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Gravitational redshift and Doppler effects give rise to an antisymmetric component of the galaxy correlation function when cross-correlating two galaxy populations or two different tracers. In this paper, we assess the detectability of these effects in the Euclid spectroscopic galaxy survey. We model the impact of gravitational redshift on the observed redshift of galaxies in the Flagship mock catalogue using a Navarro-Frenk-White profile for the host haloes. We isolate these relativistic effects, largely subdominant in the standard analysis, by splitting the galaxy catalogue into two populations of faint and bright objects and estimating the dipole of their cross-correlation in four redshift bins. In the simulated catalogue, we detect the dipole signal on scales below $30\,h^{-1}{\rm Mpc}$, with detection significances of $4\,\sigma$ and $3\,\sigma$ in the two lowest redshift bins, respectively. At higher redshifts, the detection significance drops below $2\,\sigma$. Overall, we estimate the total detection significance in the Euclid spectroscopic sample to be approximately $6\,\sigma$. We find that on small scales, the major contribution to the signal comes from the nonlinear gravitational potential. Our study on the Flagship mock catalogue shows that this observable can be detected in Euclid Data Release 2 and beyond., Comment: 21 pages, 11 figures, 1 appendix; submitted on behalf of the Euclid Collaboration

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global H\"older stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point., Comment: 24 pages. arXiv admin note: text overlap with arXiv:1502.04842

The structure of amorphous silicon (a-Si) has been studied for decades. The two main theories are based on a continuous random network and on a `paracrystalline' model, respectively -- the latter being defined as showing localized structural order resembling the crystalline state whilst retaining an overall amorphous network. However, the extent of this local order has been unclear, and experimental data have led to conflicting interpretations. Here we show that signatures of paracrystallinity in an otherwise disordered network are indeed compatible with the existing body of experimental observations for a-Si. We use quantum-mechanically accurate, machine-learning-driven simulations to systematically sample the configurational space of quenched a-Si, thereby allowing us to elucidate the boundary between amorphization and crystallization. We analyze our dataset using structural and local-energy descriptors to show that paracrystalline models are consistent with experiments in both regards. Our work provides a unified explanation for seemingly conflicting theories in one of the most widely studied amorphous networks.

Simplicial sets generalise many categories of graphs. In this paper, we give a complete characterisation of the Lawvere-Tierney topologies on (semi-)simplicial sets, on bicolored graphs, and on fuzzy sets. We apply our results to establish that 'partially simple' simplicial sets and 'partially simple' graphs form quasitoposes.

Synthetic data is becoming increasingly important for accelerating the development of language models, both large and small. Despite several successful use cases, researchers also raised concerns around model collapse and drawbacks of imitating other models. This discrepancy can be attributed to the fact that synthetic data varies in quality and diversity. Effective use of synthetic data usually requires significant human effort in curating the data. We focus on using synthetic data for post-training, specifically creating data by powerful models to teach a new skill or behavior to another model, we refer to this setting as Generative Teaching. We introduce AgentInstruct, an extensible agentic framework for automatically creating large amounts of diverse and high-quality synthetic data. AgentInstruct can create both the prompts and responses, using only raw data sources like text documents and code files as seeds. We demonstrate the utility of AgentInstruct by creating a post training dataset of 25M pairs to teach language models different skills, such as text editing, creative writing, tool usage, coding, reading comprehension, etc. The dataset can be used for instruction tuning of any base model. We post-train Mistral-7b with the data. When comparing the resulting model Orca-3 to Mistral-7b-Instruct (which uses the same base model), we observe significant improvements across many benchmarks. For example, 40% improvement on AGIEval, 19% improvement on MMLU, 54% improvement on GSM8K, 38% improvement on BBH and 45% improvement on AlpacaEval. Additionally, it consistently outperforms other models such as LLAMA-8B-instruct and GPT-3.5-turbo.

Reinforcement learning from human feedback (RLHF) has emerged as a central tool for language model alignment. We consider online exploration in RLHF, which exploits interactive access to human or AI feedback by deliberately encouraging the model to produce diverse, maximally informative responses. By allowing RLHF to confidently stray from the pre-trained model, online exploration offers the possibility of novel, potentially super-human capabilities, but its full potential as a paradigm for language model training has yet to be realized, owing to computational and statistical bottlenecks in directly adapting existing reinforcement learning techniques. We propose a new algorithm for online exploration in RLHF, Exploratory Preference Optimization (XPO), which is simple and practical -- a one-line change to (online) Direct Preference Optimization (DPO; Rafailov et al., 2023) -- yet enjoys the strongest known provable guarantees and promising empirical performance. XPO augments the DPO objective with a novel and principled exploration bonus, empowering the algorithm to explore outside the support of the initial model and human feedback data. In theory, we show that XPO is provably sample-efficient and converges to a near-optimal language model policy under natural exploration conditions, irrespective of whether the initial model has good coverage. Our analysis, which builds on the observation that DPO implicitly performs a form of $Q^{\star}$-approximation (or, Bellman error minimization), combines previously disparate techniques from language modeling and theoretical reinforcement learning in a serendipitous fashion through the perspective of KL-regularized Markov decision processes. Empirically, we find that XPO is more sample-efficient than non-exploratory DPO variants in a preliminary evaluation.

Restricted Boltzmann Machines (RBMs) are effective tools for modeling complex systems and deriving insights from data. However, training these models with highly structured data presents significant challenges due to the slow mixing characteristics of Markov Chain Monte Carlo processes. In this study, we build upon recent theoretical advancements in RBM training, to significantly reduce the computational cost of training (in very clustered datasets), evaluating and sampling in RBMs in general. The learning process is analogous to thermodynamic continuous phase transitions observed in ferromagnetic models, where new modes in the probability measure emerge in a continuous manner. Such continuous transitions are associated with the critical slowdown effect, which adversely affects the accuracy of gradient estimates, particularly during the initial stages of training with clustered data. To mitigate this issue, we propose a pre-training phase that encodes the principal components into a low-rank RBM through a convex optimization process. This approach enables efficient static Monte Carlo sampling and accurate computation of the partition function. We exploit the continuous and smooth nature of the parameter annealing trajectory to achieve reliable and computationally efficient log-likelihood estimations, enabling online assessment during the training, and propose a novel sampling strategy named parallel trajectory tempering (PTT) which outperforms previously optimized MCMC methods. Our results show that this training strategy enables RBMs to effectively address highly structured datasets that conventional methods struggle with. We also provide evidence that our log-likelihood estimation is more accurate than traditional, more computationally intensive approaches in controlled scenarios. The PTT algorithm significantly accelerates MCMC processes compared to existing and conventional methods., Comment: 31 pages, 16 figures

We present the Flagship galaxy mock, a simulated catalogue of billions of galaxies designed to support the scientific exploitation of the Euclid mission. Euclid is a medium-class mission of the European Space Agency optimised to determine the properties of dark matter and dark energy on the largest scales of the Universe. It probes structure formation over more than 10 billion years primarily from the combination of weak gravitational lensing and galaxy clustering data. The breath of Euclid's data will also foster a wide variety of scientific analyses. The Flagship simulation was developed to provide a realistic approximation to the galaxies that will be observed by Euclid and used in its scientific analyses. We ran a state-of-the-art N-body simulation with four trillion particles, producing a lightcone on the fly. From the dark matter particles, we produced a catalogue of 16 billion haloes in one octant of the sky in the lightcone up to redshift z=3. We then populated these haloes with mock galaxies using a halo occupation distribution and abundance matching approach, calibrating the free parameters of the galaxy mock against observed correlations and other basic galaxy properties. Modelled galaxy properties include luminosity and flux in several bands, redshifts, positions and velocities, spectral energy distributions, shapes and sizes, stellar masses, star formation rates, metallicities, emission line fluxes, and lensing properties. We selected a final sample of 3.4 billion galaxies with a magnitude cut of H_E<26, where we are complete. We have performed a comprehensive set of validation tests to check the similarity to observational data and theoretical models. In particular, our catalogue is able to closely reproduce the main characteristics of the weak lensing and galaxy clustering samples to be used in the mission's main cosmological analysis. (abridged), Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

The Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid satellite provides multiband photometry and R>=450 slitless grism spectroscopy in the 950-2020nm wavelength range. In this reference article we illuminate the background of NISP's functional and calibration requirements, describe the instrument's integral components, and provide all its key properties. We also sketch the processes needed to understand how NISP operates and is calibrated, and its technical potentials and limitations. Links to articles providing more details and technical background are included. NISP's 16 HAWAII-2RG (H2RG) detectors with a plate scale of 0.3" pix^-1 deliver a field-of-view of 0.57deg^2. In photo mode, NISP reaches a limiting magnitude of ~24.5AB mag in three photometric exposures of about 100s exposure time, for point sources and with a signal-to-noise ratio (SNR) of 5. For spectroscopy, NISP's point-source sensitivity is a SNR = 3.5 detection of an emission line with flux ~2x10^-16erg/s/cm^2 integrated over two resolution elements of 13.4A, in 3x560s grism exposures at 1.6 mu (redshifted Ha). Our calibration includes on-ground and in-flight characterisation and monitoring of detector baseline, dark current, non-linearity, and sensitivity, to guarantee a relative photometric accuracy of better than 1.5%, and relative spectrophotometry to better than 0.7%. The wavelength calibration must be better than 5A. NISP is the state-of-the-art instrument in the NIR for all science beyond small areas available from HST and JWST - and an enormous advance due to its combination of field size and high throughput of telescope and instrument. During Euclid's 6-year survey covering 14000 deg^2 of extragalactic sky, NISP will be the backbone for determining distances of more than a billion galaxies. Its NIR data will become a rich reference imaging and spectroscopy data set for the coming decades., Comment: Paper submitted as part of the A&A special issue 'Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information., Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

Recent breakthroughs in large models have highlighted the critical significance of data scale, labels and modals. In this paper, we introduce MS MARCO Web Search, the first large-scale information-rich web dataset, featuring millions of real clicked query-document labels. This dataset closely mimics real-world web document and query distribution, provides rich information for various kinds of downstream tasks and encourages research in various areas, such as generic end-to-end neural indexer models, generic embedding models, and next generation information access system with large language models. MS MARCO Web Search offers a retrieval benchmark with three web retrieval challenge tasks that demand innovations in both machine learning and information retrieval system research domains. As the first dataset that meets large, real and rich data requirements, MS MARCO Web Search paves the way for future advancements in AI and system research. MS MARCO Web Search dataset is available at: https://github.com/microsoft/MS-MARCO-Web-Search., Comment: 10 pages, 6 figures, for associated dataset, see http://github.com/microsoft/MS-MARCO-Web-Search

We introduce phi-3-mini, a 3.8 billion parameter language model trained on 3.3 trillion tokens, whose overall performance, as measured by both academic benchmarks and internal testing, rivals that of models such as Mixtral 8x7B and GPT-3.5 (e.g., phi-3-mini achieves 69% on MMLU and 8.38 on MT-bench), despite being small enough to be deployed on a phone. Our training dataset is a scaled-up version of the one used for phi-2, composed of heavily filtered publicly available web data and synthetic data. The model is also further aligned for robustness, safety, and chat format. We also provide parameter-scaling results with a 7B, 14B models trained for 4.8T tokens, called phi-3-small, phi-3-medium, both significantly more capable than phi-3-mini (e.g., respectively 75%, 78% on MMLU, and 8.7, 8.9 on MT-bench). To enhance multilingual, multimodal, and long-context capabilities, we introduce three models in the phi-3.5 series: phi-3.5-mini, phi-3.5-MoE, and phi-3.5-Vision. The phi-3.5-MoE, a 16 x 3.8B MoE model with 6.6 billion active parameters, achieves superior performance in language reasoning, math, and code tasks compared to other open-source models of similar scale, such as Llama 3.1 and the Mixtral series, and on par with Gemini-1.5-Flash and GPT-4o-mini. Meanwhile, phi-3.5-Vision, a 4.2 billion parameter model derived from phi-3.5-mini, excels in reasoning tasks and is adept at handling both single-image and text prompts, as well as multi-image and text prompts., Comment: 24 pages

This study is part of the debate on the efficiency of large versus small language models for text classification by prompting.We assess the performance of small language models in zero-shot text classification, challenging the prevailing dominance of large models.Across 15 datasets, our investigation benchmarks language models from 77M to 40B parameters using different architectures and scoring functions. Our findings reveal that small models can effectively classify texts, getting on par with or surpassing their larger counterparts.We developed and shared a comprehensive open-source repository that encapsulates our methodologies. This research underscores the notion that bigger isn't always better, suggesting that resource-efficient small models may offer viable solutions for specific data classification challenges.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term rewriting methods, we also describe when a minimal set of equations axiomatises the composite theory.

Intent classification and slot-filling are essential tasks of Spoken Language Understanding (SLU). In most SLUsystems, those tasks are realized by independent modules. For about fifteen years, models achieving both of themjointly and exploiting their mutual enhancement have been proposed. A multilingual module using a joint modelwas envisioned to create a touristic dialogue system for a European project, HumanE-AI-Net. A combination ofmultiple datasets, including the MEDIA dataset, was suggested for training this joint model. The MEDIA SLU datasetis a French dataset distributed since 2005 by ELRA, mainly used by the French research community and free foracademic research since 2020. Unfortunately, it is annotated only in slots but not intents. An enhanced version ofMEDIA annotated with intents has been built to extend its use to more tasks and use cases. This paper presents thesemi-automatic methodology used to obtain this enhanced version. In addition, we present the first results of SLUexperiments on this enhanced dataset using joint models for intent classification and slot-filling.

Within the current trend of Pretained Language Models (PLM), emerge more and more criticisms about the ethical andecological impact of such models. In this article, considering these critical remarks, we propose to focus on smallermodels, such as compact models like ALBERT, which are more ecologically virtuous than these PLM. However,PLMs enable huge breakthroughs in Natural Language Processing tasks, such as Spoken and Natural LanguageUnderstanding, classification, Question--Answering tasks. PLMs also have the advantage of being multilingual, and,as far as we know, a multilingual version of compact ALBERT models does not exist. Considering these facts, wepropose the free release of the first version of a multilingual compact ALBERT model, pre-trained using Wikipediadata, which complies with the ethical aspect of such a language model. We also evaluate the model against classicalmultilingual PLMs in classical NLP tasks. Finally, this paper proposes a rare study on the subword tokenizationimpact on language performances., Comment: The 2024 Joint International Conference on Computational Linguistics, Language Resources and Evaluation, May 2024, Torino, Italy

Existing question answering (QA) datasets are no longer challenging to most powerful Large Language Models (LLMs). Traditional QA benchmarks like TriviaQA, NaturalQuestions, ELI5 and HotpotQA mainly study ``known unknowns'' with clear indications of both what information is missing, and how to find it to answer the question. Hence, good performance on these benchmarks provides a false sense of security. A yet unmet need of the NLP community is a bank of non-factoid, multi-perspective questions involving a great deal of unclear information needs, i.e. ``unknown uknowns''. We claim we can find such questions in search engine logs, which is surprising because most question-intent queries are indeed factoid. We present Researchy Questions, a dataset of search engine queries tediously filtered to be non-factoid, ``decompositional'' and multi-perspective. We show that users spend a lot of ``effort'' on these questions in terms of signals like clicks and session length, and that they are also challenging for GPT-4. We also show that ``slow thinking'' answering techniques, like decomposition into sub-questions shows benefit over answering directly. We release $\sim$ 100k Researchy Questions, along with the Clueweb22 URLs that were clicked.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

The European Space Agency's Euclid mission is one of the upcoming generation of large-scale cosmology surveys, which will map the large-scale structure in the Universe with unprecedented precision. The development and validation of the SGS pipeline requires state-of-the-art simulations with a high level of complexity and accuracy that include subtle instrumental features not accounted for previously as well as faster algorithms for the large-scale production of the expected Euclid data products. In this paper, we present the Euclid SGS simulation framework as applied in a large-scale end-to-end simulation exercise named Science Challenge 8. Our simulation pipeline enables the swift production of detailed image simulations for the construction and validation of the Euclid mission during its qualification phase and will serve as a reference throughout operations. Our end-to-end simulation framework starts with the production of a large cosmological N-body & mock galaxy catalogue simulation. We perform a selection of galaxies down to I_E=26 and 28 mag, respectively, for a Euclid Wide Survey spanning 165 deg^2 and a 1 deg^2 Euclid Deep Survey. We build realistic stellar density catalogues containing Milky Way-like stars down to H<26. Using the latest instrumental models for both the Euclid instruments and spacecraft as well as Euclid-like observing sequences, we emulate with high fidelity Euclid satellite imaging throughout the mission's lifetime. We present the SC8 data set consisting of overlapping visible and near-infrared Euclid Wide Survey and Euclid Deep Survey imaging and low-resolution spectroscopy along with ground-based. This extensive data set enables end-to-end testing of the entire ground segment data reduction and science analysis pipeline as well as the Euclid mission infrastructure, paving the way to future scientific and technical developments and enhancements., Comment: 39 pages, 25 figures, A&A submitted

The remarkable abilities of large language models (LLMs) like GPT-4 partially stem from post-training processes like Reinforcement Learning from Human Feedback (RLHF) involving human preferences encoded in a reward model. However, these reward models (RMs) often lack direct knowledge of why, or under what principles, the preferences annotations were made. In this study, we identify principles that guide RMs to better align with human preferences, and then develop an axiomatic framework to generate a rich variety of preference signals to uphold them. We use these axiomatic signals to train a model for scoring answers to longform questions. Our approach yields a Preference Model with only about 220M parameters that agrees with gold human-annotated preference labels more often than GPT-4. The contributions of this work include: training a standalone preference model that can score human- and LLM-generated answers on the same scale; developing an axiomatic framework for generating training data pairs tailored to certain principles; and showing that a small amount of axiomatic signals can help small models outperform GPT-4 in preference scoring. We release our model on huggingface: https://huggingface.co/corbyrosset/axiomatic_preference_model, Comment: Accepted to EMNLP 2023

Orca 1 learns from rich signals, such as explanation traces, allowing it to outperform conventional instruction-tuned models on benchmarks like BigBench Hard and AGIEval. In Orca 2, we continue exploring how improved training signals can enhance smaller LMs' reasoning abilities. Research on training small LMs has often relied on imitation learning to replicate the output of more capable models. We contend that excessive emphasis on imitation may restrict the potential of smaller models. We seek to teach small LMs to employ different solution strategies for different tasks, potentially different from the one used by the larger model. For example, while larger models might provide a direct answer to a complex task, smaller models may not have the same capacity. In Orca 2, we teach the model various reasoning techniques (step-by-step, recall then generate, recall-reason-generate, direct answer, etc.). More crucially, we aim to help the model learn to determine the most effective solution strategy for each task. We evaluate Orca 2 using a comprehensive set of 15 diverse benchmarks (corresponding to approximately 100 tasks and over 36,000 unique prompts). Orca 2 significantly surpasses models of similar size and attains performance levels similar or better to those of models 5-10x larger, as assessed on complex tasks that test advanced reasoning abilities in zero-shot settings. make Orca 2 weights publicly available at aka.ms/orca-lm to support research on the development, evaluation, and alignment of smaller LMs, Comment: Added url to model weights fixed typo in Author name

This is the first year of the TREC Product search track. The focus this year was the creation of a reusable collection and evaluation of the impact of the use of metadata and multi-modal data on retrieval accuracy. This year we leverage the new product search corpus, which includes contextual metadata. Our analysis shows that in the product search domain, traditional retrieval systems are highly effective and commonly outperform general-purpose pretrained embedding models. Our analysis also evaluates the impact of using simplified and metadata-enhanced collections, finding no clear trend in the impact of the expanded collection. We also see some surprising outcomes; despite their widespread adoption and competitive performance on other tasks, we find single-stage dense retrieval runs can commonly be noncompetitive or generate low-quality results both in the zero-shot and fine-tuned domain., Comment: 14 pages, 4 figures, 11 tables - TREC 2023

Transformer-based language models (LMs) are inefficient in long contexts. We propose Dodo, a solution for context compression. Instead of one vector per token in a standard transformer model, Dodo represents text with a dynamic number of hidden states at each layer, reducing the cost of self-attention to a fraction of typical time and space. Moreover, off-the-shelf models such as LLaMA can be adapted to Dodo by efficient parameter tuning methods such as LoRA. In use, Dodo can act as either an autoregressive LM or a context compressor for downstream tasks. We demonstrate through experiments in language modeling, question answering, and summarization that Dodo retains capabilities in these tasks, while drastically reducing the overhead during decoding. For example, in the autoencoding task, Dodo shrinks context at a 20x compression ratio with a BLEU score of 98% for reconstruction, achieving nearly lossless encoding., Comment: ACL 2024 camera-ready. 15 pages and 7 figures

Alignment serves as an important step to steer large language models (LLMs) towards human preferences. In this paper, we propose an automatic way to construct contrastive data for LLM, using preference pairs from multiple models of varying strengths (e.g., InstructGPT, ChatGPT and GPT-4). We compare the contrastive techniques of SLiC and DPO to SFT baselines and find that DPO provides a step-function improvement even after continuing SFT saturates. We also explore a data curriculum learning scheme for contrastive post-training, which starts by learning from "easier" pairs and transitioning to "harder" ones, which further improves alignment. Finally, we scale up our experiments to train with more data and larger models like Orca. Remarkably, our automatic contrastive post-training further improves the performance of Orca, already a state-of-the-art instruction learning model tuned with GPT-4 outputs, to outperform ChatGPT., Comment: NAACL 2024 (Findings)

In this study, we address the challenge of using energy-based models to produce high-quality, label-specific data in complex structured datasets, such as population genetics, RNA or protein sequences data. Traditional training methods encounter difficulties due to inefficient Markov chain Monte Carlo mixing, which affects the diversity of synthetic data and increases generation times. To address these issues, we use a novel training algorithm that exploits non-equilibrium effects. This approach, applied on the Restricted Boltzmann Machine, improves the model's ability to correctly classify samples and generate high-quality synthetic data in only a few sampling steps. The effectiveness of this method is demonstrated by its successful application to four different types of data: handwritten digits, mutations of human genomes classified by continental origin, functionally characterized sequences of an enzyme protein family, and homologous RNA sequences from specific taxonomies., Comment: 15 pages

We consider a problem where autonomous agents enter a dynamic and unknown environment described by a network of weighted arcs. These agents move within the network from node to node according to a decentralized policy using only local information, with the goal of finding a path to an unknown sink node to leave the network. This policy makes each agent move to some adjacent node or stop at the current node. The transition along an arc is allowed or denied based on a threshold mechanism that takes into account the number of agents already accumulated in the arc's end nodes and the arc's weight. We show that this policy ensures path-length optimality in the sense that, in a finite time, all new agents entering the network reach the closer sinks by the shortest paths. Our approach is later extended to support constraints on the paths that agents can follow., Comment: This work has been submitted to the IEEE for possible publication

We present a methodology for using unlabeled data to design semi supervised learning (SSL) methods that improve the prediction performance of supervised learning for regression tasks. The main idea is to design different mechanisms for integrating the unlabeled data, and include in each of them a mixing parameter $\alpha$, controlling the weight given to the unlabeled data. Focusing on Generalized Linear Models (GLM) and linear interpolators classes of models, we analyze the characteristics of different mixing mechanisms, and prove that in all cases, it is invariably beneficial to integrate the unlabeled data with some nonzero mixing ratio $\alpha>0$, in terms of predictive performance. Moreover, we provide a rigorous framework to estimate the best mixing ratio $\alpha^*$ where mixed SSL delivers the best predictive performance, while using the labeled and unlabeled data on hand. The effectiveness of our methodology in delivering substantial improvement compared to the standard supervised models, in a variety of settings, is demonstrated empirically through extensive simulation, in a manner that supports the theoretical analysis. We also demonstrate the applicability of our methodology (with some intuitive modifications) to improve more complex models, such as deep neural networks, in real-world regression tasks., Comment: 63 pages, 10 figures

We investigate the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over $15\,000$ deg$^2$ of the sky in the redshift range $0.9\leq z<1.8$. We do this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic data set. To mitigate anisotropic selection-bias effects, we use a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allows us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock-Paczynski effect, and we study the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance $D_{\rm M}$ and Hubble distance $D_{\rm H}$ to a relative precision of about $0.3\%$, and the growth rate $f\sigma_8$ to a precision of between $5\%$ and $8\%$ in each of four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty $\Delta\Omega_\mathrm{m}=\pm0.0028$ on the matter density parameter from voids, better than can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to $6\%$ precision., Comment: 20 pages, 13 figures, accepted version

In this paper we improve the zero-shot generalization ability of language models via Mixture-Of-Memory Augmentation (MoMA), a mechanism that retrieves augmentation documents from multiple information corpora ("external memories"), with the option to "plug in" new memory at inference time. We develop a joint learning mechanism that trains the augmentation component with latent labels derived from the end retrieval task, paired with hard negatives from the memory mixture. We instantiate the model in a zero-shot dense retrieval setting by augmenting a strong T5-based retriever with MoMA. Our model, MoMA, obtains strong zero-shot retrieval accuracy on the eighteen tasks included in the standard BEIR benchmark. It outperforms systems that seek generalization from increased model parameters and computation steps. Our analysis further illustrates the necessity of augmenting with mixture-of-memory for robust generalization, the benefits of augmentation learning, and how MoMA utilizes the plug-in memory at inference time without changing its parameters. We plan to open source our code.

Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these datasets is an important task that has many practical applications. To address this challenge, we present a new and general method for building relational data trees by exploiting the learning dynamics of the Restricted Boltzmann Machine (RBM). Our method is based on the mean-field approach, derived from the Plefka expansion, and developed in the context of disordered systems. It is designed to be easily interpretable. We tested our method in an artificially created hierarchical dataset and on three different real-world datasets (images of digits, mutations in the human genome, and a homologous family of proteins). The method is able to automatically identify the hierarchical structure of the data. This could be useful in the study of homologous protein sequences, where the relationships between proteins are critical for understanding their function and evolution., Comment: Version accepted in Physical Review E

Quasitoposes encompass a wide range of structures, including various categories of graphs. They have proven to be a natural setting for reasoning about the metatheory of algebraic graph rewriting. In this paper we propose and motivate the notion of fuzzy presheaves, which generalises fuzzy sets and fuzzy graphs. We prove that fuzzy presheaves are rm-adhesive quasitoposes, proving our recent conjecture for fuzzy graphs. Furthermore, we show that simple fuzzy graphs categories are quasitoposes.

A long-standing challenge for search and conversational assistants is query intention detection in ambiguous queries. Asking clarifying questions in conversational search has been widely studied and considered an effective solution to resolve query ambiguity. Existing work have explored various approaches for clarifying question ranking and generation. However, due to the lack of real conversational search data, they have to use artificial datasets for training, which limits their generalizability to real-world search scenarios. As a result, the industry has shown reluctance to implement them in reality, further suspending the availability of real conversational search interaction data. The above dilemma can be formulated as a cold start problem of clarifying question generation and conversational search in general. Furthermore, even if we do have large-scale conversational logs, it is not realistic to gather training data that can comprehensively cover all possible queries and topics in open-domain search scenarios. The risk of fitting bias when training a clarifying question retrieval/generation model on incomprehensive dataset is thus another important challenge. In this work, we innovatively explore generating clarifying questions in a zero-shot setting to overcome the cold start problem and we propose a constrained clarifying question generation system which uses both question templates and query facets to guide the effective and precise question generation. The experiment results show that our method outperforms existing state-of-the-art zero-shot baselines by a large margin. Human annotations to our model outputs also indicate our method generates 25.2\% more natural questions, 18.1\% more useful questions, 6.1\% less unnatural and 4\% less useless questions., Comment: To appear in the Web Conference 2023

Efron's two-group model is widely used in large scale multiple testing. This model assumes that test statistics are mutually independent, however in realistic settings they are typically dependent, and taking the dependence into account can boost power. The general two-group model takes the dependence between the test statistics into account. Optimal policies in the general two-group model require calculation, for each hypothesis, of the probability that it is a true null given all test statistics, denoted local false discovery rate (locFDR). Unfortunately, calculating locFDRs under realistic dependence structures can be computationally prohibitive. We propose calculating approximate locFDRs based on a properly defined N-neighborhood for each hypothesis. We prove that by thresholding the approximate locFDRs with a fixed threshold, the marginal false discovery rate is controlled for any dependence structure. Furthermore, we prove that this is the optimal procedure in a restricted class of decision rules, where decision for each hypothesis is only guided by its N-neighborhood. We show through extensive simulations that our proposed method achieves substantial power gains compared to alternative practical approaches, while maintaining conceptual simplicity and computational feasibility. We demonstrate the utility of our method on a genome wide association study of height., Comment: 34 pages, 2 figures, 4 tables

The various Euclid imaging surveys will become a reference for studies of galaxy morphology by delivering imaging over an unprecedented area of 15 000 square degrees with high spatial resolution. In order to understand the capabilities of measuring morphologies from Euclid-detected galaxies and to help implement measurements in the pipeline, we have conducted the Euclid Morphology Challenge, which we present in two papers. While the companion paper by Merlin et al. focuses on the analysis of photometry, this paper assesses the accuracy of the parametric galaxy morphology measurements in imaging predicted from within the Euclid Wide Survey. We evaluate the performance of five state-of-the-art surface-brightness-fitting codes DeepLeGATo, Galapagos-2, Morfometryka, Profit and SourceXtractor++ on a sample of about 1.5 million simulated galaxies resembling reduced observations with the Euclid VIS and NIR instruments. The simulations include analytic S\'ersic profiles with one and two components, as well as more realistic galaxies generated with neural networks. We find that, despite some code-specific differences, all methods tend to achieve reliable structural measurements (10% scatter on ideal S\'ersic simulations) down to an apparent magnitude of about 23 in one component and 21 in two components, which correspond to a signal-to-noise ratio of approximately 1 and 5 respectively. We also show that when tested on non-analytic profiles, the results are typically degraded by a factor of 3, driven by systematics. We conclude that the Euclid official Data Releases will deliver robust structural parameters for at least 400 million galaxies in the Euclid Wide Survey by the end of the mission. We find that a key factor for explaining the different behaviour of the codes at the faint end is the set of adopted priors for the various structural parameters., Comment: Accepted by A&A. 30 pages, 23+6 figures, Euclid pre-launch key paper. Companion paper: Euclid Collaboration XXV: Merlin et al. 2022 Minor corrections after journal review

Current and future imaging surveys require photometric redshifts (photo-zs) to be estimated for millions of galaxies. Improving the photo-z quality is a major challenge but is needed to advance our understanding of cosmology. In this paper we explore how the synergies between narrow-band photometric data and large imaging surveys can be exploited to improve broadband photometric redshifts. We used a multi-task learning (MTL) network to improve broadband photo-z estimates by simultaneously predicting the broadband photo-z and the narrow-band photometry from the broadband photometry. The narrow-band photometry is only required in the training field, which also enables better photo-z predictions for the galaxies without narrow-band photometry in the wide field. This technique was tested with data from the Physics of the Accelerating Universe Survey (PAUS) in the COSMOS field. We find that the method predicts photo-zs that are 13% more precise down to magnitude i_{AB} < 23; the outlier rate is also 40% lower when compared to the baseline network. Furthermore, MTL reduces the photo-z bias for high-redshift galaxies, improving the redshift distributions for tomographic bins with z>1. Applying this technique to deeper samples is crucial for future surveys such as \Euclid or LSST. For simulated data, training on a sample with i_{AB} <23, the method reduces the photo-z scatter by 16% for all galaxies with i_{AB}<25. We also studied the effects of extending the training sample with photometric galaxies using PAUS high-precision photo-zs, which reduces the photo-z scatter by 20% in the COSMOS field., Comment: 20 pages, 16 figures

We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide quantitative upper and lower estimates for the area of the unknown defect in terms of the works exerted by the boundary data when the inclusion is present or absent., Comment: arXiv admin note: text overlap with arXiv:2209.08830

In this paper we analyze some properties of a sixth order elliptic operator arising in the framework of the strain gradient linear elasticity theory for nanoplates in flexural deformation. We first rigorously deduce the weak formulation of the underlying Neumann problem as well as its well posedness. Under some suitable smoothness assumptions on the coefficients and on the geometry we derive interior and boundary regularity estimates for the solution of the Neumann problem. Finally, for the case of isotropic materials, we obtain new Strong Unique Continuation results in the interior, in the form of doubling inequality and three spheres inequality, by a Carlemann estimates approach.

The investigation of Bell nonlocality traditionally relies on joint probabilities of observing certain measurement outcomes. In this work we explore a possibilistic approach, where only patterns of possible outcomes matter, and apply it to Bell nonlocality in networks with independent sources. We present various algorithms for determining whether a given outcome pattern can be achieved via classical resources or via non-signaling resources. Next we illustrate these methods considering the triangle and square networks (with binary outputs and no inputs), identifying patterns that are incompatible with the network structure, as well as patterns that imply nonlocality. In particular, we obtain an example of quantum nonlocality in the square network with binary outcomes. Moreover, we show how to construct certificates for detecting the nonlocality of a certain pattern, in the form of nonlinear Bell-type inequalities involving joint probabilities. Finally, we show that these inequalities remain valid in the case where the sources in the network become partially correlated., Comment: 17 pages, lots of figures, comments welcome

Cosmological constraints from key probes of the Euclid imaging survey rely critically on the accurate determination of the true redshift distributions, $n(z)$, of tomographic redshift bins. We determine whether the mean redshift, $$, of ten Euclid tomographic redshift bins can be calibrated to the Euclid target uncertainties of $\sigma()<0.002\,(1+z)$ via cross-correlation, with spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), and Euclid's NISP spectroscopic survey. We construct mock Euclid and spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshift $z<1.8$ with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to two $n(z)$ models: one is the true $n(z)$ with a free mean; the other a Gaussian Process modified to be restricted to non-negative values. We show that $$ is measured in each tomographic redshift bin to an accuracy of order 0.01 or better. By measuring the clustering redshifts on subsets of the full Flagship area, we construct scaling relations that allow us to extrapolate the method performance to larger sky areas than are currently available in the mock. For the full expected Euclid, BOSS, and DESI overlap region of approximately 6000 deg$^{2}$, the uncertainties attainable by clustering redshifts exceeds the Euclid requirement by at least a factor of three for both $n(z)$ models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration for Euclid if the sources of systematic biases can be determined and removed, or calibrated-out with sufficiently realistic simulations. We outline possible future work, in particular an extension to higher redshifts with quasar reference samples., Comment: 14 pages, 8 figures, accepted for publication in A&A

Supervised deep learning-based approaches have been applied to task-oriented dialog and have proven to be effective for limited domain and language applications when a sufficient number of training examples are available. In practice, these approaches suffer from the drawbacks of domain-driven design and under-resourced languages. Domain and language models are supposed to grow and change as the problem space evolves. On one hand, research on transfer learning has demonstrated the cross-lingual ability of multilingual Transformers-based models to learn semantically rich representations. On the other, in addition to the above approaches, meta-learning have enabled the development of task and language learning algorithms capable of far generalization. Through this context, this article proposes to investigate the cross-lingual transferability of using synergistically few-shot learning with prototypical neural networks and multilingual Transformers-based models. Experiments in natural language understanding tasks on MultiATIS++ corpus shows that our approach substantially improves the observed transfer learning performances between the low and the high resource languages. More generally our approach confirms that the meaningful latent space learned in a given language can be can be generalized to unseen and under-resourced ones using meta-learning., Comment: Accepted to the ACL workshop METANLP 2021

In the last five years, the rise of the self-attentional Transformer-based architectures led to state-of-the-art performances over many natural language tasks. Although these approaches are increasingly popular, they require large amounts of data and computational resources. There is still a substantial need for benchmarking methodologies ever upwards on under-resourced languages in data-scarce application conditions. Most pre-trained language models were massively studied using the English language and only a few of them were evaluated on French. In this paper, we propose a unified benchmark, focused on evaluating models quality and their ecological impact on two well-known French spoken language understanding tasks. Especially we benchmark thirteen well-established Transformer-based models on the two available spoken language understanding tasks for French: MEDIA and ATIS-FR. Within this framework, we show that compact models can reach comparable results to bigger ones while their ecological impact is considerably lower. However, this assumption is nuanced and depends on the considered compression method., Comment: Accepted paper at INTERSPEECH 2022

For many tasks, state-of-the-art results have been achieved with Transformer-based architectures, resulting in a paradigmatic shift in practices from the use of task-specific architectures to the fine-tuning of pre-trained language models. The ongoing trend consists in training models with an ever-increasing amount of data and parameters, which requires considerable resources. It leads to a strong search to improve resource efficiency based on algorithmic and hardware improvements evaluated only for English. This raises questions about their usability when applied to small-scale learning problems, for which a limited amount of training data is available, especially for under-resourced languages tasks. The lack of appropriately sized corpora is a hindrance to applying data-driven and transfer learning-based approaches with strong instability cases. In this paper, we establish a state-of-the-art of the efforts dedicated to the usability of Transformer-based models and propose to evaluate these improvements on the question-answering performances of French language which have few resources. We address the instability relating to data scarcity by investigating various training strategies with data augmentation, hyperparameters optimization and cross-lingual transfer. We also introduce a new compact model for French FrALBERT which proves to be competitive in low-resource settings., Comment: French compact model paper: FrALBERT, Accepted to RANLP 2021

Next generation telescopes, like Euclid, Rubin/LSST, and Roman, will open new windows on the Universe, allowing us to infer physical properties for tens of millions of galaxies. Machine learning methods are increasingly becoming the most efficient tools to handle this enormous amount of data, because they are often faster and more accurate than traditional methods. We investigate how well redshifts, stellar masses, and star-formation rates (SFR) can be measured with deep learning algorithms for observed galaxies within data mimicking the Euclid and Rubin/LSST surveys. We find that Deep Learning Neural Networks and Convolutional Neutral Networks (CNN), which are dependent on the parameter space of the training sample, perform well in measuring the properties of these galaxies and have a better accuracy than methods based on spectral energy distribution fitting. CNNs allow the processing of multi-band magnitudes together with $H_{\scriptscriptstyle\rm E}$-band images. We find that the estimates of stellar masses improve with the use of an image, but those of redshift and SFR do not. Our best results are deriving i) the redshift within a normalised error of less than 0.15 for 99.9$\%$ of the galaxies with S/N>3 in the $H_{\scriptscriptstyle\rm E}$-band; ii) the stellar mass within a factor of two ($\sim0.3 \rm dex$) for 99.5$\%$ of the considered galaxies; iii) the SFR within a factor of two ($\sim0.3 \rm dex$) for $\sim$70$\%$ of the sample. We discuss the implications of our work for application to surveys as well as how measurements of these galaxy parameters can be improved with deep learning., Comment: accepted for publication in MNRAS, 21 pages, 22 figures, 6 tables

Modern approaches to supervised learning like deep neural networks (DNNs) typically implicitly assume that observed responses are statistically independent. In contrast, correlated data are prevalent in real-life large-scale applications, with typical sources of correlation including spatial, temporal and clustering structures. These correlations are either ignored by DNNs, or ad-hoc solutions are developed for specific use cases. We propose to use the mixed models framework to handle correlated data in DNNs. By treating the effects underlying the correlation structure as random effects, mixed models are able to avoid overfitted parameter estimates and ultimately yield better predictive performance. The key to combining mixed models and DNNs is using the Gaussian negative log-likelihood (NLL) as a natural loss function that is minimized with DNN machinery including stochastic gradient descent (SGD). Since NLL does not decompose like standard DNN loss functions, the use of SGD with NLL presents some theoretical and implementation challenges, which we address. Our approach which we call LMMNN is demonstrated to improve performance over natural competitors in various correlation scenarios on diverse simulated and real datasets. Our focus is on a regression setting and tabular datasets, but we also show some results for classification. Our code is available at https://github.com/gsimchoni/lmmnn., Comment: 53 pages, 9 figures

Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting monads, distributive laws fail to exist, and this has motivated investigations into weaker notions. In this line of research, Petri\c{s}an and Sarkis recently introduced a construction called the semifree monad in order to study semialgebras for a monad and weak distributive laws. In this paper, we prove that an algebraic presentation of the semifree monad M^s on a monad M can be obtained uniformly from an algebraic presentation of M. This result was conjectured by Petri\c{s}an and Sarkis. We also show that semifree monads are ideal monads, that the semifree construction is not a monad transformer, and that the semifree construction is a comonad on the category of monads., Comment: In Proceedings of CMCS 2022

We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called PBPO+, allows more control over the embedding of the pattern in the host graph, which is important for a large class of rewrite systems. We argue that PBPO+ can be considered a unifying theory in the general setting of quasitoposes, by demonstrating that PBPO+ can define a strict superset of the rewrite relations definable by PBPO, AGREE and DPO. Additionally, we show that PBPO+ is well suited for rewriting labeled graphs and some classes of attributed graphs, by introducing a lattice structure on the label set and requiring graph morphisms to be order-preserving., Comment: This article significantly extends and improves arXiv:2010.08230. 36 pages

The purpose of this work is to contribute to the understanding and improvement of deep neural networks in the field of vocal quality. A neural network that predicts the perceptual assessment of overall severity of dysphonia in GRBAS scale is obtained. The design focuses on amplitude perturbations, frequency perturbations, and noise. Results are compared with performance of human raters on the same data. Both the precision and the mean absolute error of the neural network are close to human intra-rater performance, exceeding inter-rater performance.

Forgetting a subspace from a partial flag yields another partial flag composed of fewer subspaces. This induces a forgetful map $\pi : X \to X'$ between the corresponding flag varieties. We prove here that, for a degree large enough, the variety associated with degree d stable maps sending their marked points within Schubert varieties $X_i$ of $X$ is a rationally connected fibration over its image, which parametrizes degree $\pi_* d$ stable maps sending their marked points within the Schubert varieties $\pi(X_i)$ of $X'$. The Euler characteristic of these varieties are quantum $K$-invariants. Our result implies equalities between quantum $K$ correlators. We extend these equalities to the equivariant setting. Finally, we study the small quantum $K$-ring of the universal hyperplane $Fl_{1,n-1}$. We prove a Chevalley formula in $QK_s(Fl_{1,n-1})$ via geometrical analysis of the space of stale maps to $Fl_{1,n-1}$ and of its image via evaluation maps., Comment: PhD thesis