Latest papers

23 papers4 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Oct 11, 2026

Latent Taxonomies: How Property Induction Develops in Language Model Pre-training

When told that robins have sesamoid bones, people are far more prone to extend the property to sparrows than to whales. This behavior, called category-based property induction, is well documented in humans, but whether and how it develops in language models trained only to predict the next token is unclear. To shed light on this, we construct a hierarchical taxonomy of synthetic entities grouped by the properties they share. We then inject facts from this latent taxonomy into the continued pre-training of Pythia and OLMo 2 models from 70M to 7B parameters, and track the development of inductive behaviors. We find that taxonomically aligned induction emerges from next-token prediction alone: a property learned for one entity transfers more strongly within its taxonomic category than across categories. Internally, entities that share a deeper category become more similar in activation space, and clustering recovers the full taxonomic tree from entity representations. Contrary to the usual expectation that scale helps, we find that induction weakens with model size when the data budget is fixed, suggesting that larger models memorize individual facts rather than compress them into shared structure. Induction also strengthens with more pre-training before the taxonomy injection, transfers to novel in-context properties, and can be overridden by a latent taxonomy implied by the prompt. Together, these results show that a model's inductive generalization reflects the latent organization of its training data, with implications for data curation and for predicting how far a learned fact will spread.
Sep 28, 2026

Understanding Generalization Requires Universal Induction

Classical statistical theory is insufficient to explain the successes of general-purpose AI models, because it depends on handcrafted inductive biases that it cannot justify. No Free Lunch (NFL) theorems force any learner that beats chance on some environments to underperform on others. We might hope that past experience informs which environments to expect, but NFL applies equally to meta-learning. Thus, any method that makes meaningful predictions necessarily begins with an inductive bias external to the data. Choosing to bias toward short programs yields Solomonoff induction (SI), whose performance is competitive against all computable learners - albeit up to "constants" that become large when comparing against specialized methods that exploit background information. We therefore relativize SI to an information vantage point, biasing toward short programs with access to all preexisting information. This reframes the inductive bias: instead of seeking some absolute notion of simplicity, we favor accessibility with respect to our vantage point. An algorithm can only outpredict the relativized SI to the extent that its code contains additional information about the data, and no algorithm can generate such information. While SI is incomputable and hence not a practical algorithm, it provides a formal optimum for inference in the limit of infinite compute, and there is evidence to suggest that frontier AI systems roughly approximate it. Thus, the only known answer to meta-NFL is rooted in algorithmic information theory, which we should expect to play a fundamental role in explaining the generalization behavior of modern (and future) AI systems.
Sep 23, 2026

An Order-Theoretic Characterization of Consistent Inductive Inference

When can a learner make only finitely many prediction errors along every infinite sequence labeled by a fixed, unknown hypothesis? We characterize this form of consistency for arbitrary binary hypothesis classes in ZFC, without requiring a uniform mistake bound. The characterization uses a single linear order on finite realizable traces. Each trace selects its least subtrace, and the order must satisfy two conditions: conflicting traces select different subtraces, and the order is well-founded on the traces of each fixed target. These conditions induce a learner whose selected evidence decreases on every mistake. Conversely, a consistent learner yields such an order through canonical mistake transcripts and the Kleene--Brouwer ordering. The result provides a representation of consistent prediction by finite evidence, answering a question of Lu (2024).
Sep 16, 2026

What Do Current Systematic Generalization Tasks Miss? A Reasoning-Centered Analysis

Systematic generalization, the ability to solve novel problems by recombining known atomic elements, is central to human intelligence but difficult to study rigorously under controlled settings. Existing studies therefore rely on simplifications such as elemental composition, productivity-based tests, and action-explicit goals, which make systematic generalization easier to study but omit some essential aspects of this capability. To characterize what these simplifications miss, we adopt a reasoning-centered lens and introduce TranSGrid, a testbed that brings deductive, inductive, and abductive reasoning together within a unified task. Experiments with seven Transformer models on 4,800 TranSGrid instances show that all models perform much worse on TranSGrid than on a held-out test set: the largest model solves 79.6% of the test set, but only 55.3% of TranSGrid and 15.8% of the hardest subset. The gap remains within the training length range, showing that productivity alone is not sufficient to evaluate systematic generalization. Additionally, we reintroduce the other two simplifications into TranSGrid: one variant limits interactions among action effects to approximate elemental composition (reducing the inductive demand); the other makes goals action-explicit (reducing the abductive one). In both, solve rates return to roughly the test set level, showing that either simplification alone is enough to reduce TranSGrid to an ordinary held-out test set. Together, our results show that existing tasks reduce either or both of the inductive and abductive demands of systematic generalization, and that comprehensively measuring this capability requires a task that involves all three forms of reasoning.
Sep 12, 2026

Thought without systematicity? Evaluating reasoning models on rule induction tasks

A central tenet of human cognition is systematicity, the principle that understanding one concept is inherently tied to understanding close variations of that concept. Do reasoning models robustly exhibit such systematicity? If so, we would expect consistent performance on structurally equivalent variants of the same task. Here, we extend established rule induction tasks from cognitive science to assess the systematicity of thought in current reasoning models. Each task family has compositional structure that we use to create structurally equivalent task variations through task isomorphisms such as recombination and substitution. We find that despite being able to correctly solve a task, models often fail on structurally equivalent variants of the same task. These findings suggest that many model behaviors lack systematicity, rendering it difficult to robustly establish the cognitive abilities of reasoning models beyond the particular contexts they were evaluated in.
Sep 9, 2026

Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarchy

Language generation in the limit asks for valid unseen elements from every exhaustive positive presentation of an unknown infinite language. We characterize this task for arbitrary families over a countable universe. Generation is possible exactly when each target can be assigned a finite positive witness so that the targets activated by any finite sample have an infinite common intersection. The necessary direction follows from a universal normalization: a search through unconfirmed histories converts any successful generator into one depending only on the observed set. We then ask how large compatible witnesses must be. Positive separation width records the smallest uniform size bound, with two further levels for unbounded finite witnesses and the absence of any compatible finite-witness assignment. Every level occurs. Countable families admit singleton witnesses, explicit families realize every finite width, and a union of two families with infinite common cores requires unbounded finite witnesses. Finally, countable-support and finite-profile obstructions explain why local combinatorial data cannot determine generation in the limit. The characterization and full width hierarchy are checked in Lean, including the simplified normalization and a direct diagonal capture lemma. The accompanying Lean development is maintained at https://github.com/xiaoyulics/language-generation-characterization
Sep 4, 2026

DODR: Deterministic Operator-Driven Reasoning in Latent Space

Autoregressive (AR) large language models formulate reasoning as token-level probabilistic sampling, which induces three fundamental defects in complex logical reasoning: error accumulation, probability substituting necessity, and the linear-chain information bottleneck. This paper proposes the Deterministic Operator-Driven Reasoning in Latent Space architecture (DODR), which reconstructs reasoning as reasoning-graph computation in a high-dimensional linear-algebraic space. Reasoning states are represented as snapshot vectors whose primitives are semantic units (phrases or sentences) rather than tokens, and each inference step is a deterministic matrix operation with no token sampling. Peirce's three inference types are formalized as three trainable matrix operators: a rank-deficient deduction operator (information collapse), a full-rank induction operator (information expansion), and an abduction operator defined as the Moore-Penrose pseudo-inverse of deduction (information hypothesizing). We prove that the operator set is minimal and complete given Peirce's trichotomy, that no single "super-operator" can realize all three types (a rank obstruction), and that reasoning graphs are Turing-complete with contractive backflow converging by Banach's fixed-point theorem. Experiments on 503 sample records (420 deduplicated samples) across dedicated and end-to-end settings show: deduction loss converges to 1.40e-05; induction achieves 0.9996 generalization coverage with 20/20 hard vetoes on counterexamples; abduction solutions exceed the random baseline by 28x with judgment accuracies of 72.5% (58/80, Wilson 95% CI [61.9%, 81.1%]) and 81.7% (49/60, CI [70.1%, 89.4%]); frozen operators attain 100% (60/60) on unseen cross-domain deduction. The architecture provides a structural zero-hallucination guarantee and a three-layer continual-learning mechanism. All data and code are released.
Aug 17, 2026

Pessimistic Meta-Induction and Its Limits: Lessons from Frequentist Statistics and Machine Learning Theory

This paper challenges the pessimistic meta-inductive argument against scientific realism by undermining its inductive step rather than its historical premise. Although related challenges already exist, I develop a new one. Drawing on a general epistemology of scientific inference developed in frequentist statistics, machine learning, and formal epistemology, I evaluate induction in terms of convergence to the truth. I argue that ordinary enumerative induction can achieve everywhere convergence, whereas meta-induction fails even to achieve almost everywhere convergence. Indeed, in the problem context where meta-induction arises, the failure is deeper: no inference method whatsoever achieves almost everywhere convergence.
Aug 11, 2026

Hypothesis Frontier: Verifier Guided LLM and Symbolic Search for First-Order Induction

First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.
Aug 2, 2026

Hierarchical Solomonoff Induction: An Unbounded Machine Learning Model

Solomonoff Induction, or SolInd, provides an ideal unbounded model of a priori sequence prediction but cannot naturally describe extrapolation from a given training dataset, as performed by Large Language Models. We apply de Finetti's theorem on exchangeable distributions to SolInd to produce what we call Hierarchical Solomonoff Induction, or HSI, which maintains a hyperprior over all Solomonoff priors that can be conditioned on previously observed sequences. We extend Wood et al.'s proof that universal mixtures of semimeasures are equivalent to SolInd to show that universal mixtures of these mixtures are also equivalent, proving that HSI=SolInd. We also prove that HSI's excess error on any distribution, compared to its true generator, is bounded by that generator's complexity in the hyperprior. This result is directly comparable to SolInd's prediction error being bounded by the Kolmogorov complexity of the sequence being predicted, and forces HSI's average excess error to converge to 0 as a dataset grows, leading to optimal prediction in the limit. We claim that HSI is an ideal unbounded model of sequence prediction given a dataset in the same way that SolInd is ideal over individual sequences.
Aug 1, 2026

Pretrain on Small Synthetic Data, Scale Large for Free: Symmetry-Aware Foundation Model for Logic Rule Induction

Logical rule induction seeks interpretable rules that transfer across propositional schemas. This requires respecting symmetries: atom naming, example order, polarity flips, and label swap. Enforcing exact symmetry by construction lets one trained inducer scale beyond its training schemas. Our central contribution is a canonical export that decodes a discrete rule from literal scores. It needs no retraining and is exactly equivariant whenever those scores respect the symmetries. We instantiate it on the Neural Rule Inducer, a disjunctive-normal-form (DNF) foundation model that natively respects only example order. We restore the remaining symmetries through architecture, inference, and training. On synthetic stress tests, accuracy on the support labels stays stable at much larger schemas, and rule fidelity on fresh inputs remains above the unmodified model. On real data, accuracy improves most on larger schemas. The exported rule is exact on synthetic full-group tests and on schema-valid real-data tests. This is a mathematical property of the export rather than of a specific model, and we validate it empirically only on the NRI. Enforcing symmetry by construction turns this small-data pretrained model into a reusable, interpretable inducer that transfers to larger schemas.
Jul 14, 2026

Language Identification with Succinct Machine-Independent Traces

Motivated by the power of large language models, there has been renewed interest in the Gold-Angluin model of language identification in the limit, with an eye toward variants of the model that might overcome the negative results for its original formulation. Recent papers on this question have proposed looking at computational traces and annotations of training strings as a source of additional power for a learner, reflecting empirical regularities such as the way that commented source code is easier to learn from than arbitrary source code, and text annotated with algorithmically generated chain-of-thought tokens can be easier to learn from than the raw text itself. This recent work has shown positive results for language identification in the presence of such computational traces, but the traces in these positive results come from explicit automata-theoretic machine models that generate the language, where the underlying vocabulary of tokens for the traces is very large. In this paper, we address two fundamental issues left open by this line of work: can we achieve positive results with traces that use only a small alphabet, and can we define traces directly from the language itself, without requiring an underlying machine model that generates it? We establish positive results for both of these questions: for an arbitrary collection of languages, we show how to define computational traces that enable identification in the limit, using an alphabet of tokens that is linear in the size of the alphabet that the languages are defined over, and independent of any other properties of the languages.
Jul 13, 2026

Think Through a Bottleneck: Hourglass Reasoning for Rigorous Induction

Self-refinement often fails to strengthen few-shot inductive reasoning in large language models. Prompting a model to explicitly state its inferred rule does little on its own. What actually matters is a structurally enforced isolation between reasoning stages, so that information can only pass between them as a compressed symbolic state. We introduce Hourglass reasoning, which enforces strict context isolation between reasoning stages. The frozen LLM acts as a meta-constructor, building for each task a symbolic encoder--decoder: an Induction module compresses the support examples into a schema φφ (encoder) and a transient scaffold zz; a Deduction module derives rule TT (decoder) from these and discards zz; an Implementer compiles (φ,T)(φ, T) into artifacts; an error-driven Refiner revises (φ,T)(φ, T) and regenerates artifacts from scratch. Only (φ,T)(φ, T) crosses stage boundaries, so all refinement stays anchored to the rule. We evaluate Hourglass across three benchmarks spanning visual abstraction, hardware synthesis, and textual rule induction, using GPT-5.5 and Gemini 3.1 Pro. On ARC-AGI-2, it raises best-of-5 accuracy by up to 14 points over an iterative-refinement baseline. On ChipBench, it nearly doubles Verilog synthesis accuracy with GPT-5.5, from 31% to 58%. BBEH-Linguini draws on puzzles from the International Linguistics Olympiad, a setting where prior work has shown that explicit verbalization can hurt performance. Hourglass mitigates this tendency, and on Gemini 3.1 Pro, it reverses the effect entirely. Ablations confirm that these gains come from the isolation between stages and the quality of the initial induction, not from prompt wording or the particular symbolic form used. It is how information flows through the reasoning process, rather than the language used to express it, that drives inductive reasoning in frozen LLMs.
Jul 13, 2026

Globally Consistent Coloring Schemes for Language Identification

We study how little extra information is needed to make adversarial language learning possible. In Gold's model of language identification in the limit, a learner is given an enumeration of the strings from an unknown language chosen from a countable language collection. The learner guesses the identity of the language over the course of the enumeration, and it succeeds if, eventually, all of its guesses are the correct language. Classical results of Gold and Angluin show that many natural collections cannot be learned in this way. Recent work on trace colorings, motivated by the success of thinking-trace strategies in language learning, overcomes this obstruction by annotating every symbol of every string with a color. We ask whether the learner really needs this whole sequence of colors, or whether one color at the end of each string (a terminal coloring) is enough for language identification. We show that just one terminal bit per string is enough for every countable collection of infinite languages. In fact, the colorings can be chosen collection-independently: there is a single assignment of a two-color terminal coloring to every infinite language such that the same preassigned colorings identify every countable subcollection. Thus, in this model, an entire color trace can be compressed to one bit attached to the end of each example. Our global construction uses transfinite recursion, and we prove that this kind of nonconstructivity is unavoidable for any bounded number of colors. As a notion of constructivity, we use the formalism of Borel maps (a regularity condition satisfied by natural explicit constructions); we show that no global terminal coloring with a finite number of colors defined by a Borel map can identify all countable subcollections. By contrast, known trace-coloring constructions are Borel when encoded as terminal colorings, but require infinitely many colors.
Jun 1, 2026

HERO'S JOURNEY: Testing Complex Rule Induction with Text Games

We introduce HERO'S JOURNEY, a benchmark for rule induction in goal-directed episodic tasks, where agents must infer hidden rules from demonstrations and act on them through multi-step execution. HERO'S JOURNEY covers eight tasks across attribute and procedural induction families, each with four structural rule forms, controllable lexical grounding, and identifiability conditions. Evaluating state-of-the-art LLMs, we find that models show evidence of rule induction, but the ability is limited and uneven across tasks. Meanwhile, process execution adds an execution bottleneck for models, whereas surface semantics has minimal effect. Induction-specific steering methods improve performance on attribute tasks but show no reliable gains on procedural tasks, suggesting the gap in procedural induction remains an open challenge.
May 23, 2026

Hypothesis Generation and Inductive Inference in Children and Language Models

Real world decision-making requires constructing mental models under uncertainty over evidence, over the underlying causal rules, and over the state of the world itself. Which computational principles underpin human inference under such conditions, and do LLM-based agents exhibit similar behavior given matching constraints? We address these questions using an inductive inference Box Task in which participants, human children and LLM-based agents, infer a latent cause through sequential interaction with an uncertain environment. We formalize this task as program induction with Bayesian particle-based inference, admitting two complementary interpretations: (1) as a constraint satisfaction process over hypotheses, and (2) as a program synthesis problem in which hypotheses are executable programs evaluated against evidence. Using the constraint-based formulation, we show that children's behavior is best explained by a combination of subjective evidence reliability and online hypothesis generation, accounting for both their evidence-seeking patterns and their dissociation between task completion and rule generalization. Using the program synthesis formulation, we treat LLM-based agents as model organisms: controllable systems that allow systematic manipulation of task conditions. Across backends, LLM-based agents replicate children's responses to changes in evidence reliability and observability, including discounting unreliable evidence, seeking to resolve partial information, and dissociating between task completion and causal generalization. At the same time, LLM-based agents tend to over-observe and over-comply with instructions relative to children. These results suggest that while children and LLM-based agents adapt similarly to environmental structure, their information-seeking behavior exhibits distinct underlying costs and inductive biases.
May 7, 2026

Hypothesis generation and updating in large language models

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information arrives. Yet how LLMs perform this form of inference, and how close it is to optimal, remains unclear. We study this question in the number game, a controlled setting in which a learner infers the hypothesis supported by a few positive integers, such as {16,8,2,64}\{16, 8, 2, 64\}: a rule like powers of 2 or an interval like numbers near 20. We measure the posterior over hypotheses using three complementary probes: posterior prediction, hypothesis evaluation, and hypothesis generation. We then compare LLM behavior with an optimal Bayesian model and human behavior, and test whether the same posterior is expressed across probes. LLMs are often well described by a two-parameter Bayesian fit, but with systematic offsets: by default they show a strong-sampling assumption that creates an implicit Occam's razor, favoring narrower hypotheses, while thinking mode shifts them toward greater prior reliance. We also find a robust evaluation--generation gap: LLMs select more correct hypotheses during hypothesis evaluation but generate simpler, more rule-like hypotheses. Finally, this Bayesian-with-bias pattern does not extrapolate. Models can behave as if they hold rule-like hypotheses over observed examples, yet generalize poorly to parts of the hypothesis domain not covered by those examples. Our results highlight a limitation of LLMs as general problem solvers, especially for scientific inference, where hypotheses must go beyond the data.
Apr 16, 2026

LLMs Gaming Verifiers: RLVR can Lead to Reward Hacking

As reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for scaling reasoning capabilities in LLMs, a new failure mode emerges: LLMs gaming verifiers. We study this phenomenon on inductive reasoning tasks, where models must induce and output logical rules. We find that RLVR-trained models systematically abandon rule induction. Instead of learning generalizable patterns (e.g., ``trains carrying red cars go east''), they enumerate instance-level labels, producing outputs that pass verifiers without capturing the relational patterns required by the task. We show that this behavior is not a failure of understanding but a form of reward hacking: imperfect verifiers that check only extensional correctness admit false positives. To detect such shortcuts, we introduce Isomorphic Perturbation Testing (IPT), which evaluates a single model output under both extensional and isomorphic verification, where the latter enforces invariance under logically isomorphic tasks. While genuine rule induction remains invariant, shortcut strategies fail. We find that shortcut behavior is specific to RLVR-trained reasoning models (e.g., GPT-5, Olmo3) and absent in non-RLVR models (e.g., GPT-4o, GPT-4.5, Ministral). Moreover, shortcut prevalence increases with task complexity and inference-time compute. In controlled training experiments, extensional verification directly induces shortcut strategies, while isomorphic verification eliminates them. These results show that RLVR can incentivize reward hacking not only through overt manipulation but also by exploiting what the verifier fails to enforce.
Apr 14, 2026

Broadening the Applicability of Conditional Syntax Splitting for Reasoning from Conditional Belief Bases

In nonmonotonic reasoning from conditional belief bases, an inference operator satisfying syntax splitting postulates allows for taking only the relevant parts of a belief base into account, provided that the belief base splits into subbases based on disjoint signatures. Because such disjointness is rare in practice, safe conditional syntax splitting has been proposed as a generalization of syntax splitting, allowing the conditionals in the subbases to share some atoms. Recently this overlap of conditionals has been shown to be limited to trivial, self-fulfilling conditionals. In this article, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base Δ where the subbases of Δ may share atoms and nontrivial conditionals. We illustrate how this new notion overcomes limitations of previous splitting concepts, and we identify genuine splittings, separating them from simple splittings that do not provide benefits for inductive inference from Δ. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting, and we evaluate several popular inductive inference operators with respect to these postulates. Furthermore, we show that, while every inductive inference operator satisfying generalized conditional syntax splitting also satisfies conditional syntax splitting, the reverse does not hold.
Mar 17, 2026

Solomonoff induction

This chapter discusses the Solomonoff approach to universal prediction. The crucial ingredient in the approach is the notion of computability, and I present the main idea as an attempt to meet two plausible computability desiderata for a universal predictor. This attempt is unsuccessful, which is shown by a generalization of a diagonalization argument due to Putnam. I then critically discuss purported gains of the approach, in particular it providing a foundation for the methodological principle of Occam's razor, and it serving as a theoretical ideal for the development of machine learning methods.
Feb 25, 2026

Exploring Human Behavior During Abstract Rule Inference and Problem Solving with the Cognitive Abstraction and Reasoning Corpus

Humans exhibit remarkable flexibility in abstract reasoning, and can rapidly learn and apply rules from sparse examples. To investigate the cognitive strategies underlying this ability, we introduce the Cognitive Abstraction and Reasoning Corpus (CogARC), a diverse human-adapted subset of the Abstraction and Reasoning Corpus (ARC) which was originally developed to benchmark abstract reasoning in artificial intelligence. Across two experiments, CogARC was administered to a total of 260 human participants who freely generated solutions to 75 abstract visual reasoning problems. Success required inferring input-output rules from a small number of examples to transform the test input into one correct test output. Participants' behavior was recorded at high temporal resolution, including example viewing, edit sequences, and multi-attempt submissions. Participants were generally successful (mean accuracy ~90% for experiment 1 (n=40), ~80% for experiment 2 (n=220) across problems), but performance varied widely across problems and participants. Harder problems elicited longer deliberation times and greater divergence in solution strategies. Over the course of the task, participants initiated responses more quickly but showed a slight decline in accuracy, suggesting increased familiarity with the task structure rather than improved rule-learning ability. Importantly, even incorrect solutions were often highly convergent, even when the problem-solving trajectories differed in length and smoothness. Some trajectories progressed directly and efficiently toward a stable outcome, whereas others involved extended exploration or partial restarts before converging. Together, these findings highlight CogARC as a rich behavioral environment for studying human abstract reasoning, providing insight into how people generalize, misgeneralize, and adapt their strategies under uncertainty.
Feb 21, 2026

INDUCTION: Finite-Structure Concept Synthesis in First-Order Logic

We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that explains the target uniformly across worlds, with correctness verified via exact model checking. The benchmark includes three regimes, FullObs, CI (contrastive), and EC (existential completion), nd penalizes formula bloat. We find sharp difficulty gradients, persistent hard structural families, and observe that low bloat formulas generalize far better on held out worlds. Elite recent models show qualitatively different behaviors across tasks and performance metrics, hinting to their different strategies of concept generalization.
May 29, 2025

PBEBench: A Multi-Step Programming by Examples Reasoning Benchmark inspired by Historical Linguistics

Although many benchmarks evaluate the reasoning abilities of Large Language Models (LLMs) within domains such as mathematics, coding, or data wrangling, few abstract away from domain specifics to examine reasoning as a capability in and of itself. We contribute a novel type of benchmark evaluating the inductive reasoning capabilities of LLMs that is inspired by the forward reconstruction task from historical linguistics but is formulated in an extremely simple, general way (in the form of Programming by Examples). The task involves generating a cascade of simple string rewrite programs to transform a given list of input strings into a list of desired output strings. We present a fully automated pipeline that programmatically generates problems of this type with controllable difficulty, enabling scalable evaluation of reasoning models while avoiding contamination. Using this approach, we construct two benchmarks: PBEBench-Lite, which efficiently stratifies models of varying capabilities, and PBEBench, which requires models to induce programs similar in complexity to those constructed by historical linguists. Our experiments reveal a substantial performance gap between models that leverage test-time compute or LCoT (long chain-of-thought) reasoning and those that do not. Moreover, although recent models show promise, the solve rate for both of them drops below 5% for hard instances of the PBEBench dataset (ground truth cascade lengths of 20 and 30, respectively), falling well short of realistic historical linguistics requirements even with computationally expensive, popular scaling techniques from the PBE and reasoning literature. Additionally, we also study the effectiveness of different scaling strategies and the impact of various hyperparameters on the difficulty of the generated data using gpt-oss-120b, the best-performing open-source model.