Theory of Computing Report

Simplex is usually stated with signed quorums that anyone can forward and verify. Here we describe an information-theoretic version. Parties have authenticated point-to-point channels, but no signatures and no transferable quorums. Each party therefore acts only on quorums of messages it received directly. The motivation is practical as well as conceptual: avoiding signatures removes signature verification from the critical path. Threshold signatures and multi-signatures can reduce this overhead in signed...

By Ittai Abraham, Sourav Das, Yuval Efron, Jovan Komatovic, Gilad Stern

Authors: Jehn-Ruey Jiang

We introduce Transition states (T states), denoted by $\ket{T_k^n}$, as a class of multipartite entangled states characterized by a fixed number of state transitions between adjacent qubits. These states form equal-amplitude superpositions over all states with a specified transition count. Unlike Bell states based on two-qubit correlations, GHZ states characterized by global correlations among all qubits, and W and Dicke states based on fixed numbers of qubit excitations, T states are defined by transition counts along an ordered sequence of qubits. We prove that T states are unitarily equivalent to Dicke states through a chain of CX (controlled-X) operations, thereby establishing a direct correspondence between transition-based and excitation-based representations of multipartite entanglement.

Authors: Marcel Wild

A Boolean function in CNF format is of type Positive$\wedge$Negative} if each clause C is either positive (i.e. all literals of C are positive) or negative (i.e. all literals of C are negative). As is well known, deciding the satisfiability of such CNFs is NP-complete. We say that a CNF is of type DisjointPositive if its clauses are positive and mutually disjoint. Dually define DisjointNegative. It is shown that the satisfiability of CNFs of type DisjointPositive$\wedge$DisjointNegative can be decided in quadratic time. Moreover, the modelset can be output in polynomial total time. This is relevant since it affects not only the modelsets of CNFs of type Positive$\wedge$Negative, but more generally of type Horn$\wedge$AntiHorn. As to the latter CNFs, they e.g. occur in connection with the fixpoints of a Monotone Boolean Network.

Authors: Abhishek Indupally, Ibraheem Alawadhi, Satchit Ramnath, Jami J. Shah

Engineering design is an iterative, simulation-driven process where traditional workflows rely heavily on computationally expensive analyses such as finite element and computational fluid dynamics. Although data-driven methods have accelerated design evaluation and optimization, most existing geometric representations discard parametric and feature-level semantics, limiting their integration with CAD-driven design workflows and reducing model interpretability. To address this gap, this work introduces Attributed Feature Graphs (AFGs), a feature-based representation that encodes design features, such as extrusions, ribs, and pockets, as nodes and their geometric or dependency relations as directed edges. AFGs preserve design intent and parametric structure while remaining compatible with standard graph-based learning methods, enabling end-to-end learning directly on CAD-derived feature graphs. The paper demonstrates the proposed representation through a surrogate-modeling case study on the CarHoods10K automotive hood frame dataset, where a Graph Neural Network (GNN) is trained as an evaluation engine to predict performance metrics from AFG inputs. The learned model achieves competitive surrogate performance compared with traditional data-driven approaches, but with the added benefit that engineers can map predictions back to specific CAD features and interpret how individual design elements influence system behavior. Furthermore, because AFGs are built from native CAD features, engineers can directly edit the underlying geometry in the CAD environment and reevaluate the design through the same learned model.

Authors: Henk Mulder

The extension of the analytic fractal curve trees of (2601.17490} to analytic surface patch trees reveals a new geometric structure: branch points are replaced by interface curves that transmit the full analytical state of parent patches to their children. These interfaces prove to be central in determining the topology of the surface patch trees, including for the conditions for self-similarity of the interfaces, the patches and thus the trees. We establish the analytic conditions for the integrability and well-posedness of the surface patch trees and introduce further restrictions for conformality. We demonstrate that patch trees have a natural foliation that slices the trees into one dimensional curve trees, each of which has their own Hausdorff dimension, jointly creating a smooth dimension field. We extend the two dimensional surface model to arbitrary dimensions $n$ where $n-1$ interface manifolds transport the $n$ field state of the parent patches to their child branches. We note that the balance or discrepancy between patch field dimension and the dimensions in which the branches may evolve, determine the analytical regime from essentially geometrical to essentially operational.

Authors: Alexandre L. M. Levada

Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for datasets with more than a few dozen features. This paper introduces two complementary contributions that together reduce this cost by several orders of magnitude. The first contribution is an exact algebraic identity. This identity, derived from the orthogonality of the eigenvectors of the covariance matrix and the cyclicity of the trace operator, eliminates $H$ entirely and reduces the per-point cost to $O(m^2)$ after the eigendecomposition. The second contribution addresses the remaining $O(m^3)$ bottleneck of the full eigendecomposition. Since the local covariance matrix has rank at most $k-1 \ll m$, we replace it with a truncated SVD of the $k \times m$ centered data matrix, an $O(k^2 m)$ operation, and derive an analytical approximation for the contribution of the null-space eigenvectors based on the expected value of their outer product under the Haar measure. The resulting estimator has total cost $O(k^2 m + k m p^2)$, where $p = k-1$. Experiments on real-world datasets confirm speedups of 50 to 300 times relative to the original implementation, with negligible loss when the fast estimator is used to replace the original version. By providing a scalable and data-driven estimate of local curvature, the proposed method establishes curvature as a practical geometric feature for a broad range of machine learning tasks, from classical to modern deep learning pipelines.

Authors: Chris Kapulkin, Nathan Kershaw

We introduce a new algorithm for computing persistent homology of Vietoris--Rips filtrations, which in many cases offers a considerable speedup over the existing implementation of the persistence pairing algorithm. The key innovation, called active enumeration, is made possible by a new theoretical framework of Reduction to Zero Differentials (hence RedZeD) in which to view persistent homology.

Authors: Vinicius M. Gonçalves, João Baião, Felipe Bartelt, Douglas G. Macharet, Gustavo M. Freitas, Héctor Azpúrua, Luciano C. A. Pimenta

Vector-field-based methods are widely used for robot control and are often applied to the path-tracking problem. Some vector field approaches require repeatedly computing the distance between the robot configuration and the curve, as well as the corresponding closest point. Recently, vector fields have been extended to Lie Groups. In this case, this computation can be expensive, especially when performed at high control frequencies on embedded platforms. This paper proposes a method for efficiently computing the distance between a point and a curve represented as what is called a G-polynomial curve, which is a curve representation that generalizes polynomial curves to matrix Lie groups. The proposed approach exploits the structure of these curves to reduce the problem to a small number of polynomial root-finding computations. Simulation results show that the method significantly reduces computation time while maintaining accuracy compared to existing optimization-based approaches. Practical formulas are also provided for the case of the group SE(3), and the method is validated experimentally on a robotic manipulator. The methodology is implemented in a computational package, available online.

Authors: Márk Hunor Juhász, Péter Madarasi

We study maximum matching problems in temporal graphs whose underlying graph is a tree. We consider two temporal models. In a $Δ$-matching, selected time edges sharing an endpoint must have time ticks differing by at least $Δ$. In a $γ$-matching, the selected objects are blocks of $γ$ consecutive appearances of the same underlying edge. We also consider the related ordered static problem of $d$-distance matchings. We show that maximum $Δ$-matching remains NP-hard on temporal trees for every $Δ\geq 2$, even in the sparse case where each edge appears at most twice. Using a reduction between the temporal models, we obtain the analogous result for maximum $γ$-matching on temporal trees, even when each edge admits at most two $γ$-edges. We also show, via a reduction from $d$-distance matching, that maximum $γ$-matching is APX-hard even when the underlying graph is bipartite. Complementing these hardness results, we identify several tractable cases. We prove that maximum $Δ$-matching is polynomial-time solvable on temporal trees in which every edge appears exactly once, and that maximum $γ$-matching is polynomial-time solvable when each edge admits at most one $γ$-edge. We also give dynamic-programming algorithms under bounded local-use and local-sparsity assumptions, and derive polynomial-time solvability of maximum $d$-distance matching when the input bipartite graph is a tree. Finally, we prove that both maximum $Δ$-matching and maximum $γ$-matching admit polynomial-time approximation schemes on temporal trees.

Authors: Naixu Guo, Po-Wei Huang, Qisheng Wang, Jayne Thompson, Patrick Rebentrost, Mile Gu, Chengran Yang

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Authors: Shan Jiang, Pan Peng

Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis. To enable efficient use of such structures at scale, we study the problem of \emph{triangle cut sparsification}, which aims to reduce the graph size while approximately preserving triangle counts across every cut. We investigate \emph{quantum algorithms} for this problem, using triangle listing as our main technical ingredient. In particular, we present a quantum algorithm for triangle listing that, for a graph with $n$ vertices, $m$ edges, and $t$ triangles, runs in time $T_{\mathrm{q\text{-}list}} =$ $\widetilde{O}\bigl(\min(n^{5/4}t^{7/12} + n^{7/6}t^{7/9}, m + m^{3/4}t^{1/2},$ $n^{3/2}t^{1/2})\bigr)$, improving upon the best known classical bounds over a broad range of parameters. Our algorithm is based on a heavy-light vertex partition and an extension of triangle detection via quantum walks and Grover search. Leveraging this result, we design a quantum algorithm for constructing $\varepsilon$-triangle cut sparsifiers of size $\widetilde{O}(n/\varepsilon^2)$ in time $\widetilde{O}(T_{\mathrm{q\text{-}list}} + \sqrt{mn}/\varepsilon)$. Finally, we demonstrate applications to clustering algorithms based on triangle-related measures and prove a lower bound of $Ω(n/\varepsilon^2)$ on the size of any $\varepsilon$-triangle cut sparsifiers.

Authors: Ruize Zhao

The textbook choice B=sqrt(n) for square-root decomposition is asymptotically natural, but it is not always the fastest implementation choice. We study block-size autotuning as a reproducible algorithm-engineering problem and show that a learned workload model can improve over fixed sqrt(n) on the tested implementation. Under repeated grouped cross-validation, the best policy is a full-feature KNN-9 model that reduces mean regret from 1.2882 to 1.0646 and yields a paired geometric-mean speedup of 1.151x. A confidence gate retains most of that gain while reducing slowdowns. A family-free full-observation follow-up remains better than fixed blocking, which suggests that the model is learning from workload statistics rather than memorizing labels. In contrast, short-prefix variants do not produce a successful low-overhead online tuner in the current prototype. External validation is selective but supportive: Zipf-Hotspot is the strongest out-of-distribution case, and a six-window Baleen follow-up still improves over fixed blocking. Overall, block-size choice is workload aware and platform aware, and the fixed sqrt(n) rule leaves substantial performance on the table.

Authors: Luciano Gualà, Simone Pellegrini, Luca Pepè Sciarria, Alessandro Straziota

Motivated by the problem of detecting large and cohesive groups of vertices in real networks, the task of finding large \emph{quasi-cliques} has attracted considerable attention across different research areas. From a computational complexity perspective, strong inapproximability results are known for this problem, yet several heuristics have been proposed to identify large quasi-cliques in real-world networks. Recently, [Pang \emph{et al.}, (WWW 2024)] introduced a similarity-based approach that represents the current state of the art. In this work, we extend that approach to \emph{dynamic} networks, thereby addressing an open problem posed by [Pang \emph{et al.}, (WWW 2024)]. We first present a Baseline fully dynamic algorithm where edges of the network can be both inserted and deleted. The algorithm exactly maintains the same quasi-clique returned by the algorithm by Pang et al. on the current graph, with update time $\widetilde{O}(Δ)$, where $Δ$ is the maximum degree. We then focus on the practically relevant incremental case, where only edge insertions are allowed, and design an algorithm with $O(\log Δ)$ update time. This method leverages a novel technique for dynamically maintaining accurate estimates of vertex $γ$-degrees, a core component of framework by Pang et al., and achieves up to $207\times$ speed-up over the Baseline while preserving comparable solution quality. Finally, we extend the approach to the fully dynamic setting, supporting both insertions and deletions, obtaining up to $21\times$ speed-up with limited and acceptable loss in quasi-clique size and density. We provide a formal analysis of our algorithms and validate them through an extensive set of experiments on real-world datasets.

Authors: Marcin Zukowski

Huffman encoding has been an enduring technique for 70+ years, ubiquitous in compression algorithms since its invention. In this paper we propose a new approach to Huffman coding, based on a data structure from wavelet trees. The resulting pivot-coded Huffman (PivCo-Huffman) enables high-performance SIMD-friendly encoding and decoding operations. In our tests PivCo-Huffman consistently outperforms state-of-the-art Huffman codecs in decoding throughput. Additionally, we show how ANS-coding can be selectively applied to skewed nodes in this structure, yielding compression ratios approaching those of ANS-based codecs while preserving very high decompression speeds.

Authors: Ting Hou, Yanhao Wang, Yiping Wang, Cen Chen, Minghao Zhao, Fan Dang

In this paper, we study multi-objective submodular maximization (MOSM) subject to a cardinality constraint under differential privacy (DP). Specifically, we aim to select a set of at most $k \in \mathbb{Z}_{+}$ elements to maximize the minimum of $d > 1$ monotone submodular functions while satisfying $\varepsilon$-DP. Although extensive studies have been conducted on both differentially private single-objective submodular maximization on sensitive data and non-private MOSM, to the best of our knowledge, there has not yet been any prior work on MOSM with DP. We propose two novel algorithms: the first extends the classic greedy algorithm and the second employs a truncation technique, both of which are integrated with DP mechanisms for privacy protection and achieve approximation guarantees for MOSM. Finally, we conduct numerical experiments on two submodular maximization applications, namely maximum coverage and facility location, in multi-objective settings to validate the efficacy and efficiency of our proposed algorithms.

Authors: Josh Ascher, Eric Balkanski, Jason Chatzitheodorou, Vasilis Gkatzelis

In the classic online min-cost matching problem, the goal is to match a sequence of requests that arrive dynamically over time to a set of static servers, aiming to minimize the total cost of the matching. This assumes that there are two distinct "sides" and that only one of these sides arrives online, but many of the motivating applications violate these assumptions. We study online min-cost perfect-matching when \emph{all} participants arrive online and, upon arrival, they need to either be matched to someone from a waiting pool or to join the waiting pool. We evaluate the competitive ratios achievable in different input models and show that for both the adversarial and the random-order input models the competitive ratio of any algorithm is unbounded. In contrast, for i.i.d. arrivals we give a $O( \log^2{n})$-competitive algorithm, even if the distribution that generates these arrivals is unknown to the algorithm. This result implies a rare example of separation in the achievable competitive ratio between the random-order and the unknown-i.i.d. input models.

Authors: Lei Dong, Bowie Liu, Dennis Wong, Lin Chen, Chan-Tong Lam, Sio-Kei Im

A grand Motzkin path with air pockets is a non-empty lattice path in the first and fourth quadrant of $\mathbb{Z}^2$, starting at the origin $(0,0)$, ending on the $x$-axis, and consisting of up-steps $(1, 1)$, horizontal steps $(1, 0)$, down-steps $(1, -k)$ where $k \geq 1$, and with no consecutive down-steps. A {grand Dyck path with air pockets} is a grand Motzkin path with air pockets that uses no horizontal steps. We present the first known 2-Gray codes for grand Motzkin paths with air pockets. Setting the number of horizontal steps to zero in our algorithm yields the first known 2-Gray codes for grand Dyck paths with air pockets. Our three-stage algorithm generates each path in constant amortized time per string, using $O(n^2)$ memory. We also provide enumeration formulae for grand Motzkin paths and grand Dyck paths with air pockets.

Authors: Faruk Alpay, Levent Sarioglu

A long-running append-mostly sequence, such as an edit log, event store, or versioned working set, is usually tiered into a bounded hot stratum and colder folded summaries. This saves memory but breaks stable references: a handle minted while a record is hot may later be resolved after the record has moved into a digest, after it has been superseded, or while a fold is in flight. We define the resulting cross-tier anomalies--dangling, stale, corrupt, and snapshot-skewed resolution--and present the Cascade Log, a reference-stable tiered append structure. The structure keeps a single persistent coalescing interval map over handles as the sole authority on each live version; folding a contiguous run replaces many singleton entries by one digest-backed interval node, and immutable roots provide snapshot tokens. Its cost is characterized by the fragmentation $A$, the number of index pieces, namely live handles plus maximal same-digest runs. The index uses $Θ(A)$ space, resolves a point in $O(\log A)$, reports a $k$-handle range in $O(\log A+k)$, and performs $a$ appends and $s$ supersedes in $O((a/B+s)\log A)$ update work for fold block size $B$. Matching lower bounds show that $Ω(A)$ space and $Ω(\log A+k)$ ordered range cost are unavoidable, and an adversary can force $A=Θ(s)$. Thus the index is sublinear on append-dominated histories and grows linearly only under fragmenting edits. A reference implementation and reproducible experiments to $10^6$ records validate the anomaly-freedom and the fragmentation bounds.

Authors: Christian Coester, Alexa Tudose, Alexander Turoczy

We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.

Authors: Haoyu Wang, Guangxu Yang

In this paper, we give a one-pass quantum streaming algorithm for Max-$k$SAT that uses $\operatorname{polylog}(n)$ space and achieves a $0.7172$-approximation on instances with $n$ variables. In contrast, prior work by Chou, Golovnev, and Velusamy (FOCS 2020) implies that achieving an approximation ratio better than $\sqrt{2}/2 \approx 0.7071$ for Max-$k$SAT requires $Ω(\sqrt{n})$ space for any classical streaming algorithm. Therefore, it yields an exponential quantum space advantage for Max-$k$SAT in the streaming setting. We further give a one-pass quantum streaming algorithm for Max-2OR that uses $\operatorname{polylog}(n)$ space and achieves a $0.7425$-approximation on instances with $n$ variables. Combining with the known results, it gives a complete classification of quantum space advantages for all Boolean Max-2CSPs.

June 4-22, 2026 STOC 2026, Salt Lake City, Utah, USA, and Gather.Town https://acm-stoc.org/stoc2026/call-for-posters.html Submission deadline: June 12, 2026 As part of the STOC 2026 program, we will be hosting an online poster session from 18:30-19:30 MDT (GMT -6) on Monday, June 22, 2026 on the platform Gather.Town. Our hope is that people who cannot come … Continue reading STOC TheoryFest 2026 Online Poster Session – Call for Posters

By shacharlovett

Weighted pseudorandom generators (wPRGs) were suggested by Braverman, Cohen, and Garg (STOC, 2018) as a relaxation of pseudorandom generator (PRG) used for derandomization. We present proofs of several observations regarding wPRGs, where some of these observations are well known.

There is a tempting story you can tell about the cardiology megatrials I’ve written about in the past few posts. If you focus on a single health outcome (say, mortality) and a single disease (say, infarctus du myocarde, aka heart attack), you can optimize the treatment program by continually running randomized clinical trials. Each trial will carefully compare two nearly identical treatment regimens that differ only in a single step. Professional societies will regularly communicate the latest results and guidelines. Piecemeal improvements to the standard of care will be broadcast at meetings and on websites to keep all clinicians up to date on the best plan for every patient.

This approach can be applied to multiple diseases. With enough buy-in, these trials can be scaled up to provide personalized adjustments to the standard of care. Patients’ demographic information, family history, and behaviors can then be considered, and professional societies can craft specialized plans for each demographic bucket.

Now, statistical calculations would quickly tell you that you need far more than 8 billion people to make this optimized dream a reality. But let’s leave that aside for a minute. There’s something bizarre and alienating about this view. In this pipe dream, care becomes nothing more than a computer algorithm. A patient becomes nothing more than a classification assignment. Healthcare becomes nothing more than optimizing actuarial tables. Is this dignified? Is this care? Is this what we want the medical system to be?

There was a reactionary and revolutionary movement in the 1990s that thought yes, healthcare should be nothing more than the application of clinical data: evidence-based medicine.

EBM remains incredibly influential. I mean, who wants medicine that isn’t based on evidence, right? Back in 2020, I also had a brief moment when I thought this was a brilliant way to conceptualize medicine. For mathematically minded people, EBM has the appeal of rigor. It provides what appears to be a set of clear rules for deciding on medical treatment. There is a hierarchy of evidence. A pyramid, if you will:

Expert opinion is the lowest form of evidence. Case studies are barely better. Epidemiological studies would be of slightly higher grade, but these are too easily fooled by confounding causes. A big step above, a gold standard, is the randomized controlled trial. And at the very top, we place an even higher grade on systematic reviews of all randomized controlled trials conducted on a disease.1

Once you have this evidence in hand, you can make clear decisions. You don’t need expertise. You simply need a Meehlian formula: you plug all of the data you have about a patient into a computer. The computer spits out a treatment plan for the patient based on the highest grade evidence available. Healthcare is now solved.

You might think I’m caricaturing their position, but you can go back to the original position papers, and the quotes are even stronger than what I say. Here’s the opening paragraph of “Evidence-Based Medicine: A New Approach to Teaching the Practice of Medicine,” written by a working group chaired by EBM pioneer Gordan Guyatt:

“A new paradigm for medical practice is emerging. Evidence-based medicine de-emphasizes intuition, unsystematic clinical experience, and pathophysiologic rationale as sufficient grounds for clinical decision making and stresses the examination of evidence from clinical research. Evidence-based medicine requires new skills of the physician, including efficient literature searching and the application of formal rules of evidence evaluating the clinical literature.”

The working group was explicit about expert judgment: “The new paradigm puts a much lower value on authority. The underlying belief is that physicians can gain the skills to make independent assessments of evidence and thus evaluate the credibility of opinions being offered by experts.” In their view, expert intuition and creative care caused more harm than good. Moreover, they thought a move to computerized decision making would improve patient outcomes, writing “A final assumption of the new paradigm is that physicians whose practice is based on an understanding of the underlying evidence will provide superior patient care.”

Computerization was exactly what they had in mind. David Sackett put together a prototype treatment computer, called The Evidence Cart, in the early nineties. Check him out making a diagnosis:

Sackett stuffed the evidence cart with a compendium of information: BestEvidence, the JAMA Rational Clinical Examination series, the Cochrane Library, multiple textbooks, and material compiled by his collaborators from journal groups and other assessments. Sackett’s crew would wheel the Evidence Cart into a patient room and evaluate each decision against the best evidence.

Did it work? Hilariously, the evidence that the Evidence Cart works is a tiny, single-center observational study, not an RCT. But the influence of EBM and the goal of making Sackett’s dream a reality was undeniable. Doctors now have supercomputers in their pockets at all times. They can pull out medical calculators, reduce patients to categories, and prescribe treatment plans based on the best evidence. Every doctor-patient visit is hooked up to a different computer that serves not only as a way for doctors to keep records of how their patients are doing, but also as a way to file them as statistics in actuarial tables at insurance companies and to enter their virtualized identity into the pool of future observational studies.

Has healthcare landed in a good spot? It’s complicated. Obviously, studies are good. But the idea that you can synthesize an optimal decision from the medical literature is crazy, whether you have modern LLMs or not. You can’t do an RCT of every possible option. We’ve already seen that expert knowledge is needed to decide which RCTs to do and to make sense of RCTs that seemingly contradict each other. And the medical literature does not tell you what to do with an individual patient. Patients are not just category labels. Care is more than robotic decision-making.

I’m more sympathetic to the iatrogenic argument put forward by the EBM pioneers. Many were medical conservatives. They thought that most treatments not only lacked evidence but were also harmful. You can look at the barbarism that riddles the history of medicine and certainly see that they had a point. Medical conservatives believe that we should err on the side of treating less not more. EBM was partially a battle against the intervention bias that still plagues medicine. “We have to do something” feels right, but is often harmful. This is why the CAST trial on anti-arrhythmia drugs is a poster child for the movement.

Though well-intentioned, evidence-based medicine is one of the best case studies of how the quantification trap leads to madness. We computerize everything to displace the influence of narratives. Mechanism and natural law don’t matter. The only thing that matters is optimizing outcomes. The pursuit of medical knowledge is only to optimize actuarial tables, not to understand the human condition. Medicine becomes a video game. This is the purest form of what Jean-François Lyotard called postmodernism. Statistical thinking run amok is the postmodern condition.

Subscribe now

By Ben Recht

Authors: Qisheng Wang

Tight bounds on quantum sample complexity and quantum query complexity have been known for various computational problems in the literature, whereas tight bounds on quantum time complexity (i.e., the size of quantum circuits) remain unresolved. In this paper, we provide a framework to establish lower bounds on the quantum time complexity for testing permutation-invariant properties of quantum states, via a reduction from quantum sample complexity. As an application, we obtain a series of matching lower bounds when given sample access to the input quantum states, including: 1. The SWAP test due to Buhrman, Cleve, Watrous, and de Wolf (Phys. Rev. Lett. 2001) is time-optimal to estimate the purity $\operatorname{tr}(ρ^2)$ and the inner product $\operatorname{tr}(ρσ)$. 2. The Shift test due to Ekert, Alves, Oi, Horodecki, Horodecki, and Kwek (Phys. Rev. Lett. 2002) is time-optimal to estimate the high-order functionals $\operatorname{tr}(ρ^k)$. 3. The productness tester for multipartite pure states due to Harrow and Montanaro (J. ACM 2013) is time-optimal. 4. The LMR protocol due to Lloyd, Mohseni, and Rebentrost (Nat. Phys. 2014) is time-optimal to implement the reflection operator about a pure state. 5. The samplizer due to Wang and Zhang (IEEE Trans. Inf. Theory 2025) is time-optimal for pure states. 6. The estimator for pure-state trace distance and fidelity due to Wang and Zhang (ICALP 2026) is time-optimal. To the best of our knowledge, this is the first method that allows us to systematically establish tight lower bounds on quantum time complexity.

Authors: Fedor Kiselev

We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations.

Authors: Matthew Finlayson, Andreas Grivas, Xiang Ren, Swabha Swayamdipta

Language model parameters are known to impose unique (to each model) geometric constraints on their logit outputs, which serves as a signature that identifies the model, but also leaks the model's final layer parameters when an API distributes logits. We investigate more restrictive APIs that expose token rankings (i.e., their ordering by probability, but not the probability values) and find that rankings also constitute a signature: every model has a unique set of feasible top-$k$ rankings for sufficiently large $k$. Furthermore, the ranking signature is the first known (polynomially) unforgeable signature, since finding a model with the same set of feasible rankings is NP-hard. On the security front, we find that token rankings are already sufficient to approximately steal the final layer of the model, similar to logits, though the approximation is too coarse to forge the signature, and can be effectively countered by restricting the API to top-$k$ tokens with sufficiently small $k$. Since the top-$k$ required to present the model signature is generally smaller than the $k$ required to prevent stealing, it is possible for an API to present an unforgeable signature without leaking model parameters.

Authors: Tayfun Pay

We define a new family of complexity classes called bit-counting complexity classes, since membership depends not merely on the number of accepting paths, but also on the binary profile of that number. We study the relationship between this new family of complexity classes and the classical complexity classes. We prove that the classical complexity class ${\bf PP}$ is contained in our comparison based bit-counting complexity classes ${\bf B_{|0|=|1|}P}$, ${\bf B_{|0|<|1|}P}$ and ${\bf B_{|0|>|1|}P}$. We further show that all of these complexity classes are Turing equivalent ${\bf P}^{\bf PP} = {\bf P}^{{\bf B_{|0|=|1|}P}}={\bf P}^{{\bf B_{|0|>|1|}P}}={\bf P}^{{\bf B_{|0|<|1|}P}}$. We also prove that classical complexity classes ${\bf NP}$ and ${\bf CoNP}$ are contained in both of our parity based bit-counting complexity classes ${\bf B_{|0| \oplus}P}$ and ${\bf B_{|1| \oplus}P}$.

Authors: Hunter Monroe

Monroe (2026) shows that the nonexistence of an optimal proof system can be read as an information constraint regarding canonical hard instances: no sound arithmetic theory simulates the extensions adjoining sufficiently large, unprovable Busy Beaver values. Furthermore, if the best-known route to simulation is also necessary -- that is, if simulation requires a relative-consistency explanation over a weak base theory -- then the same constraint holds for inaccessible Kolmogorov-randomness facts. Call this Kolmogorov Hardness (KH). We argue that open questions in computational complexity can likewise be reformulated as information constraints involving Kolmogorov-random strings. Variants of KH yield, as conditional consequences, dense families of small hard tautologies, no-mutual-help phenomena for independent random axioms, PH noncollapse with explicit dense separators at each level, $SAT\notin P/poly$, and canonical disjoint NP pairs arising from random-axiom constructions. Time-bounded and sparse-support variants extend the same template to one-way functions via Liu--Pass, derandomization, natural-proofs-style limitations, and Feige-style random refutation. This framework gives a unified working model of complexity theorists' beliefs, organized around canonical hard instances. It seems self-evident that efficient proofs in a theory should not leverage true randomness facts the theory cannot verify. Yet the structural features of KH and its variants suggest they may be formally independent of standard metatheories. They behave like reflection principles; their internal readings fail in nonstandard models even when the corresponding external readings are true; and the same information constraints may apply to the metatheories themselves. We propose a research program: extend the model, resolve questions of formal independence, and identify which principles are potential new axioms.

Authors: Masahito Nakano

We study Sibley's guard-point convexity measure for simple polygons and compare it with the exterior and perimeter convexity measures. We prove the exterior inequality G(F) <= E(F) and disprove the pointwise perimeter inequality G(F) <= P(F) by an explicit nonconvex pentagon with G(F) = 62/63 and P(F) = 185/189. Nevertheless, we prove the uniform bound G(F) <= 2P(F) for every simple polygon. Thus the pointwise perimeter inequality is false, but the corresponding asymptotic non-domination conclusion remains true. We also record an auxiliary guard-point-adapted anisotropic perimeter ratio, which isolates the directional loss in the Euclidean perimeter comparison.

Authors: Minjie Tang, Xiangfei Li

Generating compact polygonal models from point clouds is a key problem in 3D vision and computer graphics. However, due to inherent limitations of LiDAR scanning (e.g. range constraints and occlusions), critical scene information is often missing, leading to degraded reconstruction accuracy. To address this, we propose a plane assembling strategy that effectively recovers missing details while maintaining model compactness. We classify all the planes extracted from the scene into three categories: highly visible, barely visible, and invisible. The invisible planes, which are recovered by scene structure analysis, indicate the missing details. The three types of planes correspond to the three growth priorities. Each plane grows according to the priority level, and the space is partitioned progressively, namely, the hierarchical partition. Subsequently, we generate a watertight polygonal mesh from the partition via a min-cut-based optimization. Finally, comparisons on public datasets show the effectiveness and superiority of our method against mainstream approaches. The project page is available at https://hsr-3dv.github.io/.

Authors: Panagiotis Simatis, Panagiotis Bouros, Nikos Mamoulis

Spatial indexing is foundational to Geographic Information Systems (GIS) and multi-dimensional data management, yet the current open-source landscape poses a significant barrier to research that employs or benchmarks spatial access methods. We observe that most of the existing open-source libraries include a single index. Some are hindered by complex dependencies, missing critical functionalities, inconsistent APIs, and rigid constraints regarding the support of spatial data types. To address this issue, we introduce Indexicon: a unified, highly portable, extendable, open-source spatial indexing library, designed specifically for rapid integration and ease of modification of main-memory spatial access methods. Indexicon provides a comprehensive suite of popular tree-based spatial access methods, including the R-tree, Quad-tree variants, and the KD-tree. Each structure is meticulously implemented as a self-contained, single-file, header-only C++ template with zero external dependencies beyond the standard library. Crucially, every index features a uniform interface, natively supporting bulk-loading, dynamic insertions/deletions, range queries, $k$-nearest neighbor ($k$NN) search, and structural statistics tracking. We also present an extensive performance evaluation of Indexicon against well-established and widely used implementations of these structures (including Boost Geometry, PCL, and Nanoflann) across six real-world geographic datasets. Our results demonstrate that Indexicon's lightweight design matches or outperforms existing state-of-the-art implementations while offering unmatched architectural flexibility. To foster reproducible spatial research, we open-source the complete library alongside our datasets and query workloads.

Authors: Shakiba Khourashahi, Ilia Jahanshahi, Bei Wang, Lin Yan

As data becomes increasingly central across engineering and scientific disciplines, effective visualization is essential for interpreting complex, high-dimensional structures. Dimensionality reduction techniques project high-dimensional data into lower dimensions while aiming to preserve structural properties such as pairwise distances and local neighborhoods. In this paper, we focus on improving homological preservation, that is, the retention of topological features such as connected components and loops, which is critical for maintaining global shape and continuity. We first introduce AdaMapper, a Mapper-based algorithm that leverages persistence diagrams to guide both skeleton construction and landmark selection. AdaMapper incorporates an adaptive refinement strategy that automatically increases cover resolution in regions exhibiting topological loops. We then propose AdaHIsomap, which extends landmark Isomap by incorporating homology-informed landmark selection and augmenting it with random anchor points to better balance distance and homology preservation. We evaluate both methods on a diverse set of datasets, including high-dimensional point clouds, scientific simulations, networks, and image data, and benchmark their performance against state-of-the-art approaches.

Authors: Anda Skeja, Daniel Gutiérrez Espinoza, Fiona Skerman, Alexander S. Wein

We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.

Authors: Tim A. Hartmann, Dániel Marx

The distance-d variants of Independent Set and Dominating Set problems have been extensively studied from different algorithmic viewpoints. In particular, the complexity of these problems are well understood on bounded-treewidth graphs [Katsikarelis, Lampis, and Paschos, Discret. Appl. Math 2022][Borradaile and Le, IPEC 2016]: given a tree decomposition of width t, the two problems can be solved in time $d^t \cdot n^{O(1)}$ and $(2d + 1)t \cdot n^{O(1)}$, respectively. Furthermore, assuming the Strong Exponential-Time Hypothesis (SETH), the base constants are best possible in these running times: they cannot be improved to $d-ε$ and $2d+1-ε$, respectively, for any $ε > 0$. We investigate continuous versions of these problems in a setting introduced by Megiddo and Tamir [SICOMP 1983], where every edge is modeled by a unit-length interval of points. In the δ-Dispersion problem, the task is to find a maximum number of points (possibly inside edges) that are pairwise at distance at least δ from each other. Similarly, in the δ-Covering problem, the task is to find a minimum number of points (possibly inside edges) such that every point of the graph (including those inside edges) is at distance at most δ from the selected point set. We provide a comprehensive understanding of these two problems on bounded-treewidth graphs.

Authors: Andrei Graur, Aaron Sidford, Ta-Wei Tu

We provide faster deterministic and randomized algorithms for exactly solving discounted Markov Decision Processes (DMDPs). We obtain our results by efficiently reducing computing optimal values and policies in DMDPs to the easier tasks of policy evaluation and computing approximately optimal values in DMDPs. We provide both a straightforward deterministic reduction and a more efficient randomized variant that, together with advances in approximately solving DMDPs, yield our results.

Authors: Deniz Elbek, Kamer Kaya

Modern GPUs have Tensor Cores (TCs) capable of extremely high-throughput matrix operations, yet graph algorithms remain difficult to accelerate because of their irregular and data-dependent execution patterns. This work presents BLEST, a TC-accelerated framework that reformulates Breadth-First Search (BFS) as a bit-level sparse matrix-vector computation while addressing the load imbalance, memory inefficiency, and synchronization overheads that limit prior approaches. BLEST introduces Binarized Virtual Slice Sets (BVSS), a graph representation that partitions work into balanced warp-level units and schedules only frontier-relevant regions of the graph. It further employs an optimized TC layout that maps neighbour checks onto binary MMA instructions without wasted outputs, reducing the number of required MMA calls by 8$\times$ compared with prior layouts. To mitigate atomic and cache bottlenecks, BLEST incorporates a lazy vertex-update scheme. We revisit the switching terminology for BFS and propose a mechanism that dynamically transitions from TCs to CUDA cores when it becomes more efficient. We also extend BLEST to multi-source BFS and closeness centrality workloads. Finally, we introduce a scalable graph reordering method that improves compression for scale-free-like graphs, while using RCM to improve locality for others. Across a broad set of real-world graphs, BLEST achieves average speedups of 22.0$\times$, 7.7$\times$, 8.1$\times$, and 5.9$\times$ over GAP, Gunrock, GSWITCH, and BerryBees, respectively, establishing a new BFS baseline on GPUs. Thanks to its high performance, BLEST can compute the exact closeness centralities of 65.6M vertices in a social network with 3.6B edges in an hour using 100 H100 GPUs.

Authors: Paul Dütting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Ola Svensson, Morteza Zadimoghaddam

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

Authors: Piotr Frydrych

Let R denote the class of all computable, causal functionals that are rate-independent in the classical sense (invariant under monotone time reparametrizations), and let Pi_n be the Preisach extremum stack of an input sequence u_{0:n}. We prove a characterization theorem establishing that every F in R satisfies Fu = f(Pi_n) for a computable f, and derive two information-theoretic results. First, under any probability measure on u_{0:n}, the equality I(u_{0:n}; Fu) = I(Pi_n; Fu) holds for every F in R and is an immediate corollary of the characterization theorem. Second, the main result: Pi_n is a Shannon-minimal sufficient statistic in the sense that I(u_{0:n}; Pi_n) <= I(u_{0:n}; S) for every random variable S from which all R-queries are computable. The proof uses the finite indicator family of [Frydrych, 2026] to reconstruct Pi_n from any sufficient S. As a corollary, online maintenance of Pi_n suffices for rate-independent estimation: the NNLS estimator of the Preisach measure mu can be assembled from the incremental stack process (Pi_t)_{t=0}^n in O(k * L^2) memory per step, where k = |Pi_t| and L is the grid resolution.

Authors: Piotr Frydrych

The Preisach extremum stack $Π_n$ is the minimal sufficient statistic for the class $\mathcal{R}$ of computable rate-independent functionals in the Kolmogorov complexity sense [1]. Its standard update algorithm runs in amortised $O(1)$ time, but adversarial inputs can force $Θ(k)$ operations per step (where $k$ is the current depth). We establish a three-level complexity picture: (i) any compact exact $\mathcal{R}$-minimal representation incurs $Θ(k)$ output changes per step in the worst case (in a model-independent output-change metric); (ii) the monotone ordering of the Preisach wiping property enables binary search, reducing boundary detection to $O(log k)$, though physical deletion remains $Θ(d)$; (iii) a finger-tree implementation achieves $O(log k)$ worst-case time per step for both search and deletion, at the cost of a more complex data structure, while maintaining exact $\mathcal{R}$-minimality with no approximation error. These results settle the worst-case complexity of the Preisach extremum stack across all three levels.

Authors: David Alemán Espinosa, Niklas Schlomberg

The multicommodity flow problem in an undirected capacitated graph $G$ is specified by a set of source-sink pairs with nonnegative demands. A flow is feasible if it routes all demands without exceeding the edge capacities, and it is unsplittable if it routes each demand along a single path. Let $α$ be the smallest value such that the existence of a feasible flow implies the existence of an unsplittable flow that exceeds the edge capacities by at most $+\,α\,d_{\max}$, where $d_{\max}$ is the maximum demand value. Schrijver, Seymour, and Winkler showed that $α\in\left[1.01,\,1.5\right]$ if $G$ is a cycle. These bounds were ultimately improved to $α\in\left[1.1,\,1.3\right]$ by Skutella and Däubel. Recently, Alemán Espinosa and Kumar extended this constant upper bound to the broader class of outerplanar graphs, and showed that if $G$ is outerplanar then $α\le 3.6$. We show that $α\in\left[\tfrac{4}{3},2\right]$ if $G$ is outerplanar. We introduce a novel technique that considers the global parameters of the instance, and that may be useful in other (more general) settings where the cut-condition is sufficient, or nearly sufficient, for the existence of a feasible flow.

Authors: Šimon Schierreich, Ildikó Schlotter

Majority illusion is an undesirable phenomenon in social networks in which agents incorrectly perceive a minority opinion as dominant. This can severely distort collective behavior and decision-making. We study the fundamental question of detecting whether a social network allows for a majority illusion. Formally, in the $q$-Majority Illusion problem, we ask whether there exists a binary labeling of agents in which at least a $q$-fraction of agents have the majority of neighbors with the minority label. We investigate how various structural properties of the underlying social network influence the tractability of this question, and provide a detailed map of its computational complexity.

Authors: Jason L. Volk

We present an algorithmic framework for incremental maintenance of first sheaf cohomology $H^1(X; \mathcal{F})$ on dynamically evolving 1-dimensional cellular complexes equipped with finite-dimensional cellular sheaves. The classical computation of $H^1$ via factorization of the coboundary matrix requires $O(n^3)$ time; when the complex evolves with a stream of $m$ edits, full recomputation after each edit costs $O(mn^3)$. Under a bounded local geometry assumption -- bounded cell size $v_{\max}$, bounded stalk dimension $d$, and bounded nerve degree $D$ -- each edit (vertex insertion, edge insertion, restriction map update) affects only a bounded set of local coboundary blocks. The algorithm therefore processes lazy streaming edits in $O(1)$ time with respect to the total complex size $n$ (with cost polynomial in the local geometry parameters $v_{\max}$, $d$, and $D$, which are treated as constants independent of $n$), deferring local eigensolves and Mayer-Vietoris global assembly to synchronization points (Flush). At synchronization, the maintained state agrees with the corresponding batch assembly of the partitioned sheaf model; we observe zero measured drift in all batch-verified runs (through $V = 10^6$). We also give an amortized $O(|E|)$ streaming construction for the cellular decomposition and discuss an adversarial algebraic-RAM barrier arguing that unpartitioned non-trivial sheaves ($d \geq 2$, non-identity restriction maps) do not admit the same locality. Experiments on Barabasi-Albert graphs with up to $5 \times 10^6$ vertices and $1.7 \times 10^7$ streaming edits show 35 $μ$s median lazy per-edit update latency (excluding flush); query time (global assembly at synchronization) is $O(n)$ per flush in the implemented full-traversal path. Exact synchronization costs are reported separately.

In this paper, we give a one-pass quantum streaming algorithm for Max-$k$SAT that uses $\operatorname{polylog}(n)$ space and achieves a $0.7172$-approximation on instances with $n$ variables. In contrast, prior work by Chou, Golovnev, and Velusamy (FOCS 2020) implies that achieving an approximation ratio better than $\sqrt{2}/2 \approx 0.7071$ for Max-$k$SAT requires $\Omega(\sqrt{n})$ space for any classical streaming algorithm. Therefore, it yields an exponential quantum space advantage for Max-$k$SAT in the streaming setting. We further give a one-pass quantum streaming algorithm for Max-2OR that uses polylog(n) space and achieves a $0.7425$-approximation on instances with $n$ variables. Combining with the known results, it gives a complete classification of quantum space advantages for all Boolean Max-2CSPs.

We show that several meta-complexity problems are NP-hard under randomized polynomial-time (half-Levin) reductions, and provably cannot be NP-hard under randomized Levin reductions, under the assumptions that (cryptography): there exists a subexponentially-secure indistinguishability obfuscator in the sense of Barak et al. (JACM 2012), and (proof complexity): there are no infinitely-often subexponentially-optimal propositional proof systems in the sense of Cook and Reckhow (J. Symb. Log. 1979) and Krajicek and Pudlak (J. Symb. Log. 1989). In particular, this is shown for (1) the problem of improper full-support PAC learning of boolean functions in P/poly, and (2) a gap-version of the Implicit Minimum Circuit Size Problem (ImpMCSP). More precisely, for item (1), we consider the following learning problem $TotL$: Given a circuit sampling a distribution $\mathcal{E}$ of labeled examples $(x, b)\in\{0,1\}^n\times\{0,1\}$ so that every $x\in\{0,1\}^n$ is in the support of $\mathcal{E}$, distinguish between the two cases: (a) there exists a circuit $C$ of size at most $s$ that, for all $(x,b)$ in the support of $\mathcal{E}$, $C(x)=b$, and (b) no circuit $C$ of size $subexp(s)$ satisfies $C(x)=b$ with probability noticeably higher than $1/2$ over samples $(x,b)$ from $\mathcal{E}$. Gap-ImpMCSP in item (2) is defined as follows. Given a circuit $C$ sampling a distribution $\mathcal{E}$ of labeled examples $(x,f(x))\in\{0,1\}^n\times\{0,1\}$ for some boolean function $f$ so that every $x\in\{0,1\}^n$ is in the support of $\mathcal{E}$, distinguish between the two cases: (a) the circuit complexity of $f$ is at most $s$, or (b) no circuit of size $subexp(s)$ can approximate $f$ over $\mathcal{E}$ with probability noticeably higher than $1/2$. We also give more examples of synergy between these two assumptions from cryptography and proof complexity. In particular, we prove that together they imply $NP\not\subseteq io SIZE[2^{n^{o(1)}}]$, and hence that subexponentially-secure one-way functions and public-key encryption exist. Our conditional NP-hardness results complement the recent results of Hirahara and Ilango (FOCS 2025) which prove conditional NP-hardness of constant-gap MCSP under quasipolynomial-time non-Levin reductions, from seemingly much stronger assumptions.

Yesterday, National Academy of Sciences President Marcia McNutt delivered her last annual State of the Sciences Address. Overall the talk basically calls us to adapt to the new reality that industrial and foundation support for research has taken a far larger role in academic research. I fear we may be losing the broad academic independence and exploration that has made our universities the envy of the world.

Government funding for research has become more challenging to receive, more bureaucratic and more political. The US Office of Management and Budget has proposed new regulations that would require all grant funding to go through political review. 

McNutt presented this graph showing the seemingly exponential growth in research requirements from zero in 1990 (when I got my first grant) to well over three hundred today. Researchers now spend close to half their time on regulatory compliance. 

Increase in regulatory requirements

McNutt mentioned six specific issues.

1. Reimagine connections between universities and industry
2. Realign the academic reward system
3. Meet the needs of the STEM workforce
4. Reduce research regulations (as in the graph above)
5. Increase the rate of innovation with the help of automation in shared facilities
6. Tackle Big Challenges

For the first, she highlighted U Washington CS where a large percentage of their faculty had half-time appointments in industry. I understand why this is necessary from both sides, but that doesn't mean it's a good thing. Academics should not have two masters. We become academics to choose our own research directions and to prepare the next generation, both more challenging when you spend half your time connected with a company. 

Even for the "big challenges" she specifically mentioned two foundation-driven projects.

McNutt has hopes that government research can be less bureaucratic and willing to take bigger risks. Outside of theoretical areas, CS conferences now have heavy industrial representation. I worry that we bend our research to fit the needs of corporations and foundations funded by wealthy donors. Welcome to the new world.

By Lance Fortnow

Authors: Xingchen Li, Kunpeng Liu, Keyou You

Computing the Lipschitz constant of the solution map of a multi-parametric quadratic program is important for the analysis of optimization-based control. This problem is governed by three factors: the parameter dimension, the number of decision variables, and the number of constraints. While empirical evidence has long suggested exponential complexity, a rigorous complexity-theoretic proof has been lacking. In this paper, we fill this gap by proving that this problem is not only NP-hard but also APX-hard. Furthermore, we reveal that: (a) the problem becomes polynomial-time solvable when the number of constraints or decision variables is fixed; and (b) both NP-hardness and APX-hardness persist even in the scalar parameter case. These results confirm that the complexity stems from the number of constraints and variables, rather than the parameter dimension. Numerical experiments further validate these theoretical findings.

Authors: Marco Benedetti, Andrej Bogdanov, Enrico M. Malatesta, Marc Mézard, Gianmarco Perrupato, Alon Rosen, Nikolaj I. Schwartzbach, Riccardo Zecchina

We initiate the study of the algorithmic complexity of finding collisions in single-layer binary neural networks. Given a random matrix $\mathbf{A} \in \mathbb{R}^{m\times n}$, an input $\mathbf{x} \in \{-1,1\}^n$ is mapped to a binary output vector $\varphi(\mathbf{A}\mathbf{x})\in \{-1,1\}^m$, where $\varphi$ is an activation function with constant behavior on $[κ, \infty)$ for some threshold $κ\geq 0$. We identify the threshold scale $κ=Θ(1/\sqrtα)$, where $α=m/n$, as separating two complementary phenomena. When $κ\ll 1/\sqrtα$, we give a simple online algorithm that efficiently produces extensive collisions. When $κ\gg 1/\sqrtα$, for a natural \emph{randomized} non-periodic activation and suitable oscillation complexity, we prove that the extensive-collision space exhibits an overlap gap property (OGP), yielding an exponential lower bound against online algorithms. Ours is the first work to use the overlap gap property as a rigorous criterion for collision resistance. The key difference between collision finding and average-case search is that collision finding has a new ``worst-case'' aspect: the collision finder has full control over the choice of colliding pairs. Our lower bound is proved in the online model; extending such guarantees to broader classes of algorithms, including spectral, algebraic, lattice-based, or quantum methods, remains an open direction.

Authors: Sreejata Kishor Bhattacharya, Farzan Byramji, Arkadev Chattopadhyay, Yogesh Dahiya, Shachar Lovett

A major open problem in quantum communication complexity is whether quantum protocols can be exponentially more efficient than classical protocols for computing total Boolean functions; the prevailing conjecture is that they cannot be so. In a seminal work, Razborov (2002) resolved this question for AND-functions of the form $$ F(x,y) = f(x_1 \land y_1, \ldots, x_n \land y_n), $$ when the outer function $f$ is symmetric, by proving that their bounded-error quantum and classical communication complexities are polynomially related. Since then, extending this result to all AND-functions has remained open and has been posed by several authors. In this work, we settle this problem in a strong way. We show that for every Boolean function $f$, the bounded-error quantum and classical deterministic communication complexities of the function $f \circ \mathrm{AND}_2$ are polynomially related, up to polylogarithmic factors in $n$. We prove this by showing that both are characterized--up to polynomial loss--by the logarithm of the De Morgan sparsity of $f$. Our results build on the recent work of Chattopadhyay, Dahiya, and Lovett (2025) on structural characterizations of non-sparse Boolean functions, which we extend to resolve the conjecture for general AND-functions.

Authors: T. S. Arthanari

The Membership Problem for Pedigree Polytope (M3P) asks, given $X\in\mathbb{Q}^{\binom{n}{3}}$, whether $X\in\mathrm{conv}(P_n)$, where $P_n$ is the set of all pedigrees. A pedigree is a structured encoding of a Hamiltonian cycle construction in $K_n$. We establish that M3P is solvable in strongly polynomial time via a recursively constructed layered network $(N_k, R_k, μ)$ and a multicommodity flow problem MCF$(k)$. The necessary and sufficient condition for membership established is that the optimal total flow in MCF$(n-1)$ equals the maximum possible flow $z_{\max}$. The complexity analysis, grounded in Tardos's strongly polynomial algorithm for combinatorial linear programs (1986), shows that this condition can be checked in strongly polynomial time in the dimension of the matrix involved. By sufficiency, this implies M3P~$\in$~P. Since the Symmetric Travelling Salesman Problem (STSP) reduces to M3P via the Multistage Insertion (MI) formulation (Arthanari 1983), STSP is solvable in polynomial time, and the P vs.NP question is resolved. The proofs leading to this result are fully machine-verified in Lean~4/Mathlib4, with zero unresolved \texttt{sorry}s in the main proof chain. The main contribution is the Lean~4 machine verification of all proofs in the main chain, resulting in \texttt{theorem p\_equals\_np}: P = NP. The Lean~4 formal verification covers the sufficiency of MCF(n-1) for membership in $\mathrm{conv}(P_n)$, and the P = NP chain via Maurras (2002), Grötschel--Lovász--Schrijver (1988), Cook (1971), and Karp (1972). The complete lean project (36 Lean~4 files, 2968/2968 build targets clean) is available at https://github.com/TiruArt/Pedigree-Polytopes-Lean4.

Authors: Riccardo Rende, Alessandro Sinibaldi, Luciano Loris Viteritti, Roeland Wiersema, Antoine Georges, Giuseppe Carleo

Scaling laws, the power-law relations between loss, architecture size, and compute observed in modern neural networks, offer a quantitative way to characterize the complexity of a learning problem, with the exponent governing the decay of the loss reflecting how rapidly additional resources translate into improved accuracy, and thus how hard the target is to learn. Whether an analogous framework can characterize the complexity of physical problems remains open. We address this question for Neural-Network Quantum States, a leading variational approach for strongly correlated quantum many-body systems. Using transformer wave functions to approximate ground states of the $J_1$-$J_2$ Heisenberg model on triangular and square lattices with up to $20\times 20$ sites, we find that the $V$-score, a measure of accuracy of a variational state, decays as a power law in training compute. Under an appropriate rescaling of compute, results for different system sizes collapse onto a single curve, analogous to scaling collapse in critical phenomena. The resulting power law is, to a good approximation, independent of the number of sites, showing that the transformer Ansatz is size-consistent for the systems considered. The exponent decreases systematically with frustration, identifying it as a quantitative measure of representational difficulty of the ground state and establishing scaling laws as a general framework for benchmarking variational ansätze.