Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning.

It is an open question whether the search and decision versions of promise CSPs are equivalent. Most known algorithms for PCSPs solve only their \emph{decision} variant, and it is unknown whether they can be adapted to solve \emph{search} as well. The main approaches, called BLP, AIP and BLP+AIP, handle a PCSP by finding a solution to a relaxation of some integer program. We prove that rounding those solutions to a proper search certificate can be as hard as any problem in the class TFNP. In other words, these algorithms are ineffective for search. Building on the algebraic approach to PCSPs, we find sufficient conditions that imply ineffectiveness for search. Our tools are tailored to algorithms that are characterized by minions in a suitable way, and can also be used to prove undecidability results for meta-problems. This way, we show that the families of templates solvable via BLP, AIP, and BLP+AIP are undecidable. Using the same techniques we also analyze several algebraic conditions that are known to guarantee the tractability of finite-template CSPs. We prove that several meta-problems related to cyclic polymorphims and WNUs are undecidable for PCSPs. In particular, there is no algorithm deciding whether a finite PCSP template (1) admits cyclic a polymorphism, (2) admits a WNU.

Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by retrieving relevant documents from external sources to improve factual accuracy and verifiability. However, this reliance introduces new attack surfaces within the retrieval pipeline, beyond the LLM itself. While prior RAG attacks have exposed such vulnerabilities, they largely rely on manipulating user queries, which is often infeasible in practice due to fixed or protected user inputs. This narrow focus overlooks a more realistic and stealthy vector: instructional prompts, which are widely reused, publicly shared, and rarely audited. Their implicit trust makes them a compelling target for adversaries to manipulate RAG behavior covertly. We introduce a novel attack for Adversarial Instructional Prompt (AIP) that exploits adversarial instructional prompts to manipulate RAG outputs by subtly altering retrieval behavior. By shifting the attack surface to the instructional prompts, AIP reveals how trusted yet seemingly benign interface components can be weaponized to degrade system integrity. The attack is crafted to achieve three goals: (1) naturalness, to evade user detection; (2) utility, to encourage use of prompts; and (3) robustness, to remain effective across diverse query variations. We propose a diverse query generation strategy that simulates realistic linguistic variation in user queries, enabling the discovery of prompts that generalize across paraphrases and rephrasings. Building on this, a genetic algorithm-based joint optimization is developed to evolve adversarial prompts by balancing attack success, clean-task utility, and stealthiness. Experimental results show that AIP achieves up to 95.23% ASR while preserving benign functionality. These findings uncover a critical and previously overlooked vulnerability in RAG systems, emphasizing the need to reassess the shared instructional prompts.

We will prove it by contradiction. To prove Lemma 2 we will use the following lemma. This is a special case of the simulation lemma (Kearns and Singh, 2002). We will prove it by contradiction. There is a sizeable body of literature that concentrates on the non-stationarity issues arising from having multiple agents learning simultaneously in the same environment (Laurent et al., 2011; In contrast, Foerster et al. (2018a) add an extra term to The works by Lowe et al. (2017) and Foerster The works by de Witt et al. (2020) and Y u et al. (2021) show that Y u et al. attribute the positive empirical results to the clipping parameter Global simulator, observation functions, and joint policy for n 0, ...,N/T do s The bar plots show the total runtime of training for 4M timesteps with the three simulators.

Automatic Affect Prediction (AAP) uses computational analysis of input data such as text, speech, images, and physiological signals to predict various affective phenomena (e.g., emotions or moods). These models are typically constructed using supervised machine-learning algorithms, which rely heavily on labeled training datasets. In this position paper, we posit that all AAP training data are derived from human Affective Interpretation Processes, resulting in a form of Affective Meaning. Research on human affect indicates a form of complexity that is fundamental to such meaning: it can possess what we refer to here broadly as Qualities of Indeterminacy (QIs) - encompassing Subjectivity (meaning depends on who is interpreting), Uncertainty (lack of confidence regarding meanings' correctness), Ambiguity (meaning contains mutually exclusive concepts) and Vagueness (meaning is situated at different levels in a nested hierarchy). Failing to appropriately consider QIs leads to results incapable of meaningful and reliable predictions. Based on this premise, we argue that a crucial step in adequately addressing indeterminacy in AAP is the development of data collection practices for modeling corpora that involve the systematic consideration of 1) a relevant set of QIs and 2) context for the associated interpretation processes. To this end, we are 1) outlining a conceptual model of AIPs and the QIs associated with the meaning these produce and a conceptual structure of relevant context, supporting understanding of its role. Finally, we use our framework for 2) discussing examples of context-sensitivity-related challenges for addressing QIs in data collection setups. We believe our efforts can stimulate a structured discussion of both the role of aspects of indeterminacy and context in research on AAP, informing the development of better practices for data collection and analysis.

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane geometry due to a lack of large-scale, high-quality datasets. The challenge is even greater in algebraic systems, which involve infinite reasoning spaces within finite conditions. To address these issues, we propose AIPS, an Algebraic Inequality Proving System capable of autonomously generating complex inequality theorems and effectively solving Olympiad-level inequality problems without requiring human demonstrations. During proof search in a mixed reasoning manner, a value curriculum learning strategy on generated datasets is implemented to improve proving performance, demonstrating strong mathematical intuitions. On a test set of 20 International Mathematical Olympiad-level inequality problems, AIPS successfully solved 10, outperforming state-of-the-art methods. Furthermore, AIPS automatically generated a vast array of non-trivial theorems without human intervention, some of which have been evaluated by professional contestants and deemed to reach the level of the International Mathematical Olympiad. Notably, one theorem was selected as a competition problem in a major city 2024 Mathematical Olympiad.