The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kind of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations.

Few-shot named entity recognition (NER) targets generalizing to unseen labels and/or domains with few labeled examples. Existing metric learning methods compute token-level similarities between query and support sets, but are not able to fully incorporate label semantics into modeling. To address this issue, we propose a simple method to largely improve metric learning for NER: 1) multiple prompt schemas are designed to enhance label semantics; 2) we propose a novel architecture to effectively combine multiple prompt-based representations. Empirically, our method achieves new state-of-the-art (SOTA) results under 16 of the 18 considered settings, substantially outperforming the previous SOTA by an average of 8.84% and a maximum of 34.51% in relative gains of micro F1. Named entity recognition (NER) is a key natural language understanding task that extracts and classifies named entities mentioned in unstructured texts into predefined categories. Few-shot NER targets generalizing to unseen categories by learning from few labeled examples. Recent advances for few-shot NER use metric learning methods which compute the token-level similarities between the query and the given support cases. Snell et al. (2017) proposed to use prototypical networks that learn prototypical representations for target classes. Later, this method was introduced to few-shot NER tasks (Fritzler et al., 2019; Hou et al., 2020).

Semantic code search is the task of retrieving a code snippet given a textual description of its functionality. Recent work has been focused on using similarity metrics between neural embeddings of text and code. However, current language models are known to struggle with longer, compositional text, and multi-step reasoning. To overcome this limitation, we propose supplementing the query sentence with a layout of its semantic structure. The semantic layout is used to break down the final reasoning decision into a series of lower-level decisions. We use a Neural Module Network architecture to implement this idea. We compare our model - NS3 (Neuro-Symbolic Semantic Search) - to a number of baselines, including state-of-the-art semantic code retrieval methods, and evaluate on two datasets - CodeSearchNet and Code Search and Question Answering. We demonstrate that our approach results in more precise code retrieval, and we study the effectiveness of our modular design when handling compositional queries.

We show two average-reward off-policy control algorithms, Differential Q-learning (Wan, Naik, & Sutton 2021a) and RVI Q-learning (Abounadi Bertsekas & Borkar 2001), converge in weakly communicating MDPs. Weakly communicating MDPs are the most general MDPs that can be solved by a learning algorithm with a single stream of experience. The original convergence proofs of the two algorithms require that the solution set of the average-reward optimality equation only has one degree of freedom, which is not necessarily true for weakly communicating MDPs. To the best of our knowledge, our results are the first showing average-reward off-policy control algorithms converge in weakly communicating MDPs. As a direct extension, we show that average-reward options algorithms for temporal abstraction introduced by Wan, Naik, & Sutton (2021b) converge if the Semi-MDP induced by options is weakly communicating.

In fighting games, individual players of the same skill level often exhibit distinct strategies from one another through their gameplay. Despite this, the majority of AI agents for fighting games have only a single strategy for each "level" of difficulty. To make AI opponents more human-like, we'd ideally like to see multiple different strategies at each level of difficulty, a concept we refer to as "multidimensional" difficulty. In this paper, we introduce a diversity-based deep reinforcement learning approach for generating a set of agents of similar difficulty that utilize diverse strategies. We find this approach outperforms a baseline trained with specialized, human-authored reward functions in both diversity and performance.

Persistent Memory (PMEM), also known as Non-Volatile Memory (NVM), can deliver higher density and lower cost per bit when compared with DRAM. Its main drawback is that it is typically slower than DRAM. On the other hand, DRAM has scalability problems due to its cost and energy consumption. Soon, PMEM will likely coexist with DRAM in computer systems but the biggest challenge is to know which data to allocate on each type of memory. This paper describes a methodology for identifying and characterizing application objects that have the most influence on the application's performance using Intel Optane DC Persistent Memory. In the first part of our work, we built a tool that automates the profiling and analysis of application objects. In the second part, we build a machine learning model to predict the most critical object within large-scale graph-based applications. Our results show that using isolated features does not bring the same benefit compared to using a carefully chosen set of features. By performing data placement using our predictive model, we can reduce the execution time degradation by 12\% (average) and 30\% (max) when compared to the baseline's approach based on LLC misses indicator.

Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a scalable way. The absence of efficient ways of computation drove the most widely used methods to focus on first-order approximations that do not capture the curvature information. In this paper, we develop HesScale, a scalable approach to approximating the diagonal of the Hessian matrix, to incorporate second-order information in a computationally efficient manner. We show that HesScale has the same computational complexity as backpropagation. Our results on supervised classification show that HesScale achieves high approximation accuracy, allowing for scalable and efficient second-order optimization. First-order optimization offers a cheap and efficient way of performing local progress in optimization problems by using gradient information. However, their performance suffers from instability or slow progress when used in ill-conditioned landscapes. Such a problem is present because firstorder methods do not capture curvature information which causes two interrelated issues. First, the updates in first-order have incorrect units (Duchi et al. 2011), which creates a scaling issue.

Fine-tuning pre-trained language models has recently become a common practice in building NLP models for various tasks, especially few-shot tasks. We argue that under the few-shot setting, formulating fine-tuning closer to the pre-training objectives shall be able to unleash more benefits from the pre-trained language models. In this work, we take few-shot named entity recognition (NER) for a pilot study, where existing fine-tuning strategies are much different from pre-training. We propose a novel few-shot fine-tuning framework for NER, FFF-NER. Specifically, we introduce three new types of tokens, "is-entity", "which-type" and bracket, so we can formulate the NER fine-tuning as (masked) token prediction or generation, depending on the choice of pre-trained language models. In our experiments, we apply FFF-NER to fine-tune both BERT and BART for few-shot NER on several benchmark datasets and observe significant improvements over existing fine-tuning strategies, including sequence labeling, prototype meta-learning, and prompt-based approaches. We further perform a series of ablation studies, showing few-shot NER performance is strongly correlated with the similarity between fine-tuning and pre-training.

We consider approximate dynamic programming in $\gamma$-discounted Markov decision processes and apply it to approximate planning with linear value-function approximation. Our first contribution is a new variant of Approximate Policy Iteration (API), called Confident Approximate Policy Iteration (CAPI), which computes a deterministic stationary policy with an optimal error bound scaling linearly with the product of the effective horizon $H$ and the worst-case approximation error $\epsilon$ of the action-value functions of stationary policies. This improvement over API (whose error scales with $H^2$) comes at the price of an $H$-fold increase in memory cost. Unlike Scherrer and Lesner [2012], who recommended computing a non-stationary policy to achieve a similar improvement (with the same memory overhead), we are able to stick to stationary policies. This allows for our second contribution, the application of CAPI to planning with local access to a simulator and $d$-dimensional linear function approximation. As such, we design a planning algorithm that applies CAPI to obtain a sequence of policies with successively refined accuracies on a dynamically evolving set of states. The algorithm outputs an $\tilde O(\sqrt{d}H\epsilon)$-optimal policy after issuing $\tilde O(dH^4/\epsilon^2)$ queries to the simulator, simultaneously achieving the optimal accuracy bound and the best known query complexity bound, while earlier algorithms in the literature achieve only one of them. This query complexity is shown to be tight in all parameters except $H$. These improvements come at the expense of a mild (polynomial) increase in memory and computational costs of both the algorithm and its output policy.

In this paper, we explore an approach to auxiliary task discovery in reinforcement learning based on ideas from representation learning. Auxiliary tasks tend to improve data efficiency by forcing the agent to learn auxiliary prediction and control objectives in addition to the main task of maximizing reward, and thus producing better representations. Typically these tasks are designed by people. Meta-learning offers a promising avenue for automatic task discovery; however, these methods are computationally expensive and challenging to tune in practice. In this paper, we explore a complementary approach to the auxiliary task discovery: continually generating new auxiliary tasks and preserving only those with high utility. We also introduce a new measure of auxiliary tasks' usefulness based on how useful the features induced by them are for the main task. Our discovery algorithm significantly outperforms random tasks, hand-designed tasks, and learning without auxiliary tasks across a suite of environments. The discovery question--what should an agent learn about--remains an open challenge for AI research. In the context of reinforcement learning, multiple components define the scope of what the agent is learning about. The agent's behavior defines its focus and attention in terms of data collection. Related exploration methods based on intrinsic rewards define what the agent chooses to do outside of reward maximization.