Search

The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through data-driven methods, these algorithms often exhibit limitations in generalizability beyond the distribution captured by training data and are not robust to changes in the nominal system dynamics induced by intrinsic or environmental factors. To overcome these limitations, this study presents an adaptive Koopman architecture capable of responding to the changes in system dynamics online. The proposed framework initially employs an autoencoder-based neural network that utilizes input-output information from the nominal system to learn the corresponding Koopman embedding offline. Subsequently, we augment this nominal Koopman architecture with a feed-forward neural network that learns to modify the nominal dynamics in response to any deviation between the predicted and observed lifted states, leading to improved generalization and robustness to a wide range of uncertainties and disturbances compared to contemporary methods. Extensive tracking control simulations, which are undertaken by integrating the proposed scheme within a Model Predictive Control framework, are used to highlight its robustness against measurement noise, disturbances, and parametric variations in system dynamics., Comment: Corrected the title

Large language models (LLMs) have recently been used as backbones for recommender systems. However, their performance often lags behind conventional methods in standard tasks like retrieval. We attribute this to a mismatch between LLMs' knowledge and the knowledge crucial for effective recommendations. While LLMs excel at natural language reasoning, they cannot model complex user-item interactions inherent in recommendation tasks. We propose bridging the knowledge gap and equipping LLMs with recommendation-specific knowledge to address this. Operations such as Masked Item Modeling (MIM) and Bayesian Personalized Ranking (BPR) have found success in conventional recommender systems. Inspired by this, we simulate these operations through natural language to generate auxiliary-task data samples that encode item correlations and user preferences. Fine-tuning LLMs on such auxiliary-task data samples and incorporating more informative recommendation-task data samples facilitates the injection of recommendation-specific knowledge into LLMs. Extensive experiments across retrieval, ranking, and rating prediction tasks on LLMs such as FLAN-T5-Base and FLAN-T5-XL show the effectiveness of our technique in domains such as Amazon Toys & Games, Beauty, and Sports & Outdoors. Notably, our method outperforms conventional and LLM-based baselines, including the current SOTA, by significant margins in retrieval, showcasing its potential for enhancing recommendation quality., Comment: Accepted to the NAACL 2024 Findings

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers., Comment: 13 pages, 16 pages. arXiv admin note: substantial text overlap with arXiv:2209.11524, arXiv:2303.15871, arXiv:2310.10839

Hallucinations and delusions are often grouped together within the positive symptoms of psychosis. However, recent evidence suggests they may be driven by distinct computational and neural mechanisms. Examining the time course of their emergence may provide insights into the relationship between these underlying mechanisms. Participants from the second (N = 719) and third (N = 699) iterations of the North American Prodrome Longitudinal Study (NAPLS 2 and 3) were assessed for timing of CHR-P-level delusion and hallucination onset. Pre-onset symptom patterns in first-episode psychosis patients (FEP) from the Prevention and Early Intervention Program for Psychosis (PEPP-Montreal; N = 694) were also assessed. Symptom onset was determined at baseline assessment and the evolution of symptom patterns examined over 24 months. In all three samples, participants were more likely to report the onset of delusion-spectrum symptoms prior to hallucination-spectrum symptoms (odds ratios (OR): NAPLS 2 = 4.09; NAPLS 3 = 4.14; PEPP, Z = 7.01, P < 0.001) and to present with only delusions compared to only hallucinations (OR: NAPLS 2 = 5.6; NAPLS 3 = 11.11; PEPP = 42.75). Re-emergence of delusions after remission was also more common than re-emergence of hallucinations (Ps < 0.05), and hallucinations more often resolved first (Ps < 0.001). In both CHR-P samples, ratings of delusional ideation fell with the onset of hallucinations (P = 0.007). Delusions tend to emerge before hallucinations and may play a role in their development. Further work should examine the relationship between the mechanisms driving these symptoms and its utility for diagnosis and treatment.

Randomly-hashed item ids are used ubiquitously in recommendation models. However, the learned representations from random hashing prevents generalization across similar items, causing problems of learning unseen and long-tail items, especially when item corpus is large, power-law distributed, and evolving dynamically. In this paper, we propose using content-derived features as a replacement for random ids. We show that simply replacing ID features with content-based embeddings can cause a drop in quality due to reduced memorization capability. To strike a good balance of memorization and generalization, we propose to use Semantic IDs -- a compact discrete item representation learned from frozen content embeddings using RQ-VAE that captures the hierarchy of concepts in items -- as a replacement for random item ids. Similar to content embeddings, the compactness of Semantic IDs poses a problem of easy adaption in recommendation models. We propose novel methods for adapting Semantic IDs in industry-scale ranking models, through hashing sub-pieces of of the Semantic-ID sequences. In particular, we find that the SentencePiece model that is commonly used in LLM tokenization outperforms manually crafted pieces such as N-grams. To the end, we evaluate our approaches in a real-world ranking model for YouTube recommendations. Our experiments demonstrate that Semantic IDs can replace the direct use of video IDs by improving the generalization ability on new and long-tail item slices without sacrificing overall model quality.

Modern recommender systems perform large-scale retrieval by first embedding queries and item candidates in the same unified space, followed by approximate nearest neighbor search to select top candidates given a query embedding. In this paper, we propose a novel generative retrieval approach, where the retrieval model autoregressively decodes the identifiers of the target candidates. To that end, we create semantically meaningful tuple of codewords to serve as a Semantic ID for each item. Given Semantic IDs for items in a user session, a Transformer-based sequence-to-sequence model is trained to predict the Semantic ID of the next item that the user will interact with. To the best of our knowledge, this is the first Semantic ID-based generative model for recommendation tasks. We show that recommender systems trained with the proposed paradigm significantly outperform the current SOTA models on various datasets. In addition, we show that incorporating Semantic IDs into the sequence-to-sequence model enhances its ability to generalize, as evidenced by the improved retrieval performance observed for items with no prior interaction history., Comment: To appear in The 37th Conference on Neural Information Processing Systems (NeurIPS 2023)

Unmanned aerial vehicles (UAVs), specifically quadrotors, have revolutionized various industries with their maneuverability and versatility, but their safe operation in dynamic environments heavily relies on effective collision avoidance techniques. This paper introduces a novel technique for safely navigating a quadrotor along a desired route while avoiding kinematic obstacles. We propose a new constraint formulation that employs control barrier functions (CBFs) and collision cones to ensure that the relative velocity between the quadrotor and the obstacle always avoids a cone of vectors that may lead to a collision. By showing that the proposed constraint is a valid CBF for quadrotors, we are able to leverage its real-time implementation via Quadratic Programs (QPs), called the CBF-QPs. Validation includes PyBullet simulations and hardware experiments on Crazyflie 2.1, demonstrating effectiveness in static and moving obstacle scenarios. Comparative analysis with literature, especially higher order CBF-QPs, highlights the proposed approach's less conservative nature. Simulation and Hardware videos are available here: https://tayalmanan28.github.io/C3BF-UAV/, Comment: Accepted at American Control Conference(ACC) 2024. 6 pages, 8 figures

Alumina forming, oxidation and thermal shock resistant MAX phases are of a high interest for high temperature applications. Herein we report, on bonding and resulting interactions between a Ni-based superalloy, NSA, and two alumina forming MAX phases. The diffusion couples Cr${_2}$AlC/Inconel-718/Ti${_2}$AlC were assembled and heated to 1000 or 1100{\deg}C in a vacuum hot press under loads corresponding to stresses of either 2 MPa or 20 MPa. The resulting interfaces were examined using X-ray diffraction, scanning electron microscopy and energy-dispersive X-ray spectroscopy. Good bonding between Cr${_2}$AlC and NSA was achieved after hot pressing at 1000{\deg}C and a contact pressure of only 2 MPa; in the case of Ti${_2}$AlC a higher temperature (1100{\deg}C) and pressure (20 MPa) were needed. In both cases, a diffusion bond was realized with no evidence of interfacial damage or cracking after cooling to room temperature. Twenty thermal cycles from room temperature to 1000{\deg}C showed that Ti${_2}$AlC is a poor oxidation barrier for Inconel-718. However, in the case of Cr${_2}$AlC no cracks, delamination nor surface degradation were observed, suggesting that this material could be used to protect Inconel-718 from oxidation.

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise" generically refers to any contribution to the data that is not captured by the low-rank model. In most applications, the noise level is large compared to the underlying signal and it is important to avoid overfitting. In order to tackle this problem, we define a regularized cost function well suited for spectral reconstruction methods. Within a random noise model, and in the large system limit, we prove that the resulting accuracy undergoes a phase transition depending on the noise level and on the fraction of observed entries. The cost function can be minimized using OPTSPACE (a manifold gradient descent algorithm). Numerical simulations show that this approach is competitive with state-of-the-art alternatives., Comment: 5 pages, 3 figures, Conference Version

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local manifold optimization, for solving the low-rank matrix completion problem. It has been shown that if the number of revealed entries is large enough, the output of singular value decomposition gives a good estimate for the original matrix, so that local optimization reconstructs the correct matrix with high probability. We present numerical results which show that this algorithm can reconstruct the low rank matrix exactly from a very small subset of its entries. We further study the robustness of the algorithm with respect to noise, and its performance on actual collaborative filtering datasets., Comment: 26 pages, 15 figures

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and wireless sensor networks. In this paper, we focus on the matrix completion problem in the case when the observed samples are corrupted by noise. We compare the performance of three state-of-the-art matrix completion algorithms (OptSpace, ADMiRA and FPCA) on a single simulation platform and present numerical results. We show that in practice these efficient algorithms can be used to reconstruct real data matrices, as well as randomly generated matrices, accurately., Comment: 7 pages, 7 figures, 47th Allerton Conference on Communication Control and Computing, 2009, invited paper

Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan et al.(2009), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances., Comment: 22 pages, 3 figures

Let M be a random (alpha n) x n matrix of rank r<

How many random entries of an n by m, rank r matrix are necessary to reconstruct the matrix within an accuracy d? We address this question in the case of a random matrix with bounded rank, whereby the observed entries are chosen uniformly at random. We prove that, for any d>0, C(r,d)n observations are sufficient. Finally we discuss the question of reconstructing the matrix efficiently, and demonstrate through extensive simulations that this task can be accomplished in nPoly(log n) operations, for small rank., Comment: 8 pages, 11 figures, Forty-sixth Allerton Conference on Communication, Control and Computing, invited paper