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In this paper, we suggest new SAT encodings of the partial-ordering based ILP model for the graph coloring problem (GCP) and the bandwidth coloring problem (BCP). The GCP asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. The BCP is a generalization, where each edge has a weight that enforces a minimal "distance" between the assigned colors, and the goal is to minimize the "largest" color used. For the widely studied GCP, we experimentally compare our new SAT encoding to the state-of-the-art approaches on the DIMACS benchmark set. Our evaluation confirms that this SAT encoding is effective for sparse graphs and even outperforms the state-of-the-art on some DIMACS instances. For the BCP, our theoretical analysis shows that the partial-ordering based SAT and ILP formulations have an asymptotically smaller size than that of the classical assignment-based model. Our practical evaluation confirms not only a dominance compared to the assignment-based encodings but also to the state-of-the-art approaches on a set of benchmark instances. Up to our knowledge, we have solved several open instances of the BCP from the literature for the first time.

In this paper, we propose a new hybrid temporal computing (HTC) framework that leverages both pulse rate and temporal data encoding to design ultra-low energy hardware accelerators. Our approach is inspired by the recently proposed temporal computing, or race logic, which encodes data values as single delays, leading to significantly lower energy consumption due to minimized signal switching. However, race logic is limited in its applications due to inherent restrictions. The new HTC framework overcomes these limitations by encoding signals in both temporal and pulse rate formats for multiplication and in temporal format for propagation. This approach maintains reduced switch energy while being general enough to implement a wide range of arithmetic operations. We demonstrate how HTC multiplication is performed for both unipolar and bipolar data encoding and present the basic designs for multipliers, adders, and MAC units. Additionally, we implement two hardware accelerators: a Finite Impulse Response (FIR) filter and a Discrete Cosine Transform (DCT)/iDCT engine for image compression and DSP applications. Experimental results show that the HTC MAC has a significantly smaller power and area footprint compared to the Unary MAC design and is orders of magnitude faster. Compared to the CBSC MAC, the HTC MAC reduces power consumption by $45.2\%$ and area footprint by $50.13\%$. For the FIR design, the HTC design significantly outperforms the Unary design on all metrics. Compared to the CBSC design, the HTC-based FIR filter reduces power consumption by $36.61\%$ and area cost by $45.85\%$. The HTC-based DCT filter retains the quality of the original image with a decent PSNR, while consuming $23.34\%$ less power and occupying $18.20\%$ less area than the CBSC MAC-based DCT filter.

In this paper, we delve into the computations performed at a node within a message-passing algorithm. We investigate low complexity/latency multi-input structures that can be adopted by the node for computing outgoing messages y = (y1, y2, . . . , yn) from incoming messages x = (x1, x2, . . . , xn), where each yj , j = 1, 2, . . . , n is computed via a multi-way tree with leaves x excluding xj . Specifically, we propose two classes of structures for different scenarios. For the scenario where complexity has a higher priority than latency, the star-tree-based structures are proposed. The complexity-optimal ones (as well as their lowest latency) of such structures are obtained, which have the near-lowest (and sometimes the lowest) complexity among all structures. For the scenario where latency has a higher priority than complexity, the isomorphic-directed-rooted-tree-based structures are proposed. The latency-optimal ones (as well as their lowest complexity) of such structures are obtained, which are proved to have the lowest latency among all structures.

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.

In this paper, we investigate the potential of image-to-image translation (I2I) techniques for transferring realism to 3D-rendered facial images in the context of Face Recognition (FR) systems. The primary motivation for using 3D-rendered facial images lies in their ability to circumvent the challenges associated with collecting large real face datasets for training FR systems. These images are generated entirely by 3D rendering engines, facilitating the generation of synthetic identities. However, it has been observed that FR systems trained on such synthetic datasets underperform when compared to those trained on real datasets, on various FR benchmarks. In this work, we demonstrate that by transferring the realism to 3D-rendered images (i.e., making the 3D-rendered images look more real), we can boost the performance of FR systems trained on these more photorealistic images. This improvement is evident when these systems are evaluated against FR benchmarks utilizing real-world data, thereby paving new pathways for employing synthetic data in real-world applications.

In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance prediction, dimension reduction, and creating data-driven parameterisations, respectively. However, as both the input and output streams of these models consist of low-level shape representations, they often fail to capture shape characteristics essential for performance analyses. Therefore, the proposed GOs exploit the differential and integral properties of shapes--accessed through Fourier descriptors, curvature integrals, geometric moments, and their invariants--to infuse high-level intrinsic geometric information and physics into the feature vector used for training, even when employing simple model architectures or low-level parametric descriptions. We showed that for surrogate modelling, along with the inclusion of the notion of physics, GOs enact regularisation to reduce over-fitting and enhance generalisation to new, unseen designs. Furthermore, through extensive experimentation, we demonstrate that for dimension reduction and generative models, incorporating the proposed GOs enriches the training data with compact global and local geometric features. This significantly enhances the quality of the resulting latent space, thereby facilitating the generation of valid and diverse designs. Lastly, we also show that GOs can enable learning parametric sensitivities to a great extent. Consequently, these enhancements accelerate the convergence rate of shape optimisers towards optimal solutions.

In this paper we consider contamination by code generation test sets, in particular in their use in modern large language models. We discuss three possible sources of such contamination and show findings supporting each of them: (i) direct data leakage, (ii) indirect data leakage through the use of synthetic data and (iii) overfitting to evaluation sets during model selection. Key to our findings is a new dataset of 161 prompts with their associated python solutions, dataset which is released at //huggingface.co/datasets/CohereForAI/lbpp .

In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that, for any $\epsilon>0$ and positive integers $n$ and $k$, with high probability, random Reed--Solomon codes of length $n$ and dimension $k$ can correct $(1-\varepsilon)n-2k+1$ adversarial insdel errors over alphabets of size $n+2^{\mathsf{poly}(1/\varepsilon)}k$. This significantly improves upon the alphabet size demonstrated in the work of Con, Shpilka, and Tamo (IEEE TIT, 2023), who showed the existence of Reed--Solomon codes with exponential alphabet size $\widetilde O\left(\binom{n}{2k-1}^2\right)$ precisely achieving the half-Singleton bound. Our methods are inspired by recent works on list-decoding Reed-Solomon codes. Brakensiek-Gopi-Makam (STOC 2023) showed that random Reed-Solomon codes are list-decodable up to capacity with exponential-sized alphabets, and Guo-Zhang (FOCS 2023) and Alrabiah-Guruswami-Li (STOC 2024) improved the alphabet-size to linear. We achieve a similar alphabet-size reduction by similarly establishing strong bounds on the probability that certain random rectangular matrices are full rank. To accomplish this in our insdel context, our proof combines the random matrix techniques from list-decoding with structural properties of Longest Common Subsequences.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.