Science & Mathematics

A Transformer is built around attention, whose cost grows with the square of the sequence length and dominates the layer on long sequences. FlashAttention made that cost manageable by tiling the attention matrix and updating the softmax as it goes, but almost all work since has targeted GPUs. On long-vector processors one vector register can hold up to 512 single-precision numbers. The savings of a vector instruction are proportional to how much of the register it uses, so the choice of which loop to vectorize is a first-order decision. We port PyTorch's CPU FlashAttention kernel to a RISC-V CPU with 2KB vector registers and find that it reaches 16.2% of peak floating-point throughput. The kernel walks each tile one query row at a time: the product against V is vectorized along the 64-element head dimension, the softmax's per-row maximum and sum are reductions that collapse a full register to a scalar, and the software exponential's polynomial coefficients compete with tile data for vector registers and cause spilling. We propose two techniques. The first transposes the score tile and the running output so that queries lie along the contiguous axis. The algorithm and its values are unchanged. A single parameter, the number of queries in a tile, now sets the vector length of every part of the kernel and can be matched to the machine. Both reductions also disappear. The second moves the polynomial's coefficients into scalar registers, removing the spills and cutting the softmax's vector memory instructions by 78.7%. On silicon the two together cut whole-kernel cycles by 1.84 to 2.08x at a head dimension of 64, raising floating-point utilization from 16.2% to 29.7% of peak. An FPGA of the same design ranks the changes identically and scores them higher, at 2.71x.

A model's failures can reveal gaps in the behavioral criteria guiding its training. We introduce RubricOpt, a framework that lets a policy revise these criteria within preference optimization. The policy diagnoses its own rubric-free outputs, retains requirements already covered by the rubric, and edits clauses that leave recurring failures unaddressed. A shared semantic representation connects task demands, preference-data contrasts, and rubric clauses, while a deterministic gate checks evidence references and fixed semantic anchors. The rubric then guides Direct Preference Optimization (DPO) during training, with preference pairs, labels, and the objective held fixed, and is removed at evaluation. Our analysis relates the local effect on rubric-free success to semantic alignment and a residual beyond the measured factors. Experiments on capability and open-ended generation benchmarks show that rubric conditioning can improve outcomes over ordinary DPO, with gains and regressions varying across models and datasets. A matched continuation isolates the contribution of revision from additional training and finds mixed incremental effects for the tested edit, whose feedback overlaps the evaluation set. RubricOpt thus brings the behavioral specification itself into the policy's feedback loop.

We determine the minimum number of directional commands needed to solve alevel of Order of the Sinking Star, modeled as a crystal-exchangepuzzle on an 11*11 board. A command swapsthe player with the nearest crystal in the selected row or column, regardlessof distance; only an empty ray permits an ordinary unit walk. Two gates admitthe player to the exit exactly while all sixteen crystals occupy their targetcells. We give an explicit 93-command solution and exclude every shortersolution by an exact, cost-bounded breadth-first search. The search representsa position by its seventeen occupied cells and one active cell. Its admissibleheuristic partitions command costs between a compressed core abstraction andresidual motion, strengthened by a necessary activation detour and a cornervisit condition. The completed computation retained 605,349,215 occupied setsand 1,863,925,136 states. We prove the reductions and pruning conditions,describe the exact storage scheme, and provide source code, execution logs,and a reproduction driver. The result is a computer-assisted proof for thespecified instance, with an explicit implementation trust boundary.

Biometric recognition often degrades under partial facial vis- ibility, where conventional facial cues are occluded. The forehead region remains consistently visible and contains distinctive crease patterns that can serve as a complementary biometric trait. We present a unified eval- uation of forehead-crease recognition across explainable zero-shot rea- soning, domain-adaptive learning, and trait-specific modeling. FIRE en- ables interpretable zero-shot verification using multimodal large language models, while pretrained face-recognition models are adapted to the fore- head domain through margin-based learning. Under open-set evaluation, the best zero-shot model GPT-4o+FIRE achieves 18.22% EER, while Edge-Forehead achieves 8.30% EER and 54.01% [email protected]% FMR. The results show that although MLLMs offer interpretable zero-shot verifi- cation, trait-specific learning remains more effective for robust forehead- crease biometric recognition.

Blockchain consensus protocols implicitly follow a client-server architecture: validators are the only active participants, while clients (i.e., users) merely submit transactions and rely on validators to include them. This abstraction obscures a fundamental question: what should a client do to guarantee the timely inclusion of its own transaction? We study this question by introducing a leaderless consensus protocol in which clients are active. We define inclusion safety: the guarantee that a client's transaction enters some of the blocks produced for an epoch, and that every block omitting it belongs to a fork that is eventually abandoned. Because every transaction carries a reference to a block of the previous epoch, clients help select the surviving fork. This yields two paths to inclusion: reaching sufficiently many honest replicas within an epoch, or relaying a block containing the transaction across epochs until the corresponding fork becomes canonical. In a generalized model spanning synchrony and asynchrony, the client's and the replicas' connectivity are substitutes for inclusion safety: it is achieved either if the client is well connected, or if the client is poorly connected but honest replicas communicate reliably, provided the client reaches at least one of them. However, the substitution is imperfect: when inclusion safety rests on the replicas' connectivity, it requires a longer epoch compared to when the client is well connected.

Process reward models (PRMs) provide fine-grained supervision for multi-step reasoning, yet obtaining reliable process labels remains a central bottleneck. Existing approaches typically rely on human annotation, rollout-based estimation, or auxiliary verification. In this work, we explore a different source of process supervision natively exposed by Mixture-of-Experts (MoE) models: expert routing. We show that simple routing statistics provide an intrinsic process-confidence signal that is competitive with conventional output-logit confidence. Building on this observation, we construct routing confidence by combining overall routing mass, head routing mass, and within-step routing variation, and introduce RoCo-Rethink, which identifies the least confident reasoning step and selectively regenerates the subsequent trajectory. We further introduce RoCo-PRM, which uses a strong MoE to automatically annotate reasoning trajectories with routing-derived step scores and distills them into a standalone PRM. Across multiple MoE architectures and diverse reasoning tasks, both RoCo-Rethink and RoCo-PRM consistently outperform strong baselines, while RoCo-PRM transfers effectively across both model architectures and tasks. Our findings suggest that expert routing is more than a computational dispatch mechanism: it provides an architecture-native source of process supervision for reasoning.

Reliable evaluation of LLM-based alpha mining requires more than positive backtest summaries. We audit a preserved project at three levels: historical run counters, outcome retention, and a separately scoped public reanalysis. Three historical runs report 67, 20, and 11 keep decisions, but the comparison mixes metric populations: a mean over kept candidates is compared with a mean of per-round maxima, and successful evaluations with all returned outcomes. These artifacts cannot identify an architecture advantage. A released 1,837-expression catalog also excludes non-positive OOS outcomes, making its zero-reversal rate non-informative. We then account for all 1,047 unique expressions in a frozen, IS-screened preserved pool using forty A-shares and 2024-2025 rank associations. A versioned public-operator correction yields 923 scorable records, 99 with insufficient valid dates, and 25 unsupported, without modifying the other 990 prior diagnostics. Among scorable records, 671 have positive and 252 negative signed mean rank-IC. Simple untrained references also show positive associations, so this distribution does not establish incremental agent skill or profitability. The case study motivates explicit metric grains, immutable cohort accounting, and provenance-aware interpretation rather than architectural rankings from incomplete records.

Parallel thinking has emerged as a promising paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs) by exploring multiple reasoning paths simultaneously. However, we identify that parallel thinking via Reinforcement Learning (RL) typically suffers from the mode collapse of reasoning paths, where parallel thinking trajectories degenerate into similar ones. This homogeneity undermines the fundamental motivation of parallel thinking, that is, maintaining multiple hypotheses concurrently to prevent premature loss into a suboptimal solution. In this paper, we propose Diverse Parallel Thinking (DPT), a simple yet effective RL approach for parallel thinking designed to encourage path diversity. DPT rewards the model to develop distinct reasoning strategies by penalizing the prefix similarity of parallel thinking paths, thereby enhancing a more comprehensive exploration of the reasoning space. We conduct various experiments and analyses across multiple reasoning benchmarks to demonstrate the effectiveness of DPT. Results show that DPT successfully outperforms previous parallel thinking methods, achieving state-of-the-art performance over baselines. We validate path diversity as a key element to improve parallel thinking. Our code is available at https://github.com/JiaruQian/DPT.

We present a scheduling framework for heterogeneous multi-accelerator systems executing both hard real-time and soft real-time QoS-aware DNN inference workloads. The framework combines an online reinforcement learning (RL) scheduler with a deterministic runtime safety layer. The RL scheduler dynamically generates candidate schedules by jointly selecting sub-job priorities and accelerator assignments, while runtime certification guarantees that all HRT deadlines remain satisfied independently of the learned policy. To enable runtime certification in heterogeneous precedence-constrained systems, we introduce a schedulability-preserving prefix replacement criterion based on machine-wise cuts. The proposed criterion guarantees that runtime-generated schedule prefixes preserve the existence of a feasible continuation without requiring complete finish-time dominance with respect to a feasible reference schedule. Experimental results on heterogeneous DNN accelerator platforms show that the proposed framework preserves HRT schedulability while improving QoS-aware deadline satisfaction, client-level service quality, and accelerator utilization compared to state-of-the-art scheduling approaches.

Time series foundation models (TSFMs) perform unevenly across forecasting tasks. Recent work uses agentic model orchestration (AMO) to select or combine TSFMs, often outperforming individual forecasters. Yet these gains may reflect stronger or more complementary candidates rather than better orchestration. To disentangle these effects, we introduce FairAMO, a controlled evaluation protocol with frozen candidate forecasts. Experiments on GIFT-Eval show that AMO improves accuracy, but its gains are bounded by the candidate TSFMs. The best orchestrators reduce MASE by less than 6% relative to the best single TSFM across all tasks. These gains depend on complementarity (different candidates excel on different tasks) rather than the number of candidates. Adding members yields diminishing returns, and a redundant member can erase these gains. The value of historical evidence also saturates quickly. A few recent windows capture all gains, and further history adds none. These findings separate system-level forecasting gains from the contribution of orchestration itself.

LEGO walkers are walking automata constructed from modular LEGO Technic bricks. They exhibit intriguing locomotion and are also highly reconfigurable through the modular Technic bricks, making them widely applicable in education, recreation, and robotics research. However, existing LEGO walkers are designed mostly by reusing existing single-actuator walking mechanisms. Although the locomotion is stable, their fixed walking gaits limit their adaptability and versatility. This paper presents the first computational solution capable of designing LEGO walkers that not only walk stably, but also support a variety of walking gaits. Our idea is twofold. First, we control the foot motion trajectory of each leg mechanically via a specifically-designed gear-linkage mechanism, in which we incorporate a pair of 3D-printed non-circular gears to work with a LEGO Technic mechanism. Second, we drive each leg by an independent motor and synchronize the timings of multiple leg motions via a simple yet adaptable control algorithm, enabling stable and versatile locomotion. Importantly, we take this modeling as a foundation to co-design the morphology and control of the LEGO walkers to meet the target locomotion and appearance. Leveraging our approach, we created a variety of LEGO walkers, demonstrating various walking gaits and appearances, and fabricated some of them to show their locomotion capability in the real world.

Approximate Bayesian computation (ABC) enables Bayesian inference for models with intractable likelihoods by estimating parameter posterior distributions from simulated data. Sequential ABC methods improve sampling efficiency by iteratively adapting the proposal distribution toward regions of high posterior probability. However, these methods typically operate in generations, where each generation must wait for its slowest simulation before the next can begin. On a parallel machine, this synchronization barrier leaves workers idle and reduces throughput, particularly when simulation runtimes vary substantially. We introduce a generation-free ABC sampler that updates its proposal when simulation results arrive and sends a new candidate to each available worker. The proposal is based on the best particles evaluated so far. To estimate the posterior, we reuse the full history and reweight particles against a reconstructed mixture of sampling proposals. We show how errors in approximating the mixture of sampling proposals affect the estimated posterior and establish consistency for the smooth-ABC posterior when the approximation becomes asymptotically exact. In our experiments, the method achieves well-calibrated posterior estimates where a pyABC baseline with the same kernel and bandwidth schedule under-covers. From the asynchronous run's timing alone, we predict how much a synchronization barrier would slow the sampler. These predictions agree with measured synchronization penalties ranging from 1.2x to 400x. On a Cellular Potts tissue simulator, the asynchronous sampler completes 2.1-2.4x as many evaluations as pyABC in the same hour, and the discrepancy threshold for its best 100 evaluations is 4.1x smaller. With the starting bandwidth set from prior-predictive discrepancies, it also produces a more concentrated two-parameter posterior with a larger effective sample size than pyABC.

Temporal reasoning is widely assumed to decompose into two modes: temporal arithmetic (date and time calculations), and temporal semantics (understanding temporal and causal relations). This dichotomy shapes how benchmarks are designed, how models are trained, and how progress is measured, yet its empirical validity has never been directly tested. We provide two lines of evidence that challenge it. First, we test whether tasks labelled as arithmetic or semantic by the benchmarks support transferable gains within their purported mode. Finetuning on these subsets yields predominantly dataset-specific gains ($+6.8$ to $+23.1$ percentage points), while transfer to a different dataset in the same mode ranges from $-3.2$ to $+1.1$ percentage points. Across the two benchmark families used in the transfer analysis, this pattern provides little evidence of coherent, transferable temporal abilities. Second, using cognitive-demand-based model evaluation, we examine which capabilities actually drive performance on these benchmarks. We find that quantitative and logical reasoning, the assumed proxies for temporal arithmetic and temporal semantics, are not the primary drivers; knowledge is. Together, these findings show that current temporal reasoning benchmarks do not cleanly realise the arithmetic-semantics distinction and instead largely reward models for remembering how time typically works.

Real-world datasets often follow a long-tailed distribution, making generalization to tail classes difficult. We revisit this problem through the lens of shortcut learning, where models prefer the easiest predictive cues (e.g., background or textures) over object-centric semantics, especially under scarce and biased supervision. We find that this tendency is amplified for tail classes: limited examples often share similar contexts, making non-semantic signals highly correlated and thus tempting shortcuts, whereas head classes with diverse appearances and environments encourage more stable object-focused representations. Motivated by this observation, we propose Shortcut-Resistant CAM Distillation (SRCD), a plug-and-play framework that transfers object-focused explanations from head to tail classes. SRCD operates in the Class Activation Map (CAM) space, where a CAM provides a class-specific spatial evidence map for a prediction. SRCD aggregates CAMs from a small set of head-class candidates into a shortcut-resistant teacher using an energy-model weighting based on coherence and concentration, and distills it to the tail-class CAM. We provide a theoretical analysis that quantifies shortcut reliance as shortcut-region evidence mass in CAM space and shows that SRCD suppresses tail shortcuts. Extensive experiments on long-tailed benchmarks consistently improve strong baselines. The code is available at https://github.com/Haifeng3/SRCD.

In this paper, we develop a unified framework connecting proper scoring rules and Stein's method for the estimation of unnormalized models. We construct a class of proper scoring rules that encompasses score matching, ratio matching, pseudolikelihood, and noise contrastive estimation. We show that these proper scoring rules naturally induce Stein operators. This connection yields a new construction principle for Stein operators, and enables us to study estimators based on these scoring rules through the geometry associated with the induced Stein operators. Using this geometric perspective, we provide a unified characterization of the asymptotic efficiency of the resulting estimators.