Linear scalarization, i.e., combining all loss functions by a weighted sum, has been the default choice in the literature of multi-task learning (MTL) since its inception. In recent years, there is a surge of interest in developing Specialized Multi-Task Optimizers (SMTOs) that treat MTL as a multi-objective optimization problem. However, it remains open whether there is a fundamental advantage of SMTOs over scalarization. In fact, heated debates exist in the community comparing these two types of algorithms, mostly from an empirical perspective. To approach the above question, in this paper, we revisit scalarization from a theoretical perspective. We focus on linear MTL models and study whether scalarization is capable of fully exploring the Pareto front. Our findings reveal that, in contrast to recent works that claimed empirical advantages of scalarization, scalarization is inherently incapable of full exploration, especially for those Pareto optimal solutions that strike the balanced trade-offs between multiple tasks. More concretely, when the model is under-parametrized, we reveal a multi-surface structure of the feasible region and identify necessary and sufficient conditions for full exploration. This leads to the conclusion that scalarization is in general incapable of tracing out the Pareto front. Our theoretical results partially answer the open questions in Xin et al. (2021), and provide a more intuitive explanation on why scalarization fails beyond non-convexity. We additionally perform experiments on a real-world dataset using both scalarization and state-of-the-art SMTOs. The experimental results not only corroborate our theoretical findings, but also unveil the potential of SMTOs in finding balanced solutions, which cannot be achieved by scalarization.
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In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response, or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example.
We propose Multiplier-less INTeger (MINT) quantization, a uniform quantization scheme that efficiently compresses weights and membrane potentials in spiking neural networks (SNNs). Unlike previous SNN quantization methods, MINT quantizes memory-intensive membrane potentials to an extremely low precision (2-bit), significantly reducing the memory footprint. MINT also shares the quantization scaling factor between weights and membrane potentials, eliminating the need for multipliers required in conventional uniform quantization. Experimental results show that our method matches the accuracy of full-precision models and other state-of-the-art SNN quantization techniques while surpassing them in memory footprint reduction and hardware cost efficiency at deployment. For example, 2-bit MINT VGG-16 achieves 90.6% accuracy on CIFAR-10, with roughly 93.8% reduction in memory footprint from the full-precision model and 90% reduction in computation energy compared to vanilla uniform quantization at deployment. The code is available at //github.com/Intelligent-Computing-Lab-Yale/MINT-Quantization.
We introduce AdaSub, a stochastic optimization algorithm that computes a search direction based on second-order information in a low-dimensional subspace that is defined adaptively based on available current and past information. Compared to first-order methods, second-order methods exhibit better convergence characteristics, but the need to compute the Hessian matrix at each iteration results in excessive computational expenses, making them impractical. To address this issue, our approach enables the management of computational expenses and algorithm efficiency by enabling the selection of the subspace dimension for the search. Our code is freely available on GitHub, and our preliminary numerical results demonstrate that AdaSub surpasses popular stochastic optimizers in terms of time and number of iterations required to reach a given accuracy.
Semantic textual similarity (STS), a cornerstone task in NLP, measures the degree of similarity between a pair of sentences, and has broad application in fields such as information retrieval and natural language understanding. However, sentence similarity can be inherently ambiguous, depending on the specific aspect of interest. We resolve this ambiguity by proposing a novel task called Conditional STS (C-STS) which measures sentences' similarity conditioned on an feature described in natural language (hereon, condition). As an example, the similarity between the sentences "The NBA player shoots a three-pointer." and "A man throws a tennis ball into the air to serve." is higher for the condition "The motion of the ball" (both upward) and lower for "The size of the ball" (one large and one small). C-STS's advantages are two-fold: (1) it reduces the subjectivity and ambiguity of STS and (2) enables fine-grained language model evaluation through diverse natural language conditions. We put several state-of-the-art models to the test, and even those performing well on STS (e.g. SimCSE, Flan-T5, and GPT-4) find C-STS challenging; all with Spearman correlation scores below 50. To encourage a more comprehensive evaluation of semantic similarity and natural language understanding, we make nearly 19K C-STS examples and code available for others to train and test their models.
Student attention is an indispensable input for uncovering their goals, intentions, and interests, which prove to be invaluable for a multitude of research areas, ranging from psychology to interactive systems. However, most existing methods to classify attention fail to model its complex nature. To bridge this gap, we propose AttentioNet, a novel Convolutional Neural Network-based approach that utilizes Electroencephalography (EEG) data to classify attention into five states: Selective, Sustained, Divided, Alternating, and relaxed state. We collected a dataset of 20 subjects through standard neuropsychological tasks to elicit different attentional states. The average across-student accuracy of our proposed model at this configuration is 92.3% (SD=3.04), which is well-suited for end-user applications. Our transfer learning-based approach for personalizing the model to individual subjects effectively addresses the issue of individual variability in EEG signals, resulting in improved performance and adaptability of the model for real-world applications. This represents a significant advancement in the field of EEG-based classification. Experimental results demonstrate that AttentioNet outperforms a popular EEGnet baseline (p-value < 0.05) in both subject-independent and subject-dependent settings, confirming the effectiveness of our proposed approach despite the limitations of our dataset. These results highlight the promising potential of AttentioNet for attention classification using EEG data.
Considerable research efforts have been devoted to the development of motion planning algorithms, which form a cornerstone of the autonomous driving system (ADS). However, obtaining an interactive and secure trajectory for the ADS remains a formidable task, especially in scenarios with significant interaction complexities. Many contemporary prediction-based planning methods frequently overlook interaction modeling, leading to less effective planning performance. This paper introduces a novel prediction-based interactive planning framework that explicitly and mathematically models interactions among traffic entities during the planning process. Our method incorporates interaction reasoning into spatio-temporal (s-t) planning by defining interaction conditions and constraints. Furthermore, it records and continually updates interaction relations for each planned state throughout the forward search. We assess the performance of our approach alongside state-of-the-art methods using a series of experiments conducted in both single and multi-modal scenarios. These experiments encompass variations in the accuracy of prediction outcomes and different degrees of planner aggressiveness. The experimental findings demonstrate the effectiveness and robustness of our method, yielding insights applicable to the wider field of autonomous driving. For the community's reference, our code is accessible at //github.com/ChenYingbing/IR-STP-Planner.
In the field of reinforcement learning (RL), representation learning is a proven tool for complex image-based tasks, but is often overlooked for environments with low-level states, such as physical control problems. This paper introduces SALE, a novel approach for learning embeddings that model the nuanced interaction between state and action, enabling effective representation learning from low-level states. We extensively study the design space of these embeddings and highlight important design considerations. We integrate SALE and an adaptation of checkpoints for RL into TD3 to form the TD7 algorithm, which significantly outperforms existing continuous control algorithms. On OpenAI gym benchmark tasks, TD7 has an average performance gain of 276.7% and 50.7% over TD3 at 300k and 5M time steps, respectively, and works in both the online and offline settings.
Activation functions are the linchpins of deep learning, profoundly influencing both the representational capacity and training dynamics of neural networks. They shape not only the nature of representations but also optimize convergence rates and enhance generalization potential. Appreciating this critical role, we present the Linear Oscillation (LoC) activation function, defined as $f(x) = x \times \sin(\alpha x + \beta)$. Distinct from conventional activation functions which primarily introduce non-linearity, LoC seamlessly blends linear trajectories with oscillatory deviations. The nomenclature "Linear Oscillation" is a nod to its unique attribute of infusing linear activations with harmonious oscillations, capturing the essence of the "Importance of Confusion". This concept of "controlled confusion" within network activations is posited to foster more robust learning, particularly in contexts that necessitate discerning subtle patterns. Our empirical studies reveal that, when integrated into diverse neural architectures, the LoC activation function consistently outperforms established counterparts like ReLU and Sigmoid. The stellar performance exhibited by the avant-garde Vision Transformer model using LoC further validates its efficacy. This study illuminates the remarkable benefits of the LoC over other prominent activation functions. It champions the notion that intermittently introducing deliberate complexity or "confusion" during training can spur more profound and nuanced learning. This accentuates the pivotal role of judiciously selected activation functions in shaping the future of neural network training.
Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.
The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provides a comprehensive survey on works that employ Deep Learning models to solve the task of MOT on single-camera videos. Four main steps in MOT algorithms are identified, and an in-depth review of how Deep Learning was employed in each one of these stages is presented. A complete experimental comparison of the presented works on the three MOTChallenge datasets is also provided, identifying a number of similarities among the top-performing methods and presenting some possible future research directions.
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