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The accuracy of binary classification systems is defined as the proportion of correct predictions - both positive and negative - made by a classification model or computational algorithm. A value between 0 (no accuracy) and 1 (perfect accuracy), the accuracy of a classification model is dependent on several factors, notably: the classification rule or algorithm used, the intrinsic characteristics of the tool used to do the classification, and the relative frequency of the elements being classified. Several accuracy metrics exist, each with its own advantages in different classification scenarios. In this manuscript, we show that relative to a perfect accuracy of 1, the positive prevalence threshold ($\phi_e$), a critical point of maximum curvature in the precision-prevalence curve, bounds the $F{_{\beta}}$ score between 1 and 1.8/1.5/1.2 for $\beta$ values of 0.5/1.0/2.0, respectively; the $F_1$ score between 1 and 1.5, and the Fowlkes-Mallows Index (FM) between 1 and $\sqrt{2} \approx 1.414$. We likewise describe a novel $negative$ prevalence threshold ($\phi_n$), the level of sharpest curvature for the negative predictive value-prevalence curve, such that $\phi_n$ $>$ $\phi_e$. The area between both these thresholds bounds the Matthews Correlation Coefficient (MCC) between $\sqrt{2}/2$ and $\sqrt{2}$. Conversely, the ratio of the maximum possible accuracy to that at any point below the prevalence threshold, $\phi_e$, goes to infinity with decreasing prevalence. Though applications are numerous, the ideas herein discussed may be used in computational complexity theory, artificial intelligence, and medical screening, amongst others. Where computational time is a limiting resource, attaining the prevalence threshold in binary classification systems may be sufficient to yield levels of accuracy comparable to that under maximum prevalence.

We consider the dynamic pricing problem with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is jointly determined by the price and an observable covariate vector $x_t\in\mathbb{R}^d$ through an unknown generalized linear model. Most of the existing literature assumes the covariate vectors $x_t$'s are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper we show that a simple pricing algorithm has an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$ (which can even be arbitrarily chosen). The upper bound on the regret matches the lower bound (even under the i.i.d. assumption) up to logarithmic factors. Our paper thus shows that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the $x_t$'s, a quantity present in previous bounds. Furthermore, we discuss a condition under which a better regret is achievable and how a Thompson sampling algorithm can be applied to give an efficient computation of the prices.

In communication complexity the Arthur-Merlin (AM) model is the most natural one that allows both randomness and non-determinism. Presently we do not have any super-logarithmic lower bound for the AM-complexity of an explicit function. Obtaining such a bound is a fundamental challenge to our understanding of communication phenomena. In this article we explore the gap between the known techniques and the complexity class AM. In the first part we define a new natural class, Small-advantage Layered Arthur-Merlin (SLAM), that has the following properties: - SLAM is (strictly) included in AM and includes all previously known subclasses of AM with non-trivial lower bounds. - SLAM is qualitatively stronger than the union of those classes. - SLAM is a subject to the discrepancy bound: in particular, the inner product function does not have an efficient SLAM-protocol. Structurally this can be summarised as SBP $\cup$ UAM $\subset$ SLAM $\subseteq$ AM $\cap$ PP. In the second part we ask why proving a lower bound of $\omega(\sqrt n)$ on the MA-complexity of an explicit function seems to be difficult. Both of these results are related to the notion of layer complexity, which is, informally, the number of "layers of non-determinism" used by a protocol.

Simulations of high-energy particle collisions, such as those used at the Large Hadron Collider, are based on quantum field theory; however, many approximations are made in practice. For example, the simulation of the parton shower, which gives rise to objects called `jets', is based on a semi-classical approximation that neglects various interference effects. While there is a desire to incorporate interference effects, new computational techniques are needed to cope with the exponential growth in complexity associated to quantum processes. We present a classical algorithm called the quantum trellis to efficiently compute the un-normalized probability density over N-body phase space including all interference effects, and we pair this with an MCMC-based sampling strategy. This provides a potential path forward for classical computers and a strong baseline for approaches based on quantum computing.

Recent advances in Transformer models allow for unprecedented sequence lengths, due to linear space and time complexity. In the meantime, relative positional encoding (RPE) was proposed as beneficial for classical Transformers and consists in exploiting lags instead of absolute positions for inference. Still, RPE is not available for the recent linear-variants of the Transformer, because it requires the explicit computation of the attention matrix, which is precisely what is avoided by such methods. In this paper, we bridge this gap and present Stochastic Positional Encoding as a way to generate PE that can be used as a replacement to the classical additive (sinusoidal) PE and provably behaves like RPE. The main theoretical contribution is to make a connection between positional encoding and cross-covariance structures of correlated Gaussian processes. We illustrate the performance of our approach on the Long-Range Arena benchmark and on music generation.

In this paper, we investigate a new variant of neural architecture search (NAS) paradigm -- searching with random labels (RLNAS). The task sounds counter-intuitive for most existing NAS algorithms since random label provides few information on the performance of each candidate architecture. Instead, we propose a novel NAS framework based on ease-of-convergence hypothesis, which requires only random labels during searching. The algorithm involves two steps: first, we train a SuperNet using random labels; second, from the SuperNet we extract the sub-network whose weights change most significantly during the training. Extensive experiments are evaluated on multiple datasets (e.g. NAS-Bench-201 and ImageNet) and multiple search spaces (e.g. DARTS-like and MobileNet-like). Very surprisingly, RLNAS achieves comparable or even better results compared with state-of-the-art NAS methods such as PC-DARTS, Single Path One-Shot, even though the counterparts utilize full ground truth labels for searching. We hope our finding could inspire new understandings on the essential of NAS.

We describe an algorithm for automatic classification of idiomatic and literal expressions. Our starting point is that words in a given text segment, such as a paragraph, that are highranking representatives of a common topic of discussion are less likely to be a part of an idiomatic expression. Our additional hypothesis is that contexts in which idioms occur, typically, are more affective and therefore, we incorporate a simple analysis of the intensity of the emotions expressed by the contexts. We investigate the bag of words topic representation of one to three paragraphs containing an expression that should be classified as idiomatic or literal (a target phrase). We extract topics from paragraphs containing idioms and from paragraphs containing literals using an unsupervised clustering method, Latent Dirichlet Allocation (LDA) (Blei et al., 2003). Since idiomatic expressions exhibit the property of non-compositionality, we assume that they usually present different semantics than the words used in the local topic. We treat idioms as semantic outliers, and the identification of a semantic shift as outlier detection. Thus, this topic representation allows us to differentiate idioms from literals using local semantic contexts. Our results are encouraging.

We present assertion based question answering (ABQA), an open domain question answering task that takes a question and a passage as inputs, and outputs a semi-structured assertion consisting of a subject, a predicate and a list of arguments. An assertion conveys more evidences than a short answer span in reading comprehension, and it is more concise than a tedious passage in passage-based QA. These advantages make ABQA more suitable for human-computer interaction scenarios such as voice-controlled speakers. Further progress towards improving ABQA requires richer supervised dataset and powerful models of text understanding. To remedy this, we introduce a new dataset called WebAssertions, which includes hand-annotated QA labels for 358,427 assertions in 55,960 web passages. To address ABQA, we develop both generative and extractive approaches. The backbone of our generative approach is sequence to sequence learning. In order to capture the structure of the output assertion, we introduce a hierarchical decoder that first generates the structure of the assertion and then generates the words of each field. The extractive approach is based on learning to rank. Features at different levels of granularity are designed to measure the semantic relevance between a question and an assertion. Experimental results show that our approaches have the ability to infer question-aware assertions from a passage. We further evaluate our approaches by incorporating the ABQA results as additional features in passage-based QA. Results on two datasets show that ABQA features significantly improve the accuracy on passage-based~QA.

We study response generation for open domain conversation in chatbots. Existing methods assume that words in responses are generated from an identical vocabulary regardless of their inputs, which not only makes them vulnerable to generic patterns and irrelevant noise, but also causes a high cost in decoding. We propose a dynamic vocabulary sequence-to-sequence (DVS2S) model which allows each input to possess their own vocabulary in decoding. In training, vocabulary construction and response generation are jointly learned by maximizing a lower bound of the true objective with a Monte Carlo sampling method. In inference, the model dynamically allocates a small vocabulary for an input with the word prediction model, and conducts decoding only with the small vocabulary. Because of the dynamic vocabulary mechanism, DVS2S eludes many generic patterns and irrelevant words in generation, and enjoys efficient decoding at the same time. Experimental results on both automatic metrics and human annotations show that DVS2S can significantly outperform state-of-the-art methods in terms of response quality, but only requires 60% decoding time compared to the most efficient baseline.