text
stringlengths 137
2.43k
| field
stringclasses 2
values | label
int64 0
1
|
|---|---|---|
Title: CARAT: Contrastive Feature Reconstruction and Aggregation for Multi-modal Multi-label Emotion Recognition
Abstract: Multi-modal multi-label emotion recognition (MMER) aims to identify relevant emotions from multiple modalities. The challenge of MMER is how to effectively capture discriminative features for multiple labels from heterogeneous data. Recent studies are mainly devoted to exploring various fusion strategies to integrate multi-modal information into a unified representation for all labels. However, such a learning scheme not only overlooks the specificity of each modality but also fails to capture individual discriminative features for different labels. Moreover, dependencies of labels and modalities cannot be effectively modeled. To address these issues, this paper presents ContrAstive feature Reconstruction and AggregaTion (CARAT) for the MMER task. Specifically, we devise a reconstruction-based fusion mechanism to better model fine-grained modality-to-label dependencies by contrastively learning modal-separated and label-specific features. To further exploit the modality complementarity, we introduce a shuffle-based aggregation strategy to enrich co-occurrence collaboration among labels. Experiments on two benchmark datasets CMU-MOSEI and M3ED demonstrate the effectiveness of CARAT over state-of-the-art methods. Code is available at https://github.com/chengzju/CARAT. | cs | 0 |
Title: Deutsch paths and their enumeration
Abstract: A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection. | math | 1 |
Title: Learning to Generalize towards Unseen Domains via a Content-Aware Style Invariant Model for Disease Detection from Chest X-rays
Abstract: Performance degradation due to distribution discrepancy is a longstanding challenge in intelligent imaging, particularly for chest X-rays (CXRs). Recent studies have demonstrated that CNNs are biased toward styles (e.g., uninformative textures) rather than content (e.g., shape), in stark contrast to the human vision system. Radiologists tend to learn visual cues from CXRs and thus perform well across multiple domains. Motivated by this, we employ the novel on-the-fly style randomization modules at both image (SRM-IL) and feature (SRM-FL) levels to create rich style perturbed features while keeping the content intact for robust cross-domain performance. Previous methods simulate unseen domains by constructing new styles via interpolation or swapping styles from existing data, limiting them to available source domains during training. However, SRM-IL samples the style statistics from the possible value range of a CXR image instead of the training data to achieve more diversified augmentations. Moreover, we utilize pixel-wise learnable parameters in the SRM-FL compared to pre-defined channel-wise mean and standard deviations as style embeddings for capturing more representative style features. Additionally, we leverage consistency regularizations on global semantic features and predictive distributions from with and without style-perturbed versions of the same CXR to tweak the model's sensitivity toward content markers for accurate predictions. Our proposed method, trained on CheXpert and MIMIC-CXR datasets, achieves 77.32$\pm$0.35, 88.38$\pm$0.19, 82.63$\pm$0.13 AUCs(%) on the unseen domain test datasets, i.e., BRAX, VinDr-CXR, and NIH chest X-ray14, respectively, compared to 75.56$\pm$0.80, 87.57$\pm$0.46, 82.07$\pm$0.19 from state-of-the-art models on five-fold cross-validation with statistically significant results in thoracic disease classification. | cs | 0 |
Title: GUESS:GradUally Enriching SyntheSis for Text-Driven Human Motion Generation
Abstract: In this paper, we propose a novel cascaded diffusion-based generative framework for text-driven human motion synthesis, which exploits a strategy named GradUally Enriching SyntheSis (GUESS as its abbreviation). The strategy sets up generation objectives by grouping body joints of detailed skeletons in close semantic proximity together and then replacing each of such joint group with a single body-part node. Such an operation recursively abstracts a human pose to coarser and coarser skeletons at multiple granularity levels. With gradually increasing the abstraction level, human motion becomes more and more concise and stable, significantly benefiting the cross-modal motion synthesis task. The whole text-driven human motion synthesis problem is then divided into multiple abstraction levels and solved with a multi-stage generation framework with a cascaded latent diffusion model: an initial generator first generates the coarsest human motion guess from a given text description; then, a series of successive generators gradually enrich the motion details based on the textual description and the previous synthesized results. Notably, we further integrate GUESS with the proposed dynamic multi-condition fusion mechanism to dynamically balance the cooperative effects of the given textual condition and synthesized coarse motion prompt in different generation stages. Extensive experiments on large-scale datasets verify that GUESS outperforms existing state-of-the-art methods by large margins in terms of accuracy, realisticness, and diversity. Code is available at https://github.com/Xuehao-Gao/GUESS. | cs | 0 |
Title: On broadcast channels with binary inputs and symmetric outputs
Abstract: We study the capacity regions of broadcast channels with binary inputs and symmetric outputs. We study the partial order induced by the more capable ordering of broadcast channels for channels belonging to this class. This study leads to some surprising connections regarding various notions of dominance of receivers. The results here also help us isolate some classes of symmetric channels where the best known inner and outer bounds differ. | cs | 1 |
Title: On the $k$-measure of partitions and distinct partitions
Abstract: The $k$-measure of an integer partition was recently introduced by Andrews, Bhattacharjee and Dastidar. In this paper, we establish trivariate generating function identities counting both the length and the $k$-measure for partitions and distinct partitions, respectively. The $2$-measure case for partitions extends a result of Andrews, Bhattacharjee and Dastidar. | math | 1 |
Title: Identifying contact graphs of sphere packings with generic radii
Abstract: Ozkan et al. conjectured that any packing of $n$ spheres with generic radii will be stress-free, and hence will have at most $3n-6$ contacts. In this paper we prove that this conjecture is true for any sphere packing with contact graph of the form $G \oplus K_2$, i.e., the graph formed by connecting every vertex in a graph $G$ to every vertex in the complete graph with two vertices. We also prove the converse of the conjecture holds in this special case: specifically, a graph $G \oplus K_2$ is the contact graph of a generic radii sphere packing if and only if $G$ is a penny graph with no cycles. | math | 0 |
Title: Iyama-Solberg correspondence for exact dg categories
Abstract: We generalize the notions of $d$-cluster tilting pair and $d$-Auslander exact dg category to $d$-precluster tilting triple and $d$-minimal Auslander--Gorenstein exact dg category. We give a bijection between equivalence classes of $d$-precluster tilting triples and equivalence classes of $d$-minimal Auslander--Gorenstein exact dg categories. Our bijection generalizes Iyama--Solberg correspondence for module categories. | math | 0 |
Title: Reversible Joint Hilbert and Linear Canonical Transform Without Distortion
Abstract: Generalized analytic signal associated with the linear canonical transform (LCT) was proposed recently by Fu and Li ["Generalized Analytic Signal Associated With Linear Canonical Transform," Opt. Commun., vol. 281, pp. 1468-1472, 2008]. However, most real signals, especially for baseband real signals, cannot be perfectly recovered from their generalized analytic signals. Therefore, in this paper, the conventional Hilbert transform (HT) and analytic signal associated with the LCT are concerned. To transform a real signal into the LCT of its HT, two integral transforms (i.e., the HT and LCT) are required. The goal of this paper is to simplify cascades of multiple integral transforms, which may be the HT, analytic signal, LCT or inverse LCT. The proposed transforms can reduce the complexity when realizing the relationships among the following six kinds of signals: a real signal, its HT and analytic signal, and the LCT of these three signals. Most importantly, all the proposed transforms are reversible and undistorted. Using the proposed transforms, several signal processing applications are discussed and show the advantages and flexibility over simply using the analytic signal or the LCT. | cs | 1 |
Title: A Quasi Curtis-Tits-Phan theorem for the symplectic group
Abstract: We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry. | math | 1 |
Title: Non-holomorphic Kaehler submanifolds of Euclidean space
Abstract: This paper is about non-holomorphic isometric immersions of Kaehler manifolds into Euclidean space $f\colon M^{2n}\to\R^{2n+p}$, $p\leq n-1$, with low codimension $p\leq 11$. In particular, it addresses a conjecture proposed by J. Yan and F. Zheng. The claim that if the index of complex relative nullity of the submanifold satisfies $\nu_f^c<2n-2p$ at any point, then $f(M)$ can be realized as a holomorphic submanifold of a non-holomorphic Kaehler submanifold of $\R^{2n+p}$ of larger dimension and some large index of complex relative nullity. This conjecture had previously been confirmed by Dajczer-Gromoll for codimension $p=3$, and then by Yan-Zheng for $p=4$. For codimension $p\leq 11$, we already showed that the pointwise structure of the second fundamental form of the submanifold aligns with the anticipated characteristics, assuming the validity of the conjecture. In this paper, we confirm the conjecture until codimension $p=6$, whereas for codimensions $7\leq p\leq 9$ it is also possible that the submanifold exhibits a complex ruled structure with rulings of a specific dimension. Moreover, we prove that the claim of the conjecture holds for codimensions $7\leq p\leq 11$ albeit subject to an additional assumption. | math | 0 |
Title: Pattern avoidance in ascent sequences
Abstract: Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and various other combinatorial structures. We study pattern avoidance in ascent sequences, giving several results for patterns of lengths up to 4, for Wilf equivalence and for growth rates. We establish bijective connections between pattern avoiding ascent sequences and various other combinatorial objects, in particular with set partitions. We also make a number of conjectures related to all of these aspects. | math | 1 |
Title: Compensating trajectory bias for unsupervised patient stratification using adversarial recurrent neural networks
Abstract: Electronic healthcare records are an important source of information which can be used in patient stratification to discover novel disease phenotypes. However, they can be challenging to work with as data is often sparse and irregularly sampled. One approach to solve these limitations is learning dense embeddings that represent individual patient trajectories using a recurrent neural network autoencoder (RNN-AE). This process can be susceptible to unwanted data biases. We show that patient embeddings and clusters using previously proposed RNN-AE models might be impacted by a trajectory bias, meaning that results are dominated by the amount of data contained in each patients trajectory, instead of clinically relevant details. We investigate this bias on 2 datasets (from different hospitals) and 2 disease areas as well as using different parts of the patient trajectory. Our results using 2 previously published baseline methods indicate a particularly strong bias in case of an event-to-end trajectory. We present a method that can overcome this issue using an adversarial training scheme on top of a RNN-AE. Our results show that our approach can reduce the trajectory bias in all cases. | cs | 1 |
Title: Parallel Integer Sort: Theory and Practice
Abstract: Integer sorting is a fundamental problem in computer science. This paper studies parallel integer sort both in theory and in practice. In theory, we show tighter bounds for a class of existing practical integer sort algorithms, which provides a solid theoretical foundation for their widespread usage in practice and strong performance. In practice, we design a new integer sorting algorithm, \textsf{DovetailSort}, that is theoretically-efficient and has good practical performance. In particular, \textsf{DovetailSort} overcomes a common challenge in existing parallel integer sorting algorithms, which is the difficulty of detecting and taking advantage of duplicate keys. The key insight in \textsf{DovetailSort} is to combine algorithmic ideas from both integer- and comparison-sorting algorithms. In our experiments, \textsf{DovetailSort} achieves competitive or better performance than existing state-of-the-art parallel integer and comparison sorting algorithms on various synthetic and real-world datasets. | cs | 0 |
Title: On the displacement of generators of free Fuchsian groups
Abstract: We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $\log (2k-1)$ Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of closed curves, which improves a result of Buser's. | math | 1 |
Title: Legendrians with vanishing Shelukhin-Chekanov-Hofer metric
Abstract: We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang. | math | 0 |
Title: Answering Queries with Negation over Existential Rules
Abstract: Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon semantics or standard implementation. Stratification, as used for Datalog, is not enough for existential rules, since the latter still admit multiple universal models that can differ on negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we identify syntactic descriptions of queries that can equivalently be answered over other types of models. This leads to fragments of queries with negation that can safely be evaluated by current chase implementations. We establish new techniques to estimate how the core model differs from other universal models, and we incorporate our findings into a new reasoning approach for existential rules with negation. | cs | 1 |
Title: How does Observational Learning Impact Crowdfunding Outcomes for Backers, Project Creators and Platforms?
Abstract: Reward-based crowdfunding platforms are becoming increasingly popular to finance projects proposing innovative products, e.g., Kickstarter. One important challenge of this form of financing is the uncertainty in the quality of projects. To mitigate the negative effects of this uncertainty for backers, platforms share information regarding the decisions of earlier backers visiting the project campaign pages. This allows backers not only to rely on their expertise to identify project qualities but also to learn from the decisions of their fellow backers who might be more informed. Current studies on observational learning (OL) in crowdfunding mainly focus on predicting the success chances of projects, and there is a lack of understanding of how OL affects crowdfunding dynamics for backers, project creators and platforms. This paper aims to fill this gap by using a theoretical OL model involving two projects competing for funding from backers who may have differentiated expertness in identifying project quality. By introducing various performance measures for backers, creators and platforms and comparing these measures under OL to the case without learning, we provide a thorough analysis of how OL impacts crowdfunding outcomes. We find that information sharing and OL always benefit backers, especially when the early backers are experts. Regarding the impact of OL on creators and platforms, our analysis reveals two understudied but important aspects: the tightness of the competition for projects according to the availability of funding, and the quality difference among the proposed projects. Additionally, we investigate how OL affects the quality decisions of creators and show that OL increases the incentive for high-quality products, especially in situations where funding is scarce. | math | 0 |
Title: A Truthful Referral Auction Over Networks
Abstract: This paper studies a mechanism design problem over a network, where agents can only participate by referrals. The Bulow-Klemberer theorem proposes that expanding the number of participants is a more effective approach to increase revenue than modifying the auction format. However, agents lack the motivation to invite others because doing so intensifies competition among them. On the other hand, misreporting social networks is also a common problem that can reduce revenue. Examples of misreporting include Sybil attacks (an agent pretending to be multiple bidders) and coalition groups (multiple agents pretending to be an agent). To address these challenges, we introduce a novel mechanism called the Truthful Referral Diffusion Mechanism (TRDM). TRDM incentivizes agents to report their social networks truthfully, and some of them are rewarded by the seller for improving revenue. In spite of the fact that some agents overbid in TRDM, the revenue is fixed, and it is higher than the revenue of any mechanism without referrals. TRDM is budget-balanced (non-negative revenue) and generates an efficient outcome (maximized social welfare), making it attractive for both the seller and the buyers as it improves revenue and reward. | cs | 1 |
Title: On infinitesimal generators of sublinear Markov semigroups
Abstract: We establish a Dynkin formula and a Courr\`ege-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator $A$ on $C_c^{\infty}(\mathbb{R}^d)$ satisfying the positive maximum principle can be represented as supremum of a family of pseudo-differential operators: $$Af(x) = \sup_{\alpha \in I} (-q_{\alpha}(x,D) f)(x).$$ As an immediate consequence, we obtain a representation formula for infinitesimal generators of sublinear Markov semigroups with a sufficiently rich domain. We give applications in the theory of non-linear Hamilton--Jacobi--Bellman equations and L\'evy processes for sublinear expectations. | math | 1 |
Title: Stochastic Coalitional Games for Cooperative Random Access in M2M Communications
Abstract: In this paper, the problem of random access contention between machine type devices (MTDs) in the uplink of a wireless cellular network is studied. In particular, the possibility of forming cooperative groups to coordinate the MTDs' requests for the random access channel (RACH) is analyzed. The problem is formulated as a stochastic coalition formation game in which the MTDs are the players that seek to form cooperative coalitions to optimize a utility function that captures each MTD's energy consumption and time-varying queue length. Within each coalition, an MTD acts as a coalition head that sends the access requests of the coalition members over the RACH. One key feature of this game is its ability to cope with stochastic environments in which the arrival requests of MTDs and the packet success rate over RACH are dynamically time-varying. The proposed stochastic coalitional is composed of multiple stages, each of which corresponds to a coalitional game in stochastic characteristic form that is played by the MTDs at each time step. To solve this game, a novel distributed coalition formation algorithm is proposed and shown to converge to a stable MTD partition. Simulation results show that, on the average, the proposed stochastic coalition formation algorithm can reduce the average fail ratio and energy consumption of up to 36% and 31% for a cluster-based distribution of MTDs, respectively, compared with a noncooperative case. Moreover, when the MTDs are more sensitive to the energy consumption (queue length), the coalitions' size will increase (decrease). | cs | 1 |
Title: Popularity of patterns over $d$-equivalence classes of words and permutations
Abstract: Two same length words are $d$-equivalent if they have same descent set and same underlying alphabet. In particular, two same length permutations are $d$-equivalent if they have same descent set. The popularity of a pattern in a set of words is the overall number of copies of the pattern within the words of the set. We show the far-from-trivial fact that two patterns are $d$-equivalent if and only if they are equipopular over any $d$-equivalence class, and this equipopularity does not follow obviously from a trivial equidistribution. | cs | 1 |
Title: Second homotopy classes associated with non-cancellative monoids
Abstract: We construct second homotopy classes associated with twins of non-cancellative tuples of a monoid, where the monoid is defined by the semi-positive fundamental relations of the fundamental group of a CW-complex. As an application, we reconstruct the second homotopy classes for the complement of generic lines arrangement studied by Akio Hattori. | math | 0 |
Title: A note on the growth of regularity with respect to Frobenius
Abstract: Let $R=k[x_1,\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\dots,x_n)$ by $\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension. | math | 1 |
Title: Microlocal Morse theory of wrapped Fukaya categories
Abstract: The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize this correspondence to incorporate the infinite-dimensional spaces of morphisms 'at infinity', given on the Floer side by Reeb trajectories (also known as "wrapping") and on the sheaf side by allowing unbounded infinite rank sheaves which are categorically compact. When combined with existing sheaf theoretic computations, our results confirm many new instances of homological mirror symmetry. More precisely, given a real analytic manifold $M$ and a subanalytic isotropic subset $\Lambda$ of its co-sphere bundle $S^*M$, we show that the partially wrapped Fukaya category of $T^*M$ stopped at $\Lambda$ is equivalent to the category of compact objects in the unbounded derived category of sheaves on $M$ with microsupport inside $\Lambda$. By an embedding trick, we also deduce a sheaf theoretic description of the wrapped Fukaya category of any Weinstein sector admitting a stable polarization. | math | 1 |
Title: Elementary SFT Spectral Gaps And The Strong Closing Property
Abstract: We formulate elementary SFT spectral invariants of a large class of symplectic cobordisms and stable Hamiltonian manifolds, in any dimension. We give criteria for the strong closing property using these invariants, and verify these criteria for Hofer near periodic systems. This extends the class of symplectic dynamical systems in any dimension that satisfy the strong closing property. | math | 0 |
Title: P-TimeSync: A Precise Time Synchronization Simulation with Network Propagation Delays
Abstract: Time serves as the foundation of modern society and will continue to grow in value in the future world. Unlike previous research papers, authors delve into various time sources, ranging from atomic time and GPS time to quartz time. Specifically, we explore the time uncertainty associated with the four major Global Navigation Satellite Systems. Additionally, we provide a summary of eight metrics used to evaluate time accuracy. In existing time synchronization simulations provide partial usages. However, our research introduces a comprehensive and precise time synchronization simulation named P-TimeSync, leading to a better understanding of time synchronization in distributed environments. It is a state-of-the-art simulation tool for time because (1) it can simulate atomic clocks and quartz clocks with user-defined software clock algorithms, (2) the simulation provides nanosecond-level precision time across different network propagation paths and distances, (3) the tool offers a visualization platform with classic algorithms for distributed time synchronization, such as Cristian's algorithm and Berkeley algorithm, and (4) the simulation includes three time-sync attack functions, including distributed denial-of-service (DDoS) attack, IP spoofer, and router hijacker. The simulation easily allows for the redefinition of configurations and functions, supporting advanced research and development. The simulation tool could be downloaded via the website: https://github.com/rui5097/purdue_timesync | cs | 0 |
Title: Density bounds for unit ball packings relative to their outer parallel domains
Abstract: We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This generalizes some earlier (classical) results. Sharp upper bounds are proved for the analogue problem on congruent circular disks in the spherical (resp., hyperbolic) plane and on congruent balls in Euclidean $3$-space. | math | 0 |
Title: Homology spheres and property R
Abstract: We present infinitely many homology spheres which contain two distinct knots whose 0-surgeries are $S^1 \times S^2$. This resolves a question posed by Kirby and Melvin in 1978. | math | 1 |
Title: InternVid: A Large-scale Video-Text Dataset for Multimodal Understanding and Generation
Abstract: This paper introduces InternVid, a large-scale video-centric multimodal dataset that enables learning powerful and transferable video-text representations for multimodal understanding and generation. The InternVid dataset contains over 7 million videos lasting nearly 760K hours, yielding 234M video clips accompanied by detailed descriptions of total 4.1B words. Our core contribution is to develop a scalable approach to autonomously build a high-quality video-text dataset with large language models (LLM), thereby showcasing its efficacy in learning video-language representation at scale. Specifically, we utilize a multi-scale approach to generate video-related descriptions. Furthermore, we introduce ViCLIP, a video-text representation learning model based on ViT-L. Learned on InternVid via contrastive learning, this model demonstrates leading zero-shot action recognition and competitive video retrieval performance. Beyond basic video understanding tasks like recognition and retrieval, our dataset and model have broad applications. They are particularly beneficial for generating interleaved video-text data for learning a video-centric dialogue system, advancing video-to-text and text-to-video generation research. These proposed resources provide a tool for researchers and practitioners interested in multimodal video understanding and generation. | cs | 0 |
Title: SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations
Abstract: Learning representations on large-sized graphs is a long-standing challenge due to the inter-dependence nature involved in massive data points. Transformers, as an emerging class of foundation encoders for graph-structured data, have shown promising performance on small graphs due to its global attention capable of capturing all-pair influence beyond neighboring nodes. Even so, existing approaches tend to inherit the spirit of Transformers in language and vision tasks, and embrace complicated models by stacking deep multi-head attentions. In this paper, we critically demonstrate that even using a one-layer attention can bring up surprisingly competitive performance across node property prediction benchmarks where node numbers range from thousand-level to billion-level. This encourages us to rethink the design philosophy for Transformers on large graphs, where the global attention is a computation overhead hindering the scalability. We frame the proposed scheme as Simplified Graph Transformers (SGFormer), which is empowered by a simple attention model that can efficiently propagate information among arbitrary nodes in one layer. SGFormer requires none of positional encodings, feature/graph pre-processing or augmented loss. Empirically, SGFormer successfully scales to the web-scale graph ogbn-papers100M and yields up to 141x inference acceleration over SOTA Transformers on medium-sized graphs. Beyond current results, we believe the proposed methodology alone enlightens a new technical path of independent interest for building Transformers on large graphs. | cs | 0 |
Title: Exponential sums, twisted multiplicativity and moments
Abstract: We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of exponential sums associated to different suitably unrelated and generic polynomials. The proofs combine analytic arguments with the algebraic interpretation of exponential sums and their monodromy groups. | math | 1 |
Title: Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
Abstract: The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{\'c} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \url{https://github.com/jakobrunge/tigramite}. | cs | 1 |
Title: Explicit characterisation of the fractional power spaces of the Dirichlet Laplacian and Stokes operators
Abstract: We identify explicitly the fractional power spaces for the $L^2$ Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new, but we hope that our arguments are relatively accessible. | math | 1 |
Title: Frechet differentiability of the metric projection operator in Banach spaces
Abstract: In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and convex subsets, we find the exact expressions for Frechet derivatives and Gateaux directional derivatives of the metric projection operator. | math | 0 |
Title: On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy
Abstract: We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov\'{a}sz--Schrijver SDP operator $\text{LS}_+$, with a particular focus on finding and characterizing the smallest graphs with a given $\text{LS}_+$-rank (the least number of iterations of the $\text{LS}_+$ operator on the fractional stable set polytope to compute the stable set polytope). We introduce a generalized vertex-stretching operation that appears to be promising in generating $\text{LS}_+$-minimal graphs and study its properties. We also provide several new $\text{LS}_+$-minimal graphs, most notably the first known instances of $12$-vertex graphs with $\text{LS}_+$-rank $4$, which provides the first advance in this direction since Escalante, Montelar, and Nasini's discovery of a $9$-vertex graph with $\text{LS}_+$-rank $3$ in 2006. | cs | 0 |
Title: Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field
Abstract: Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $\kappa$-density, for $\rm{Re}(\kappa)\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\rm{Bun}$ is $\kappa$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $\kappa\in\mathbb{C}$. | math | 0 |
Title: Basmajian-type identities and Hausdorff dimension of limit sets
Abstract: In this paper, we study Basmajian-type series identities on holomorphic families of Cantor sets associated to one-dimensional complex dynamical systems. We show that the series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is strictly less than one. Throughout the domain of convergence, these identities can be analytically continued and they exhibit nontrivial monodromy. | math | 1 |
Title: Quotients of Special Classes of Positroids
Abstract: In this paper, we give a complete characterization of rank $k-1$ positroids that are quotients of the uniform matroid $U_{k,n}$, completing a partial result by Bendetti-Chavez-Jim\'enez. Furthermore, we show that any pair of concordant positroids with adjacent ranks are related by a cyclic shift on their decorated permutations. We also use the concept of conecklaces to give a full characterization of concordant lattice path matroids (LPMs). | math | 0 |
Title: Quasitriangular structure and twisting of the 2+1 bicrossproduct model
Abstract: We show that the bicrossproduct model $C[SU_2^*]{\blacktriangleright\!\!\triangleleft} U(su_2)$ quantum Poincare group in 2+1 dimensions acting on the quantum spacetime $[x_i,t]=\imath\lambda x_i$ is related by a Drinfeld and module-algebra twist to the quantum double $U(su_2)\ltimes C[SU_2]$ acting on the quantum spacetime $[x_\mu,x_\nu]=\imath\lambda\epsilon_{\mu\nu\rho}x_\rho$. We obtain this twist by taking a scaling limit as $q\to 1$ of the $q$-deformed version of the above where it corresponds to a previous theory of $q$-deformed Wick rotation from $q$-Euclidean to $q$-Minkowski space. We also recover the twist result at the Lie bialgebra level. | math | 1 |
Title: Transfer Regression via Pairwise Similarity Regularization
Abstract: Transfer learning methods address the situation where little labeled training data from the "target" problem exists, but much training data from a related "source" domain is available. However, the overwhelming majority of transfer learning methods are designed for simple settings where the source and target predictive functions are almost identical, limiting the applicability of transfer learning methods to real world data. We propose a novel, weaker, property of the source domain that can be transferred even when the source and target predictive functions diverge. Our method assumes the source and target functions share a Pairwise Similarity property, where if the source function makes similar predictions on a pair of instances, then so will the target function. We propose Pairwise Similarity Regularization Transfer, a flexible graph-based regularization framework which can incorporate this modeling assumption into standard supervised learning algorithms. We show how users can encode domain knowledge into our regularizer in the form of spatial continuity, pairwise "similarity constraints" and how our method can be scaled to large data sets using the Nystrom approximation. Finally, we present positive and negative results on real and synthetic data sets and discuss when our Pairwise Similarity transfer assumption seems to hold in practice. | cs | 1 |
Title: On the associativity of the addition on elliptic curves
Abstract: In this short note we give a simple elementary proof of the associativity of the addition on elliptic curves. We do this by providing an explicit formula for the sum of three points, using the explicit definition of the group structure. | math | 0 |
Title: A Three-Valued Semantics for Typed Logic Programming
Abstract: Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we define a new semantics for logic programming, where programs evaluate to true, false, and to a new semantic value called wrong, corresponding to a run-time type error. We then have a type language with a separated semantics of types. Finally, we define a type system for logic programming and prove that it is semantically sound with respect to a semantic relation between programs and types where, if a program has a type, then its semantics is not wrong. Our work follows Milner's approach for typed functional languages where the semantics of programs is independent from the semantic of types, and the type system is proved to be sound with respect to a relation between both semantics. | cs | 1 |
Title: Positive Semidefinite Metric Learning with Boosting
Abstract: The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time. | cs | 1 |
Title: 3D Open-Vocabulary Panoptic Segmentation with 2D-3D Vision-Language Distillation
Abstract: 3D panoptic segmentation is a challenging perception task, which aims to predict both semantic and instance annotations for 3D points in a scene. Although prior 3D panoptic segmentation approaches have achieved great performance on closed-set benchmarks, generalizing to novel categories remains an open problem. For unseen object categories, 2D open-vocabulary segmentation has achieved promising results that solely rely on frozen CLIP backbones and ensembling multiple classification outputs. However, we find that simply extending these 2D models to 3D does not achieve good performance due to poor per-mask classification quality on novel categories. In this paper, we propose the first method to tackle 3D open-vocabulary panoptic segmentation. Our model takes advantage of the fusion between learnable LiDAR features and dense frozen vision CLIP features, using a single classification head to make predictions for both base and novel classes. To further improve the classification performance on novel classes and leverage the CLIP model, we propose two novel loss functions: object-level distillation loss and voxel-level distillation loss. Our experiments on the nuScenes and SemanticKITTI datasets show that our method outperforms strong baselines by a large margin. | cs | 0 |
Title: Relations Between $p$-Means of Convex Bodies and a New Suggestion for the Definition of the Geometric Mean
Abstract: In light of the log-Brunn-Minkowski conjecture, various attempts have been made to define the geometric mean of convex bodies. Many of these constructions are fairly complex and/or fail to satisfy some natural properties one would expect of such a mean. We remedy this by providing a new geometric mean that is both technically simple and inherits all the natural properties expected. To improve our understanding of potential geometric mean definitions, we first study general $p$-means of convex bodies, with the usual definition extended to two series ranging over all $p \in [-\infty,\infty]$. We characterize their equality cases and obtain (in almost all instances tight) inequalities that quantify how well these means approximate each other. As a corollary, we establish that every Minkowski centered body is equidistant from all its $p$-symmetrizations with respect to the Banach-Mazur distance. Finally, we show that our geometric mean satisfies all the properties considered in recent literature and extend this list with some properties regarding symmetrization and asymmetry. | math | 0 |
Title: The Effect of Learning Strategy versus Inherent Architecture Properties on the Ability of Convolutional Neural Networks to Develop Transformation Invariance
Abstract: As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on understanding the mechanisms behind how neural networks generalize to spatial transformations of complex objects. While humans excel at discriminating between objects shown at new positions, orientations, and scales, past results demonstrate that this may be limited to familiar objects - humans demonstrate low tolerance of spatial-variances for purposefully constructed novel objects. Because training artificial neural networks from scratch is similar to showing novel objects to humans, we seek to understand the factors influencing the tolerance of CNNs to spatial transformations. We conduct a thorough empirical examination of seven Convolutional Neural Network (CNN) architectures. By training on a controlled face image dataset, we measure model accuracy across different degrees of 5 transformations: position, size, rotation, Gaussian blur, and resolution transformation due to resampling. We also examine how learning strategy affects generalizability by examining how different amounts of pre-training have on model robustness. Overall, we find that the most significant contributor to transformation invariance is pre-training on a large, diverse image dataset. Moreover, while AlexNet tends to be the least robust network, VGG and ResNet architectures demonstrate higher robustness for different transformations. Along with kernel visualizations and qualitative analyses, we examine differences between learning strategy and inherent architectural properties in contributing to invariance of transformations, providing valuable information towards understanding how to achieve greater robustness to transformations in CNNs. | cs | 1 |
Title: Directed Homology and Persistence Modules
Abstract: In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some exact sequences. | math | 0 |
Title: A Comprehensive Survey on Graph Summarization with Graph Neural Networks
Abstract: As large-scale graphs become more widespread, more and more computational challenges with extracting, processing, and interpreting large graph data are being exposed. It is therefore natural to search for ways to summarize these expansive graphs while preserving their key characteristics. In the past, most graph summarization techniques sought to capture the most important part of a graph statistically. However, today, the high dimensionality and complexity of modern graph data are making deep learning techniques more popular. Hence, this paper presents a comprehensive survey of progress in deep learning summarization techniques that rely on graph neural networks (GNNs). Our investigation includes a review of the current state-of-the-art approaches, including recurrent GNNs, convolutional GNNs, graph autoencoders, and graph attention networks. A new burgeoning line of research is also discussed where graph reinforcement learning is being used to evaluate and improve the quality of graph summaries. Additionally, the survey provides details of benchmark datasets, evaluation metrics, and open-source tools that are often employed in experimentation settings, along with a detailed comparison, discussion, and takeaways for the research community focused on graph summarization. Finally, the survey concludes with a number of open research challenges to motivate further study in this area. | cs | 0 |
Title: Efficient computation of the cumulative distribution function of a linear mixture of independent random variables
Abstract: For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional correctness, i.e. the convergence of the computed distribution function towards the true distribution function (given the observations) as the algorithm resolution is increased to infinity. The algorithm (like its predecessor version) bears elements which are closely related to early known methods for numerical inversion of the characteristic function of a probability distribution, however here efficiently computes the complete distribution function. Possible applications are in computing the distribution of the bootstrap estimate in any linear bootstrap method (e.g. in the block bootstrap for the mean as parameter of interest, or residual bootstrap in linear regression with fixed design), or in elementary analysis-of-variance hypothesis testing. | math | 1 |
Title: Efficient Detection of Botnet Traffic by features selection and Decision Trees
Abstract: Botnets are one of the online threats with the biggest presence, causing billionaire losses to global economies. Nowadays, the increasing number of devices connected to the Internet makes it necessary to analyze large amounts of network traffic data. In this work, we focus on increasing the performance on botnet traffic classification by selecting those features that further increase the detection rate. For this purpose we use two feature selection techniques, Information Gain and Gini Importance, which led to three pre-selected subsets of five, six and seven features. Then, we evaluate the three feature subsets along with three models, Decision Tree, Random Forest and k-Nearest Neighbors. To test the performance of the three feature vectors and the three models we generate two datasets based on the CTU-13 dataset, namely QB-CTU13 and EQB-CTU13. We measure the performance as the macro averaged F1 score over the computational time required to classify a sample. The results show that the highest performance is achieved by Decision Trees using a five feature set which obtained a mean F1 score of 85% classifying each sample in an average time of 0.78 microseconds. | cs | 1 |
Title: A dilation theoretic approach to approximation by inner functions
Abstract: Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction and the realization formula for functions in the unit ball of $H^\infty$. We first prove a generalization of a result of Carath\'eodory. This generalization has many applications. A uniform approximation result for matrix-valued holomorphic functions which extend continuously to the unit circle is proved using the Potapov factorization. This generalizes a theorem due to Fisher. Approximation results are proved for matrix-valued functions for whom a naturally associated kernel has finitely many negative squares. This uses the Krein-Langer factorization. Approximation results for $J$-contractive meromorphic functions where $J$ induces an indefinite metric on $\mathbb C^N$ are proved using the Potapov-Ginzburg Theorem. Moreover, approximation results for holomorphic functions on the unit disc with values in certain other domains of interest are also proved. | math | 1 |
Title: The automatic solution of partial differential equations using a global spectral method
Abstract: A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method. If a partial differential operator is of splitting rank $2$, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree $(n_x,n_y)$ is computed in $\mathcal{O}((n_x n_y)^{3/2})$ operations. Partial differential operators of splitting rank $\geq 3$ are solved via a linear system involving a block-banded matrix in $\mathcal{O}(\min(n_x^{3} n_y,n_x n_y^{3}))$ operations. Numerical examples demonstrate the applicability of our 2D spectral method to a broad class of PDEs, which includes elliptic and dispersive time-evolution equations. The resulting PDE solver is written in MATLAB and is publicly available as part of CHEBFUN. It can resolve solutions requiring over a million degrees of freedom in under $60$ seconds. An experimental implementation in the Julia language can currently perform the same solve in $10$ seconds. | math | 1 |
Title: Theta divisors whose Gauss map has a fiber of positive dimension
Abstract: We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci. | math | 1 |
Title: On knots that divide ribbon knotted surfaces
Abstract: We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of which K is a cross-section. We compute this genus for all prime knots up to 12 crossings, and many 13-crossing knots. The same approach yields new computations of the doubly slice genus. We also introduce the half fusion number of a knot K, that measures the complexity of ribbon 2-knots of which K is a cross-section. We show that it is bounded from below by the Levine-Tristram signatures, and differs from the standard fusion number by an arbitrarily large amount. | math | 1 |
Title: Stanley--Elder--Fine theorems for colored partitions
Abstract: We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored partitions (or prefabs). More specifically, we give analogous results for $b$-colored partitions, where each part occurs in $b$ colors; for $b$-colored partitions with odd parts (or distinct parts); for partitions where the part $k$ comes in $k$ colors; and, overpartitions. | math | 1 |
Title: View-based Explanations for Graph Neural Networks
Abstract: Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable. We propose GVEX, a novel paradigm that generates Graph Views for EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is $\Sigma^2_P$-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4 approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX. | cs | 0 |
Title: Constrained quantization for a uniform distribution
Abstract: Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. In this paper, for a uniform distribution with support lying on a side of an equilateral triangle, and the constraint as the union of the other two sides, we obtain the optimal sets of $n$-points and the $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient. | math | 0 |
Title: On Augmenting Scenario-Based Modeling with Generative AI
Abstract: The manual modeling of complex systems is a daunting task; and although a plethora of methods exist that mitigate this issue, the problem remains very difficult. Recent advances in generative AI have allowed the creation of general-purpose chatbots, capable of assisting software engineers in various modeling tasks. However, these chatbots are often inaccurate, and an unstructured use thereof could result in erroneous system models. In this paper, we outline a method for the safer and more structured use of chatbots as part of the modeling process. To streamline this integration, we propose leveraging scenario-based modeling techniques, which are known to facilitate the automated analysis of models. We argue that through iterative invocations of the chatbot and the manual and automatic inspection of the resulting models, a more accurate system model can eventually be obtained. We describe favorable preliminary results, which highlight the potential of this approach. | cs | 0 |
Title: Image classification and retrieval with random depthwise signed convolutional neural networks
Abstract: We propose a random convolutional neural network to generate a feature space in which we study image classification and retrieval performance. Put briefly we apply random convolutional blocks followed by global average pooling to generate a new feature, and we repeat this k times to produce a k-dimensional feature space. This can be interpreted as partitioning the space of image patches with random hyperplanes which we formalize as a random depthwise convolutional neural network. In the network's final layer we perform image classification and retrieval with the linear support vector machine and k-nearest neighbor classifiers and study other empirical properties. We show that the ratio of image pixel distribution similarity across classes to within classes is higher in our network's final layer compared to the input space. When we apply the linear support vector machine for image classification we see that the accuracy is higher than if we were to train just the final layer of VGG16, ResNet18, and DenseNet40 with random weights. In the same setting we compare it to an unsupervised feature learning method and find our accuracy to be comparable on CIFAR10 but higher on CIFAR100 and STL10. We see that the accuracy is not far behind that of trained networks, particularly in the top-k setting. For example the top-2 accuracy of our network is near 90% on both CIFAR10 and a 10-class mini ImageNet, and 85% on STL10. We find that k-nearest neighbor gives a comparable precision on the Corel Princeton Image Similarity Benchmark than if we were to use the final layer of trained networks. As with other networks we find that our network fails to a black box attack even though we lack a gradient and use the sign activation. We highlight sensitivity of our network to background as a potential pitfall and an advantage. Overall our work pushes the boundary of what can be achieved with random weights. | cs | 1 |
Title: Some remarks on Grothendieck pairs
Abstract: We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We also show that various groups are left and/or right Grothendieck rigid and, in particular, all ascending HNN extensiona of finitely generated free groups are right Grothendieck rigid. Along the way we present a number of questions and suggestions for further research. | math | 0 |
Title: Concentration-compactness at the mountain pass level in semilinear elliptic problems
Abstract: The concentration compactness framework for semilinear elliptic equations without compactness, set originally by P.-L.Lions for constrained minimization in the case of homogeneous nonlinearity, is extended here to the case of general nonlinearities in the standard mountain pass setting of Ambrosetti-Rabinowitz. In these setting, existence of solutions at the mountain pass level is verified under a single penalty condition analogous to that in the Lions' case. Problems on the whole space and problems with critical nonlinearity are considered. Particular attention is given to nonhomogeneous critical nonlinearities that oscillate about the "critical stem". | math | 1 |
Title: Solving a Random Asymmetric TSP Exactly in Quasi-Polynomial Time w.h.p
Abstract: Let the costs $A(i,j)$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent exponential mean one random variables. We describe an enumerative algorithm that solves ATSP exactly in time $e^{\log^{3+o(1)}n}$. | cs | 0 |
Title: Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem
Abstract: In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator. | math | 0 |
Title: Algebraic trace functions over the primes
Abstract: We study sums over primes of trace functions of $\ell$-adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann Hypothesis over finite fields, we prove general estimates with power-saving for such sums. We then derive various concrete applications. | math | 1 |
Title: Particle systems and kinetic equations modeling interacting agents in high dimension
Abstract: In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such systems, one has to deal with a large number of agents (typically millions) in spaces of parameters describing each agent of high dimension (thousands or more). Even with today's powerful computers, numerical simulations of such systems are prohibitively expensive. We propose an approach for the simulation of dynamical systems governed by functions of adjacency matrices in high dimension, by random projections via Johnson-Lindenstrauss embeddings, and recovery by compressed sensing techniques. We show how these concepts can be generalized to work for associated kinetic equations, by addressing the phenomenon of the delayed curse of dimension, known in information-based complexity for optimal numerical integration problems in high dimensions. | math | 1 |
Title: Matchings and loose cycles in the semirandom hypergraph model
Abstract: We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching, and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within $\Theta(n)$ steps. Both results extend to $s$-uniform hypergraphs. Much of the analysis is done on an auxiliary graph that is a uniform $k$-out subgraph of a random bipartite graph, and this tool may be useful in other contexts. | math | 0 |
Title: On volumes of hyperbolic right-angled polyhedra
Abstract: In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite (or usual) vertices, and for finite volume polyhedra with vertices of both types. | math | 1 |
Title: Legendre-Moment Transform for Linear Ensemble Control and Computation
Abstract: Ensemble systems, pervasive in diverse scientific and engineering domains, pose challenges to existing control methods due to their massive scale and underactuated nature. This paper presents a dynamic moment approach to addressing theoretical and computational challenges in systems-theoretic analysis and control design for linear ensemble systems. We introduce the Legendre-moments and Legendre-moment transform, which maps an ensemble system defined on the $L^2$-space to a Legendre-moment system defined on the $\ell^2$-space. We show that this pair of systems is of one-to-one correspondence and shares the same controllability property. This equivalence admits the control of an ensemble system through the control of the corresponding Legendre-moment system and inspires a unified control design scheme for linear ensemble systems using structured truncated moment systems. In particular, we develop a sampling-free ensemble control design algorithm, then conduct error analysis for control design using truncated moment systems and derive error bounds with respect to the truncation orders, which are illustrated with numerical examples. | math | 0 |
Title: Offline Policy Optimization with Eligible Actions
Abstract: Offline policy optimization could have a large impact on many real-world decision-making problems, as online learning may be infeasible in many applications. Importance sampling and its variants are a commonly used type of estimator in offline policy evaluation, and such estimators typically do not require assumptions on the properties and representational capabilities of value function or decision process model function classes. In this paper, we identify an important overfitting phenomenon in optimizing the importance weighted return, in which it may be possible for the learned policy to essentially avoid making aligned decisions for part of the initial state space. We propose an algorithm to avoid this overfitting through a new per-state-neighborhood normalization constraint, and provide a theoretical justification of the proposed algorithm. We also show the limitations of previous attempts to this approach. We test our algorithm in a healthcare-inspired simulator, a logged dataset collected from real hospitals and continuous control tasks. These experiments show the proposed method yields less overfitting and better test performance compared to state-of-the-art batch reinforcement learning algorithms. | cs | 1 |
Title: An entropy bound due to symmetries
Abstract: Let $H$ be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime $\mathbb{R}^{d+1}$, covariant with respect to a positive energy, unitary representation $U$ of the Poincar\'e group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy $S_H(\phi|\! | C)$ of a vector in a region $C$ that depends only on $U$ and the PCT anti-unitary canonically associated with $H$. A similar result holds for local, M\"obius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the $U(1)$-current derivatives. | math | 0 |
Title: Symbolic dynamics and rotation symmetric Boolean functions
Abstract: We identify the weights $wt(f_n)$ of a family $\{f_n\}$ of rotation symmetric Boolean functions with the cardinalities of the sets of $n$-periodic points of a finite-type shift, recovering the second author's result that said weights satisfy a linear recurrence. Similarly, the weights of idempotent functions $f_n$ defined on finite fields can be recovered as the cardinalities of curves over those fields and hence satisfy a linear recurrence as a consequence of the rationality of curves' zeta functions. Weil's Riemann hypothesis for curves then provides additional information about $wt(f_n)$. We apply our results to the case of quadratic functions and considerably extend the results in an earlier paper of ours. | cs | 1 |
Title: Efficient UAVs Deployment and Resource Allocation in UAV-Relay Assisted Public Safety Networks for Video Transmission
Abstract: Wireless communication highly depends on the cellular ground base station (GBS). A failure of the cellular GBS, fully or partially, during natural or man-made disasters creates a communication gap in the disaster-affected areas. In such situations, public safety communication (PSC) can significantly save the national infrastructure, property, and lives. Throughout emergencies, the PSC can provide mission-critical communication and video transmission services in the affected area. Unmanned aerial vehicles (UAVs) as flying base stations (UAV-BSs) are particularly suitable for PSC services as they are flexible, mobile, and easily deployable. This manuscript considers a multi-UAV-assisted PSC network with an observational UAV receiving videos from the affected area's ground users (AGUs) and transmitting them to the nearby GBS via a relay UAV. The objective of the proposed study is to maximize the average utility of the video streams generated by the AGUs upon reaching the GBS. This is achieved by optimizing the positions of the observational and relay UAVs, as well as the distribution of communication resources, such as bandwidth, and transmit power, while satisfying the system-designed constraints, such as transmission rate, rate outage probability, transmit power budget, and available bandwidth. To this end, a joint UAVs placement and resource allocation problem is mathematically formulated. The proposed problem poses a significant challenge for a solution. Considering the block coordinate descent and successive convex approximation techniques, an efficient iterative algorithm is proposed. Finally, simulation results are provided which show that our proposed approach outperforms the existing methods. | cs | 0 |
Title: Unicron: Economizing Self-Healing LLM Training at Scale
Abstract: Training large-scale language models is increasingly critical in various domains, but it is hindered by frequent failures, leading to significant time and economic costs. Current failure recovery methods in cloud-based settings inadequately address the diverse and complex scenarios that arise, focusing narrowly on erasing downtime for individual tasks without considering the overall cost impact on a cluster. We introduce Unicron, a workload manager designed for efficient self-healing in large-scale language model training. Unicron optimizes the training process by minimizing failure-related costs across multiple concurrent tasks within a cluster. Its key features include in-band error detection for real-time error identification without extra overhead, a dynamic cost-aware plan generation mechanism for optimal reconfiguration, and an efficient transition strategy to reduce downtime during state changes. Deployed on a 128-GPU distributed cluster, Unicron demonstrates up to a 1.9x improvement in training efficiency over state-of-the-art methods, significantly reducing failure recovery costs and enhancing the reliability of large-scale language model training. | cs | 0 |
Title: Byzantine-Resilient Gradient Coding through Local Gradient Computations
Abstract: We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers each partial gradient is computed by. In this work, we propose a way to reduce the replication to $s+1$ instead of $2s+1$ in the presence of $s$ malicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense of $s$ additional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers. | cs | 0 |
Title: Sampling Acquisition Functions for Batch Bayesian Optimization
Abstract: We present Acquisition Thompson Sampling (ATS), a novel technique for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model hyper-parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function or to make existing parallel methods scale further. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the advantages of ATS with respect to classical parallel Thompson Sampling for BO, its competitiveness with two state-of-the-art batch BO methods, and its effectiveness if applied to existing parallel BO algorithms. | cs | 1 |
Title: SyCoCa: Symmetrizing Contrastive Captioners with Attentive Masking for Multimodal Alignment
Abstract: Multimodal alignment between language and vision is the fundamental topic in current vision-language model research. Contrastive Captioners (CoCa), as a representative method, integrates Contrastive Language-Image Pretraining (CLIP) and Image Caption (IC) into a unified framework, resulting in impressive results. CLIP imposes a bidirectional constraints on global representation of entire images and sentences. Although IC conducts an unidirectional image-to-text generation on local representation, it lacks any constraint on local text-to-image reconstruction, which limits the ability to understand images at a fine-grained level when aligned with texts. To achieve multimodal alignment from both global and local perspectives, this paper proposes Symmetrizing Contrastive Captioners (SyCoCa), which introduces bidirectional interactions on images and texts across the global and local representation levels. Specifically, we expand a Text-Guided Masked Image Modeling (TG-MIM) head based on ITC and IC heads. The improved SyCoCa can further leverage textual cues to reconstruct contextual images and visual cues to predict textual contents. When implementing bidirectional local interactions, the local contents of images tend to be cluttered or unrelated to their textual descriptions. Thus, we employ an attentive masking strategy to select effective image patches for interaction. Extensive experiments on five vision-language tasks, including image-text retrieval, image-captioning, visual question answering, and zero-shot/finetuned image classification, validate the effectiveness of our proposed method. | cs | 0 |
Title: A spectral theorem for compact representations and non-unitary cusp forms
Abstract: We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. | math | 0 |
Title: Returns to the origin of the Pólya walk with stochastic resetting
Abstract: We consider the simple random walk (or P\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers ${\mathcal{N}}_t^{\times}$ of spontaneous returns of the walker to the origin and ${\mathcal{N}}_t^{\bullet}$ of resetting events up to some observation time $t$. These numbers are extensive in time in a strong sense: all their joint cumulants grow linearly in $t$, with explicitly computable amplitudes, and their fluctuations are described by a smooth bivariate large deviation function. A non-trivial crossover phenomenon takes place in the regime of weak resetting and late times. Remarkably, the time intervals between spontaneous returns to the origin of the reset random walk form a renewal process described in terms of a single `dressed' probability distribution. These time intervals are probabilistic copies of the first one, the `dressed' first-passage time. The present work follows a broader study, covered in a companion paper, on general nested renewal processes. | math | 0 |
Title: On the support of the Kloosterman paths
Abstract: We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of our earlier functional limit theorem for Kloosterman paths. | math | 1 |
Title: Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
Abstract: The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications, including regression and classification tasks. Furthermore, it is valid for real-valued neural networks and some hypercomplex-valued neural networks such as complex-, quaternion-, tessarine-, and Clifford-valued neural networks. However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties. This paper extends the universal approximation theorem for a wide range of vector-valued neural networks, including hypercomplex-valued models as particular instances. Precisely, we introduce the concept of non-degenerate algebra and state the universal approximation theorem for neural networks defined on such algebras. | cs | 0 |
Title: Potentially crystalline deformation rings in the ordinary case
Abstract: We study potentially crystalline deformation rings for a residual, ordinary Galois representation $\overline{\rho}: G_{\mathbb{Q}_p}\rightarrow \mathrm{GL}_3(\mathbb{F}_p)$. We consider deformations with Hodge-Tate weights $(0,1,2)$ and inertial type chosen to contain exactly one Fontaine-Laffaille modular weight for $\overline{\rho}$. We show that, in this setting, the potentially crystalline deformation space is formally smooth over $\mathbb{Z}_p$ and any potentially crystalline lift is ordinary. The proof requires an understanding of the condition imposed by the monodromy operator on Breuil modules with descent datum, in particular, that this locus mod p is formally smooth. | math | 1 |
Title: UstanceBR: a multimodal language resource for stance prediction
Abstract: This work introduces UstanceBR, a multimodal corpus in the Brazilian Portuguese Twitter domain for target-based stance prediction. The corpus comprises 86.8 k labelled stances towards selected target topics, and extensive network information about the users who published these stances on social media. In this article we describe the corpus multimodal data, and a number of usage examples in both in-domain and zero-shot stance prediction based on text- and network-related information, which are intended to provide initial baseline results for future studies in the field. | cs | 0 |
Title: Linear inverse problems for Markov processes and their regularisation
Abstract: We study the solutions of the inverse problem \[ g(z)=\int f(y) P_T(z,dy) \] for a given $g$, where $(P_t(\cdot,\cdot))_{t \geq 0}$ is the transition function of a given Markov process, $X$, and $T$ is a fixed deterministic time, which is linked to the solutions of the ill-posed Cauchy problem \[ u_t + A u=0, \qquad u(0,\cdot)=g, \] where $A$ is the generator of $X$. A necessary and sufficient condition ensuring square integrable solutions is given. Moreover, a family of regularisations for the above problems is suggested. We show in particular that these inverse problems have a solution when $X$ is replaced by $\xi X + (1-\xi)J$, where $\xi$ is a Bernoulli random variable, whose probability of success can be chosen arbitrarily close to $1$, and $J$ is a suitably constructed jump process. | math | 1 |
Title: Are LLMs Robust for Spoken Dialogues?
Abstract: Large Pre-Trained Language Models have demonstrated state-of-the-art performance in different downstream tasks, including dialogue state tracking and end-to-end response generation. Nevertheless, most of the publicly available datasets and benchmarks on task-oriented dialogues focus on written conversations. Consequently, the robustness of the developed models to spoken interactions is unknown. In this work, we have evaluated the performance of LLMs for spoken task-oriented dialogues on the DSTC11 test sets. Due to the lack of proper spoken dialogue datasets, we have automatically transcribed a development set of spoken dialogues with a state-of-the-art ASR engine. We have characterized the ASR-error types and their distributions and simulated these errors in a large dataset of dialogues. We report the intrinsic (perplexity) and extrinsic (human evaluation) performance of fine-tuned GPT-2 and T5 models in two subtasks of response generation and dialogue state tracking, respectively. The results show that LLMs are not robust to spoken noise by default, however, fine-tuning/training such models on a proper dataset of spoken TODs can result in a more robust performance. | cs | 0 |
Title: Littlewood's problem for sets with multidimensional structure
Abstract: We give $L^1$-norm estimates for exponential sums of a finite sets $A$ consisting of integers or lattice points. Under the assumption that $A$ possesses sufficient multidimensional structure, our estimates are stronger than those of McGehee-Pigno-Smith and Konyagin. These theorems improve upon past work of Petridis. | math | 1 |
Title: Some Inequalities Related to the Seysen Measure of a Lattice
Abstract: Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the orthogonality measure $S(B)=\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced by M. Seysen in 1993. This measure is at the heart of the Seysen lattice reduction algorithm and is linked with different geometrical properties of the basis. In this paper, we explicit different expressions for this measure as well as new inequalities. | math | 1 |
Title: On the minimal set for counterexamples to the local-global principle
Abstract: We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous criterion for the validity of the principle. We also give an example that shows that the assumptions of our criterion are necessary. | math | 1 |
Title: Dataset Difficulty and the Role of Inductive Bias
Abstract: Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call "example difficulty scores", are typically used to rank or categorize examples, but the consistency of rankings between different training runs, scoring methods, and model architectures is generally unknown. To determine how example rankings vary due to these random and controlled effects, we systematically compare different formulations of scores over a range of runs and model architectures. We find that scores largely share the following traits: they are noisy over individual runs of a model, strongly correlated with a single notion of difficulty, and reveal examples that range from being highly sensitive to insensitive to the inductive biases of certain model architectures. Drawing from statistical genetics, we develop a simple method for fingerprinting model architectures using a few sensitive examples. These findings guide practitioners in maximizing the consistency of their scores (e.g. by choosing appropriate scoring methods, number of runs, and subsets of examples), and establishes comprehensive baselines for evaluating scores in the future. | cs | 0 |
Title: Efficient Algorithms for Learning from Coarse Labels
Abstract: For many learning problems one may not have access to fine grained label information; e.g., an image can be labeled as husky, dog, or even animal depending on the expertise of the annotator. In this work, we formalize these settings and study the problem of learning from such coarse data. Instead of observing the actual labels from a set $\mathcal{Z}$, we observe coarse labels corresponding to a partition of $\mathcal{Z}$ (or a mixture of partitions). Our main algorithmic result is that essentially any problem learnable from fine grained labels can also be learned efficiently when the coarse data are sufficiently informative. We obtain our result through a generic reduction for answering Statistical Queries (SQ) over fine grained labels given only coarse labels. The number of coarse labels required depends polynomially on the information distortion due to coarsening and the number of fine labels $|\mathcal{Z}|$. We also investigate the case of (infinitely many) real valued labels focusing on a central problem in censored and truncated statistics: Gaussian mean estimation from coarse data. We provide an efficient algorithm when the sets in the partition are convex and establish that the problem is NP-hard even for very simple non-convex sets. | cs | 1 |
Title: 2-Rainbow domination number of circulant graphs C(n; {1,4})
Abstract: Let $k$ be a positive integer. A $k$-rainbow domination function (kRDF) of a graph $G$ is a function $f$ from $V(G)$ to the set of all subsets of $\{1,2,\dots,k\}$ such that every vertex $v \in V(G)$ with $f(v) = \emptyset$ satisfies $\bigcup_{u \in N(v)} f(u) = \{1,2,\dots,k\}$. The weight of a $k$RDF is defined as $w(f)= \sum_{v \in V(G)} |f(v)|$. The $k$-rainbow domination number of $G$, denoted by $\gamma_{rk}(G)$, is the minimum weight of all kRDFs of $G$. In this paper, we determine the exact value of the 2-rainbow domination number of circulant graphs $C(n; \{1,4\})$, which is $\gamma_{r2}(C(n; \{1,4\})) = \lceil n/3 \rceil + \alpha$, where $\alpha = 0$ for $n \equiv 0 \pmod{6}$, $\alpha = 1$ for $n \equiv 1,2,3,5 \pmod{6}$, and $\alpha = 2$ for $n \equiv 4 \pmod{6}$. | math | 0 |
Title: ChartAssisstant: A Universal Chart Multimodal Language Model via Chart-to-Table Pre-training and Multitask Instruction Tuning
Abstract: Charts play a vital role in data visualization, understanding data patterns, and informed decision-making. However, their unique combination of graphical elements (e.g., bars, lines) and textual components (e.g., labels, legends) poses challenges for general-purpose multimodal models. While vision-language models trained on chart data excel in comprehension, they struggle with generalization and require task-specific fine-tuning. To address these challenges, we propose ChartAssistant, a chart-based vision-language model for universal chart comprehension and reasoning. ChartAssistant leverages ChartSFT, a comprehensive dataset covering diverse chart-related tasks with basic and specialized chart types. It undergoes a two-stage training process, starting with pre-training on chart-to-table parsing to align chart and text, followed by multitask instruction-following fine-tuning. This approach enables ChartAssistant to achieve competitive performance across various chart tasks without task-specific fine-tuning. Experimental results demonstrate significant performance gains over the state-of-the-art UniChart method, outperforming OpenAI's GPT-4V(ision) on real-world chart data. The code and data are available at https://github.com/OpenGVLab/ChartAst. | cs | 0 |
Title: Approximation in Hölder Spaces
Abstract: For a modulus of continuity $\omega$ and Banach spaces $X,Y$ we introduce and study the subspaces $\dot{\operatorname{VC}}^{0,\omega}_{\Upsilon}(X,Y)$ of vanishing scales $\Upsilon\in \{\operatorname{small},\operatorname{large},\operatorname{far}\}$ of the homogeneous H\"{o}lder space $\dot{C}^{0,\omega}(X,Y).$ For a wide class of couples $X$ and $Y$, we characterize the subspaces of functions approximable by smooth and Lipschitz and boundedly supported functions in terms of these three vanishing scales. In the particular case $X=\mathbb{R}^n,$ we identify the spaces $\dot{\operatorname{VC}}^{0,\omega}_{\Upsilon}(\mathbb{R}^n,Y)$ with the corresponding vanishing mean oscillation spaces $\operatorname{VMO}^{\omega}_{\Upsilon}(\mathbb{R}^n,Y)$, thus providing a proof for the density of test functions also on these spaces. | math | 0 |
Title: Anisotropy of quadratic forms over a global field of odd characteristic is diophantine
Abstract: We prove that the anisotropy of quadratic forms over any global field of characteristic not equal to 2 is diophantine, by using a generalization of the method of Koenigsmann and some known results in diophantine sets and quadratic forms. | math | 0 |
Title: On Codes for the Noisy Substring Channel
Abstract: We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems, interest in this channel has renewed in recent years. In contrast to existing literature, we consider a noisy channel model where information is subject to noise before its substrings are sampled, motivated by in-vivo storage. We study two separate noise models, substitutions or deletions. In both cases, we examine families of codes which may be utilized for error-correction and present combinatorial bounds on their sizes. Through a generalization of the concept of repeat-free strings, we show that the added required redundancy due to this imperfect observation assumption is sublinear, either when the fraction of errors in the observed substring length is sufficiently small, or when that length is sufficiently long. This suggests that no asymptotic cost in rate is incurred by this channel model in these cases. Moreover, we develop an efficient encoder for such constrained strings in some cases. Finally, we show how a similar encoder can be used to avoid formation of secondary-structures in coded DNA strands, even when accounting for imperfect structures. | cs | 1 |
Title: On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
Abstract: In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erd\H{o}s and Rado, concerning their interrelation with several weak choice forms. | math | 0 |
Title: Towards Computing an Optimal Abstraction for Structural Causal Models
Abstract: Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we focus on the problem of learning abstractions. We start by defining the learning problem formally in terms of the optimization of a standard measure of consistency. We then point out the limitation of this approach, and we suggest extending the objective function with a term accounting for information loss. We suggest a concrete measure of information loss, and we illustrate its contribution to learning new abstractions. | cs | 1 |
Title: Understanding Softmax Confidence and Uncertainty
Abstract: It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuitions about softmax confidence are misleading. Diagnostic experiments quantify reasons softmax confidence can fail, finding that extrapolations are less to blame than overlap between training and OOD data in final-layer representations. Pre-trained/fine-tuned networks reduce this overlap. | cs | 1 |
Title: A collection of integrals, products and series
Abstract: This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental constants. | math | 0 |
Title: Approximate innerness and central triviality of endomorphisms
Abstract: We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in automorphism case. | math | 1 |