Neural processes amortize Gaussian process inference, replacing the exact $O(n^3)$ posterior with a learned $O(n)$ map from context sets to predictive distributions. For a class of latent neural processes, we bound the Kullback--Leibler (KL) divergence between the GP and LNP predictives, decomposing it into three interpretable sources, namely label contamination as the neural process uses label values to estimate a quantity that is label-independent in the exact GP, an information bottleneck because the finite-dimensional representation cannot resolve the full context geometry, and amortization error from a single encoder network shared across all contexts. The bottleneck truncation term decays in the representation dimension $d$ as $O(e^{-cd^{2/d_x}})$ for squared-exponential kernels on $\mathbb{R}^{d_x}$ where $c > 0$ is a kernel-dependent constant and as $O(d^{-2ν/d_x})$ for Matérn-$ν$ kernels, directly linking architecture sizing to kernel smoothness and input dimension. The label contamination term is $O(1)$ in general, with only the observation-noise component decaying as $O(1/n)$, identifying a persistent cost of routing uncertainty estimation through a label-dependent representation. These results characterize the costs of amortization within the analyzed class and yield architectural recommendations to predict variance from context locations alone in the GP-amortization regime, and replace mean aggregation with second-order pooling to close the dominant amortization gap.

Optimal transport (OT) has emerged as a fundamental tool in modern machine learning, yet its computational cost remains a significant bottleneck for large-scale applications. While harnessing the massive parallelism of modern GPU hardware is critical for efficiency, the de facto standard Sinkhorn algorithm, despite its ease of parallelization, often suffers from slow convergence in challenging problems. More recently, the sparse-plus-low-rank quasi-Newton method offers a balance between convergence rate and per-iteration complexity; however, its efficiency on GPUs is severely hindered by the serial nature of sparse matrix symbolic analysis and irregular memory access patterns. To bridge this gap, we present cuRegOT, a high-performance GPU solver tailored for entropic-regularized OT. We introduce a suite of algorithmic and architectural optimizations, including an amortized symbolic analysis strategy to mitigate CPU bottlenecks, an asynchronous Sinkhorn iterates generation mechanism, and a fused kernel for bandwidth-efficient gradient evaluation. These strategies are backed by rigorous theoretical guarantees ensuring algorithmic convergence. Extensive numerical experiments demonstrate that cuRegOT achieves significant speedups over state-of-the-art GPU-based solvers across a variety of benchmark tasks.

Large language models hallucinate in predictable ways: attention routing fails by over-concentrating on a narrow set of positions, or by spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport capacity; we prove that every transpose-invariant spectral diagnostic of this operator is structurally orientation-blind (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a quantitative converse establishing the asymmetry coefficient $G$ as the unique control parameter for direction. Pairing this with a closed-form bipartite-Cheeger landscape for canonical causal architectures, we show that uniform causal attention satisfies an $n$-independent floor $ϕ\ge 1/5$ with worst cut at $t^\ast/n \approx 0.32$, while window attention pierces the floor as $O(w/n)$; failure modes are shape-different, not just value-different. The resulting two-axis diagnostic ($ϕ$ for capacity, $G$ for direction) yields a falsifiable polarity prediction: bottleneck- and diffuse-dominated benchmarks should exhibit opposite polarity. Under length-controlled evaluation, transport features retain interpretable signal (LC-AUROC from 0.62 to 0.84) on tested models up to 8B parameters, with polarity reversing as predicted between HaluEval and MedHallu.

Appendix382 AAdditional Experiments3383 A.1 Experiments on the ETT datasets384 In the main body, we present a comparison of the benchmark methods on the ETTm2 dataset. In this385 section, we extend our analysis to the remaining three ETT datasets, namely ETTh1, ETTh2, and386 ETTm1, as summarized in Table 7. Our experimental results reveal that Basisformer outperforms all387 other methods in terms of MSE and MAE. In all experiments, lower MSE values indicate better model performance, and we present the best results in boldface. Experimental results with longer length input setting391 Throughout our research, we maintain consistency in our experimental settings by fixing the input392 length to be 96(with a reduced input length of 36for the illness dataset), instead of using a longer393 length.

Recent work has demonstrated the effectiveness of formulating decision making as supervised learning on offline-collected trajectories. Powerful sequence models, such as GPT or BERT, are often employed to encode the trajectories. However, the benefits of performing sequence modeling on trajectory data remain unclear. In this work, we investigate whether sequence modeling has the ability to condense trajectories into useful representations that enhance policy learning. We adopt a two-stage framework that first leverages sequence models to encode trajectory-level representations, and then learns a goal-conditioned policy employing the encoded representations as its input.

Knowledge editing technology has received widespread attention for low-cost updates of incorrect or outdated knowledge in large-scale language models. However, recent research has found that edited models often exhibit varying degrees of performance degradation. The reasons behind this phenomenon and potential solutions have not yet been provided. In order to investigate the reasons for the performance decline of the edited model and optimize the editing method, this work explores the underlying reasons from both data and model perspectives.

We introduce the Block Transformer which adopts hierarchical global-to-local modeling to autoregressive transformers to mitigate the inference bottlenecks associated with self-attention. Self-attention requires the key-value (KV) cache of all previous sequences to be retrieved from memory at every decoding step to retrieve context information, leading to two primary bottlenecks during batch inference. First, there is a significant delay in obtaining the first token, as the information of the entire prompt must first be processed to prefill the KV cache. Second, computation of subsequent tokens is bottlenecked by the high memory I/O demand of fetching the entire KV cache, which grows linearly with sequence length, incurring quadratic memory reads overall. We design the Block Transformer to strategically mitigate these costs, by incorporating coarsity and locality into an integrated global-to-local architecture. At the lower layers, we aggregate tokens into fixed size blocks to apply attention across the entire sequence at coarse-grained detail, to capture the global context while minimizing KV cache overhead. At upper layers, we apply attention within each block to decode individual tokens, to model fine-grained details with a lightweight local KV cache. We pretrain vanilla and Block Transformers from scratch and demonstrate that Block Transformers reach 10--20x inference throughput compared to vanilla transformers with equivalent perplexity and zero-shot task performance.