arXiv subjects
Publications and source records attributed to Tomáš Gavenčiak.
Suppose that each of $n$ players rolls a different die and the players are ordered by their rolls. Can the dice use disjoint labels such that ties are impossible, while all $n!$ orders remain equally likely? We give two general constructions of such dice and solve some related problems.
As AI systems become more capable, training procedures that optimize for downstream outcomes risk introducing implicit agency: goal-directed behavior that designers never specified. We present a formal safety argument for the Scientist AI (SAI) Predictor, trained to approximate the Bayesian posterior conditioned on a dataset of "epistemically contextualized" natural-language statements. We argue that such a Predictor can honestly predict agents, actions, and their consequences without itself being an agent that selects outputs to achieve goals. This rests on data representation and on the training procedure. Epistemic contextualization of text distinguishes latent factual claims from communication acts, so expressions of goals are treated as evidence to be explained rather than drives the model adopts. With a posterior-seeking training objective, this is intended to drive the Predictor toward calibrated, cautious predictions. Training proceeds so downstream effects of deploying a prediction never serve as a reward signal; any agency the system needs is supplied by explicit scaffolding constrained by guardrails. We prove that, under assumptions on the training dynamics and on the argued sparsity of dangerous Predictors, the probability that training produces a Predictor whose guarded deployment carries residual harm above a specified threshold is small: a dangerous Predictor would have to underestimate harm in a coordinated way across many queries while such coordinated patterns are rare under the initialization distribution and receive no direct training signal. Safety and accuracy are jointly supported in this framework, since the constraints that secure accuracy are the same ones that make coordinated deception costly. These guarantees against misalignment and agency arising from within the Predictor itself do not preclude the use of the Predictor as part of an agentic system.
This position paper argues that the dominant paradigm of AI evaluation (which focuses on superhuman autonomous performance and so implicitly targets the goal of replacing humans) is guiding AI development in the wrong direction. Instead, the AI community should pivot to evaluating the performance of human--AI teams. We argue that this collaborative shift will foster AI systems that act as true complements to human capabilities and therefore lead to far better societal outcomes than will the current process.
If LLM training data is polluted with benchmark test data, then benchmark performance gives biased estimates of out-of-distribution (OOD) generalization. Typical decontamination filters use n-gram matching which fail to detect semantic duplicates: sentences with equivalent (or near-equivalent) content that are not close in string space. We study this soft contamination of training data by semantic duplicates. Among other experiments, we embed the Olmo3 training corpus and find that: 1) contamination remains widespread, e.g. we find semantic duplicates for 78% of CodeForces and exact duplicates for 50% of ZebraLogic problems; 2) including semantic duplicates of benchmark data in training does improve benchmark performance; and 3) when finetuning on duplicates of benchmark datapoints, performance also improves on truly-held-out datapoints from the same benchmark. We argue that recent benchmark gains are thus confounded: the prevalence of soft contamination means gains reflect both genuine capability improvements and the accumulation of test data and effective test data in growing training corpora.
This paper offers a roadmap for the development of scalable aligned artificial intelligence (AI) from first principle descriptions of natural intelligence. In brief, a possible path toward scalable aligned AI rests upon enabling artificial agents to learn a good model of the world that includes a good model of our preferences. For this, the main objective is creating agents that learn to represent the world and other agents' world models; a problem that falls under structure learning (a.k.a. causal representation learning or model discovery). We expose the structure learning and alignment problems with this goal in mind, as well as principles to guide us forward, synthesizing various ideas across mathematics, statistics, and cognitive science. 1) We discuss the essential role of core knowledge, information geometry and model reduction in structure learning, and suggest core structural modules to learn a wide range of naturalistic worlds. 2) We outline a way toward aligned agents through structure learning and theory of mind. As an illustrative example, we mathematically sketch Asimov's Laws of Robotics, which prescribe agents to act cautiously to minimize the ill-being of other agents. We supplement this example by proposing refined approaches to alignment. These observations may guide the development of artificial intelligence in helping to scale existing -- or design new -- aligned structure learning systems.
Are large language models (LLMs) biased in favor of communications produced by LLMs, leading to possible antihuman discrimination? Using a classical experimental design inspired by employment discrimination studies, we tested widely used LLMs, including GPT-3.5, GPT-4 and a selection of recent open-weight models in binary choice scenarios. These involved LLM-based assistants selecting between goods (the goods we study include consumer products, academic papers, and film-viewings) described either by humans or LLMs. Our results show a consistent tendency for LLM-based AIs to prefer LLM-presented options. This suggests the possibility of future AI systems implicitly discriminating against humans as a class, giving AI agents and AI-assisted humans an unfair advantage.
The rapid development of advanced AI agents and the imminent deployment of many instances of these agents will give rise to multi-agent systems of unprecedented complexity. These systems pose novel and under-explored risks. In this report, we provide a structured taxonomy of these risks by identifying three key failure modes (miscoordination, conflict, and collusion) based on agents' incentives, as well as seven key risk factors (information asymmetries, network effects, selection pressures, destabilising dynamics, commitment problems, emergent agency, and multi-agent security) that can underpin them. We highlight several important instances of each risk, as well as promising directions to help mitigate them. By anchoring our analysis in a range of real-world examples and experimental evidence, we illustrate the distinct challenges posed by multi-agent systems and their implications for the safety, governance, and ethics of advanced AI.
The broad capabilities of Language Models (LMs) can be limited by their sensitivity to distractor tasks: LMs can infer secondary tasks from the prompt in addition to the intended one, leading to unwanted outputs. For example, prompt injection attacks can cause models to deviate from explicit directives. In some 'inverse scaling' cases, this unwanted behaviour actually worsens as models scale up to at least 540B parameters. We present a theoretical framework that interprets LMs as a product of experts that combine multiple data generation processes. Based on this framework, we demonstrate prior-aware decoding (PAD) - a simple contrastive inference method to reduce the influence of distractor tasks. We apply PAD to eleven models, across four datasets, and find improvements in 41 out of 44 task-model combinations, with a median increase in task completion proportion of 40%. The results suggest a promising direction for further development towards more reliable language models.
Self-modification of agents embedded in complex environments is hard to avoid, whether it happens via direct means (e.g. own code modification) or indirectly (e.g. influencing the operator, exploiting bugs or the environment). It has been argued that intelligent agents have an incentive to avoid modifying their utility function so that their future instances work towards the same goals. Everitt et al. (2016) formally show that providing an option to self-modify is harmless for perfectly rational agents. We show that this result is no longer true for agents with bounded rationality. In such agents, self-modification may cause exponential deterioration in performance and gradual misalignment of a previously aligned agent. We investigate how the size of this effect depends on the type and magnitude of imperfections in the agent's rationality (1-4 below). We also discuss model assumptions and the wider problem and framing space. We examine four ways in which an agent can be bounded-rational: it either (1) doesn't always choose the optimal action, (2) is not perfectly aligned with human values, (3) has an inaccurate model of the environment, or (4) uses the wrong temporal discounting factor. We show that while in the cases (2)-(4) the misalignment caused by the agent's imperfection does not increase over time, with (1) the misalignment may grow exponentially.
To what extent are effectiveness estimates of nonpharmaceutical interventions (NPIs) against COVID-19 influenced by the assumptions our models make? To answer this question, we investigate 2 state-of-the-art NPI effectiveness models and propose 6 variants that make different structural assumptions. In particular, we investigate how well NPI effectiveness estimates generalise to unseen countries, and their sensitivity to unobserved factors. Models that account for noise in disease transmission compare favourably. We further evaluate how robust estimates are to different choices of epidemiological parameters and data. Focusing on models that assume transmission noise, we find that previously published results are remarkably robust across these variables. Finally, we mathematically ground the interpretation of NPI effectiveness estimates when certain common assumptions do not hold.
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While this problem is very well explored in e.g. uniform numerical data processing, structural data applications (e.g. on huge graphs) require different algorithm-dependent approaches. Separable graph classes (i.e. graph classes with balanced separators of size $\mathcal{O}(n^c)$ with $c < 1$) include planar graphs, bounded genus graphs, and minor-free graphs. In this article we present two generalizations of the separator theorem, to partitions with small regions only on average and to weighted graphs. Then we propose I/O-efficient succinct representation and memory layout for random walks in(weighted) separable graphs in the pointer machine model, including an efficient algorithm to compute them. Finally, we present a worst-case I/O-optimal tree layout algorithm for root-leaf path traversal, show an additive (+1)-approximation of optimal compact layout and contrast this with NP-completeness proof of finding an optimal compact layout.
Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed dimension, there is still little understanding in the parameterized complexity community of the strengths and limitations of the available tools. This is understandable: it is often difficult to infer exact runtimes or even the distinction between FPT and XP algorithms, and some knowledge is simply unwritten folklore in a different community. We wish to make a step in remedying this situation. To that end, we first provide an easy to navigate quick reference guide of integer programming algorithms from the perspective of parameterized complexity. Then, we show their applications in three case studies, obtaining FPT algorithms with runtime $f(k)poly(n)$. We focus on: * Modeling: since the algorithmic results follow by applying existing algorithms to new models, we shift the focus from the complexity result to the modeling result, highlighting common patterns and tricks which are used. * Optimality program: after giving an FPT algorithm, we are interested in reducing the dependence on the parameter; we show which algorithms and tricks are often useful for speed-ups. * Minding the poly(n): reducing $f(k)$ often has the unintended consequence of increasing poly(n); so we highlight the common trade-offs and show how to get the best of both worlds. Specifically, we consider graphs of bounded neighborhood diversity which are in a sense the simplest of dense graphs, and we show several FPT algorithms for Capacitated Dominating Set, Sum Coloring, and Max-q-Cut by modeling them as convex programs in fixed dimension, n-fold integer programs, bounded dual treewidth programs, and indefinite quadratic programs in fixed dimension.
We present LemmaTag, a featureless neural network architecture that jointly generates part-of-speech tags and lemmas for sentences by using bidirectional RNNs with character-level and word-level embeddings. We demonstrate that both tasks benefit from sharing the encoding part of the network, predicting tag subcategories, and using the tagger output as an input to the lemmatizer. We evaluate our model across several languages with complex morphology, which surpasses state-of-the-art accuracy in both part-of-speech tagging and lemmatization in Czech, German, and Arabic.
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in the presence of noisy comparisons. As quality measure, we compute the expected fitness of the stationary distribution. To measure the runtime, we compute the minimal number of steps after which the average fitness approximates the expected fitness of the stationary distribution. We study the process where in each round a random pair of elements at distance at most $r$ are compared. We give theoretical results for the extreme cases $r=1$ and $r=n$, and experimental results for the intermediate cases. We find a trade-off between faster convergence (for large $r$) and better quality of the solution after convergence (for small $r$).
The cop number of a graph $G$ is the smallest $k$ such that $k$ cops win the game of cops and robber on $G$. We investigate the maximum cop number of geometric intersection graphs, which are graphs whose vertices are represented by geometric shapes and edges by their intersections. We establish the following dichotomy for previously studied classes of intersection graphs: The intersection graphs of arc-connected sets in the plane (called string graphs) have cop number at most 15, and more generally, the intersection graphs of arc-connected subsets of a surface have cop number at most $10g+15$ in case of orientable surface of genus $g$, and at most $10g'+15$ in case of non-orientable surface of Euler genus $g'$. For more restricted classes of intersection graphs, we obtain better bounds: the maximum cop number of interval filament graphs is two, and the maximum cop number of outer-string graphs is between 3 and 4. The intersection graphs of disconnected 2-dimensional sets or of 3-dimensional sets have unbounded cop number even in very restricted settings. For instance, we show that the cop number is unbounded on intersection graphs of two-element subsets of a line, as well as on intersection graphs of 3-dimensional unit balls, of 3-dimensional unit cubes or of 3-dimensional axis-aligned unit segments.
We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance constrained graph labeling problem as a specific uniform variant of the Channel Assignment problem and show that this problem is fixed parameter tractable when parameterized by the neighborhood diversity together with the largest weight. Consequently, every $L(p_1, p_2, \dots, p_k)$-labeling problem is FPT when parameterized by the neighborhood diversity, the maximum $p_i$ and $k.$ Our results yield also FPT algorithms for all $L(p_1, p_2, \dots, p_k)$-labeling problems when parameterized by the size of a minimum vertex cover, answering an open question of Fiala et al.: Parameterized complexity of coloring problems: Treewidth versus vertex cover. The same consequence applies on Channel Assignment when the maximum weight is additionally included among the parameters. Finally, we show that the uniform variant of the Channel Assignment problem becomes NP-complete when generalized to graphs of bounded clique width.