The encounter of artificial intelligence with consciousness research is often framed as a challenge: could this science determine whether such systems are conscious? We suggest it is equally an opportunity to expand and test the scope of existing theories of consciousness. Current approaches remain polarized. Computational functionalism emphasizes abstract organization, often realized through neural correlates of consciousness, while biological naturalism insists that consciousness is tied to living embodiment. Both positions risk anthropocentrism and limit the possibility of recognizing non-biological forms of subjectivity. To move beyond this impasse, we propose a dual-resolution framework that defines the ontological and epistemic conditions for consciousness. This approach combines the Information Theory of Individuality, which defines the ontological conditions of informational autonomy and self-maintenance, with the Moment-to-Moment theory, which specifies the epistemic conditions of temporal updating and phenomenological unfolding. This integration reframes consciousness as the epistemic expression of individuated systems in substrate-independent informational terms, offering a generalizable theory of consciousness and positioning AI as a promising testbed for its emergence.

Generative large language models (LLMs) have become central to everyday life, producing human-like text across diverse domains. A growing body of research investigates whether these models also exhibit personality- and demographic-like characteristics in their language. In this work, we introduce a novel, data-driven methodology for assessing LLM personality without relying on self-report questionnaires, applying instead automatic personality and gender classifiers to model replies on open-ended questions collected from Reddit. Comparing six widely used models to human-authored responses, we find that LLMs systematically express higher Agreeableness and lower Neuroticism, reflecting cooperative and stable conversational tendencies. Gendered language patterns in model text broadly resemble those of human writers, though with reduced variation, echoing prior findings on automated agents. We contribute a new dataset of human and model responses, along with large-scale comparative analyses, shedding new light on the topic of personality and demographic patterns of generative AI.

Explainable AI (XAI) methods typically focus on identifying essential input features or more abstract concepts for tasks like image or text classification. However, for algorithmic tasks like combinatorial optimization, these concepts may depend not only on the input but also on the current state of the network, like in the graph neural networks (GNN) case. This work studies concept learning for an existing GNN model trained to solve Boolean satisfiability (SAT). \textcolor{black}{Our analysis reveals that the model learns key concepts matching those guiding human-designed SAT heuristics, particularly the notion of 'support.' We demonstrate that these concepts are encoded in the top principal components (PCs) of the embedding's covariance matrix, allowing for unsupervised discovery. Using sparse PCA, we establish the minimality of these concepts and show their teachability through a simplified GNN. Two direct applications of our framework are (a) We improve the convergence time of the classical WalkSAT algorithm and (b) We use the discovered concepts to "reverse-engineer" the black-box GNN and rewrite it as a white-box textbook algorithm. Our results highlight the potential of concept learning in understanding and enhancing algorithmic neural networks for combinatorial optimization tasks.

The Kneser graph $K(n,k)$ is defined for integers $n$ and $k$ with $n \geq 2k$ as the graph whose vertices are all the $k$-subsets of $\{1,2,\ldots,n\}$ where two such sets are adjacent if they are disjoint. A classical result of Lovász asserts that the chromatic number of $K(n,k)$ is $n-2k+2$. In the computational Kneser problem, we are given an oracle access to a coloring of the vertices of $K(n,k)$ with $n-2k+1$ colors, and the goal is to find a monochromatic edge. We present a randomized algorithm for the Kneser problem with running time $n^{O(1)} \cdot k^{O(k)}$. This shows that the problem is fixed-parameter tractable with respect to the parameter $k$. The analysis involves structural results on intersecting families and on induced subgraphs of Kneser graphs. We also study the Agreeable-Set problem of assigning a small subset of a set of $m$ items to a group of $\ell$ agents, so that all agents value the subset at least as much as its complement. As an application of our algorithm for the Kneser problem, we obtain a randomized polynomial-time algorithm for the Agreeable-Set problem for instances that satisfy $\ell \geq m - O(\frac{\log m}{\log \log m})$. We further show that the Agreeable-Set problem is at least as hard as a variant of the Kneser problem with an extended access to the input coloring.

Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another, while the latter specifically quantifies the number of insertions and deletions. Many algorithmic solutions explicitly address one of these measures, and frequently techniques applicable to one can also be adapted to work with the other. In this paper, we investigate whether there exists a standardized approach for applying results from one setting to another. Specifically, we demonstrate the capability to reduce questions regarding string similarity over arbitrary alphabets to equivalent questions over a binary alphabet. Furthermore, we illustrate how to transform questions concerning indel distance into equivalent questions based on edit distance. This complements an earlier result of Tiskin (2007) which addresses the inverse direction.

Harary and Lauri conjectured that the class reconstruction number of trees is 2, that is, each tree has two unlabelled vertex-deleted subtrees that are not both in the deck of any other tree. We show that each tree $T$ can be reconstructed up to isomorphism given two of its unlabelled subgraphs $T-u$ and $T-v$ under the assumption that $u$ and $v$ are chosen in a particular way. Our result does not completely resolve the conjecture of Harary and Lauri since the special property defining $u$ and $v$ cannot be recognised from the given subtrees $T-u$ and $T-v$.

We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the adaptive query model, recently proposed for the greedy forward selection for submodular functions, to the faster paradigm of Orthogonal Matching Pursuit for non-submodular functions. The proposed algorithm achieves exponentially fast parallel run time in the adaptive query model, scaling much better than prior work. Furthermore, our extension allows the use of downward-closed constraints, which can be used to encode certain fairness criteria into the feature selection process. We prove strong approximation guarantees for the algorithm based on standard assumptions. These guarantees are applicable to many parametric models, including Generalized Linear Models. Finally, we demonstrate empirically that the proposed algorithm competes favorably with state-of-the-art techniques for feature selection, on real-world and synthetic datasets.

Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.

We initiate the study of the binary and Boolean rank of $0,1$ matrices that have a small rank over the reals. The relationship between these three rank functions is an important open question, and here we prove that when the real rank $d$ is a small constant, the gap between the real and the binary and Boolean rank is a small constant. We give tight upper and lower bounds on the Boolean and binary rank of matrices with real rank $1 \leq d \leq 4$, as well as determine the size of the maximal isolation set in each case. Furthermore, we prove that for $d = 3,4$, the circulant matrix defined by a row with $d-1$ consecutive ones followed by $d-1$ zeros, is the only matrix of size $(2d-2)\times (2d-2)$ with real rank $d$ and Boolean and binary rank and maximal isolation set of size $2d-2$, and this matrix achieves the maximal gap possible between the real and the binary and Boolean rank for these values of $d$. Our results can also be interpreted in other equivalent terms, such as finding the minimal number of bicliques needed to partition or cover the edges of a bipartite graph whose reduced adjacency matrix has real rank $1 \leq d \leq 4$. We use a combination of combinatorial and algebraic techniques combined with the assistance of a computer program.

The minrank over a field $\mathbb{F}$ of a graph $G$ on the vertex set $\{1,2,\ldots,n\}$ is the minimum possible rank of a matrix $M \in \mathbb{F}^{n \times n}$ such that $M_{i,i} \neq 0$ for every $i$, and $M_{i,j}=0$ for every distinct non-adjacent vertices $i$ and $j$ in $G$. For an integer $n$, a graph $H$, and a field $\mathbb{F}$, let $g(n,H,\mathbb{F})$ denote the maximum possible minrank over $\mathbb{F}$ of an $n$-vertex graph whose complement contains no copy of $H$. In this paper we study this quantity for various graphs $H$ and fields $\mathbb{F}$. For finite fields, we prove by a probabilistic argument a general lower bound on $g(n,H,\mathbb{F})$, which yields a nearly tight bound of $\Omega(\sqrt{n}/\log n)$ for the triangle $H=K_3$. For the real field, we prove by an explicit construction that for every non-bipartite graph $H$, $g(n,H,\mathbb{R}) \geq n^\delta$ for some $\delta = \delta(H)>0$. As a by-product of this construction, we disprove a conjecture of Codenotti, Pudlák, and Resta. The results are motivated by questions in information theory, circuit complexity, and geometry.

We present a novel approach to automating the identification of risk factors for diseases from medical literature, leveraging pre-trained models in the bio-medical domain, while tuning them for the specific task. Faced with the challenges of the diverse and unstructured nature of medical articles, our study introduces a multi-step system to first identify relevant articles, then classify them based on the presence of risk factor discussions and, finally, extract specific risk factor information for a disease through a question-answering model. Our contributions include the development of a comprehensive pipeline for the automated extraction of risk factors and the compilation of several datasets, which can serve as valuable resources for further research in this area. These datasets encompass a wide range of diseases, as well as their associated risk factors, meticulously identified and validated through a fine-grained evaluation scheme. We conducted both automatic and thorough manual evaluation, demonstrating encouraging results. We also highlight the importance of improving models and expanding dataset comprehensiveness to keep pace with the rapidly evolving field of medical research.

The minrank over a field $\mathbb{F}$ of a graph $G$ on the vertex set $\{1,2,\ldots,n\}$ is the minimum possible rank of a matrix $M \in \mathbb{F}^{n \times n}$ such that $M_{i,i} \neq 0$ for every $i$, and $M_{i,j}=0$ for every distinct non-adjacent vertices $i$ and $j$ in $G$. For an integer $n$, a graph $H$, and a field $\mathbb{F}$, let $g(n,H,\mathbb{F})$ denote the maximum possible minrank over $\mathbb{F}$ of an $n$-vertex graph whose complement contains no copy of $H$. In this paper we study this quantity for various graphs $H$ and fields $\mathbb{F}$. For finite fields, we prove by a probabilistic argument a general lower bound on $g(n,H,\mathbb{F})$, which yields a nearly tight bound of $\Omega(\sqrt{n}/\log n)$ for the triangle $H=K_3$. For the real field, we prove by an explicit construction that for every non-bipartite graph $H$, $g(n,H,\mathbb{R}) \geq n^\delta$ for some $\delta = \delta(H)>0$. As a by-product of this construction, we disprove a conjecture of Codenotti, Pudlák, and Resta. The results are motivated by questions in information theory, circuit complexity, and geometry.

A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$and parameters$k$and$d$, we prove a strong upper bound on the number of $k$-Fourier-sparse Boolean functions that disagree with $f$ on at most $d$ inputs. Our bound implies that the number of uniform and independent random samples needed for learning the class of $k$-Fourier-sparse Boolean functions on $n$ variables exactly is at most $O(n \cdot k \log k)$. As an application, we prove an upper bound on the query complexity of testing Booleanity of Fourier-sparse functions. Our bound is tight up to a logarithmic factor and quadratically improves on a result due to Gur and Tamuz (Chicago J. Theor. Comput. Sci., 2013).

The edit distance is a way of quantifying how similar two strings are to one another by counting the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. A simple dynamic programming computes the edit distance between two strings of length $n$ in $O(n^2)$ time, and a more sophisticated algorithm runs in time $O(n+t^2)$ when the edit distance is $t$ [Landau, Myers and Schmidt, SICOMP 1998]. In pursuit of obtaining faster running time, the last couple of decades have seen a flurry of research on approximating edit distance, including polylogarithmic approximation in near-linear time [Andoni, Krauthgamer and Onak, FOCS 2010], and a constant-factor approximation in subquadratic time [Chakrabarty, Das, Goldenberg, Kouck\'y and Saks, FOCS 2018]. We study sublinear-time algorithms for small edit distance, which was investigated extensively because of its numerous applications. Our main result is an algorithm for distinguishing whether the edit distance is at most $t$ or at least $t^2$ (the quadratic gap problem) in time $\tilde{O}(\frac{n}{t}+t^3)$. This time bound is sublinear roughly for all $t$ in $[\omega(1), o(n^{1/3})]$, which was not known before. The best previous algorithms solve this problem in sublinear time only for $t=\omega(n^{1/3})$ [Andoni and Onak, STOC 2009]. Our algorithm is based on a new approach that adaptively switches between uniform sampling and reading contiguous blocks of the input strings. In contrast, all previous algorithms choose which coordinates to query non-adaptively. Moreover, it can be extended to solve the $t$ vs $t^{2-\epsilon}$ gap problem in time $\tilde{O}(\frac{n}{t^{1-\epsilon}}+t^3)$.

Factuality assesses the extent to which a language utterance relates to real-world information; it determines whether utterances correspond to facts, possibilities, or imaginary situations, and as such, it is instrumental for fact checking. Factuality is a complex notion that relies on multiple linguistic signals, and has been studied in various disciplines. We present a complex, multi-faceted annotation scheme of factuality that combines concepts from a variety of previous works. We developed the scheme for Hebrew, but we trust that it can be adapted to other languages. We also present a set of almost 5,000 sentences in the domain of parliamentary discourse that we manually annotated according to this scheme. We report on inter-annotator agreement, and experiment with various approaches to automatically predict (some features of) the scheme, in order to extend the annotation to a large corpus.

We study the problem of approximating edit distance in sublinear time. This is formalized as the $(k,k^c)$-Gap Edit Distance problem, where the input is a pair of strings $X,Y$ and parameters k,c&gt;1, and the goal is to return YES if $ED(X,Y)\leq k$, NO if ED(X,Y)&gt; k^c, and an arbitrary answer when $k < ED(X,Y) \le k^c$. Recent years have witnessed significant interest in designing sublinear-time algorithms for Gap Edit Distance. In this work, we resolve the non-adaptive query complexity of Gap Edit Distance for the entire range of parameters, improving over a sequence of previous results. Specifically, we design a non-adaptive algorithm with query complexity $\tilde{O}(n/k^{c-0.5})$, and we further prove that this bound is optimal up to polylogarithmic factors. Our algorithm also achieves optimal time complexity $\tilde{O}(n/k^{c-0.5})$ whenever $c\geq 1.5$. For $1

We present the Knesset Corpus, a corpus of Hebrew parliamentary proceedings containing over 30 million sentences (over 384 million tokens) from all the (plenary and committee) protocols held in the Israeli parliament between 1998 and 2022. Sentences are annotated with morpho-syntactic information and are associated with detailed meta-information reflecting demographic and political properties of the speakers, based on a large database of parliament members and factions that we compiled. We discuss the structure and composition of the corpus and the various processing steps we applied to it. To demonstrate the utility of this novel dataset we present two use cases. We show that the corpus can be used to examine historical developments in the style of political discussions by showing a reduction in lexical richness in the proceedings over time. We also investigate some differences between the styles of men and women speakers. These use cases exemplify the potential of the corpus to shed light on important trends in the Israeli society, supporting research in linguistics, political science, communication, law, etc.

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic programming algorithm that runs in quadratic time. Andoni, Krauthgamer, and Onak (2010) gave a nearly linear time algorithm that approximates edit distance within an approximation factor $\text{poly}(\log n)$. In this paper, we provide an algorithm with running time $\tilde{O}(n^{2-2/7})$ that approximates the edit distance within a constant factor.

We show that the Consensus Division theorem implies lower bounds on the chromatic number of Kneser hypergraphs, offering a novel proof for a result of Alon, Frankl, and Lovász (Trans. Amer. Math. Soc., 1986) and for its generalization by Kř\'ıž (Trans. Amer. Math. Soc., 1992). Our approach is applied to study the computational complexity of the total search problem Kneser$^p$, which given a succinct representation of a coloring of a $p$-uniform Kneser hypergraph with fewer colors than its chromatic number, asks to find a monochromatic hyperedge. We prove that for every prime $p$, the Kneser$^p$ problem with an extended access to the input coloring is efficiently reducible to a quite weak approximation of the Consensus Division problem with $p$ shares. In particular, for $p=2$, the problem is efficiently reducible to any non-trivial approximation of the Consensus Halving problem on normalized monotone functions. We further show that for every prime $p$, the Kneser$^p$ problem lies in the complexity class $\mathsf{PPA}$-$p$. As an application, we establish limitations on the complexity of the Kneser$^p$ problem, restricted to colorings with a bounded number of colors.

The Nystr\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of square matrices. We take as an input a matrix $M\in \mathbb{R}^{m\times n}$, a user defined integer$s\leq min(m,n)$and$A_M \in \mathbb{R}^{s\times s}$, a matrix sampled from the columns and rows of$M$. These are used to construct an approximate rank-$s$ SVD of $M$ in $O\left(s^2\left(m+n\right)\right)$ operations. If $M$ is square, the rank-$s$ EVD can be similarly constructed in $O\left(s^2 n\right)$ operations. Thus, the matrix $A_M$ is a compressed version of $M$. We discuss the choice of $A_M$ and propose an algorithm that selects a good initial sample for a pivoted version of $M$. The proposed algorithm performs well for general matrices and kernel matrices whose spectra exhibit fast decay.