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Despite the efficacy of graph-based algorithms for Approximate Nearest Neighbor (ANN) searches, the optimal tuning of such systems remains unclear. This study introduces a method to tune the performance of off-the-shelf graph-based indexes, focusing on the dimension of vectors, database size, and entry points of graph traversal. We utilize a black-box optimization algorithm to perform integrated tuning to meet the required levels of recall and Queries Per Second (QPS). We applied our approach to Task A of the SISAP 2023 Indexing Challenge and got second place in the 10M and 30M tracks. It improves performance substantially compared to brute force methods. This research offers a universally applicable tuning method for graph-based indexes, extending beyond the specific conditions of the competition to broader uses.

Whilst contrastive learning yields powerful representations by matching different augmented views of the same instance, it lacks the ability to capture the similarities between different instances. One popular way to address this limitation is by learning global features (after the global pooling) to capture inter-instance relationships based on knowledge distillation, where the global features of the teacher are used to guide the learning of the global features of the student. Inspired by cross-modality learning, we extend this existing framework that only learns from global features by encouraging the global features and intermediate layer features to learn from each other. This leads to our novel self-supervised framework: cross-context learning between global and hypercolumn features (CGH), that enforces the consistency of instance relations between low- and high-level semantics. Specifically, we stack the intermediate feature maps to construct a hypercolumn representation so that we can measure instance relations using two contexts (hypercolumn and global feature) separately, and then use the relations of one context to guide the learning of the other. This cross-context learning allows the model to learn from the differences between the two contexts. The experimental results on linear classification and downstream tasks show that our method outperforms the state-of-the-art methods.

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper addresses this computational challenge through the development of a novel generalised Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalised posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant. The statistical properties of the generalised posterior are analysed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalised posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalised Bayesian inference at low computational cost.

In randomized experiments, the classic stable unit treatment value assumption (SUTVA) states that the outcome for one experimental unit does not depend on the treatment assigned to other units. However, the SUTVA assumption is often violated in applications such as online marketplaces and social networks where units interfere with each other. We consider the estimation of the average treatment effect in a network interference model using a mixed randomization design that combines two commonly used experimental methods: Bernoulli randomized design, where treatment is independently assigned for each individual unit, and cluster-based design, where treatment is assigned at an aggregate level. Essentially, a mixed randomization experiment runs these two designs simultaneously, allowing it to better measure the effect of network interference. We propose an unbiased estimator for the average treatment effect under the mixed design and show the variance of the estimator is bounded by $O({d^2}n^{-1}p^{-1})$ where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the probability of treatment. We also establish a lower bound of $\Omega(d^{1.5}n^{-1}p^{-1})$ for the variance of any mixed design. For a family of sparse networks characterized by a growth constant $\kappa \leq d$, we improve the upper bound to $O({\kappa^7 d}n^{-1}p^{-1})$. Furthermore, when interference weights on the edges of the network are unknown, we propose a weight-invariant design that achieves a variance bound of $O({d^3}n^{-1}p^{-1})$.

Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, an important tool for simulating quantum circuits in the tractable regime. We first show that although DDs were suggested to succinctly represent important quantum states, they actually require exponential space for certain stabilizer states. To remedy this, we introduce a more powerful decision diagram variant, called Local Invertible Map-DD (LIMDD). We prove that the set of quantum states represented by poly-sized LIMDDs strictly contains the union of stabilizer states and other decision diagram variants. Finally, there exist circuits which LIMDDs can efficiently simulate, while their output states cannot be succinctly represented by two state-of-the-art simulation paradigms: the stabilizer decomposition techniques for Clifford + $T$ circuits and Matrix-Product States. By uniting two successful approaches, LIMDDs thus pave the way for fundamentally more powerful solutions for simulation and analysis of quantum computing.

We study methods to manipulate weights in stress-graph embeddings to improve convex straight-line planar drawings of 3-connected planar graphs. Stress-graph embeddings are weighted versions of Tutte embeddings, where solving a linear system places vertices at a minimum-energy configuration for a system of springs. A major drawback of the unweighted Tutte embedding is that it often results in drawings with exponential area. We present a number of approaches for choosing better weights. One approach constructs weights (in linear time) that uniformly spread all vertices in a chosen direction, such as parallel to the $x$- or $y$-axis. A second approach morphs $x$- and $y$-spread drawings to produce a more aesthetically pleasing and uncluttered drawing. We further explore a "kaleidoscope" paradigm for this $xy$-morph approach, where we rotate the coordinate axes so as to find the best spreads and morphs. A third approach chooses the weight of each edge according to its depth in a spanning tree rooted at the outer vertices, such as a Schnyder wood or BFS tree, in order to pull vertices closer to the boundary.

Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are hard to decode efficiently. This motivated several previous works to study the problem of partially derandomizing RLCs, by applying certain operations to an explicit mother code. Among them, one of the most well studied operations is random puncturing, where a series of works culminated in the work of Guruswami and Mosheiff (FOCS' 22), which showed that a random puncturing of a low-biased code is likely to possess almost all interesting local properties of RLCs. In this work, we provide an in-depth study of another, dual operation of random puncturing, known as random shortening, which can be viewed equivalently as random puncturing on the dual code. Our main results show that for any small $\varepsilon$, by starting from a mother code with certain weaker conditions (e.g., having a large distance) and performing a random (or even pseudorandom) shortening, the new code is $\varepsilon$-biased with high probability. Our results hold for any field size and yield a shortened code with constant rate. This can be viewed as a complement to random puncturing, and together, we can obtain codes with properties like RLCs from weaker initial conditions. Our proofs involve several non-trivial methods of estimating the weight distribution of codewords, which may be of independent interest.

Unstructured meshes are characterized by data points irregularly distributed in the Euclidian space. Due to the irregular nature of these data, computing connectivity information between the mesh elements requires much more time and memory than on uniformly distributed data. To lower storage costs, dynamic data structures have been proposed. These data structures compute connectivity information on the fly and discard them when no longer needed. However, on-the-fly computation slows down algorithms and results in a negative impact on the time performance. To address this issue, we propose a new task-parallel approach to proactively compute mesh connectivity. Unlike previous approaches implementing data-parallel models, where all threads run the same type of instructions, our task-parallel approach allows threads to run different functions. Specifically, some threads run the algorithm of choice while other threads compute connectivity information before they are actually needed. The approach was implemented in the new Accelerated Clustered TOPOlogical (ACTOPO) data structure, which can support any processing algorithm requiring mesh connectivity information. Our experiments show that ACTOPO combines the benefits of state-of-the-art memory-efficient (TTK CompactTriangulation) and time-efficient (TTK ExplicitTriangulation) topological data structures. It occupies a similar amount of memory as TTK CompactTriangulation while providing up to 5x speedup. Moreover, it achieves comparable time performance as TTK ExplicitTriangulation while using only half of the memory space.

Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.