Which Coauthor Should I Nominate in My 99 ICLR Submissions? A Mathematical Analysis of the ICLR 2026 Reciprocal Reviewer Nomination Policy

The rapid growth of AI conference submissions has created an overwhelming reviewing burden. To alleviate this, recent venues such as ICLR 2026 introduced a reviewer nomination policy: each submission must nominate one of its authors as a reviewer, and any paper nominating an irresponsible reviewer is desk-rejected. We study this new policy from the perspective of author welfare. Assuming each author carries a probability of being irresponsible, we ask: how can authors (or automated systems) nominate reviewers to minimize the risk of desk rejections? We formalize and analyze three variants of the desk-rejection risk minimization problem. The basic problem, which minimizes expected desk rejections, is solved optimally by a simple greedy algorithm. We then introduce hard and soft nomination limit variants that constrain how many papers may nominate the same author, preventing widespread failures if one author is irresponsible. These formulations connect to classical optimization frameworks, including minimum-cost flow and linear programming, allowing us to design efficient, principled nomination strategies. Our results provide the first theoretical study for reviewer nomination policies, offering both conceptual insights and practical directions for authors to wisely choose which co-author should serve as the nominated reciprocal reviewer.

Evaluating Frontier LLMs on PhD-Level Mathematical Reasoning: A Benchmark on a Textbook in Theoretical Computer Science about Randomized Algorithms

The rapid advancement of large language models (LLMs) has led to significant breakthroughs in automated mathematical reasoning and scientific discovery. Georgiev, G${ó}$mez-Serrano, Tao, and Wagner [GGSTW+25] demonstrate that AI systems can explore new constructions and improve existing bounds, illustrating the growing potential of LLMs to accelerate mathematical discovery. Similarly, Bubeck et al. [BCE+25] show that GPT-5 can meaningfully contribute to scientific workflows, from proposing hypotheses to generating proofs and analyses. Despite these advances, a rigorous evaluation of these models on canonical, graduate-level mathematical theory remains necessary to understand their baseline reasoning capabilities. In this paper, we present a comprehensive benchmark of four frontier models: GPT-5-Thinking, Gemini-3-Pro, Claude-Sonnet-4.5-Thinking, and Grok-4 against the classic curriculum of Randomized Algorithms by Motwani and Raghavan [MR95]. We tasked each model with generating formal LaTeX proofs for a series of lemmas and exercises spanning the textbook. We find that while the top-tier models (Gemini, and Claude) achieve a high accuracy rate (approx. 66%), demonstrating a robust grasp of probabilistic method and formal logic, other models lag significantly in consistency (approx. 40%). We provide a qualitative analysis of the generated proofs, highlighting differences in conciseness, hallucination rates, and logical structure. Our results suggest that while frontier models have reached a threshold of proficiency suitable for graduate-level pedagogical assistance and formalization, significant variance exists in their reliability for rigorous mathematical derivation. The code and the full set of LLM-generated responses are open-sourced and publicly available at https://github.com/magiclinux/math_benchmark_probability.

Social welfare optimisation in well-mixed and structured populations

Research on promoting cooperation among autonomous, self-regarding agents has often focused on the bi-objective optimisation problem: minimising the total incentive cost while maximising the frequency of cooperation. However, the optimal value of social welfare under such constraints remains largely unexplored. In this work, we hypothesise that achieving maximal social welfare is not guaranteed at the minimal incentive cost required to drive agents to a desired cooperative state. To address this gap, we adopt to a single-objective approach focused on maximising social welfare, building upon foundational evolutionary game theory models that examined cost efficiency in finite populations, in both well-mixed and structured population settings. Our analytical model and agent-based simulations show how different interference strategies, including rewarding local versus global behavioural patterns, affect social welfare and dynamics of cooperation. Our results reveal a significant gap in the per-individual incentive cost between optimising for pure cost efficiency or cooperation frequency and optimising for maximal social welfare. Overall, our findings indicate that incentive design, policy, and benchmarking in multi-agent systems and human societies should prioritise welfare-centric objectives over proxy targets of cost or cooperation frequency.

Your Vision-Language Model Can't Even Count to 20: Exposing the Failures of VLMs in Compositional Counting

Vision-Language Models (VLMs) have become a central focus of today's AI community, owing to their impressive abilities gained from training on large-scale vision-language data from the Web. These models have demonstrated strong performance across diverse tasks, including image understanding, video understanding, complex visual reasoning, and embodied AI. Despite these noteworthy successes, a fundamental question remains: Can VLMs count objects correctly? In this paper, we introduce a simple yet effective benchmark, VLMCountBench, designed under a minimalist setting with only basic geometric shapes (e.g., triangles, circles) and their compositions, focusing exclusively on counting tasks without interference from other factors. We adopt strict independent variable control and systematically study the effects of simple properties such as color, size, and prompt refinement in a controlled ablation. Our empirical results reveal that while VLMs can count reliably when only one shape type is present, they exhibit substantial failures when multiple shape types are combined (i.e., compositional counting). This highlights a fundamental empirical limitation of current VLMs and motivates important directions for future research.

A Theoretical Analysis of Discrete Flow Matching Generative Models

We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network to approximate the transformative velocity field. Our analysis establishes a clear chain of guarantees by decomposing the final distribution estimation error. We first prove that the total variation distance between the generated and target distributions is controlled by the risk of the learned velocity field. We then bound this risk by analyzing its two primary sources: (i) Approximation Error, where we quantify the capacity of the Transformer architecture to represent the true velocity, and (ii) Estimation Error, where we derive statistical convergence rates that bound the error from training on a finite dataset. By composing these results, we provide the first formal proof that the distribution generated by a trained DFM model provably converges to the true data distribution as the training set size increases.

Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria

Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient single-step sampling. In this work, we introduce a theoretical study on Second-Order MeanFlow, a novel extension that incorporates average acceleration fields into the MeanFlow objective. We first establish the feasibility of our approach by proving that the average acceleration satisfies a generalized consistency condition analogous to first-order MeanFlow, thereby supporting stable, one-step sampling and tractable loss functions. We then characterize its expressivity via circuit complexity analysis, showing that under mild assumptions, the Second-Order MeanFlow sampling process can be implemented by uniform threshold circuits within the $\mathsf{TC}^0$ class. Finally, we derive provably efficient criteria for scalable implementation by leveraging fast approximate attention computations: we prove that attention operations within the Second-Order MeanFlow architecture can be approximated to within $1/\mathrm{poly}(n)$ error in time $n^{2+o(1)}$. Together, these results lay the theoretical foundation for high-order flow matching models that combine rich dynamics with practical sampling efficiency.

T2VWorldBench: A Benchmark for Evaluating World Knowledge in Text-to-Video Generation

Text-to-video (T2V) models have shown remarkable performance in generating visually reasonable scenes, while their capability to leverage world knowledge for ensuring semantic consistency and factual accuracy remains largely understudied. In response to this challenge, we propose T2VWorldBench, the first systematic evaluation framework for evaluating the world knowledge generation abilities of text-to-video models, covering 6 major categories, 60 subcategories, and 1,200 prompts across a wide range of domains, including physics, nature, activity, culture, causality, and object. To address both human preference and scalable evaluation, our benchmark incorporates both human evaluation and automated evaluation using vision-language models (VLMs). We evaluated the 10 most advanced text-to-video models currently available, ranging from open source to commercial models, and found that most models are unable to understand world knowledge and generate truly correct videos. These findings point out a critical gap in the capability of current text-to-video models to leverage world knowledge, providing valuable research opportunities and entry points for constructing models with robust capabilities for commonsense reasoning and factual generation.

Thinking Isn't an Illusion: Overcoming the Limitations of Reasoning Models via Tool Augmentations

Large Reasoning Models (LRMs) have become a central focus in today's large language model (LLM) research, where models are designed to output a step-by-step thinking process before arriving at a final answer to handle complex reasoning tasks. Despite their promise, recent empirical studies (e.g., [Shojaee et al., 2025] from Apple) suggest that this thinking process may not actually enhance reasoning ability, where LLMs without explicit reasoning actually outperform LRMs on tasks with low or high complexity. In this work, we revisit these findings and investigate whether the limitations of LRMs persist when tool augmentations are introduced. We incorporate two types of tools, Python interpreters and scratchpads, and evaluate three representative LLMs and their LRM counterparts on Apple's benchmark reasoning puzzles. Our results show that, with proper tool use, LRMs consistently outperform their non-reasoning counterparts across all levels of task complexity. These findings challenge the recent narrative that reasoning is an illusion and highlight the potential of tool-augmented LRMs for solving complex problems.

Minimalist Softmax Attention Provably Learns Constrained Boolean Functions

We study the computational limits of learning $k$-bit Boolean functions (specifically, $\mathrm{AND}$, $\mathrm{OR}$, and their noisy variants), using a minimalist single-head softmax-attention mechanism, where $k=\Theta(d)$ relevant bits are selected from $d$ inputs. We show that these simple $\mathrm{AND}$ and $\mathrm{OR}$ functions are unsolvable with a single-head softmax-attention mechanism alone. However, with teacher forcing, the same minimalist attention is capable of solving them. These findings offer two key insights: Architecturally, solving these Boolean tasks requires only minimalist attention, without deep Transformer blocks or FFNs. Methodologically, one gradient descent update with supervision suffices and replaces the multi-step Chain-of-Thought (CoT) reasoning scheme of [Kim and Suzuki, ICLR 2025] for solving Boolean problems. Together, the bounds expose a fundamental gap between what this minimal architecture achieves under ideal supervision and what is provably impossible under standard training.

Only Large Weights (And Not Skip Connections) Can Prevent the Perils of Rank Collapse

Attention mechanisms lie at the heart of modern large language models (LLMs). Straightforward algorithms for forward and backward (gradient) computation take quadratic time, and a line of work initiated by [Alman and Song NeurIPS 2023] and [Alman and Song NeurIPS 2024] has shown that quadratic time is necessary unless the model weights are small, in which case almost linear time algorithms are possible. In this paper, we show that large weights are necessary to avoid a strong preclusion to representational strength we call layer collapse, which means that the entire network can be approximated well by a network with only a single layer. Thus, the quadratic running time of attention is unavoidable for expressive transformers. The notion of layer collapse that we introduce is a variant on the notion of rank collapse from the work of [Dong, Cordonnier, and Loukas ICML 2021]. They showed that in Self Attention Networks with small weights and with skip connections, rank collapse must occur. This is typically interpreted as justifying the necessity of skip connections in expressive networks. However, our result shows that even with skip connections, if the weights are small, then layer collapse still occurs. Thus, only large weights, and not skip connections, can prevent these representational weaknesses.