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This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…
We introduce a compressed representation of sets of sets that exploits how much they differ from each other. Our representation supports access, membership, predecessor and successor queries on the sets within logarithmic time. In addition,…
Instruction following is one of the fundamental capabilities of large language models (LLMs). As the ability of LLMs is constantly improving, they have been increasingly applied to deal with complex human instructions in real-world…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Recent work shows Large Language Models (LLMs) struggle to understand natural language constraints for various text generation tasks in zero- and few-shot settings. While, in the code domain, there is wide usage of constraints in code…
Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction…
The ability to follow instructions is crucial for Large Language Models (LLMs) to handle various real-world applications. Existing benchmarks primarily focus on evaluating pure response quality, rather than assessing whether the response…
In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…
Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated…
We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study…
It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…
Large language models (LLMs) are increasingly expected to tackle complex tasks, driven by their expanding applications and users' growing proficiency in crafting sophisticated prompts. However, as the number of explicitly stated…
High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse…
Streaming video understanding with large vision-language models (VLMs) requires a compact memory that can support future reasoning over an ever-growing visual history. A common solution is to compress the key-value (KV) cache, but existing…
Large language models (LLMs) are commonly trained on datasets consisting of fixed-length token sequences. These datasets are created by randomly concatenating documents of various lengths and then chunking them into sequences of a…
Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…
Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…
Large language models (LLMs) have shown remarkable capabilities across various tasks, that are learned from massive amounts of text-based data. Although LLMs can control output sequence length, particularly in instruction-based settings,…