---
title: 'BeyondBench: Dynamic Reasoning Benchmark'
url: https://www.emergentmind.com/topics/beyondbench
type: topic
---

# BeyondBench: Dynamic Reasoning Benchmark

BeyondBench is a contamination-resistant, dynamically generated benchmark for evaluating the reasoning of language models through algorithmic problem generation rather than fixed test sets [2509.24210]. It is designed to measure a model’s true algorithmic reasoning power rather than its memorization capacity by creating mathematically grounded problems on the fly, verifying solutions deterministically, and scaling instance difficulty to fit model-specific context constraints [2509.24210]. In the reported study, the framework covers 44 algorithmic tasks with 117 total variations, organized into Easy, Medium, and Hard suites, and is used to evaluate 101 language models spanning open-source and closed-source families [2509.24210].

## 1. Definition and motivating problem

BeyondBench is introduced in response to a central evaluation problem for contemporary language models: static benchmarks available on the internet risk contamination by training data, making it unclear whether strong scores reflect reasoning or answer recall [2509.24210]. Its defining move is to replace fixed benchmark items with parameterized generators that instantiate fresh problems at evaluation time. This keeps each test uncontaminated in the intended sense and shifts the target of measurement from benchmark exposure to algorithmic competence [2509.24210].

The framework is organized around three stated pillars: on-the-fly instance generation from enormous parameter spaces, formal verification of unique (or exhaustively enumerated) solutions, and token-budget-aware difficulty scaling [2509.24210]. These design choices jointly address three failure modes of static evaluation: item memorization, unverifiable open-ended outputs, and accidental mismatch between task instance size and model context budget.

A potential misconception is that “benchmark-free evaluation” implies the absence of a benchmark structure. BeyondBench instead retains a formal evaluation framework, task taxonomy, and explicit metrics; what it avoids is reliance on a static, internet-exposed collection of benchmark items [2509.24210].

## 2. Problem generation, verification, and token-aware scaling

For each task $\tau$, BeyondBench defines a generator
$$
G_\tau : \Theta_\tau \times \mathcal{R} \to \mathcal{P}_\tau
$$
mapping a finite “size-and-rule” parameter $\theta \in \Theta_\tau$ and random seed $r \in \mathcal{R}$ to a problem instance $p \in \mathcal{P}_\tau$ [2509.24210]. The construction is explicitly parameterized so that the instance space is extremely large. The paper gives the example $\Theta_\tau \approx [-10^6,10^6]^n$ for list tasks and states that one can ensure
$$
|\Theta_\tau \times \mathcal{R}| > 10^{15},
$$
yielding
$$
P(\mathrm{collide}) \le (1-10^{-15})^N \approx \exp(-N \cdot 10^{-15}) < 10^{-3}
$$
for a static training corpus $\mathcal{C}$ with $|\mathcal{C}| < 10^{12}$ [2509.24210].

Each generated instance is paired with a solver or CSP/SAT-based checker $V_\tau$ such that either
$$
|\{s : V_\tau(s,p)=1\}| = 1,
$$
or all valid solutions $S_p$ are exhaustively enumerated [2509.24210]. This is the framework’s formal verification layer. The paper states that verification costs remain polynomial, for example $O(n^3)$ or better, even when the solution space is exponential [2509.24210]. In operational terms, this allows BeyondBench to score model outputs against mathematically defined ground truth rather than heuristic answer matching.

Difficulty is additionally constrained by context length. For a model $M$ with context budget $C_M$, BeyondBench estimates required tokens by
$$
T_p(n)=T_{\mathrm{prompt}}(n)+T_{\mathrm{response}}(n)+T_{\mathrm{buffer}}, \qquad T_{\mathrm{buffer}}=0.15 \cdot C_M
$$
and enforces $T_p(n)\le C_M$ by iteratively reducing size parameters, for example $n \leftarrow \lfloor 0.8 \cdot n \rfloor$ [2509.24210]. After inference, actual token counts are measured with model-specific tokenizers, specifically tiktoken for GPT models and Hugging Face tokenizers for open-source models, and responses exceeding $0.95\,C_M$ are flagged [2509.24210]. This makes token budget a first-class constraint in task generation rather than an after-the-fact artifact of prompting.

## 3. Task taxonomy and difficulty structure

BeyondBench organizes 44 base tasks into three suites with 117 total variations [2509.24210]. The taxonomy is intended to separate relatively routine polynomial-time problems from sequence-based exponential reasoning tasks and from NP-complete or CSP-heavy problems.

| Suite | Scope | Representative tasks |
|---|---|---|
| Easy Suite | 29 tasks; polynomial-time problems $(O(n^k), k \le 2)$ | arithmetic, sorting, max/min, parity, perfect squares, palindromic numbers, mean, median, mode |
| Medium Suite | 5 tasks, 49 variations; exponential $(O(2^n)$–$O(n!))$ sequence continuation | linear recurrences, geometric/exponential sequences, prime/number-theoretic patterns, composite patterns, algebraic/transcendental nests |
| Hard Suite | 10 tasks, 68 variations; NP-complete and beyond | Tower of Hanoi, N-Queens, Graph Coloring, Boolean SAT, Sudoku, Cryptarithmetic, Matrix Chain Multiplication, Modular Systems, Constraint Optimization, Logic Grid Puzzles |

The Easy Suite contains 29 tasks for basic arithmetic and statistics, including sum $\sum x_i$, product $\prod x_i$, difference, division with tolerance $\epsilon = 10^{-2}$, sorting, max/min, parity, perfect squares, palindromic numbers, mean, median, and mode [2509.24210]. These are described as polynomial-time problems with $k \le 2$ in $O(n^k)$ [2509.24210].

The Medium Suite comprises 5 tasks with 49 variations and focuses on sequence continuation whose generation or inference can involve exponential complexity from $O(2^n)$ to $O(n!)$ [2509.24210]. The listed categories include Fibonacci and general linear recurrences of the form
$$
F_n = \sum a_i \cdot F_{n-i},
$$
geometric and exponential sequences
$$
g_n = g_1 \cdot r^{n-1},
$$
prime and number-theoretic patterns such as sieve, $\phi(n)$, $\sigma(n)$, and Mersenne tests, as well as complex composite patterns and algebraic or transcendental nests including $\lfloor \sqrt{(n+\sqrt{n})} \rfloor$ and continued fractions [2509.24210].

The Hard Suite comprises 10 tasks with 68 variations and targets NP-complete and related forms of combinatorial reasoning [2509.24210]. Its tasks include Tower of Hanoi with $T(n)=2^n-1$ moves and PSPACE-complete variants; N-Queens with conflict constraints
$$
x_i \ne x_j \wedge |i-j| \ne |x_i-x_j|;
$$
Graph Coloring with chromatic number $\chi(G)$ under the $\Delta(G)+1$ bound and Brooks’ theorem; Boolean SAT with formula $\wedge C_i$, search space $2^n$, and phase transition at $m/n \approx 4.267$; Sudoku in 4×4, 6×6, 9×9, irregular, and diagonal forms; Cryptarithmetic with letter-to-digit bijections and carry propagation; Matrix Chain Multiplication with
$$
m[i,j] = \min_k (m[i,k]+\ldots+d_{i-1}\cdot d_k \cdot d_j)
$$
in $O(n^3)$; Modular Systems; Constraint Optimization; and Logic Grid Puzzles as Latin-square-style CSPs with directed and conditional clues [2509.24210].

## 4. Evaluation protocol, model coverage, and metrics

The reported evaluation spans 101 models, including 85 open-source and 16 closed-source systems, with model sizes from 0.5B to 141B parameters and multiple quantization schemes [2509.24210]. For each of the 117 variations, 1,000 distinct instances with seed $=42$ were generated for each open-source model, while proprietary models were evaluated on 100 instances per variation to reduce API cost [2509.24210].

The open-source families listed in the paper include Qwen3 (0.6B–32B, MoE, thinking/math variants), Qwen2.5 (0.5B–72B, math-fine-tuned), Llama-3.x (1B–70B), Phi3/Phi4 (3.8B–14B), Gemma (1–27B), Mistral (7B–176B MoE), and Smollm2/3 [2509.24210]. The closed-source families include OpenAI’s GPT-4/4o and GPT-5 in full, mini, and nano variants, as well as Gemini-2.0 and Gemini-2.5 in pro, flash, and lite variants [2509.24210]. The paper further reports that FP8 and GPTQ 8-bit/4-bit variants exhibited less than 3% average accuracy drop [2509.24210].

BeyondBench defines three metrics for each suite and task. Accuracy is the percentage of instances for which
$$
V_\tau(\mathrm{parse}(\mathrm{response}), p)=1.
$$
Instruction Following is the percentage of outputs matching the prescribed `\boxed{…}` format. Token Usage is mean output length [2509.24210]. These metrics combine semantic correctness, formatting compliance, and generation length.

Tool usage is treated as an explicit evaluation variable. Proprietary models were evaluated both with their full toolchain and in a language-only setting [2509.24210]. This distinction becomes central to the interpretation of hard-suite performance because the paper reports substantial differences between tool-augmented and language-only inference.

## 5. Empirical results and observed failure modes

The principal empirical pattern reported by BeyondBench is a sharp degradation in performance as task complexity increases from polynomial to exponential [2509.24210]. The paper states that even 120B-parameter open-source models achieve greater than 90% on the Easy Suite but fall to 20–40% on the Hard Suite [2509.24210]. This is presented as evidence of consistent reasoning deficiencies across model families rather than isolated weaknesses of a single architecture.

The paper gives several concrete examples. Qwen-OSS-120B achieves Easy 93.5%, Medium 75.1%, Hard 59.6%; Llama-3.3-70B achieves Easy 74.6%, Medium 46.7%, Hard 26.9%; and Gemini-2.5-pro achieves Easy 89.2%, Medium 77.2%, Hard 56.4% [2509.24210]. In the abstract, the corresponding hard-suite averages are given as 56.38% for Gemini-2.5-pro, 26.91% for Llama-3.3-70B, and 33.60% for Qwen2.5-72B [2509.24210]. These figures show that models that are strong on arithmetic and structured sequence tasks do not maintain comparable performance on NP-complete and CSP-style tasks.

The paper also identifies a steep hard-suite cliff on specific problems, especially Sudoku and N-Queens [2509.24210]. It states that models often exceed 80% on 4×4 Sudoku but fall below 20% on 9×9 [2509.24210]. This suggests that BeyondBench is not only measuring whether a model can solve a problem family at all, but whether it preserves competence under scaling within that family.

Scaling with parameter count exhibits diminishing returns. The paper gives the example that increasing Qwen3 from 0.6B to 1.7B adds approximately 17 percentage points on Hard tasks, whereas increasing from 14B to 32B adds less than 2 percentage points [2509.24210]. A plausible implication is that BeyondBench exposes a saturation regime in which larger parameter count alone does not yield proportional gains on combinatorial reasoning.

## 6. Tool use, reproducibility, and relation to benchmark science

Tool augmentation materially changes outcomes on hard tasks. For the GPT-5 family, the paper reports that use of tools improves hard-suite results by 6–12 points and gives a concrete comparison: GPT-5 with tools scores 97.3% / 81.6% / 71.8% and 83.6% overall, whereas GPT-5 with no tools scores 88.4% / 61.6% / 50.3% and 66.8% overall [2509.24210]. The hard-suite drop is stated as $\Delta = 16.8\%$ for GPT-5, 15.9% for GPT-5-mini, and 47.6% for GPT-5-nano; the abstract gives the corresponding declines as 16.81%, 28.05%, and 47.59% on the hard suite for GPT-5, GPT-5-mini, and GPT-5-nano [2509.24210]. The exact percentages differ slightly between the abstract and detailed summary, but both passages agree that language-only performance drops drastically without tool usage.

All problems, code, and up-to-date leaderboards are publicly available at `https://ctrl-gaurav.github.io/BeyondBench/`, and the framework provides an API through which new models can generate fresh instances and compare against the 117-variation, 44-task suite without risk of contamination [2509.24210]. In this sense, reproducibility is tied not to a frozen item set but to a reproducible generation-and-verification process.

BeyondBench can also be situated in a broader line of work on benchmark methodology. “A BenchCouncil View on Benchmarking Emerging and Future Computing” formalizes a benchmark as
$$
B=(P,I,M,U,T),
$$
where $P$ is a problem definition, $I$ a solution instantiation, $M$ a measurement function, and $U$ and $T$ the measurement standard and tool [2205.07769]. That paper argues that benchmark properties are extrinsic rather than inherent and emphasizes the entanglement of definition, instantiation, and measurement, together with risks of technology inertia and instantiation bias [2205.07769]. BeyondBench’s emphasis on parameterized generation, formal checking, traceable measurement, and publicly available tooling is consistent with that broader benchmark-science perspective. This suggests that BeyondBench is not only a reasoning evaluation suite but also an example of a more general shift away from static benchmark artifacts toward dynamically instantiated, formally verifiable evaluation regimes [2205.07769].

Source: https://www.emergentmind.com/topics/beyondbench