The increasing size of language models necessitates a thorough analysis across multiple dimensions to assess trade-offs among crucial hardware metrics such as latency, energy consumption, GPU memory usage, and performance. Identifying optimal model configurations under specific hardware constraints is becoming essential but remains challenging due to the computational load of exhaustive training and evaluation on multiple devices. To address this, we introduce HW-GPT-Bench, a hardware-aware benchmark that utilizes surrogate predictions to approximate various hardware metrics across 13 devices of architectures in the GPT-2 family, with architectures containing up to 774M parameters. Our surrogates, via calibrated predictions and reliable uncertainty estimates, faithfully model the heteroscedastic noise inherent in the energy and latency measurements. To estimate perplexity, we employ weight-sharing techniques from Neural Architecture Search (NAS), inheriting pretrained weights from the largest GPT-2 model. Finally, we demonstrate the utility of HW-GPT-Bench by simulating optimization trajectories of various multi-objective optimization algorithms in just a few seconds.

Asynchronous Bayesian optimization is a recently implemented technique that allows for parallel operation of experimental systems and disjointed workflows. Contrasting with serial Bayesian optimization which individually selects experiments one at a time after conducting a measurement for each experiment, asynchronous policies sequentially assign multiple experiments before measurements can be taken and evaluate new measurements continuously as they are made available. This technique allows for faster data generation and therefore faster optimization of an experimental space. This work extends the capabilities of asynchronous optimization methods beyond prior studies by evaluating four additional policies that incorporate pessimistic predictions in the training data set. Combined with a conventional greedy policy, the five total policies were evaluated in a simulated environment and benchmarked with serial sampling. Under some conditions and parameter space dimensionalities, the pessimistic asynchronous policy reached optimum experimental conditions in significantly fewer experiments than equivalent serial policies and proved to be less susceptible to convergence onto local optima at higher dimensions. Without accounting for the faster sampling rate, the pessimistic asynchronous algorithm presented in this work could result in more efficient algorithm driven optimization of high-cost experimental spaces. Accounting for sampling rate, the presented asynchronous algorithm could allow for faster optimization in experimental spaces where multiple experiments can be run before results are collected.

Vehicle Routing Problems (VRPs) are optimization problems with significant real-world implications in logistics, transportation, and supply chain management. Despite the recent progress made in learning to solve individual VRP variants, there is a lack of a unified approach that can effectively tackle a wide range of tasks, which is crucial for real-world impact. This paper introduces RouteFinder, a framework for developing foundation models for VRPs. Our key idea is that a foundation model for VRPs should be able to model variants by treating each variant as a subset of a larger VRP problem, equipped with different attributes. We introduce a parallelized environment that can handle any combination of attributes at the same time in a batched manner, and an efficient sampling procedure to train on a mix of problems at each optimization step that can greatly improve convergence robustness. We also introduce novel Global Feature Embeddings that project instance-wise attributes efficiently onto the latent space and help the model understand different VRP variants. Finally, we introduce Efficient Adapter Layers, a simple yet effective technique to finetune pre-trained RouteFinder models to solve novel variants with previously unseen attributes outside of the original feature space.

Training with mixed data distributions is a common and important part of creating multi-task and instruction-following models. The diversity of the data distributions and cost of joint training makes the optimization procedure extremely challenging. Data mixing methods partially address this problem, albeit having a sub-optimal performance across data sources and require multiple expensive training runs. In this paper, we propose a simple and efficient alternative for better optimization of the data sources by combining models individually trained on each data source with the base model using basic element-wise vector operations. The resulting model, namely Distribution Edited Model (DEM), is 11x cheaper than standard data mixing and outperforms strong baselines on a variety of benchmarks, yielding up to 6.2% improvement on MMLU, 11.5% on BBH, 16.1% on DROP, and 9.3% on HELM with models of size 3B to 13B. Notably, DEM does not require full re-training when modifying a single data-source, thus making it very flexible and scalable for training with diverse data sources.

The rapid research and development of generative artificial intelligence has enabled the generation of high-quality images, text, and 3D models from text prompts. This advancement impels an inquiry into whether these models can be leveraged to create digital artifacts for both creative and engineering applications. Drawing on innovative designs from other domains may be one answer to this question, much like the historical practice of ``bionics", where humans have sought inspiration from nature's exemplary designs. This raises the intriguing possibility of using generative models to simultaneously tackle design tasks across multiple domains, facilitating cross-domain learning and resulting in a series of innovative design solutions. In this paper, we propose LLM2FEA as the first attempt to discover novel designs in generative models by transferring knowledge across multiple domains. By utilizing a multi-factorial evolutionary algorithm (MFEA) to drive a large language model, LLM2FEA integrates knowledge from various fields to generate prompts that guide the generative model in discovering novel and practical objects. Experimental results in the context of 3D aerodynamic design verify the discovery capabilities of the proposed LLM2FEA. The designs generated by LLM2FEA not only satisfy practicality requirements to a certain degree but also feature novel and aesthetically pleasing shapes, demonstrating the potential applications of LLM2FEA in discovery tasks.

Differentiable optimization is a powerful new paradigm capable of reconciling model-based and learning-based approaches in robotics. However, the majority of robotics optimization problems are non-convex and current differentiable optimization techniques are therefore prone to convergence to local minima. When this occurs, the gradients provided by these existing solvers can be wildly inaccurate and will ultimately corrupt the training process. On the other hand, many non-convex robotics problems can be framed as polynomial optimization problems and, in turn, admit convex relaxations that can be used to recover a global solution via so-called certifiably correct methods. We present SDPRLayers, an approach that leverages these methods as well as state-of-the-art convex implicit differentiation techniques to provide certifiably correct gradients throughout the training process. We introduce this approach and showcase theoretical results that provide conditions under which correctness of the gradients is guaranteed. We first demonstrate our approach on two simple-but-demonstrative simulated examples, which expose the potential pitfalls of existing, state-of-the-art, differentiable optimization methods. We then apply our method in a real-world application: we train a deep neural network to detect image keypoints for robot localization in challenging lighting conditions. We provide our open-source, PyTorch implementation of SDPRLayers and our differentiable localization pipeline.

In this paper, we study the contextual multinomial logit (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a significant discrepancy between lower and upper regret bounds, particularly regarding the maximum assortment size $K$. Additionally, the variation in reward structures between these bounds complicates the quest for optimality. Under uniform rewards, where all items have the same expected reward, we establish a regret lower bound of $\Omega(d\sqrt{\smash[b]{T/K}})$ and propose a constant-time algorithm, OFU-MNL+, that achieves a matching upper bound of $\tilde{O}(d\sqrt{\smash[b]{T/K}})$. Under non-uniform rewards, we prove a lower bound of $\Omega(d\sqrt{T})$ and an upper bound of $\tilde{O}(d\sqrt{T})$, also achievable by OFU-MNL+. Our empirical studies support these theoretical findings. To the best of our knowledge, this is the first work in the contextual MNL bandit literature to prove minimax optimality -- for either uniform or non-uniform reward setting -- and to propose a computationally efficient algorithm that achieves this optimality up to logarithmic factors.

The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then interpolating between the subset of the best evaluated trade-off points. In this work, we propose to parameterise the Pareto front surface using polar coordinates. More precisely, we show that any Pareto front surface can be equivalently represented using a scalar-valued length function which returns the projected length along any positive radial direction. We then use this representation in order to rigorously develop the theory and applications of stochastic Pareto front surfaces. In particular, we derive many Pareto front surface statistics of interest such as the expectation, covariance and quantiles. We then discuss how these can be used in practice within a design of experiments setting, where the goal is to both infer and use the Pareto front surface distribution in order to make effective decisions. Our framework allows for clear uncertainty quantification and we also develop advanced visualisation techniques for this purpose. Finally we discuss the applicability of our ideas within multivariate extreme value theory and illustrate our methodology in a variety of numerical examples, including a case study with a real-world air pollution data set.

In this paper, we develop a decision support system for the hierarchical text classification. We consider text collections with a fixed hierarchical structure of topics given by experts in the form of a tree. The system sorts the topics by relevance to a given document. The experts choose one of the most relevant topics to finish the classification. We propose a weighted hierarchical similarity function to calculate topic relevance. The function calculates the similarity of a document and a tree branch. The weights in this function determine word importance. We use the entropy of words to estimate the weights. The proposed hierarchical similarity function formulates a joint hierarchical thematic classification probability model of the document topics, parameters, and hyperparameters. The variational Bayesian inference gives a closed-form EM algorithm. The EM algorithm estimates the parameters and calculates the probability of a topic for a given document. Compared to hierarchical multiclass SVM, hierarchical PLSA with adaptive regularization, and hierarchical naive Bayes, the weighted hierarchical similarity function has better improvement in ranking accuracy in an abstract collection of a major conference EURO and a website collection of industrial companies.

Enabling robots to autonomously perform hybrid motions in diverse environments can be beneficial for long-horizon tasks such as material handling, household chores, and work assistance. This requires extensive exploitation of intrinsic motion capabilities, extraction of affordances from rich environmental information, and planning of physical interaction behaviors. Despite recent progress has demonstrated impressive humanoid whole-body control abilities, they struggle to achieve versatility and adaptability for new tasks. In this work, we propose HYPERmotion, a framework that learns, selects and plans behaviors based on tasks in different scenarios. We combine reinforcement learning with whole-body optimization to generate motion for 38 actuated joints and create a motion library to store the learned skills. We apply the planning and reasoning features of the large language models (LLMs) to complex loco-manipulation tasks, constructing a hierarchical task graph that comprises a series of primitive behaviors to bridge lower-level execution with higher-level planning. By leveraging the interaction of distilled spatial geometry and 2D observation with a visual language model (VLM) to ground knowledge into a robotic morphology selector to choose appropriate actions in single- or dual-arm, legged or wheeled locomotion. Experiments in simulation and real-world show that learned motions can efficiently adapt to new tasks, demonstrating high autonomy from free-text commands in unstructured scenes. Videos and website: hy-motion.github.io/