction branch, using ERA5 data from 2015--2021. After 2,500 optimizer updates, including warm-up, the selected model achieves substantial improvements relative to the uncorrected GraphCast backbone. It reduces the GraphCast loss (normalized weighted mean-squared error; MSE) by 14.42% when aggregated over the full ten-day forecast and by 21.66% at day 10 (240 h after forecast initialization). At this final forecast lead time, root-mean-square error (RMSE) decreases by 7.09--14.60% across all 11 evaluated variable groups, spanning temperature, wind, pressure, geopotential, specific humidity, and precipitation. These results demonstrate broad improvements in ten-day weather forecasts through a short correction-training schedule while retaining the pretrained backbone.