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In this work, we significantly expand the web of T-dualities among heterotic NS5-brane theories with eight supercharges. This is achieved by introducing twists involving outer automorphisms of discrete gauge/flavor factors and tensor multiplet permutations along the compactification circle. We assemble field theory data that we propose as invariants across T-dual theories, comprised of twisted Coulomb branch dimensions, higher group structures and flavor symmetry ranks. Using this data, we establish a detailed field theory correspondence between singularities of the compactification space, the number five-branes in the theory, and the flavor symmetry factors. The twisted theories are realized via M-theory compactifications on non-compact genus-one fibered Calabi-Yau threefolds without section. This approach allows us to prove duality of twisted and (un-)twisted theories by leveraging M/F-theory duality and identifying inequivalent torus fibrations in the same geometry. We construct several new 5D theories, including a novel type of CHL-like twisted theory where the two M9 branes are identified. Using their field theory invariants, we also construct their dual theories., Comment: 62 pages, 2 figures, 12 tables

Recent advancements have enabled Large Language Models (LLMs) to function as agents that can perform actions using external tools. This requires registering, i.e., integrating tool information into the LLM context prior to taking actions. Current methods indiscriminately incorporate all candidate tools into the agent's context and retain them across multiple reasoning steps. This process remains opaque to LLM agents and is not integrated into their reasoning procedures, leading to inefficiencies due to increased context length from irrelevant tools. To address this, we introduce EcoAct, a tool using algorithm that allows LLMs to selectively register tools as needed, optimizing context use. By integrating the tool registration process into the reasoning procedure, EcoAct reduces computational costs by over 50% in multiple steps reasoning tasks while maintaining performance, as demonstrated through extensive experiments. Moreover, it can be plugged into any reasoning pipeline with only minor modifications to the prompt, making it applicable to LLM agents now and future., Comment: 16 pages, 10 figures

A central challenge towards developing robots that can relate human language to their perception and actions is the scarcity of natural language annotations in diverse robot datasets. Moreover, robot policies that follow natural language instructions are typically trained on either templated language or expensive human-labeled instructions, hindering their scalability. To this end, we introduce NILS: Natural language Instruction Labeling for Scalability. NILS automatically labels uncurated, long-horizon robot data at scale in a zero-shot manner without any human intervention. NILS combines pretrained vision-language foundation models in order to detect objects in a scene, detect object-centric changes, segment tasks from large datasets of unlabelled interaction data and ultimately label behavior datasets. Evaluations on BridgeV2, Fractal, and a kitchen play dataset show that NILS can autonomously annotate diverse robot demonstrations of unlabeled and unstructured datasets while alleviating several shortcomings of crowdsourced human annotations, such as low data quality and diversity. We use NILS to label over 115k trajectories obtained from over 430 hours of robot data. We open-source our auto-labeling code and generated annotations on our website: http://robottasklabeling.github.io., Comment: Project Website at https://robottasklabeling.github.io/

The increasing prevalence of large language models (LLMs) such as GPT-4 in various applications has led to a surge in the size of prompts required for optimal performance, leading to challenges in computational efficiency. Prompt compression aims to reduce the inference cost by minimizing input tokens without compromising on the task performance. However, existing prompt compression techniques either rely on sub-optimal metrics such as information entropy or model it as a task-agnostic token classification problem that fails to capture task-specific information. To address these issues, we propose a novel and efficient reinforcement learning (RL) based task-aware prompt compression method. To ensure low latency requirements, we leverage existing Transformer encoder-based token classification model while guiding the learning process with task-specific reward signals using lightweight REINFORCE algorithm. We evaluate the performance of our method on three diverse and challenging tasks including text summarization, question answering and code summarization. We demonstrate that our RL-guided compression method improves the task performance by 8% - 260% across these three scenarios over state-of-the-art compression techniques while satisfying the same compression rate and latency requirements.

Large Language Model (LLM) workloads have distinct prefill and decode phases with different compute and memory requirements which should ideally be accounted for when scheduling input queries across different LLM instances in a cluster. However existing scheduling algorithms treat LLM workloads as monolithic jobs without considering the distinct characteristics of the two phases in each workload. This leads to sub-optimal scheduling and increased response latency. In this work, we propose a heuristic-guided reinforcement learning-based intelligent router for data-driven and workload-aware scheduling. Our router leverages a trainable response-length predictor, and a novel formulation for estimating the impact of mixing different workloads to schedule queries across LLM instances and achieve over 11\% lower end-to-end latency than existing approaches., Comment: 16 pages, 8 figures

We connect recent conjectures and observations pertaining to geodesics, attractor flows, Laplacian eigenvalues and the geometry of moduli spaces by using that attractor flows are geodesics. For toroidal compactifications, attractor points are related to (degenerate) masses of the Laplacian on the target space, and also to the Laplacian on the moduli space. We also explore compactifications of M-Theory to $5$D on a Calabi-Yau threefold and argue that geodesics are unique in a special set of classes, providing further evidence for a recent conjecture by Raman and Vafa. Finally, we describe the role of the marked moduli space in $4$d $\mathcal{N} = 2$ compactifications. We study split attractor flows in an explicit example of the one-parameter family of quintics and discuss setups where flops to isomorphic Calabi-Yau manifolds exist.

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form., Comment: 36 pages and appendices. V2: minor corrections and explanations added

Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching billions of parameters. These huge models are memory hungry and incur significant inference latency even on cutting edge AI-accelerators, such as GPUs. Specifically, the time and memory complexity of the attention operation is quadratic in terms of the total context length, i.e., prompt and output tokens. Thus, several optimizations such as key-value tensor caching and FlashAttention computation have been proposed to deliver the low latency demands of applications relying on such large models. However, these techniques do not cater to the computationally distinct nature of different phases during inference. To that end, we propose LeanAttention, a scalable technique of computing self-attention for the token-generation phase (decode-phase) of decoder-only transformer models. LeanAttention enables scaling the attention mechanism implementation for the challenging case of long context lengths by re-designing the execution flow for the decode-phase. We identify that the associative property of online softmax can be treated as a reduction operation thus allowing us to parallelize the attention computation over these large context lengths. We extend the "stream-K" style reduction of tiled calculation to self-attention to enable parallel computation resulting in an average of 2.6x attention execution speedup over FlashAttention-2 and up to 8.33x speedup for 512k context lengths., Comment: 13 pages, 10 figures

In clinical settings, we often face the challenge of building prediction models based on small observational data sets. For example, such a data set might be from a medical center in a multi-center study. Differences between centers might be large, thus requiring specific models based on the data set from the target center. Still, we want to borrow information from the external centers, to deal with small sample sizes. There are approaches that either assign weights to each external data set or each external observation. To incorporate information on differences between data sets and observations, we propose an approach that combines both into weights that can be incorporated into a likelihood for fitting regression models. Specifically, we suggest weights at the data set level that incorporate information on how well the models that provide the observation weights distinguish between data sets. Technically, this takes the form of inverse probability weighting. We explore different scenarios where covariates and outcomes differ among data sets, informing our simulation design for method evaluation. The concept of effective sample size is used for understanding the effectiveness of our subgroup modeling approach. We demonstrate our approach through a clinical application, predicting applied radiotherapy doses for cancer patients. Generally, the proposed approach provides improved prediction performance when external data sets are similar. We thus provide a method for quantifying similarity of external data sets to the target data set and use this similarity to include external observations for improving performance in a target data set prediction modeling task with small data., Comment: minor update of affiliations and funding

We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using F-/M-theory. By exploiting anomaly inflow and unitarity of the LST worldsheet theory, we derive strong conditions on the possible 6D bulk theories and their flavor algebras. These constraints continue to apply if gravity is coupled to the theory. We also study the higher form symmetry structure of these theories and show how they get exchanged under T-duality. Finally, we comment on seemingly consistent bottom-up Little String Theories that cannot be constructed from the top-down approach., Comment: 58 pages, 3 appendices, 10 tables

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs., Comment: 48 pages, 20 figures. Codes are available at https://github.com/KindXiaoming/pykan

Safety-critical applications such as autonomous driving require robust 3D environment perception algorithms capable of handling diverse and ambiguous surroundings. The predictive performance of classification models is heavily influenced by the dataset and the prior knowledge provided by the annotated labels. While labels guide the learning process, they often fail to capture the inherent relationships between classes that are naturally understood by humans. We propose a training strategy for a 3D LiDAR semantic segmentation model that learns structural relationships between classes through abstraction. This is achieved by implicitly modeling these relationships using a learning rule for hierarchical multi-label classification (HMC). Our detailed analysis demonstrates that this training strategy not only improves the model's confidence calibration but also retains additional information useful for downstream tasks such as fusion, prediction, and planning.

We study the duality between the Spin$(32)/\mathbb{Z}_2$ heterotic string without vector structure and F-theory with frozen singularities. We give a complete description in theories with $6$d $\mathcal{N}=(1,0)$ supersymmetry and identify the duals of Spin$(32)/\mathbb{Z}_2$-instantons on ADE singularities without vector structure in the frozen phase of F-theory using an ansatz introduced by Bhardwaj, Morrison, Tachikawa, and Tomasiello. As a consequence, we obtain a strongly coupled description of orbifold phases of type I string theory without vector structure, substantially expanding the list of known examples of $6$d F-theory compactifications with frozen singularities. Supergravity theories can be fused from these instanton theories, in a way that commutes with switching off vector structure, which we use to propose new consistency checks via neutral hypermultiplet counting. Finally, we describe various Higgsings of this duality, and comment on constraints on higher form symmetries., Comment: 42 pages, 1 figure, 1 appendix

This paper focuses on task-agnostic prompt compression for better generalizability and efficiency. Considering the redundancy in natural language, existing approaches compress prompts by removing tokens or lexical units according to their information entropy obtained from a causal language model such as LLaMa-7B. The challenge is that information entropy may be a suboptimal compression metric: (i) it only leverages unidirectional context and may fail to capture all essential information needed for prompt compression; (ii) it is not aligned with the prompt compression objective. To address these issues, we propose a data distillation procedure to derive knowledge from an LLM to compress prompts without losing crucial information, and meantime, introduce an extractive text compression dataset. We formulate prompt compression as a token classification problem to guarantee the faithfulness of the compressed prompt to the original one, and use a Transformer encoder as the base architecture to capture all essential information for prompt compression from the full bidirectional context. Our approach leads to lower latency by explicitly learning the compression objective with smaller models such as XLM-RoBERTa-large and mBERT. We evaluate our method on both in-domain and out-of-domain datasets, including MeetingBank, LongBench, ZeroScrolls, GSM8K, and BBH. Despite its small size, our model shows significant performance gains over strong baselines and demonstrates robust generalization ability across different LLMs. Additionally, our model is 3x-6x faster than existing prompt compression methods, while accelerating the end-to-end latency by 1.6x-2.9x with compression ratios of 2x-5x. Our code is available at https://aka.ms/LLMLingua-2., Comment: Accepted at Findings of ACL 2024

Finding string backgrounds with de Sitter spacetime, where all approximations and corrections are controlled, is an open problem. We revisit the search for de Sitter solutions in the classical regime for specific type IIB supergravity compactifications on group manifolds, an under-explored corner of the landscape that offers an interesting testing ground for swampland conjectures. While the supergravity de Sitter solutions we obtain numerically are ambiguous in terms of their classicality, we find an analytic scaling that makes four out of six compactification radii, as well as the overall volume, arbitrarily large. This potentially provides parametric control over corrections. If we could show that these solutions, or others to be found, are fully classical, they would constitute a counterexample to conjectures stating that asymptotic de Sitter solutions do not exist. We discuss this point in great detail., Comment: Six notebooks are provided as ancillary files; v2: minor corrections

Machine learning techniques are increasingly powerful, leading to many breakthroughs in the natural sciences, but they are often stochastic, error-prone, and blackbox. How, then, should they be utilized in fields such as theoretical physics and pure mathematics that place a premium on rigor and understanding? In this Perspective we discuss techniques for obtaining rigor in the natural sciences with machine learning. Non-rigorous methods may lead to rigorous results via conjecture generation or verification by reinforcement learning. We survey applications of these techniques-for-rigor ranging from string theory to the smooth $4$d Poincar\'e conjecture in low-dimensional topology. One can also imagine building direct bridges between machine learning theory and either mathematics or theoretical physics. As examples, we describe a new approach to field theory motivated by neural network theory, and a theory of Riemannian metric flows induced by neural network gradient descent, which encompasses Perelman's formulation of the Ricci flow that was utilized to resolve the $3$d Poincar\'e conjecture., Comment: 13 pages. Preprint of edited version in Nature Reviews Physics. Please cite journal version

We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-K\"ahler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent $\text{Spin(32)}/\mathbb{Z}_2$ models that are dual to the same $\text{E}_8 \times \text{E}_8$ theory, and a family of self-T-dual models., Comment: 33+7 pages , 4 figures, 4 tables

We develop a general theory of flows in the space of Riemannian metrics induced by neural network gradient descent. This is motivated in part by recent advances in approximating Calabi-Yau metrics with neural networks and is enabled by recent advances in understanding flows in the space of neural networks. We derive the corresponding metric flow equations, which are governed by a metric neural tangent kernel, a complicated, non-local object that evolves in time. However, many architectures admit an infinite-width limit in which the kernel becomes fixed and the dynamics simplify. Additional assumptions can induce locality in the flow, which allows for the realization of Perelman's formulation of Ricci flow that was used to resolve the 3d Poincar\'e conjecture. We demonstrate that such fixed kernel regimes lead to poor learning of numerical Calabi-Yau metrics, as is expected since the associated neural networks do not learn features. Conversely, we demonstrate that well-learned numerical metrics at finite-width exhibit an evolving metric-NTK, associated with feature learning. Our theory of neural network metric flows therefore explains why neural networks are better at learning Calabi-Yau metrics than fixed kernel methods, such as the Ricci flow., Comment: 32 pages + references. Published in Machine Learning: Science and Technology

We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincar\'e conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings., Comment: 23 pages, 10 figures

We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau $n$-folds in P^{n+1}. It was previously observed that some eigenmodes get lighter while others get heavier as a function of these moduli, which leads to eigenvalue crossing. We identify the cause for this behavior for the torus. We then show that at points in a sublocus of complex structure moduli space where Laplacian eigenmodes cross, the torus has complex multiplication. We speculate that the generalization to arbitrary Calabi-Yau manifolds could be that level crossing is related to rank one attractor points. To test this, we compute the eigenmodes numerically for the quartic K3 and the quintic threefold, and match crossings to CM and attractor points in these varieties. To quantify the error of our numerical methods, we also study the dependence of the numerical spectrum on the quality of the Calabi-Yau metric approximation, the number of points sampled from the Calabi-Yau variety, the truncation of the eigenbasis, and the the distance from degeneration points in complex structure moduli space., Comment: 30 pages, 8 figures

Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kahler cone made up from an infinite number of individual Kahler cones. These cones are related by reflection symmetries across flop walls. We study the implications of this cone structure for mirror symmetry, by considering the instanton part of the prepotential in Calabi-Yau threefolds. We show that such isomorphic flops across facets of the Kahler cone boundary give rise to symmetry groups isomorphic to Coxeter groups. In the dual Mori cone, non-flopping curve classes that are identified under these groups have the same Gopakumar-Vafa invariants. This leads to instanton prepotentials invariant under Coxeter groups, which we make manifest by introducing appropriate invariant functions. For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold., Comment: 20+4 pages, 4 figures, added some remarks and references

The LOPES experiment was a radio interferometer built at the existing air shower array KASCADE-Grande in Karlsruhe, Germany. The last configuration of LOPES was called LOPES 3D and consisted of ten tripole antennas. Each of these antennas consisted of three crossed dipoles east-west, north-south, and vertically aligned. With this, LOPES 3D had the unique possibility to study the benefits of measurements with vertically aligned antennas in the environment of the well understood and calibrated particle detector array KASCADE-Grande. The measurements with three spatially coincident antennas allows a redundant reconstruction of the electric field vector. Several methods to exploit the redundancy were developed and tested. Furthermore, for the first time in LOPES, the background noise could be studied polarization- and direction dependent. With LOPES 3D it could be demonstrated that radio detection reaches a higher efficiency for inclined showers when including measurements with vertically aligned antennas and that the vertical component gets more important for the measurement of inclined showers. In this contribution we discuss a weighting scheme for the best combination of three redundant reconstructed electric field vectors. Furthermore, we discuss the influence of these weighting schemes on the ability to reconstruct air showers using the radio method. We show an estimate of the radio efficiency for inclined showers with focus on the benefits of measurements with vertically aligned antennas and we present the direction dependent noise in the different polarizations., Comment: Submission to the proceedings of the ARENA2014 workshop, which unfortunately were never published; thus documented here for reference