Pater's (2019) target article proposes that neural networks will provide theories of learning that generative grammar lacks. We argue that his enthusiasm is premature since the biases of neural networks are largely unknown, and he disregards decades of work on machine learning and learnability. Learning biases form a two-way street: all learners have biases, and those biases constrain the space of learnable grammars in mathematically measurable ways. Analytical methods from the related fields of computational learning theory and grammatical inference allow one to study language learning, neural networks, and linguistics at an appropriate level of abstraction. The only way to satisfy our hunger and to make progress on the science of language learning is to confront these core issues directly.

The target article (Pater 2019) proposes to use neural networks to model learning within existing grammatical frameworks. This is easier said than done. There is a fundamental gap to be bridged that does not receive attention in the article: how can we use neural networks to examine whether it is possible to learn some linguistic representation (a tree, for example) when, after learning is finished, we cannot even tell if this is the type of representation that has been learned (all we see is a sequence of numbers)? Drawing a correspondence between an abstract linguistic representational system and an opaque parameter vector that can (or perhaps cannot) be seen as an instance of such a representation is an implementational mapping problem. Rather than relying on existing frameworks that propose partial solutions to this problem, such as harmonic grammar, I suggest that fusional research of the kind proposed needs to directly address how to ‘find’ linguistic representations in neural network representations.

Joe Pater's (2019) target article calls for greater interaction between neural network research and linguistics. I expand on this call and show how such interaction can benefit both fields. Linguists can contribute to research on neural networks for language technologies by clearly delineating the linguistic capabilities that can be expected of such systems, and by constructing controlled experimental paradigms that can determine whether those desiderata have been met. In the other direction, neural networks can benefit the scientific study of language by providing infrastructure for modeling human sentence processing and for evaluating the necessity of particular innate constraints on language acquisition.

From my perspective, Pater's (2019) target article does a great service both to researchers who work in generative linguistics and to researchers who utilize neural networks—and especially to researchers who might find themselves wanting to do both by harnessing the insights of each tradition. The fusion of theories of linguistic representation and probabilistic learning techniques has certainly led to many interesting and valuable insights about the nature of both linguistic representation and the language acquisition process. However, I feel that the most exciting aspect of Pater's article is the increasing interpretability of neural network models, especially when combined with insights from the theoretical framework of generative linguistics. This allows for the possibility that neural networks could be used to actually generate new theories of representation. I describe how I think this theory-generation process might work with interpretable neural networks.

The birthdate of both generative linguistics and neural networks can be taken as 1957, the year of the publication of foundational work by both Noam Chomsky and Frank Rosenblatt. This article traces the development of these two approaches to cognitive science, from their largely autonomous early development in the first thirty years, through their collision in the 1980s around the past-tense debate (Rumelhart & McClelland 1986, Pinker & Prince 1988) and their integration in much subsequent work up to the present. Although this integration has produced a considerable body of results, the continued general gulf between these two lines of research is likely impeding progress in both: on learning in generative linguistics, and on the representation of language in neural modeling. The article concludes with a brief argument that generative linguistics is unlikely to fulfill its promise of accounting for language learning if it continues to maintain its distance from neural and statistical approaches to learning.

Breast cancer is the second leading cause of cancer-related deaths among women globally and the most prevalent cancer in women. Artificial intelligence (AI)-based frameworks have shown great promise in correctly classifying breast carcinomas, particularly those that may have been difficult to discern through routine microscopy. Additionally, mitotic number quantification utilizing AI technology is more accurate than manual counting. With its many advantages, such as improved accuracy, efficiency and consistency as shown in this literature review, AI has promise for significantly enhancing breast cancer diagnosis in the clinical world despite the paramount obstacles that must be addressed. Ongoing research and innovation are essential for overcoming these challenges and effectively harnessing AI’s transformative potential in breast cancer detection and assessment.

In deep learning (DL), the instability phenomenon is widespread and well documented, and the most commonly used measure of stability is the Lipschitz constant. While a small Lipchitz constant is traditionally viewed as guarantying stability, it does not capture the instability phenomenon in DL for classification well. The reason is that a classification function – which is the target function to be approximated – is necessarily discontinuous, thus having an ‘infinite’ Lipchitz constant. As a result, the classical approach will deem every classification function unstable, yet basic classification functions a la ‘is there a cat in the image?’ will typically be locally very ‘flat’ – and thus locally stable – except at the decision boundary. The lack of an appropriate measure of stability hinders a rigorous theory for stability in DL, and consequently, there are no proper approximation theoretic results that can guarantee the existence of stable networks for classification functions. In this paper, we introduce a novel stability measure $\mathcal{S}(f)$, for any classification function $f$, appropriate to study the stability of classification functions and their approximations. We further prove two approximation theorems: First, for any $\epsilon \gt 0$ and any classification function $f$ on a compact set, there is a neural network (NN) $\psi$, such that $\psi - f \neq 0$ only on a set of measure $\lt \epsilon$; moreover, $\mathcal{S}(\psi ) \geq \mathcal{S}(f) - \epsilon$ (as accurate and stable as $f$ up to $\epsilon$). Second, for any classification function $f$ and $\epsilon \gt 0$, there exists a NN $\psi$ such that $\psi = f$ on the set of points that are at least $\epsilon$ away from the decision boundary.

In deep learning, interval neural networks are used to quantify the uncertainty of a pre-trained neural network. Suppose we are given a computational problem $P$ and a pre-trained neural network $\Phi _P$ that aims to solve $P$. An interval neural network is then a pair of neural networks $(\underline {\phi }, \overline {\phi })$, with the property that $\underline {\phi }(y) \leq \Phi _P(y) \leq \overline {\phi }(y)$ for all inputs $y$, where the inequalities are meant componentwise. $(\underline {\phi }, \overline {\phi })$ are specifically trained to quantify the uncertainty of $\Phi _P$, in the sense that the size of the interval $[\underline {\phi }(y),\overline {\phi }(y)]$ quantifies the uncertainty of the prediction $\Phi _P(y)$. In this paper, we investigate the phenomenon when algorithms cannot compute interval neural networks in the setting of inverse problems. We show that in the typical setting of a linear inverse problem, the problem of constructing an optimal pair of interval neural networks is non-computable, even with the assumption that the pre-trained neural network $\Phi _P$ is an optimal solution. In other words, there exist classes of training sets $\Omega$, such that there is no algorithm, even randomised (with probability $p \geq 1/2$), that computes an optimal pair of interval neural networks for each training set ${\mathcal{T}} \in \Omega$. This phenomenon happens even when we are given a pre-trained neural network $\Phi _{{\mathcal{T}}}$ that is optimal for $\mathcal{T}$. This phenomenon is intimately linked to instability in deep learning.

Psychiatric disorders lead to disability, premature mortality and economic burden, highlighting the urgent need for more effective treatments. The understanding of psychiatric disorders as conditions of large-scale brain networks has created new opportunities for developing targeted, personalised, and mechanism-based therapeutic interventions. Non-invasive brain stimulation (NIBS) techniques, such as transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), can directly modulate dysfunctional neural networks, enabling treatments tailored to the individual’s unique functional network patterns.

As NIBS techniques depend on our understanding of the neural networks involved in psychiatric disorders, this review offers a neural network-informed perspective on their applications. We focus on key disorders, including depression, schizophrenia, and obsessive-compulsive disorder, and examine the role of NIBS on cognitive impairment, a transdiagnostic feature that does not respond to conventional treatments. We discuss the advancements in identifying NIBS response biomarkers with the use of electrophysiology and neuroimaging, which can inform the development of optimised, mechanism-based, personalised NIBS treatment protocols.

We address key challenges, including the need for more precise, individualised targeting of dysfunctional networks through integration of neurophysiological, neuroimaging and genetic data and the use of emerging techniques, such as low- intensity focused ultrasound, which has the potential to improve spatial precision and target access. We finally explore future directions to improve treatment protocols and promote widespread clinical use of NIBS as a safe, effective and patient-centred treatment for psychiatric disorders.

Ethnicity and race are vital for understanding representation, yet individual-level data are often unavailable. Recent methodological advances have allowed researchers to impute racial and ethnic classifications based on publicly available information, but predictions vary in their accuracy and can introduce statistical biases in downstream analyses. We provide an overview of common estimation methods, including Bayesian approaches and machine learning techniques that use names or images as inputs. We propose and test a hybrid approach that combines surname-based Bayesian estimation with the use of publicly available images in a convolutional neural network. We find that the proposed approach not only reduces statistical bias in downstream analyses but also improves accuracy in a sample of over 16,000 local elected officials. We conclude with a discussion of caveats and describe settings where the hybrid approach is especially suitable.

Language models can produce fluent, grammatical text. Nonetheless, some maintain that language models don’t really learn language and also that, even if they did, that would not be informative for the study of human learning and processing. On the other side, there have been claims that the success of LMs obviates the need for studying linguistic theory and structure. We argue that both extremes are wrong. LMs can contribute to fundamental questions about linguistic structure, language processing, and learning. They force us to rethink arguments and ways of thinking that have been foundational in linguistics. While they do not replace linguistic structure and theory, they serve as model systems and working proofs of concept for gradient, usage-based approaches to language. We offer an optimistic take on the relationship between language models and linguistics.