arXiv subjects

Jayson Lynch

Publications and source records attributed to Jayson Lynch.

At least 19 recordsLinked to original sources

arXiv2026

Two AI Metrics Diverged: Will it Make All the Difference?

As exponential compute scaling continues, will the capabilities of frontier AI models outstrip what is accessible to developers on a small fixed budget? Or will capabilities converge, with "meek models inheriting the earth"? Building on Gundlach et al. (2025b), we show that the answer depends on how we value and measure AI capabilities. We discuss conventional performance measures and show that, while validation loss shows a shrinking gap, on other metrics frontier models grow their lead forever. Classifying performance metrics by their functional forms in relation to training (and inference) compute, we provide tight mathematical conditions for determining which metrics favor meek models, and show that bounded performance metrics always do. But careful interpretation of performance metrics is essential: we show that many common bounded metrics have closely-related counterpart metrics that are unbounded (and vice versa). Determining the apt metric in a domain is a prerequisite for policy, since bounded and unbounded metrics may suggest opposing policy responses. If a particular capability -- like software engineering, synthetic biology, or rhetorical persuasiveness -- is unbounded when measured in the terms we care about, frontier-level capability will likely be concentrated in the hands of a few wealthy actors. Conversely, if that capability is instead bounded, frontier-level capabilities proliferate through meek models into the hands of the many.

cs.AI↗

arXiv2026

The Impact of Approximation on Algorithmic Progress

In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of size 1 million. A natural response to such limits is to try to find new algorithms or to parallelize existing ones, but many algorithms are already at their theoretically-optimal level and parallelization is often impossible or prohibitively expensive. Starting in the 1960's, computer scientists pursued another solution: allowing solutions to have a small amount of error (i.e. approximating them). In this paper, we survey 118 of the most important algorithm problems in computer science, quantifying the gains and tradeoffs from approximation that have been discovered over the history of the field. Overall, only $\approx$20\% of problems have benefited from approximation. However, those with good approximate algorithms can be dramatically faster to compute with little cost to accuracy. For example, a quarter of computationally intractable problems (e.g. those that take exponential time to compute) have polynomial time approximate algorithms. Approximation also increases the number of algorithms that can run in linear time by 23\%, opening up new computational opportunities for those working in the big data regime. This work also sheds light on what should be expected from progress in AI, where approximation is at the heart of how deep learning works.

cs.DS↗

arXiv2025

The Price of Progress: Price Performance and the Future of AI

Language models have seen enormous progress on advanced benchmarks in recent years, but much of this progress has only been possible by using more costly models. Benchmarks may therefore present a warped picture of progress in practical capabilities *per dollar*. To remedy this, we use data from Artificial Analysis and Epoch AI to form the largest dataset of current and historical prices to run benchmarks to date. We find that the price for a given level of benchmark performance has decreased remarkably fast, around $5\times$ to $10\times$ per year, for frontier models on knowledge, reasoning, math, and software engineering benchmarks. These reductions in the cost of AI inference are due to economic forces, hardware efficiency improvements, and algorithmic efficiency improvements. Isolating out open models to control for competition effects and dividing by hardware price declines, we estimate that algorithmic efficiency progress is around $3\times$ per year. However, at the same time, the price of running frontier models is rising between $3\times$ to $18\times$ per year due to bigger models and larger reasoning demands. Finally, we recommend that evaluators both publicize and take into account the price of benchmarking as an essential part of measuring the real-world impact of AI.

cs.LG↗

arXiv2025

How fast are algorithms reducing the demands on memory? A survey of progress in space complexity

Algorithm research focuses primarily on how many operations processors need to do (time complexity). But for many problems, both the runtime and energy used are dominated by memory accesses. In this paper, we present the first broad survey of how algorithmic progress has improved memory usage (space complexity). We analyze 118 of the most important algorithm problems in computer science, reviewing the 800+ algorithms used to solve them. Our results show that space complexity has become much more important in recent years as worries have arisen about memory access bottle-necking performance (the ``memory wall''). In 20% of cases we find that space complexity improvements for large problems (n=1 billion) outpaced improvements in DRAM access speed, suggesting that for these problems algorithmic progress played a larger role than hardware progress in minimizing memory access delays. Increasingly, we also see the emergence of algorithmic Pareto frontiers, where getting better asymptotic time complexity for a problem requires getting worse asymptotic space complexity, and vice-versa. This tension implies that programmers will increasingly need to consider multiple algorithmic options to understand which is best for their particular problem. To help theorists and practitioners alike consider these trade-offs, we have created a reference for them at https://algorithm-wiki.csail.mit.edu.

cs.DS↗

arXiv2025

On the Origin of Algorithmic Progress in AI

Algorithms have been estimated to increase AI training FLOP efficiency by a factor of 22,000 between 2012 and 2023 [Ho et al., 2024]. Running small-scale ablation experiments on key innovations from this time period, we are able to account for less than 10x of these gains. Surveying the broader literature, we estimate that additional innovations not included in our ablations account for less than 10x, yielding a total under 100x. This leads us to conduct scaling experiments, which reveal that much of this efficiency gap can be explained by algorithms with scale-dependent efficiency improvements. In particular, we conduct scaling experiments between LSTMs and Transformers, finding exponent differences in their compute-optimal scaling law while finding little scaling difference for many other innovations. These experiments demonstrate that - contrary to standard assumptions - an algorithm's efficiency gains are tied to compute scale. Using experimental extrapolation and literature estimates, we account for 6,930x efficiency gains over the same time period, with the scale-dependent LSTM-to-Transformer transition accounting for the majority of gains. Our results indicate that algorithmic progress for small models has been far slower than previously assumed, and that measures of algorithmic efficiency are strongly reference-dependent.

cs.LG↗

arXiv2025

EvilGenie: A Reward Hacking Benchmark

We introduce EvilGenie, a benchmark for reward hacking in programming settings. We source problems from LiveCodeBench and create an environment in which agents can easily reward hack, such as by hardcoding test cases or editing the testing files. We measure reward hacking in three ways: held out unit tests, LLM judges, and test file edit detection. We verify these methods against human review and each other. We find the LLM judge to be highly effective at detecting reward hacking in unambiguous cases, and observe only minimal improvement from the use of held out test cases. In addition to testing many models using Inspect's basic\_agent scaffold, we also measure reward hacking rates for three popular proprietary coding agents: OpenAI's Codex, Anthropic's Claude Code, and Google's Gemini CLI. We observe explicit reward hacking by both Codex and Claude Code, and misaligned behavior by all three agents. Our codebase can be found at https://github.com/JonathanGabor/evilgenie_inspect .

cs.LG↗

arXiv2025

Quantum Deep Learning Still Needs a Quantum Leap

Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion based on a first-of-its-kind survey of quantum algorithms and how they match potential deep learning applications. This survey reveals three important areas where quantum computing could potentially accelerate deep learning, each of which faces a challenging roadblock to realizing its potential. First, quantum algorithms for matrix multiplication and other algorithms central to deep learning offer small theoretical improvements in the number of operations needed, but this advantage is overwhelmed on practical problem sizes by how slowly quantum computers do each operation. Second, some promising quantum algorithms depend on practical Quantum Random Access Memory (QRAM), which is underdeveloped. Finally, there are quantum algorithms that offer large theoretical advantages, but which are only applicable to special cases, limiting their practical benefits. In each of these areas, we support our arguments using quantitative forecasts of quantum advantage that build on the work by Choi et al. [2023] as well as new research on limitations and quantum hardware trends. Our analysis outlines the current scope of quantum deep learning and points to research directions that could lead to greater practical advances in the field.

quant-ph↗

arXiv2025

Who Needs Crossings?: Noncrossing Linkages are Universal, and Deciding (Global) Rigidity is Hard

We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs, with unit-length edges and where only noncrossing configurations are considered; and unrestricted graphs (crossings allowed) with unit edge lengths (or in the global rigidity case, edge lengths in $\{1,2\}$). We show that all nine of these questions are complete for the class $\exists\mathbb{R}$, defined by the Existential Theory of the Reals, or its complement $\forall\mathbb{R}$; in particular, each problem is (co)NP-hard. One of these nine results--that realization of unit-distance graphs is $\exists\mathbb{R}$-complete--was shown previously by Schaefer (2013), but the other eight are new. We strengthen several prior results. Matchstick graph realization was known to be NP-hard (Eades \& Wormald 1990, or Cabello et al.\ 2007), but its membership in NP remained open; we show it is complete for the (possibly) larger class $\exists\mathbb{R}$. Global rigidity of graphs with edge lengths in $\{1,2\}$ was known to be coNP-hard (Saxe 1979); we show it is $\forall\mathbb{R}$-complete. The majority of the paper is devoted to proving an analog of Kempe's Universality Theorem--informally, "there is a linkage to sign your name"--for globally noncrossing linkages. In particular, we show that any polynomial curve $\phi(x,y)=0$ can be traced by a noncrossing linkage, settling an open problem from 2004. More generally, we show that the regions in the plane that may be traced by a noncrossing linkage are precisely the compact semialgebraic regions (plus the trivial case of the entire plane). Thus, no drawing power is lost by restricting to noncrossing linkages. We prove analogous results for matchstick linkages and unit-distance linkages as well.

cs.CG↗

arXiv2025

Undecidability of Tiling with a Tromino

Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling. By contrast, the problem becomes decidable if the initial placement is finite, or if the tile is a domino instead of a tromino (in any dimension). As a consequence, tiling a given periodic subset of the plane with a given tromino (L or I) is co-RE-complete. We also prove co-RE-completeness of tiling the entire plane with two polyominoes (one of which is disconnected and the other of which has constant size), and of tiling 3D space with two connected polycubes (one of which has constant size). If we restrict to tiling by translation only (no rotation), then we obtain co-RE-completeness with one more tile: two trominoes for a periodic subset of 2D, three polyominoes for the 2D plane, and three connected polycubes for 3D space. Along the way, we prove several new complexity and algorithmic results about periodic (infinite) graphs. Notably, we prove that Periodic Planar (1-in-)3SAT-3, 3DM, and Graph Orientation are co-RE-complete in 2D and PSPACE-complete in 1D; we extend basic results in graph drawing to 2D periodic graphs; and we give a polynomial-time algorithm for perfect matching in bipartite periodic graphs.

cs.CG↗

arXiv2025

Quantum Advantage in Computational Chemistry?

For decades, computational chemistry has been posited as one of the areas in which quantum computing would revolutionize. However, the algorithmic advantages that fault-tolerant quantum computers have for chemistry can be overwhelmed by other disadvantages, such as error correction, processor speed, etc. To assess when quantum computing will be disruptive to computational chemistry, we compare a wide range of classical methods to quantum computational methods by extending the framework proposed by Choi, Moses, and Thompson. Our approach accounts for the characteristics of classical and quantum algorithms, and hardware, both today and as they improve. We find that in many cases, classical computational chemistry methods will likely remain superior to quantum algorithms for at least the next couple of decades. Nevertheless, quantum computers are likely to make important contributions in two important areas. First, for simulations with tens or hundreds of atoms, highly accurate methods such as Full Configuration Interaction are likely to be surpassed by quantum phase estimation in the coming decade. Secondly, in cases where quantum phase estimation is most efficient less accurate methods like Couple Cluster and Moller-Plesset, could be surpassed in fifteen to twenty years if the technical advancements for quantum computers are favorable. Overall, we find that in the next decade or so, quantum computing will be most impactful for highly accurate computations with small to medium-sized molecules, whereas classical computers will likely remain the typical choice for calculations of larger molecules.

quant-ph↗

arXiv2025

Introducing the Quantum Economic Advantage Online Calculator

Developing a systematic view of where quantum computers will outperform classical ones is important for researchers, policy makers and business leaders. But developing such a view is challenging because quantum advantage analyses depend not only on algorithm properties, but also on a host of technical characteristics (error correction, gate speeds, etc.). Because various analyses make different assumptions about these technical characteristics, it can be challenging to make comparisons across them. In this paper, we introduce an open-access web-tool designed to make such comparisons easy. Built on the framework introduced by Choi, Moses, and Thompson (2023), it calculates when quantum systems will outperform classical computers for a given algorithmic problem. These estimates can be easily updated based on various assumptions for error correction, overhead, and connectivity. Different hardware roadmaps can also be used and algorithm running times can be customized to particular applications. It can currently be accessed at https://futuretech.mit.edu/quantum-economic-advantage-calculator. This integrated prediction tool also allows us to explore which technical factors are most important for quantum ``economic" advantage (outperforming on a cost-equivalent basis). Overall, we find that for some algorithms (e.g. Shor's) the timing of advantage is quite robust, whereas for others (e.g. Grover's) it is contingent, with numerous technical characteristics substantially impacting these dates. In the paper, we discuss both why this occurs and what we can learn from it.

quant-ph↗

arXiv2025

Pushing Blocks without Fixed Walls via Checkable Gizmos: Push-1 is PSPACE-Complete

We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In particular, we remove the need for fixed (immovable) walls from a 2022 result. This fundamental model of block pushing, introduced in 1999, abstracts the mechanics of many video games. It was shown NP-hard in 2000, but its final complexity remained open for 25 years. Our result uses a new framework for checkable gadgets/gizmos, extending a prior framework for checkable gadgets to handle reconfiguration problems, at the cost of requiring a stronger auxiliary gadget. We also introduce a new connection between the motion-planning-through-gadgets framework (with an agent) and the Graph Orientation Reconfiguration Problem (with no agent), including Nondeterministic Constraint Logic.

cs.CC↗

arXiv2025

Subquadratic Approximation Algorithms for Separating Two Points with Objects in the Plane

The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has shown that the point-separation problem can be characterized as a type of shortest-path problem in a geometric intersection graph within a special lifted space. However, all known solutions to this problem essentially reduce to some form of APSP, and hence take at least quadratic time, even for special object types. We improve the conditional quadratic lower bounds for this problem, but our main results are positive: We bypass this barrier by providing subquadratic algorithms to produce solutions of size $\text{OPT}+1$ or $(1+\varepsilon)\text{OPT}+1$. Our algorithms are fundamentally different from the APSP-based approach. In particular, we give Monte Carlo randomized additive $+1$ approximation algorithms running in $\widetilde{\mathcal{O}}(n^{\frac32})$ time for disks, axis-aligned line segments and constant-complexity rectilinear polylines, and $\widetilde{\mathcal{O}}(n^{\frac{11}6})$ time for line segments and constant-complexity polylines. We will also give deterministic multiplicative-additive approximation algorithms that, for any value $\varepsilon>0$, guarantee a solution of size $(1+\varepsilon)\text{OPT}+1$ while running in $\widetilde{\mathcal{O}}\left(n/\varepsilon\right)$ time for disks, axis-aligned line segments and constant-complexity rectilinear polylines, and $\widetilde{\mathcal{O}}\left(n^{4/3}/\varepsilon\right)$ time for line segments and constant-complexity polylines.

cs.CG↗

arXiv2025

Meek Models Shall Inherit the Earth

The past decade has seen incredible scaling of AI systems by a few companies, leading to inequality in AI model performance. This paper argues that, contrary to prevailing intuition, the diminishing returns to compute scaling will lead to a convergence of AI model capabilities. In other words, meek models (those with limited computation budget) shall inherit the earth, approaching the performance level of the best models overall. We develop a model illustrating that under a fixed-distribution next-token objective, the marginal capability returns to raw compute shrink substantially. Given current scaling practices, we argue that these diminishing returns are strong enough that even companies that can scale their models exponentially faster than other organizations will eventually have little advantage in capabilities. As part of our argument, we give several reasons that proxies like training loss differences capture important capability measures using evidence from benchmark data and theoretical performance models. In addition, we analyze empirical data on the capability difference of AI models over time. Finally, in light of the increasing ability of meek models, we argue that AI strategy and policy require reexamination, and we outline the areas this shift will affect.

cs.AI↗

arXiv2025

All Polyhedral Manifolds are Connected by a 2-Step Refolding

We prove that, for any two polyhedral manifolds $\mathcal P, \mathcal Q$, there is a polyhedral manifold $\mathcal I$ such that $\mathcal P, \mathcal I$ share a common unfolding and $\mathcal I,\mathcal Q$ share a common unfolding. In other words, we can unfold $\mathcal P$, refold (glue) that unfolding into $\mathcal I$, unfold $\mathcal I$, and then refold into $\mathcal Q$. Furthermore, if $\mathcal P, \mathcal Q$ have no boundary and can be embedded in 3D (without self-intersection), then so does $\mathcal I$. These results generalize to $n$ given manifolds $\mathcal P_1, \mathcal P_2, \dots, \mathcal P_n$; they all have a common unfolding with the same intermediate manifold $\mathcal I$. Allowing more than two unfold/refold steps, we obtain stronger results for two special cases: for doubly covered convex planar polygons, we achieve that all intermediate polyhedra are planar; and for tree-shaped polycubes, we achieve that all intermediate polyhedra are tree-shaped polycubes.

cs.CG↗

arXiv2025

Quasigeodesics on the Cube

A quasigeodesic is a curve on the surface of a convex polyhedron that has $\le \pi$ surface to each side at every point. In contrast, a geodesic has exactly $\pi$ to each side and so can never pass through a vertex, whereas quasigeodesics can. Although it is known that every convex polyhedron has at least three simple closed quasigeodesics, little else is known. Only tetrahedra have been thoroughly studied. In this paper we explore the quasigeodesics on a cube, which have not been previously enumerated. We prove that the cube has exactly $15$ simple closed quasigeodesics (beyond the three known simple closed geodesics). For the lower bound we detail $15$ simple closed quasigeodesics. Our main contribution is establishing a matching upper bound. For general convex polyhedra, there is no known upper bound.

math.MG↗

arXiv2025

Slant/Gokigen Naname is NP-complete, and Some Variations are in P

In this paper we show that a generalized version of the Nikoli puzzle Slant is NP-complete. We also give polynomial time algorithms for versions of the puzzle where some constraints are omitted. These problems correspond to simultaneously satisfying connectivity and vertex degree constraints in a grid graph and its dual.

cs.DM↗

arXiv2025

EnigmaEval: A Benchmark of Long Multimodal Reasoning Challenges

As language models master existing reasoning benchmarks, we need new challenges to evaluate their cognitive frontiers. Puzzle-solving events are rich repositories of challenging multimodal problems that test a wide range of advanced reasoning and knowledge capabilities, making them a unique testbed for evaluating frontier language models. We introduce EnigmaEval, a dataset of problems and solutions derived from puzzle competitions and events that probes models' ability to perform implicit knowledge synthesis and multi-step deductive reasoning. Unlike existing reasoning and knowledge benchmarks, puzzle solving challenges models to discover hidden connections between seemingly unrelated pieces of information to uncover solution paths. The benchmark comprises 1184 puzzles of varying complexity -- each typically requiring teams of skilled solvers hours to days to complete -- with unambiguous, verifiable solutions that enable efficient evaluation. State-of-the-art language models achieve extremely low accuracy on these puzzles, even lower than other difficult benchmarks such as Humanity's Last Exam, unveiling models' shortcomings when challenged with problems requiring unstructured and lateral reasoning.

cs.AI↗