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We study a natural Hodge theoretic generalization of rational (or $\mathbb{Q}$-)homology manifolds through an invariant ${\rm HRH(Z)}$ where $Z$ is a complex algebraic variety. The defining property of this notion encodes the difference between higher Du Bois and higher rational singularities for local complete intersections, which are two classes of singularities that have recently gained much attention. We show that ${\rm HRH(Z)}$ can be characterized when the variety $Z$ is embedded into a smooth variety using the local cohomology mixed Hodge modules. Near a point, this is also characterized by the local cohomology of $Z$ at the point, and hence, by the cohomology of the link. We give an application to partial Poincar\'{e} duality. In the case of local complete intersection subvarieties, we relate ${\rm HRH(Z)}$ to various invariants. In the hypersurface case it turns out that ${\rm HRH(Z)}$ can be completely characterized by these invariants. However, for higher codimension subvarieties, the behavior is rather subtle, and in this case we relate ${\rm HRH(Z)}$ to these invariants through inequalities and give some conditions on when equality holds., Comment: 62 pages

The bulk photovoltaic effect (BPVE) offers a promising avenue to surpass the efficiency limitations of current solar cell technology. However, disentangling intrinsic and extrinsic contributions to photocurrent remains a significant challenge. Here, we fabricate high-quality, lateral devices based on atomically thin ReS2 with minimal contact resistance, providing an optimal platform for distinguishing intrinsic bulk photovoltaic signals from other extrinsic photocurrent contributions originating from interfacial effects. Our devices exhibit large bulk photovoltaic performance with intrinsic responsivities of 1 mA/W in the visible range, without the need for external tuning knobs such as strain engineering. Our experimental findings are supported by theoretical calculations. Furthermore, our approach can be extrapolated to investigate the intrinsic BPVE in other non-centrosymmetric van der Waals materials, paving the way for a new generation of efficient light-harvesting devices.

We study generalized $V$-filtrations, defined by Sabbah, on $\mathcal D$-modules underlying mixed Hodge modules on $X\times \mathbf A^r$. Using cyclic covers, we compare these filtrations to the usual $V$-filtration, which is better understood. The main result shows that these filtrations can be used to compute $\sigma^!$, where $\sigma \colon X \times \{0\} \to X \times \mathbf A^r$ is the inclusion of the zero section. As an application, we use the restriction result to study singularities of complete intersection subvarieties. These filtrations can be used to study the local cohomology mixed Hodge module. In particular, we classify when weighted homogeneous isolated complete intersection singularities in $\mathbf A^n$ are $k$-Du Bois and $k$-rational., Comment: 36 pages

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

Given a sufficiently positive embedding $X\subset\mathbb{P}^N$ of a smooth projective variety $X$, we consider its secant variety $\Sigma$ that comes equipped with the embedding $\Sigma\subset\mathbb{P}^N$ by its construction. In this article, we determine the local cohomological dimension $\textrm{lcd}(\mathbb{P}^N,\Sigma)$ of this embedding, as well as the generation level of the Hodge filtration on the topmost non-vanishing local cohomology module $\mathcal{H}^{q}_{\Sigma}(\mathcal{O}_{\mathbb{P}^N})$, i.e., when $q=\textrm{lcd}(\mathbb{P}^N,\Sigma)$. Additionally, we show that $\Sigma$ has quotient singularities (in which case the equality $\textrm{lcd}(\mathbb{P}^N,\Sigma)=\textrm{codim}_{\mathbb{P}^N}(\Sigma)$ is known to hold) if and only if $X\cong\mathbb{P}^1$. We also provide a complete classification of $(X,L)$ for which $\Sigma$ has ($\mathbb{Q}$-)Gorentein singularities. As a consequence, we deduce that if $\Sigma$ is a local complete intersection, then either $X$ is isomorphic to $\mathbb{P}^1$, or an elliptic curve., Comment: 30 pages

Captum is a comprehensive library for model explainability in PyTorch, offering a range of methods from the interpretability literature to enhance users' understanding of PyTorch models. In this paper, we introduce new features in Captum that are specifically designed to analyze the behavior of generative language models. We provide an overview of the available functionalities and example applications of their potential for understanding learned associations within generative language models.

We present a method for identifying groups of test examples -- slices -- on which a model under-performs, a task now known as slice discovery. We formalize coherence -- a requirement that erroneous predictions, within a slice, should be wrong for the same reason -- as a key property that any slice discovery method should satisfy. We then use influence functions to derive a new slice discovery method, InfEmbed, which satisfies coherence by returning slices whose examples are influenced similarly by the training data. InfEmbed is simple, and consists of applying K-Means clustering to a novel representation we deem influence embeddings. We show InfEmbed outperforms current state-of-the-art methods on 2 benchmarks, and is effective for model debugging across several case studies., Comment: NeuRIPs 2023 conference paper

We study the singularities of secant varieties of smooth projective varieties using methods from birational geometry when the embedding line bundle is sufficiently positive. More precisely, we study the Du Bois complex of secant varieties and its relationship with the sheaves of differential forms. Through this analysis, we give a necessary and sufficient condition for these varieties to have $p$-Du Bois singularities (in a sense that was proposed in [SVV23]). In addition, we show that the singularities of these varieties are never higher rational, by giving a classification of the cases when they are pre-1-rational. From these results, we deduce several consequences, including a Kodaira-Akizuki-Nakano type vanishing result for the reflexive differential forms of the secant varieties., Comment: 32 pages; v.2: Final version. Improved exposition and minor typos corrected, to appear in Proc. Lond. Math. Soc

With the proliferation of hate speech on social networks under different formats, such as abusive language, cyberbullying, and violence, etc., people have experienced a significant increase in violence, putting them in uncomfortable situations and threats. Plenty of efforts have been dedicated in the last few years to overcome this phenomenon to detect hate speech in different structured languages like English, French, Arabic, and others. However, a reduced number of works deal with Arabic dialects like Tunisian, Egyptian, and Gulf, mainly the Algerian ones. To fill in the gap, we propose in this work a complete approach for detecting hate speech on online Algerian messages. Many deep learning architectures have been evaluated on the corpus we created from some Algerian social networks (Facebook, YouTube, and Twitter). This corpus contains more than 13.5K documents in Algerian dialect written in Arabic, labeled as hateful or non-hateful. Promising results are obtained, which show the efficiency of our approach.

We present a ceramic material based on hematite (Fe$_2$O$_3$) and zirconia stabilized with yttria at 8% molar (YSZ), that exhibits stable electrical properties with transported charge and that can be tuned to the resistivities necessary to induce spark-quenching in gaseous detectors ($\rho = 10^9-10^{12}$ $\Omega \cdot$cm), from room temperature down to the liquid-vapor coexistence point of nitrogen (77 K). It, thus, allows covering the operating temperatures of most immediate interest to gaseous instrumentation. The ceramics have been produced in a region of mass concentrations far from what has been usually explored in literature: optimal characteristics are achieved for Fe$_2$O$_3$ concentrations of 75%wt (LAr boiling temperature), 35%wt (LXe boiling temperature), and 100%wt (room temperature). The nine order of magnitude enhancement observed for the electrical conductivity of the mixed phases relative to that of pure Fe$_2$O$_3$ is startling, however it can be qualitatively understood based on existing literature. Plates of 4 cm x 4 cm have been manufactured and, prior to this work, operated in-detector at the LXe boiling point (165 K), demonstrating spark-free operation. Preliminary results obtained for the first time on a spark-protected amplification structure (RP-WELL) at around the LAr boiling point (90 K) are now presented, too.

Cryogenic versions of Resistive WELL (RWELL) and Resistive Plate WELL (RPWELL) detectors have been developed, aimed at stable avalanche multiplication of ionization electrons in dual-phase TPCs. In the RWELL, a thin resistive layer deposited on top of an insulator is inserted in between the electron multiplier (THGEM) and the readout anode; in the RPWELL, a resistive plate is directly coupled to the THGEM. Radiation-induced ionization electrons in the liquid are extracted into the gaseous phase. They drift into the THGEM's holes where they undergo charge multiplication. Embedding resistive materials into the multiplier proved to enhance operation stability due to the mitigation of electrical discharges - thus allowing operation at higher charge gain compared to standard THGEM (a.k.a. LEM) multipliers. We present the detector concepts and report on the main preliminary results.

Interpretable entity representations (IERs) are sparse embeddings that are "human-readable" in that dimensions correspond to fine-grained entity types and values are predicted probabilities that a given entity is of the corresponding type. These methods perform well in zero-shot and low supervision settings. Compared to standard dense neural embeddings, such interpretable representations may permit analysis and debugging. However, while fine-tuning sparse, interpretable representations improves accuracy on downstream tasks, it destroys the semantics of the dimensions which were enforced in pre-training. Can we maintain the interpretable semantics afforded by IERs while improving predictive performance on downstream tasks? Toward this end, we propose Intermediate enTity-based Sparse Interpretable Representation Learning (ItsIRL). ItsIRL realizes improved performance over prior IERs on biomedical tasks, while maintaining "interpretability" generally and their ability to support model debugging specifically. The latter is enabled in part by the ability to perform "counterfactual" fine-grained entity type manipulation, which we explore in this work. Finally, we propose a method to construct entity type based class prototypes for revealing global semantic properties of classes learned by our model., Comment: Accepted into BlackBox NLP Workshop at EMNLP 2022