Temporal knowledge graphs represent temporal facts $(s,p,o,\tau)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $\tau$, where $\tau$ could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.
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Semantic segmentation is a key prerequisite to robust image understanding for applications in \acrlong{ai} and Robotics. \acrlong{fss}, in particular, concerns the extension and optimization of traditional segmentation methods in challenging conditions where limited training examples are available. A predominant approach in \acrlong{fss} is to rely on a single backbone for visual feature extraction. Choosing which backbone to leverage is a deciding factor contributing to the overall performance. In this work, we interrogate on whether fusing features from different backbones can improve the ability of \acrlong{fss} models to capture richer visual features. To tackle this question, we propose and compare two ensembling techniques-Independent Voting and Feature Fusion. Among the available \acrlong{fss} methods, we implement the proposed ensembling techniques on PANet. The module dedicated to predicting segmentation masks from the backbone embeddings in PANet avoids trainable parameters, creating a controlled `in vitro' setting for isolating the impact of different ensembling strategies. Leveraging the complementary strengths of different backbones, our approach outperforms the original single-backbone PANet across standard benchmarks even in challenging one-shot learning scenarios. Specifically, it achieved a performance improvement of +7.37\% on PASCAL-5\textsuperscript{i} and of +10.68\% on COCO-20\textsuperscript{i} in the top-performing scenario where three backbones are combined. These results, together with the qualitative inspection of the predicted subject masks, suggest that relying on multiple backbones in PANet leads to a more comprehensive feature representation, thus expediting the successful application of \acrlong{fss} methods in challenging, data-scarce environments.
Whether based on models, training data or a combination, classifiers place (possibly complex) input data into one of a relatively small number of output categories. In this paper, we study the structure of the boundary--those points for which a neighbor is classified differently--in the context of an input space that is a graph, so that there is a concept of neighboring inputs, The scientific setting is a model-based naive Bayes classifier for DNA reads produced by Next Generation Sequencers. We show that the boundary is both large and complicated in structure. We create a new measure of uncertainty, called Neighbor Similarity, that compares the result for a point to the distribution of results for its neighbors. This measure not only tracks two inherent uncertainty measures for the Bayes classifier, but also can be implemented, at a computational cost, for classifiers without inherent measures of uncertainty.
Large language models (LLMs) have revolutionized natural language processing (NLP) by excelling at understanding and generating human-like text. However, their widespread deployment can be prohibitively expensive. SortedNet is a recent training technique for enabling dynamic inference by leveraging the modularity in networks and sorting sub-models based on computation/accuracy in a nested manner. We extend SortedNet to generative NLP tasks, making large language models dynamic without any Pre-Training and by only replacing Standard Fine-Tuning (SFT) with Sorted Fine-Tuning (SoFT). Our approach boosts model efficiency, eliminating the need for multiple models for various scenarios during inference. We show that this approach can unlock the power of intermediate layers of transformers in generating the target output. Our sub-models remain integral components of the original model, minimizing storage requirements and transition costs between different computational/latency budgets. The efficacy of our proposed method was demonstrated by applying it to tune LLaMA 2 13B on the Stanford Alpaca dataset for instruction following and TriviaQA for closed-book question answering. Our results show the superior performance of sub-models in comparison to Standard Fine-Tuning and SFT+ICT (Early-Exit), all achieved with efficient tuning and without additional memory usage during inference.
In fair division of a connected graph $G = (V, E)$, each of $n$ agents receives a share of $G$'s vertex set $V$. These shares partition $V$, with each share required to induce a connected subgraph. Agents use their own valuation functions to determine the non-negative numerical values of the shares, which determine whether the allocation is fair in some specified sense. We introduce forbidden substructures called graph cutsets, which block divisions that are fair in the EF1 (envy-free up to one item) sense by cutting the graph into "too many pieces". Two parameters - gap and valence - determine blocked values of $n$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations that are CA (common and additive), then $G$ contains no elementary cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. If $G$ guarantees connected EF1 allocations for $n$ agents with valuations in the broader CM (common and monotone) class, then $G$ contains no cutset of gap $k \ge 2$ and valence in the interval $\[n - k + 1, n - 1\]$. These results rule out the existence of connected EF1 allocations in a variety of situations. For some graphs $G$ we can, with help from some new positive results, pin down $G$'s spectrum - the list of exactly which values of $n$ do/do not guarantee connected EF1 allocations. Examples suggest a conjectured common spectral pattern for all graphs. Further, we show that it is NP-hard to determine whether a graph admits a cutset. We also provide an example of a (non-traceable) graph on eight vertices that has no cutsets of gap $\ge 2$ at all, yet fails to guarantee connected EF1 allocations for three agents with CA preferences.
Referring expression segmentation (RES), a task that involves localizing specific instance-level objects based on free-form linguistic descriptions, has emerged as a crucial frontier in human-AI interaction. It demands an intricate understanding of both visual and textual contexts and often requires extensive training data. This paper introduces RESMatch, the first semi-supervised learning (SSL) approach for RES, aimed at reducing reliance on exhaustive data annotation. Extensive validation on multiple RES datasets demonstrates that RESMatch significantly outperforms baseline approaches, establishing a new state-of-the-art. Although existing SSL techniques are effective in image segmentation, we find that they fall short in RES. Facing the challenges including the comprehension of free-form linguistic descriptions and the variability in object attributes, RESMatch introduces a trifecta of adaptations: revised strong perturbation, text augmentation, and adjustments for pseudo-label quality and strong-weak supervision. This pioneering work lays the groundwork for future research in semi-supervised learning for referring expression segmentation.
The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the input is a vertex-weighted tree, as a measure of average/expected search length in a partially ordered set. The EPT-sum of a graph $G$ is defined as the minimum sum of the depth of every leaf in an edge partition tree (EPT), a rooted tree where leaves correspond to vertices in $G$ and internal nodes correspond to edges in $G$. A simple algorithm that approximates EPT-sum on trees is given by recursively choosing the most balanced edge in the input tree $G$ to build an EPT of $G$. Due to its fast runtime, this balanced cut algorithm is used in practice. In this paper, we show that the balanced cut algorithm gives a 1.5-approximation of EPT-sum on trees, which amounts to a tight analysis and answers a question posed by Cicalese et al. in 2014.
A graph $G=(V,E)$ is said to be distance magic if there is a bijection $f$ from a vertex set of $G$ to the first $|V(G)|$ natural numbers such that for each vertex $v$, its weight given by $\sum_{u \in N(v)}f(u)$ is constant, where $N(v)$ is an open neighborhood of a vertex $v$. In this paper, we introduce the concept of $p$-distance magic labeling and establish the necessary and sufficient condition for a graph to be distance magic. Additionally, we introduce necessary and sufficient conditions for a connected regular graph to exhibit distance magic properties in terms of the eigenvalues of its adjacency and Laplacian matrices. Furthermore, we study the spectra of distance magic graphs, focusing on singular distance magic graphs. Also, we show that the number of distance magic labelings of a graph is, at most, the size of its automorphism group.
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have substantial overlap with the true groundstate -- is BQP-complete for $k \geq 6$ when the required precision is inverse polynomial in the system size $n$, and remains hard even when the overlap of the guiding state with the groundstate is close to a constant $\left(\frac12 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)\right)$. We improve upon this result in three ways: by showing that it remains BQP-complete when i) the Hamiltonian is 2-local, ii) the overlap between the guiding state and target eigenstate is as large as $1 - \Omega\left(\frac{1}{\mathop{poly}(n)}\right)$, and iii) when one is interested in estimating energies of excited states, rather than just the groundstate. Interestingly, iii) is only made possible by first showing that ii) holds.
Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering and recommendation systems, etc. According to the graph types, the existing KGR models can be roughly divided into three categories, \textit{i.e.,} static models, temporal models, and multi-modal models. The early works in this domain mainly focus on static KGR and tend to directly apply general knowledge graph embedding models to the reasoning task. However, these models are not suitable for more complex but practical tasks, such as inductive static KGR, temporal KGR, and multi-modal KGR. To this end, multiple works have been developed recently, but no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the preliminaries, summaries of KGR models, and typical datasets are introduced and discussed consequently. Moreover, we discuss the challenges and potential opportunities. The corresponding open-source repository is shared on GitHub: //github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.
Visual dialogue is a challenging task that needs to extract implicit information from both visual (image) and textual (dialogue history) contexts. Classical approaches pay more attention to the integration of the current question, vision knowledge and text knowledge, despising the heterogeneous semantic gaps between the cross-modal information. In the meantime, the concatenation operation has become de-facto standard to the cross-modal information fusion, which has a limited ability in information retrieval. In this paper, we propose a novel Knowledge-Bridge Graph Network (KBGN) model by using graph to bridge the cross-modal semantic relations between vision and text knowledge in fine granularity, as well as retrieving required knowledge via an adaptive information selection mode. Moreover, the reasoning clues for visual dialogue can be clearly drawn from intra-modal entities and inter-modal bridges. Experimental results on VisDial v1.0 and VisDial-Q datasets demonstrate that our model outperforms exiting models with state-of-the-art results.
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