First, we construct asmall world graphrepresentation [31, 32] of a vocabulary. The nodes inthegraph arewords, each being represented using acontinuous vector transformed from its word embedding vector in the NLM.

Neural Information Processing Systems http://nips.cc/

Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected

The rise of Artificial Intelligence and Large Language Models is driving increased GPU usage in data centers for complex training and inference tasks, impacting operational costs, energy demands, and the environmental footprint of large-scale computing infrastructures. This work addresses the online scheduling problem in GPU datacenters, which involves scheduling tasks without knowledge of their future arrivals. We focus on two objectives: minimizing GPU fragmentation and reducing power consumption. GPU fragmentation occurs when partial GPU allocations hinder the efficient use of remaining resources, especially as the datacenter nears full capacity. A recent scheduling policy, Fragmentation Gradient Descent (FGD), leverages a fragmentation metric to address this issue. Reducing power consumption is also crucial due to the significant power demands of GPUs. To this end, we propose PWR, a novel scheduling policy to minimize power usage by selecting power-efficient GPU and CPU combinations. This involves a simplified model for measuring power consumption integrated into a Kubernetes score plugin. Through an extensive experimental evaluation in a simulated cluster, we show how PWR, when combined with FGD, achieves a balanced trade-off between reducing power consumption and minimizing GPU fragmentation.

Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that the prediction error of FGD is, however, by a factor $d$ slower than the prediction error of stochastic gradient descent (SGD). In this paper we show that by computing $\ell$ FGD steps based on each training sample, this suboptimality factor becomes $d/(\ell \wedge d)$ and thus the suboptimality of the rate disappears if $\ell \gtrsim d.$ We also show that FGD with repeated sampling can adapt to low-dimensional structure in the input distribution. The main mathematical challenge lies in controlling the dependencies arising from the repeated sampling process.

There has been a recent explosion in research into machine-learning-based generative modeling to tackle computational challenges for simulations in high energy physics (HEP). In order to use such alternative simulators in practice, we need well-defined metrics to compare different generative models and evaluate their discrepancy from the true distributions. We present the first systematic review and investigation into evaluation metrics and their sensitivity to failure modes of generative models, using the framework of two-sample goodness-of-fit testing, and their relevance and viability for HEP. Inspired by previous work in both physics and computer vision, we propose two new metrics, the Fr\'echet and kernel physics distances (FPD and KPD, respectively), and perform a variety of experiments measuring their performance on simple Gaussian-distributed, and simulated high energy jet datasets. We find FPD, in particular, to be the most sensitive metric to all alternative jet distributions tested and recommend its adoption, along with the KPD and Wasserstein distances between individual feature distributions, for evaluating generative models in HEP. We finally demonstrate the efficacy of these proposed metrics in evaluating and comparing a novel attention-based generative adversarial particle transformer to the state-of-the-art message-passing generative adversarial network jet simulation model. The code for our proposed metrics is provided in the open source JetNet Python library.

Long document retrieval aims to fetch query-relevant documents from a large-scale collection, where knowledge distillation has become de facto to improve a retriever by mimicking a heterogeneous yet powerful cross-encoder. However, in contrast to passages or sentences, retrieval on long documents suffers from the scope hypothesis that a long document may cover multiple topics. This maximizes their structure heterogeneity and poses a granular-mismatch issue, leading to an inferior distillation efficacy. In this work, we propose a new learning framework, fine-grained distillation (FGD), for long-document retrievers. While preserving the conventional dense retrieval paradigm, it first produces global-consistent representations crossing different fine granularity and then applies multi-granular aligned distillation merely during training. In experiments, we evaluate our framework on two long-document retrieval benchmarks, which show state-of-the-art performance.

Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected noise (such as the Gaussian noise in Langevin dynamics). In this paper, we introduce a new discrete data-dependent prior to the PAC-Bayesian framework, and prove a high probability generalization bound of order $O(\frac{1}{n}\cdot \sum_{t=1}^T(\gamma_t/\varepsilon_t)^2\left\|{\mathbf{g}_t}\right\|^2)$ for Floored GD (i.e. a version of gradient descent with precision level $\varepsilon_t$), where $n$ is the number of training samples, $\gamma_t$ is the learning rate at step $t$, $\mathbf{g}_t$ is roughly the difference of the gradient computed using all samples and that using only prior samples. $\left\|{\mathbf{g}_t}\right\|$ is upper bounded by and and typical much smaller than the gradient norm $\left\|{\nabla f(W_t)}\right\|$. We remark that our bound holds for nonconvex and nonsmooth scenarios. Moreover, our theoretical results provide numerically favorable upper bounds of testing errors (e.g., $0.037$ on MNIST). Using a similar technique, we can also obtain new generalization bounds for certain variants of SGD. Furthermore, we study the generalization bounds for gradient Langevin Dynamics (GLD). Using the same framework with a carefully constructed continuous prior, we show a new high probability generalization bound of order $O(\frac{1}{n} + \frac{L^2}{n^2}\sum_{t=1}^T(\gamma_t/\sigma_t)^2)$ for GLD. The new $1/n^2$ rate is due to the concentration of the difference between the gradient of training samples and that of the prior.

One of the key challenges of learning an online recommendation model is the temporal domain shift, which causes the mismatch between the training and testing data distribution and hence domain generalization error. To overcome, we propose to learn a meta future gradient generator that forecasts the gradient information of the future data distribution for training so that the recommendation model can be trained as if we were able to look ahead at the future of its deployment. Compared with Batch Update, a widely used paradigm, our theory suggests that the proposed algorithm achieves smaller temporal domain generalization error measured by a gradient variation term in a local regret. We demonstrate the empirical advantage by comparing with various representative baselines.