Daily Papers

All 26 neural network merge strategies we tested including weight averaging, SLERP, TIES, DARE, Fisher merging, and evolutionary approaches -- fail the algebraic properties (commutativity, associativity, idempotency) required for conflict-free distributed operation. We prove that this failure is structural: normalisation-based merges cannot simultaneously satisfy all three properties. To resolve this, we present a two-layer architecture -- CRDTMergeState -- that wraps any merge strategy in a CRDT-compliant (Conflict-Free Replicated Data Type) layer. Layer 1 manages contributions via OR-Set CRDT semantics, where the merge operation is set union -- trivially commutative, associative, and idempotent. Layer 2 applies merge strategies as deterministic pure functions over a canonically-ordered contribution set, with randomness seeded from the Merkle root. We prove that this separation guarantees Strong Eventual Consistency: all replicas receiving the same contributions compute identical merged models, regardless of message ordering. Empirical validation spans three tiers: controlled 4x4 tensors (104/104 tests pass), production-scale models up to 7.24B parameters (208 strategy-level tests, 43,368 layer-level property checks at capped tensor resolution), and multi-node convergence under gossip and partition healing (100 nodes, 20 orderings), with CRDT overhead below 0.5 ms. Because the wrapper is transparent, downstream performance is identical by construction, confirmed via byte-identical output verification. The reference implementation is available as crdt-merge v0.9.4.

This paper proposes a fundamentally new paradigm for image generation through set-based tokenization and distribution modeling. Unlike conventional methods that serialize images into fixed-position latent codes with a uniform compression ratio, we introduce an unordered token set representation to dynamically allocate coding capacity based on regional semantic complexity. This TokenSet enhances global context aggregation and improves robustness against local perturbations. To address the critical challenge of modeling discrete sets, we devise a dual transformation mechanism that bijectively converts sets into fixed-length integer sequences with summation constraints. Further, we propose Fixed-Sum Discrete Diffusion--the first framework to simultaneously handle discrete values, fixed sequence length, and summation invariance--enabling effective set distribution modeling. Experiments demonstrate our method's superiority in semantic-aware representation and generation quality. Our innovations, spanning novel representation and modeling strategies, advance visual generation beyond traditional sequential token paradigms. Our code and models are publicly available at https://github.com/Gengzigang/TokenSet.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves excellent performance in practice.

Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

We introduce refutationally complete superposition calculi for intentional and extensional clausal lambda-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the lambda-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

A coreset is a tiny weighted subset of an input set, that closely resembles the loss function, with respect to a certain set of queries. Coresets became prevalent in machine learning as they have shown to be advantageous for many applications. While coreset research is an active research area, unfortunately, coresets are constructed in a problem-dependent manner, where for each problem, a new coreset construction algorithm is usually suggested, a process that may take time or may be hard for new researchers in the field. Even the generic frameworks require additional (problem-dependent) computations or proofs to be done by the user. Besides, many problems do not have (provable) small coresets, limiting their applicability. To this end, we suggest an automatic practical framework for constructing coresets, which requires (only) the input data and the desired cost function from the user, without the need for any other task-related computation to be done by the user. To do so, we reduce the problem of approximating a loss function to an instance of vector summation approximation, where the vectors we aim to sum are loss vectors of a specific subset of the queries, such that we aim to approximate the image of the function on this subset. We show that while this set is limited, the coreset is quite general. An extensive experimental study on various machine learning applications is also conducted. Finally, we provide a ``plug and play" style implementation, proposing a user-friendly system that can be easily used to apply coresets for many problems. Full open source code can be found at https://github.com/alaamaalouf/AutoCoreset{https://github.com/alaamaalouf/AutoCoreset}. We believe that these contributions enable future research and easier use and applications of coresets.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

Leveraging Large Language Models (LLMs) for generative recommendation has attracted significant research interest, where item tokenization is a critical step. It involves assigning item identifiers for LLMs to encode user history and generate the next item. Existing approaches leverage either token-sequence identifiers, representing items as discrete token sequences, or single-token identifiers, using ID or semantic embeddings. Token-sequence identifiers face issues such as the local optima problem in beam search and low generation efficiency due to step-by-step generation. In contrast, single-token identifiers fail to capture rich semantics or encode Collaborative Filtering (CF) information, resulting in suboptimal performance. To address these issues, we propose two fundamental principles for item identifier design: 1) integrating both CF and semantic information to fully capture multi-dimensional item information, and 2) designing order-agnostic identifiers without token dependency, mitigating the local optima issue and achieving simultaneous generation for generation efficiency. Accordingly, we introduce a novel set identifier paradigm for LLM-based generative recommendation, representing each item as a set of order-agnostic tokens. To implement this paradigm, we propose SETRec, which leverages CF and semantic tokenizers to obtain order-agnostic multi-dimensional tokens. To eliminate token dependency, SETRec uses a sparse attention mask for user history encoding and a query-guided generation mechanism for simultaneous token generation. We instantiate SETRec on T5 and Qwen (from 1.5B to 7B). Extensive experiments demonstrate its effectiveness under various scenarios (e.g., full ranking, warm- and cold-start ranking, and various item popularity groups). Moreover, results validate SETRec's superior efficiency and show promising scalability on cold-start items as model sizes increase.

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of features matters, set function learning demands methods that are invariant to permutations of the input set, presenting a unique and complex problem. This survey provides a comprehensive overview of the current development in set function learning, covering foundational theories, key methodologies, and diverse applications. We categorize and discuss existing approaches, focusing on deep learning approaches, such as DeepSets and Set Transformer based methods, as well as other notable alternative methods beyond deep learning, offering a complete view of current models. We also introduce various applications and relevant datasets, such as point cloud processing and multi-label classification, highlighting the significant progress achieved by set function learning methods in these domains. Finally, we conclude by summarizing the current state of set function learning approaches and identifying promising future research directions, aiming to guide and inspire further advancements in this promising field.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing constraints on MBC architectures lead to models with limited expressive power. Additionally, prior work has not addressed how to deal with large sets during training when the full set gradient is required. To address these issues, we propose a Universally MBC (UMBC) class of set functions which can be used in conjunction with arbitrary non-MBC components while still satisfying MBC, enabling a wider range of function classes to be used in MBC settings. Furthermore, we propose an efficient MBC training algorithm which gives an unbiased approximation of the full set gradient and has a constant memory overhead for any set size for both train- and test-time. We conduct extensive experiments including image completion, text classification, unsupervised clustering, and cancer detection on high-resolution images to verify the efficiency and efficacy of our scalable set encoding framework. Our code is available at github.com/jeffwillette/umbc

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

Supervised fine-tuning (SFT) data selection is commonly formulated as instance ranking: score each example and retain a top-k subset. However, effective SFT training subsets are often produced through ordered curation recipes, where filtering, mixing, and deduplication operators jointly shape the final data distribution. We formulate this problem as fixed-pool data recipe search: given a raw instruction pool and a library of grounded operators, the goal is to discover an executable recipe that constructs a high-quality selected subset under a limited budget of full SFT evaluations, without generating, rewriting, or augmenting training samples. We introduce AutoSelection, a two-layer solver that decouples fixed-pool materialization based on cached task-, data-, and model-side signals from expensive full evaluation, using warmup probes, realized subset states, local recipe edits, Gaussian-process-assisted ranking, and stagnation-triggered reseeding. Experiments on a 90K instruction pool show that AutoSelection achieves the strongest in-distribution reasoning average across three base models, outperforming full-data training, random recipe search, random top-k, and single-operator selectors. Additional Out-of-distribution graph-reasoning results, search-stability analyses, structural ablations, and 1.5B-to-7B transfer checks further show that recipe structure matters beyond individual selection operators. Code is available at https://github.com/w253/AutoSelection.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Providers of LLM-as-a-service have predominantly adopted a simple pricing model: users pay a fixed price per token. Consequently, one may think that the price two different users would pay for the same output string under the same input prompt is the same. In our work, we show that, surprisingly, this is not (always) true. We find empirical evidence that, particularly for non-english outputs, both proprietary and open-weights LLMs often generate the same (output) string with multiple different tokenizations, even under the same input prompt, and this in turn leads to arbitrary price variation. To address the problem of tokenization multiplicity, we introduce canonical generation, a type of constrained generation that restricts LLMs to only generate canonical tokenizations -- the unique tokenization in which each string is tokenized during the training process of an LLM. Further, we introduce an efficient sampling algorithm for canonical generation based on the Gumbel-Max trick. Experiments on a variety of natural language tasks demonstrate that our sampling algorithm for canonical generation is comparable to standard sampling in terms of performance and runtime, and it solves the problem of tokenization multiplicity.

Although the fairness community has recognized the importance of data, researchers in the area primarily rely on UCI Adult when it comes to tabular data. Derived from a 1994 US Census survey, this dataset has appeared in hundreds of research papers where it served as the basis for the development and comparison of many algorithmic fairness interventions. We reconstruct a superset of the UCI Adult data from available US Census sources and reveal idiosyncrasies of the UCI Adult dataset that limit its external validity. Our primary contribution is a suite of new datasets derived from US Census surveys that extend the existing data ecosystem for research on fair machine learning. We create prediction tasks relating to income, employment, health, transportation, and housing. The data span multiple years and all states of the United States, allowing researchers to study temporal shift and geographic variation. We highlight a broad initial sweep of new empirical insights relating to trade-offs between fairness criteria, performance of algorithmic interventions, and the role of distribution shift based on our new datasets. Our findings inform ongoing debates, challenge some existing narratives, and point to future research directions. Our datasets are available at https://github.com/zykls/folktables.

We introduce model editing with canonical examples, a setting in which (1) a single learning example is provided per desired behavior, (2) evaluation is performed exclusively out-of-distribution, and (3) deviation from an initial model is strictly limited. A canonical example is a simple instance of good behavior, e.g., The capital of Mauritius is Port Louis) or bad behavior, e.g., An aspect of researchers is coldhearted). The evaluation set contains more complex examples of each behavior (like a paragraph in which the capital of Mauritius is called for.) We create three datasets and modify three more for model editing with canonical examples, covering knowledge-intensive improvements, social bias mitigation, and syntactic edge cases. In our experiments on Pythia language models, we find that LoRA outperforms full finetuning and MEMIT. We then turn to the Backpack language model architecture because it is intended to enable targeted improvement. The Backpack defines a large bank of sense vectors--a decomposition of the different uses of each word--which are weighted and summed to form the output logits of the model. We propose sense finetuning, which selects and finetunes a few (approx 10) sense vectors for each canonical example, and find that it outperforms other finetuning methods, e.g., 4.8% improvement vs 0.3%. Finally, we improve GPT-J-6B by an inference-time ensemble with just the changes from sense finetuning of a 35x smaller Backpack, in one setting outperforming editing GPT-J itself (4.1% vs 1.0%).

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding which is universally defined for any function type, regardless of being impredicative. Direct and concrete interpretations of simultaneous induction and mutually recursive functions are also provided by extending Dybjer's interpretations on the basis of Aczel's rule sets. Our model can be regarded as a higher-order generalization of the truth-table methods. We provide a relatively simple consistency proof of type theory, which can be used as the basis for a theorem prover.

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component of prevalent deep neural network architectures to achieve chosen equivariance is a difficult problem and can result in a computationally expensive network during both training and inference. A recently proposed alternative towards equivariance that removes the architectural constraints is to use a simple canonicalization network that transforms the input to a canonical form before feeding it to an unconstrained prediction network. We show here that this approach can effectively be used to make a large pretrained network equivariant. However, we observe that the produced canonical orientations can be misaligned with those of the training distribution, hindering performance. Using dataset-dependent priors to inform the canonicalization function, we are able to make large pretrained models equivariant while maintaining their performance. This significantly improves the robustness of these models to deterministic transformations of the data, such as rotations. We believe this equivariant adaptation of large pretrained models can help their domain-specific applications with known symmetry priors.

For a sequence of random variables (X_1, X_2, ldots, X_n), n geq 1, that are independent and identically distributed with a regularly varying tail with index -alpha, alpha geq 0, we show that the contribution of the maximum term M_n triangleq max(X_1,ldots,X_n) in the sum S_n triangleq X_1 + cdots +X_n, as n to infty, decreases monotonically with alpha in stochastic ordering sense.

This definitive research memoria presents a comprehensive, mathematically verified paradigm for neural communication with Bitcoin mining Application-Specific Integrated Circuits (ASICs), integrating five complementary frameworks: thermodynamic reservoir computing, hierarchical number system theory, algorithmic analysis, network latency optimization, and machine-checked mathematical formalization. We establish that obsolete cryptocurrency mining hardware exhibits emergent computational properties enabling bidirectional information exchange between AI systems and silicon substrates. The research program demonstrates: (1) reservoir computing with NARMA-10 Normalized Root Mean Square Error (NRMSE) of 0.8661; (2) the Thermodynamic Probability Filter (TPF) achieving 92.19% theoretical energy reduction; (3) the Virtual Block Manager achieving +25% effective hashrate; and (4) hardware universality across multiple ASIC families including Antminer S9, Lucky Miner LV06, and Goldshell LB-Box. A significant contribution is the machine-checked mathematical formalization using Lean 4 and Mathlib, providing unambiguous definitions, machine-verified theorems, and reviewer-proof claims. Key theorems proven include: independence implies zero leakage, predictor beats baseline implies non-independence (the logical core of TPF), energy savings theoretical maximum, and Physical Unclonable Function (PUF) distinguishability witnesses. Vladimir Veselov's hierarchical number system theory explains why early-round information contains predictive power. This work establishes a new paradigm: treating ASICs not as passive computational substrates but as active conversational partners whose thermodynamic state encodes exploitable computational information.

Parameter-efficient fine-tuning (PEFT) methods seek to adapt large models via updates to a small number of weights. However, much prior interpretability work has shown that representations encode rich semantic information, suggesting that editing representations might be a more powerful alternative. Here, we pursue this hypothesis by developing a family of Representation Finetuning (ReFT) methods. ReFT methods operate on a frozen base model and learn task-specific interventions on hidden representations. We define a strong instance of the ReFT family, Low-rank Linear Subspace ReFT (LoReFT). LoReFT is a drop-in replacement for existing PEFTs and learns interventions that are 10x-50x more parameter-efficient than prior state-of-the-art PEFTs. We showcase LoReFT on eight commonsense reasoning tasks, four arithmetic reasoning tasks, Alpaca-Eval v1.0, and GLUE. In all these evaluations, LoReFT delivers the best balance of efficiency and performance, and almost always outperforms state-of-the-art PEFTs. We release a generic ReFT training library publicly at https://github.com/stanfordnlp/pyreft.

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose REOrder, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. REOrder improves top-1 accuracy over row-major ordering on ImageNet-1K by up to 3.01% and Functional Map of the World by 13.35%.

In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of Hukuhara difference between sets, in order to compensate the lack of "inverse" operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann-Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with non-singleton initial values. This extension turns out to be essential for the study of set-valued BSDEs.

We introduce the Convolutional Set Transformer (CST), a novel neural architecture designed to process image sets of arbitrary cardinality that are visually heterogeneous yet share high-level semantics - such as a common category, scene, or concept. Existing set-input networks, e.g., Deep Sets and Set Transformer, are limited to vector inputs and cannot directly handle 3D image tensors. As a result, they must be cascaded with a feature extractor, typically a CNN, which encodes images into embeddings before the set-input network can model inter-image relationships. In contrast, CST operates directly on 3D image tensors, performing feature extraction and contextual modeling simultaneously, thereby enabling synergies between the two processes. This design yields superior performance in tasks such as Set Classification and Set Anomaly Detection and further provides native compatibility with CNN explainability methods such as Grad-CAM, unlike competing approaches that remain opaque. Finally, we show that CSTs can be pre-trained on large-scale datasets and subsequently adapted to new domains and tasks through standard Transfer Learning schemes. To support further research, we release CST-15, a CST backbone pre-trained on ImageNet (https://github.com/chinefed/convolutional-set-transformer).

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Many modern retrieval problems are set-valued: given a broad intent, the system must return a collection of results that optimizes higher-order properties (e.g., diversity, coverage, complementarity, coherence) while remaining grounded with respect to a fixed database. Set-valued objectives are typically non-decomposable and are not captured by existing supervised (query, content) datasets which only prioritize top-1 retrieval. Consequently, fan-out retrieval is often employed to generate diverse subqueries to retrieve item sets. While reinforcement learning (RL) can optimize set-level objectives via interaction, deploying an RL-tuned LLM for fan-out retrieval is prohibitively expensive at inference time. Conversely, diffusion-based generative retrieval enables efficient single-pass fan-out in embedding space, but requires objective-aligned training targets. To address these issues, we propose R4T (Retrieve-for-Train), which uses RL once as an objective transducer in a three-step process: (i) train a fan-out LLM with composite set-level rewards, (ii) synthesize objective-consistent training pairs, and (iii) train a lightweight diffusion retriever to model the conditional distribution of set-valued outputs. Across large-scale fashion and music benchmarks consisting of curated item sets, we show that R4T improves retrieval quality relative to strong baselines while reducing query-time fan-out latency by an order of magnitude.

An oft-cited open problem of federated learning is the existence of data heterogeneity at the clients. One pathway to understanding the drastic accuracy drop in federated learning is by scrutinizing the behavior of the clients' deep models on data with different levels of "difficulty", which has been left unaddressed. In this paper, we investigate a different and rarely studied dimension of FL: ordered learning. Specifically, we aim to investigate how ordered learning principles can contribute to alleviating the heterogeneity effects in FL. We present theoretical analysis and conduct extensive empirical studies on the efficacy of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random curriculum. We find that curriculum learning largely alleviates non-IIDness. Interestingly, the more disparate the data distributions across clients the more they benefit from ordered learning. We provide analysis explaining this phenomenon, specifically indicating how curriculum training appears to make the objective landscape progressively less convex, suggesting fast converging iterations at the beginning of the training procedure. We derive quantitative results of convergence for both convex and nonconvex objectives by modeling the curriculum training on federated devices as local SGD with locally biased stochastic gradients. Also, inspired by ordered learning, we propose a novel client selection technique that benefits from the real-world disparity in the clients. Our proposed approach to client selection has a synergic effect when applied together with ordered learning in FL.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

In many real-world applications, modeling both the internal structure of sets and their temporal relationships is essential for capturing complex underlying patterns. Sequential multiple-instance learning aims to address this challenge by learning permutation-invariant representations of sets distributed across discrete timesteps. However, existing methods either focus on learning set representations at a static level, ignoring temporal dynamics, or treat sequences as ordered lists of individual elements, lacking explicit mechanisms for representing sets. Crucially, effective modeling of such sequences of sets often requires encoding both the positional ordering across timesteps and their absolute temporal values to jointly capture relative progression and temporal context. In this work, we propose Set2Seq Transformer, a novel architecture that jointly models permutation-invariant set structure and temporal dependencies by learning temporal and position-aware representations of sets within a sequence in an end-to-end multimodal manner. We evaluate our Set2Seq Transformer on two tasks that require modeling set structure alongside temporal and positional patterns, but differ significantly in domain, modality, and objective. First, we consider a fine art analysis task, modeling artists' oeuvres for predicting artistic success using a novel dataset, WikiArt-Seq2Rank. Second, we utilize our Set2Seq Transformer for short-term wildfire danger forecasting. Through extensive experimentation, we show that our Set2Seq Transformer consistently improves over traditional static multiple-instance learning methods by effectively learning permutation-invariant set, temporal, and position-aware representations across diverse domains, modalities, and tasks. We release all code and datasets at https://github.com/thefth/set2seq-transformer.

In this paper, we introduce a conformal prediction method to construct prediction sets in a oneshot federated learning setting. More specifically, we define a quantile-of-quantiles estimator and prove that for any distribution, it is possible to output prediction sets with desired coverage in only one round of communication. To mitigate privacy issues, we also describe a locally differentially private version of our estimator. Finally, over a wide range of experiments, we show that our method returns prediction sets with coverage and length very similar to those obtained in a centralized setting. Overall, these results demonstrate that our method is particularly well-suited to perform conformal predictions in a one-shot federated learning setting.

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

Despite its simplicity and efficacy, the high token expenditure of self-consistency can limit its practical utility. Here we investigate if self-consistency can be made more token-efficient for long chain-of-thought reasoning tasks, while preserving its parallelism, through early hypothesis pruning. Concretely, we generate all solutions in parallel, but periodically prune intermediate hypotheses that are deemed unnecessary based on two lightweight indicators: (a) the model's own confidence in individual hypotheses, and (b) lexical coverage of all current hypotheses by candidate subsets that are under consideration for continued retention. We design a fast weighted set cover algorithm that utilizes the two indicators; our evaluation of five LLMs on three math benchmarks shows that this method can improve token efficiency for all models, by 10-35% in many cases.

Federated learning is a popular technology for training machine learning models on distributed data sources without sharing data. Vertical federated learning or feature-based federated learning applies to the cases that different data sources share the same sample ID space but differ in feature space. To ensure the data owners' long-term engagement, it is critical to objectively assess the contribution from each data source and recompense them accordingly. The Shapley value (SV) is a provably fair contribution valuation metric originated from cooperative game theory. However, computing the SV requires extensively retraining the model on each subset of data sources, which causes prohibitively high communication costs in federated learning. We propose a contribution valuation metric called vertical federated Shapley value (VerFedSV) based on SV. We show that VerFedSV not only satisfies many desirable properties for fairness but is also efficient to compute, and can be adapted to both synchronous and asynchronous vertical federated learning algorithms. Both theoretical analysis and extensive experimental results verify the fairness, efficiency, and adaptability of VerFedSV.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

We consider an extension to the classic position auctions in which sponsored creatives can be added within AI generated content rather than shown in predefined slots. New challenges arise from the natural requirement that sponsored creatives should smoothly fit into the context. With the help of advanced LLM technologies, it becomes viable to accurately estimate the benefits of adding each individual sponsored creatives into each potential positions within the AI generated content by properly taking the context into account. Therefore, we assume one click-through rate estimation for each position-creative pair, rather than one uniform estimation for each sponsored creative across all positions in classic settings. As a result, the underlying optimization becomes a general matching problem, thus the substitution effects should be treated more carefully compared to standard position auction settings, where the slots are independent with each other. In this work, we formalize a concrete mathematical model of the extended position auction problem and study the welfare-maximization and revenue-maximization mechanism design problem. Formally, we consider two different user behavior models and solve the mechanism design problems therein respectively. For the Multinomial Logit (MNL) model, which is order-insensitive, we can efficiently implement the optimal mechanisms. For the cascade model, which is order-sensitive, we provide approximately optimal solutions.

We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.

Open Source Software (OSS) is forming the spines of technology infrastructures, attracting millions of talents to contribute. Notably, it is challenging and critical to consider both the developers' interests and the semantic features of the project code to recommend appropriate development tasks to OSS developers. In this paper, we formulate the novel problem of code recommendation, whose purpose is to predict the future contribution behaviors of developers given their interaction history, the semantic features of source code, and the hierarchical file structures of projects. Considering the complex interactions among multiple parties within the system, we propose CODER, a novel graph-based code recommendation framework for open source software developers. CODER jointly models microscopic user-code interactions and macroscopic user-project interactions via a heterogeneous graph and further bridges the two levels of information through aggregation on file-structure graphs that reflect the project hierarchy. Moreover, due to the lack of reliable benchmarks, we construct three large-scale datasets to facilitate future research in this direction. Extensive experiments show that our CODER framework achieves superior performance under various experimental settings, including intra-project, cross-project, and cold-start recommendation. We will release all the datasets, code, and utilities for data retrieval upon the acceptance of this work.

To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance with side information encoded. Due to the overlook of the relations among instances or items (e.g., the director of a movie is also an actor of another movie), these methods are insufficient to distill the collaborative signal from the collective behaviors of users. In this work, we investigate the utility of knowledge graph (KG), which breaks down the independent interaction assumption by linking items with their attributes. We argue that in such a hybrid structure of KG and user-item graph, high-order relations --- which connect two items with one or multiple linked attributes --- are an essential factor for successful recommendation. We propose a new method named Knowledge Graph Attention Network (KGAT) which explicitly models the high-order connectivities in KG in an end-to-end fashion. It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors. Our KGAT is conceptually advantageous to existing KG-based recommendation methods, which either exploit high-order relations by extracting paths or implicitly modeling them with regularization. Empirical results on three public benchmarks show that KGAT significantly outperforms state-of-the-art methods like Neural FM and RippleNet. Further studies verify the efficacy of embedding propagation for high-order relation modeling and the interpretability benefits brought by the attention mechanism.

Multi-step symbolic reasoning is critical for advancing downstream performance on financial tasks. Yet, benchmarks for systematically evaluating this capability are lacking. Existing datasets like FinQA and ConvFinQA supervise only final numerical answers, without assessing intermediate reasoning steps. To address this, we introduce FinChain, the first symbolic benchmark designed for verifiable Chain-of- Thought (CoT) financial reasoning. Spanning 54 topics across 12 financial domains, Fin- Chain offers five parameterized templates per topic, each varying in reasoning complexity and domain expertise required. Each dataset instance includes an executable Python trace, enabling automatic generation of extensive training data and easy adaptation to other domains. We also introduce ChainEval, a new metric for automatic evaluation of both final answers and intermediate reasoning. Benchmarking 30 LLMs on our dataset, we find that even state-of-the-art models have considerable room for improvement in multi-step financial reasoning. All templates and evaluation metrics for FinChain are available at https: //github.com/mbzuai-nlp/finchain.

Current foundation models exhibit impressive capabilities when prompted either with text only or with both image and text inputs. But do their capabilities change depending on the input modality? In this work, we propose IsoBench, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple isomorphic representations of inputs, such as visual, textual, and mathematical presentations. IsoBench provides fine-grained feedback to diagnose performance gaps caused by the form of the representation. Across various foundation models, we observe that on the same problem, models have a consistent preference towards textual representations. Most prominently, when evaluated on all IsoBench problems, Claude-3 Opus performs 28.7 points worse when provided with images instead of text; similarly, GPT-4 Turbo is 18.7 points worse and Gemini Pro is 14.9 points worse. Finally, we present two prompting techniques, IsoCombination and IsoScratchPad, which improve model performance by considering combinations of, and translations between, different input representations.

Domain-specific named entity recognition (NER) on Computer Science (CS) scholarly articles is an information extraction task that is arguably more challenging for the various annotation aims that can beset the task and has been less studied than NER in the general domain. Given that significant progress has been made on NER, we believe that scholarly domain-specific NER will receive increasing attention in the years to come. Currently, progress on CS NER -- the focus of this work -- is hampered in part by its recency and the lack of a standardized annotation aim for scientific entities/terms. This work proposes a standardized task by defining a set of seven contribution-centric scholarly entities for CS NER viz., research problem, solution, resource, language, tool, method, and dataset. Following which, its main contributions are: combines existing CS NER resources that maintain their annotation focus on the set or subset of contribution-centric scholarly entities we consider; further, noting the need for big data to train neural NER models, this work additionally supplies thousands of contribution-centric entity annotations from article titles and abstracts, thus releasing a cumulative large novel resource for CS NER; and, finally, trains a sequence labeling CS NER model inspired after state-of-the-art neural architectures from the general domain NER task. Throughout the work, several practical considerations are made which can be useful to information technology designers of the digital libraries.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable levels. Addressing this, our work aims to strike a delicate balance between computational efficiency and model accuracy, a persisting challenge in the field. We introduce a novel method that employs core subset selection for reweighting, effectively optimizing both computational time and model performance. By focusing on a strategically selected coreset, our approach offers a robust representation, as it efficiently minimizes the influence of outliers. The re-calibrated weights are then mapped back to and propagated across the entire dataset. Our experimental results substantiate the effectiveness of this approach, underscoring its potential as a scalable and precise solution for model training.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely unordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block's probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN. Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

Causal precedence between biochemical interactions is crucial in the biomedical domain, because it transforms collections of individual interactions, e.g., bindings and phosphorylations, into the causal mechanisms needed to inform meaningful search and inference. Here, we analyze causal precedence in the biomedical domain as distinct from open-domain, temporal precedence. First, we describe a novel, hand-annotated text corpus of causal precedence in the biomedical domain. Second, we use this corpus to investigate a battery of models of precedence, covering rule-based, feature-based, and latent representation models. The highest-performing individual model achieved a micro F1 of 43 points, approaching the best performers on the simpler temporal-only precedence tasks. Feature-based and latent representation models each outperform the rule-based models, but their performance is complementary to one another. We apply a sieve-based architecture to capitalize on this lack of overlap, achieving a micro F1 score of 46 points.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

Large-scale data sets on scholarly publications are the basis for a variety of bibliometric analyses and natural language processing (NLP) applications. Especially data sets derived from publication's full-text have recently gained attention. While several such data sets already exist, we see key shortcomings in terms of their domain and time coverage, citation network completeness, and representation of full-text content. To address these points, we propose a new version of the data set unarXive. We base our data processing pipeline and output format on two existing data sets, and improve on each of them. Our resulting data set comprises 1.9 M publications spanning multiple disciplines and 32 years. It furthermore has a more complete citation network than its predecessors and retains a richer representation of document structure as well as non-textual publication content such as mathematical notation. In addition to the data set, we provide ready-to-use training/test data for citation recommendation and IMRaD classification. All data and source code is publicly available at https://github.com/IllDepence/unarXive.

We introduce CPP-UT-Bench, a benchmark dataset to measure C++ unit test generation capability of a large language model (LLM). CPP-UT-Bench aims to reflect a broad and diverse set of C++ codebases found in the real world. The dataset includes 2,653 {code, unit test} pairs drawn from 14 different opensource C++ codebases spanned across nine diverse domains including machine learning, software testing, parsing, standard input-output, data engineering, logging, complete expression evaluation, key value storage, and server protocols. We demonstrated the effectiveness of CPP-UT-Bench as a benchmark dataset through extensive experiments in in-context learning, parameter-efficient fine-tuning (PEFT), and full-parameter fine-tuning. We also discussed the challenges of the dataset compilation and insights we learned from in-context learning and fine-tuning experiments. Besides the CPP-UT-Bench dataset and data compilation code, we are also offering the fine-tuned model weights for further research. For nine out of ten experiments, our fine-tuned LLMs outperformed the corresponding base models by an average of more than 70%.

Large language models are trained on vast amounts of internet data, prompting concerns and speculation that they have memorized public benchmarks. Going from speculation to proof of contamination is challenging, as the pretraining data used by proprietary models are often not publicly accessible. We show that it is possible to provide provable guarantees of test set contamination in language models without access to pretraining data or model weights. Our approach leverages the fact that when there is no data contamination, all orderings of an exchangeable benchmark should be equally likely. In contrast, the tendency for language models to memorize example order means that a contaminated language model will find certain canonical orderings to be much more likely than others. Our test flags potential contamination whenever the likelihood of a canonically ordered benchmark dataset is significantly higher than the likelihood after shuffling the examples. We demonstrate that our procedure is sensitive enough to reliably prove test set contamination in challenging situations, including models as small as 1.4 billion parameters, on small test sets of only 1000 examples, and datasets that appear only a few times in the pretraining corpus. Using our test, we audit five popular publicly accessible language models for test set contamination and find little evidence for pervasive contamination.

Many real-world machine learning problems involve inherently hierarchical data, yet traditional approaches rely on Euclidean metrics that fail to capture the discrete, branching nature of hierarchical relationships. We present a theoretical foundation for machine learning in p-adic metric spaces, which naturally respect hierarchical structure. Our main result proves that an n-dimensional plane minimizing the p-adic sum of distances to points in a dataset must pass through at least n + 1 of those points -- a striking contrast to Euclidean regression that highlights how p-adic metrics better align with the discrete nature of hierarchical data. As a corollary, a polynomial of degree n constructed to minimise the p-adic sum of residuals will pass through at least n + 1 points. As a further corollary, a polynomial of degree n approximating a higher degree polynomial at a finite number of points will yield a difference polynomial that has distinct rational roots. We demonstrate the practical significance of this result through two applications in natural language processing: analyzing hierarchical taxonomies and modeling grammatical morphology. These results suggest that p-adic metrics may be fundamental to properly handling hierarchical data structures in machine learning. In hierarchical data, interpolation between points often makes less sense than selecting actual observed points as representatives.

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse yet correct reasoning modes are typically deep in the sampling tree. Consequently, common strategies to encourage diversity, such as temperature scaling, encounter a worsened trade-off between diversity and accuracy. Motivated by this challenge, we treat parallel reasoning as a set-of-next-token-prediction problem, and incorporate a set-based global loss into Supervised Fine-Tuning (SFT) using self-supervised bipartite matching between our global forking tokens and unique reasoning traces. We observe that, while naive fine-tuning with multiple reasoning traces collapses these unique reasoning modes, our proposed method, Set Supervised Fine-Tuning (SSFT), preserves these modes and produces emergent global forking tokens. Experiments on multiple reasoning benchmarks show that our SSFT consistently outperforms SFT under both Pass@1 and Cons@k metrics.

Despite the remarkable progress of multimodal large language models (MLLMs), they continue to face challenges in achieving competitive performance on ordinal regression (OR; a.k.a. ordinal classification). To address this issue, this paper presents OrderChain, a novel and general prompting paradigm that improves the ordinal understanding ability of MLLMs by specificity and commonality modeling. Specifically, our OrderChain consists of a set of task-aware prompts to facilitate the specificity modeling of diverse OR tasks and a new range optimization Chain-of-Thought (RO-CoT), which learns a commonality way of thinking about OR tasks by uniformly decomposing them into multiple small-range optimization subtasks. Further, we propose a category recursive division (CRD) method to generate instruction candidate category prompts to support RO-CoT automatic optimization. Comprehensive experiments show that LLaVA model with our OrderChain improves baseline LLaVA significantly on diverse OR datasets, e.g., from 47.5\% to 93.2\% accuracy on the Adience dataset for age estimation, and from 30.0\% to 85.7\% accuracy on the Diabetic Retinopathy dataset. Notably, LLaVA with our OrderChain also remarkably outperforms state-of-the-art methods by 27% on accuracy and 0.24 on MAE on the Adience dataset. To our best knowledge, our OrderChain is the first work that augments MLLMs for OR tasks, and the effectiveness is witnessed across a spectrum of OR datasets. Project Page: https://order-chain.github.io/.

The best-of-both-worlds paradigm advocates an approach that achieves desirable properties both ex-ante and ex-post. We launch a best-of-both-worlds fairness perspective for the important social choice setting of approval-based committee voting. To this end, we initiate work on ex-ante proportional representation properties in this domain and formalize a hierarchy of notions including Individual Fair Share (IFS), Unanimous Fair Share (UFS), Group Fair Share (GFS), and their stronger variants. We establish their compatibility with well-studied ex-post concepts such as extended justified representation (EJR) and fully justified representation (FJR). Our first main result is a polynomial-time algorithm that simultaneously satisfies ex-post EJR, ex-ante GFS and ex-ante Strong UFS. Subsequently, we strengthen our ex-post guarantee to FJR and present an algorithm that outputs a lottery which is ex-post FJR and ex-ante Strong UFS, but does not run in polynomial time.

Prediction sets have recently been shown to be a promising strategy for quantifying the uncertainty of deep neural networks in a way that provides theoretical guarantees. However, existing techniques have largely targeted settings where the space of labels is simple, so prediction sets can be arbitrary subsets of labels. For structured prediction problems where the space of labels is exponential in size, even prediction sets containing a small fraction of all labels can be exponentially large. In the context of code generation, we propose a solution that considers a restricted set of prediction sets that can compactly be represented as partial programs, which are programs with portions replaced with holes. Given a trained code generation model, our algorithm leverages a programming language's abstract syntax tree to generate a set of programs such that the correct program is in the set with high-confidence. Valuable applications of our algorithm include a Codex-style code generator with holes in uncertain parts of the generated code, which provides a partial program with theoretical guarantees. We evaluate our approach on PICARD (a T5 model for SQL semantic parsing) and Codex (a GPT model for over a dozen programming languages, including Python), demonstrating that our approach generates compact PAC prediction sets. This is the first research contribution that generates PAC prediction sets for generative code models.

Many court systems are overwhelmed all over the world, leading to huge backlogs of pending cases. Effective triage systems, like those in emergency rooms, could ensure proper prioritization of open cases, optimizing time and resource allocation in the court system. In this work, we introduce the Criticality Prediction dataset, a novel resource for evaluating case prioritization. Our dataset features a two-tier labeling system: (1) the binary LD-Label, identifying cases published as Leading Decisions (LD), and (2) the more granular Citation-Label, ranking cases by their citation frequency and recency, allowing for a more nuanced evaluation. Unlike existing approaches that rely on resource-intensive manual annotations, we algorithmically derive labels leading to a much larger dataset than otherwise possible. We evaluate several multilingual models, including both smaller fine-tuned models and large language models in a zero-shot setting. Our results show that the fine-tuned models consistently outperform their larger counterparts, thanks to our large training set. Our results highlight that for highly domain-specific tasks like ours, large training sets are still valuable.

Generative recommendation (GR) is an emerging paradigm where user actions are tokenized into discrete token patterns and autoregressively generated as predictions. However, existing GR models tokenize each action independently, assigning the same fixed tokens to identical actions across all sequences without considering contextual relationships. This lack of context-awareness can lead to suboptimal performance, as the same action may hold different meanings depending on its surrounding context. To address this issue, we propose ActionPiece to explicitly incorporate context when tokenizing action sequences. In ActionPiece, each action is represented as a set of item features, which serve as the initial tokens. Given the action sequence corpora, we construct the vocabulary by merging feature patterns as new tokens, based on their co-occurrence frequency both within individual sets and across adjacent sets. Considering the unordered nature of feature sets, we further introduce set permutation regularization, which produces multiple segmentations of action sequences with the same semantics. Experiments on public datasets demonstrate that ActionPiece consistently outperforms existing action tokenization methods, improving NDCG@10 by 6.00% to 12.82%.

Autoregressive next token prediction language models offer powerful capabilities but face significant challenges in practical deployment due to the high computational and memory costs of inference, particularly during the decoding stage. We introduce Set Block Decoding (SBD), a simple and flexible paradigm that accelerates generation by integrating standard next token prediction (NTP) and masked token prediction (MATP) within a single architecture. SBD allows the model to sample multiple, not necessarily consecutive, future tokens in parallel, a key distinction from previous acceleration methods. This flexibility allows the use of advanced solvers from the discrete diffusion literature, offering significant speedups without sacrificing accuracy. SBD requires no architectural changes or extra training hyperparameters, maintains compatibility with exact KV-caching, and can be implemented by fine-tuning existing next token prediction models. By fine-tuning Llama-3.1 8B and Qwen-3 8B, we demonstrate that SBD enables a 3-5x reduction in the number of forward passes required for generation while achieving same performance as equivalent NTP training.

Supervised fine-tuning (SFT) is a commonly used technique to adapt large language models (LLMs) to downstream tasks. In practice, SFT on a full dataset is computationally expensive and sometimes suffers from overfitting or bias amplification. This facilitates the rise of data curation in SFT, which prioritizes the most valuable data to optimze. This work studies the online batch selection family that dynamically scores and filters samples during the training process. However, existing popular methods often (i) rely merely on the utility of data to select a subset while neglecting other crucial factors like diversity, (ii) rely on external resources such as reference models or validation sets, and (iii) incur extra training time over full-dataset training. To address these limitations, this work develops UDS (Utility-Diversity Sampling), a framework for efficient online batch selection in SFT. UDS leverages the nuclear norm of the logits matrix to capture both data utility and intra-sample diversity, while estimating inter-sample diversity through efficient low-dimensional embedding comparisons with a lightweight memory buffer of historical samples. Such a design eliminates the need for external resources and unnecessary backpropagation, securing computational efficiency. Experiments on multiple benchmarks demonstrate that UDS consistently outperforms state-of-the-art online batch selection methods under varying data budgets, and significantly reduces training time compared to full-dataset fine-tuning. Code is available at https://github.com/gfyddha/UDS.

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present DeepWeightFlow, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by DeepWeightFlow do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

This work addresses a fundamental barrier in recommender systems: the inability to generalize across domains without extensive retraining. Traditional ID-based approaches fail entirely in cold-start and cross-domain scenarios where new users or items lack sufficient interaction history. Inspired by foundation models' cross-domain success, we develop a foundation model for sequential recommendation that achieves genuine zero-shot generalization capabilities. Our approach fundamentally departs from existing ID-based methods by deriving item representations exclusively from textual features. This enables immediate embedding of any new item without model retraining. We introduce unified item tokenization with Finite Scalar Quantization that transforms heterogeneous textual descriptions into standardized discrete tokens. This eliminates domain barriers that plague existing systems. Additionally, the framework features hybrid bidirectional-causal attention that captures both intra-item token coherence and inter-item sequential dependencies. An efficient catalog-aware beam search decoder enables real-time token-to-item mapping. Unlike conventional approaches confined to their training domains, RecGPT naturally bridges diverse recommendation contexts through its domain-invariant tokenization mechanism. Comprehensive evaluations across six datasets and industrial scenarios demonstrate consistent performance advantages.

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.

We introduce XiSort, a deterministic and reproducible sorting algorithm for floating-point sequences based on IEEE-754 total ordering and entropy minimization. XiSort guarantees bit-for-bit stability across runs and platforms by resolving tie-breaking via information-theoretic and symbolic methods. The algorithm supports both in-memory and external (out-of-core) operation, offering consistent performance on large datasets. We formalize a curved variant of the sorting metric that integrates into the Alpay Algebra framework, treating XiSort as a recursive operator with provable convergence and symbolic idempotence. This model preserves state-space closure while minimizing local disorder, interpretable as symbolic entropy. Empirical benchmarks demonstrate that XiSort achieves competitive throughput (e.g., sorting 10^8 doubles in approximately 12 seconds in-memory, and 100 GB at around 100 MB/s on SSDs), with applications in scientific computing, high-frequency finance, and reproducible numerical workflows. The results position XiSort as a principled tool for stable data alignment, symbolic preprocessing, and cross-platform float ordering. Keywords: deterministic sorting, IEEE-754, entropy minimization, symbolic algebra, reproducibility, external memory, Alpay Algebra, data pipelines

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.

Benchmark datasets for table structure recognition (TSR) must be carefully processed to ensure they are annotated consistently. However, even if a dataset's annotations are self-consistent, there may be significant inconsistency across datasets, which can harm the performance of models trained and evaluated on them. In this work, we show that aligning these benchmarksx2014removing both errors and inconsistency between themx2014improves model performance significantly. We demonstrate this through a data-centric approach where we adopt a single model architecture, the Table Transformer (TATR), that we hold fixed throughout. Baseline exact match accuracy for TATR evaluated on the ICDAR-2013 benchmark is 65% when trained on PubTables-1M, 42% when trained on FinTabNet, and 69% combined. After reducing annotation mistakes and inter-dataset inconsistency, performance of TATR evaluated on ICDAR-2013 increases substantially to 75% when trained on PubTables-1M, 65% when trained on FinTabNet, and 81% combined. We show through ablations over the modification steps that canonicalization of the table annotations has a significantly positive effect on performance, while other choices balance necessary trade-offs that arise when deciding a benchmark dataset's final composition. Overall we believe our work has significant implications for benchmark design for TSR and potentially other tasks as well. All dataset processing and training code will be released.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

The Shapley value is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, which has recently been used intensively in explainable artificial intelligence. The meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley values, most of them revolve around the notion of an agent's marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contributions. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

In this brief technical report we introduce the CINIC-10 dataset as a plug-in extended alternative for CIFAR-10. It was compiled by combining CIFAR-10 with images selected and downsampled from the ImageNet database. We present the approach to compiling the dataset, illustrate the example images for different classes, give pixel distributions for each part of the repository, and give some standard benchmarks for well known models. Details for download, usage, and compilation can be found in the associated github repository.

Integer sequences are of central importance to the modeling of concepts admitting complete finitary descriptions. We introduce a novel view on the learning of such concepts and lay down a set of benchmarking tasks aimed at conceptual understanding by machine learning models. These tasks indirectly assess model ability to abstract, and challenge them to reason both interpolatively and extrapolatively from the knowledge gained by observing representative examples. To further aid research in knowledge representation and reasoning, we present FACT, the Finitary Abstraction Comprehension Toolkit. The toolkit surrounds a large dataset of integer sequences comprising both organic and synthetic entries, a library for data pre-processing and generation, a set of model performance evaluation tools, and a collection of baseline model implementations, enabling the making of the future advancements with ease.

Engineering efficient implementations of compact and succinct structures is a time-consuming and challenging task, since there is no standard library of easy-to- use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is a difficult task, since older base- line implementations may not rely on the same basic components, and reimplementing from scratch can be very time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing succinct solutions for document retrieval.

We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence p^{1/T} propto softmax(z/T) is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence itself. The framework comprises four core components: (i) operator-agnostic bias--variance decompositions that characterize when sparse students outperform dense teachers, (ii) a homotopy path formalization of multi-stage pruning in function space explaining why iterative compression succeeds where one-shot pruning fails, (iii) convergence guarantees establishing O(1/n) rates for n-stage distillation with explicit parameter dependence, and (iv) equivalence class characterizations identifying distinct probability-domain operators that yield identical student models under capacity constraints. We introduce an axiomatic definition of probability-domain softening operators based on ranking preservation, continuity, entropy monotonicity, identity, and boundary behavior, and show that multiple non-equivalent operator families satisfy these axioms. All learning-theoretic guarantees are shown to hold uniformly across this operator class, independent of implementation details. These results provide theoretical grounding for black-box teacher distillation, partial-access settings such as top-k truncation and text-only outputs, and privacy-preserving model compression.

Near-term quantum workloads are shaped by coupled compilation and execution choices: qubit layout, routing, basis translation, gate suppression, measurement mitigation, shot budget, and artifact reproducibility. This paper analyzes QBalance, a Python workflow library for dataset-level selection among quantum compilation, noise-suppression, and error-mitigation strategies built on the Qiskit ecosystem. The contribution is formulated as a finite multi-objective strategy-selection problem over circuits, backends, and transformation policies. The manuscript derives the implemented weighted objective, non-dominated selection rule, survival-product error proxy, Bayesian linear candidate-ordering surrogate, and distributional diagnostics. It also positions the system relative to established work on Qiskit pass-manager compilation, SABRE-style routing, randomized compiling, dynamical decoupling, zero-noise extrapolation, matrix-free measurement mitigation, circuit cutting, and Thompson sampling. The analysis shows that QBalance provides a reproducible orchestration and artifact model for quantum workflow studies. It also establishes precise limitations: the current bandit mechanism orders candidates but does not reduce the number of candidate evaluations, the custom layout heuristic is greedy and only partially topology-aware, the implemented ZNE helper is parity-centered, and the cutting integration is a hook rather than a full reconstruction pipeline.

Conventional Sequential Recommender Systems (SRS) typically assign unique Hash IDs (HID) to construct item embeddings. These HID embeddings effectively learn collaborative information from historical user-item interactions, making them vulnerable to situations where most items are rarely consumed (the long-tail problem). Recent methods that incorporate auxiliary information often suffer from noisy collaborative sharing caused by co-occurrence signals or semantic homogeneity caused by flat dense embeddings. Semantic IDs (SIDs), with their capability of code sharing and multi-granular semantic modeling, provide a promising alternative. However, the collaborative overwhelming phenomenon hinders the further development of SID-based methods. The quantization mechanisms commonly compromise the uniqueness of identifiers required for modeling head items, creating a performance seesaw between head and tail items. To address this dilemma, we propose \name, a novel framework that harmonizes the SID and HID. Specifically, we devise a dual-branch modeling architecture that enables the model to capture both the multi-granular semantics within SID while preserving the unique collaborative identity of HID. Furthermore, we introduce a dual-level alignment strategy that bridges the two representations, facilitating knowledge transfer and supporting robust preference modeling. Extensive experiments on three real-world datasets show that \name~ effectively balances recommendation quality for both head and tail items while surpassing the existing baselines. The implementation code can be found onlinehttps://github.com/ziwliu8/H2Rec.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Preference learning has gained significant attention in tasks involving subjective human judgments, such as speech emotion recognition (SER) and image aesthetic assessment. While pairwise frameworks such as RankNet offer robust modeling of relative preferences, they are inherently limited to local comparisons and struggle to capture global ranking consistency. To address these limitations, we propose RankList, a novel listwise preference learning framework that generalizes RankNet to structured list-level supervision. Our formulation explicitly models local and non-local ranking constraints within a probabilistic framework. The paper introduces a log-sum-exp approximation to improve training efficiency. We further extend RankList with skip-wise comparisons, enabling progressive exposure to complex list structures and enhancing global ranking fidelity. Extensive experiments demonstrate the superiority of our method across diverse modalities. On benchmark SER datasets (MSP-Podcast, IEMOCAP, BIIC Podcast), RankList achieves consistent improvements in Kendall's Tau and ranking accuracy compared to standard listwise baselines. We also validate our approach on aesthetic image ranking using the Artistic Image Aesthetics dataset, highlighting its broad applicability. Through ablation and cross-domain studies, we show that RankList not only improves in-domain ranking but also generalizes better across datasets. Our framework offers a unified, extensible approach for modeling ordered preferences in subjective learning scenarios.

Over the past decade, tremendous progress has been made in Recommender Systems (RecSys) for well-known tasks such as next-item and next-basket prediction. On the other hand, the recently proposed next-period recommendation (NPR) task is not covered as much. Current works about NPR are mostly based around distinct problem formulations, methods, and proprietary datasets, making solutions difficult to reproduce. In this article, we aim to fill the gap in RecSys methods evaluation on the NPR task using publicly available datasets and (1) introduce the TTRS, a large-scale financial transactions dataset suitable for RecSys methods evaluation; (2) benchmark popular RecSys approaches on several datasets for the NPR task. When performing our analysis, we found a strong repetitive consumption pattern in several real-world datasets. With this setup, our results suggest that the repetitive nature of data is still hard to generalize for the evaluated RecSys methods, and novel item prediction performance is still questionable.

Code editing plays a vital role in software engineering, requiring developers to adjust existing code according to natural language instructions while keeping functionality intact and avoiding unnecessary modifications. However, commit-based datasets commonly used for this task are often noisy, lack diversity, and fail to reflect the style of real-world edit instructions. To address this, we introduce CanItEdit, an open-source pipeline that leverages multiple LLMs to synthesize realistic code-edit triplets. The pipeline produces both concise "lazy" instructions and more detailed "descriptive" ones, and applies filtering based on diffs and topics to guarantee data quality and variety. Using this process, we construct OCEDataFT, a curated dataset of 20K samples. Fine-tuning three advanced base models on OCEDataFT leads to significant performance boosts on the CanItEdit benchmark, with relative pass@1 improvements ranging from 4.50% to 20.79%. Notably, the resulting models achieve performance close to closed-source systems, narrowing the gap to GPT-4 to just 3.54%, without relying on proprietary resources or manual annotation.

The way in which data are shared can affect their utility and reusability. Here, we demonstrate how data that we had previously shared in bulk can be mobilized further through a knowledge graph that allows for much more granular exploration and interrogation. The original dataset is about the computational reproducibility of GitHub-hosted Jupyter notebooks associated with biomedical publications. It contains rich metadata about the publications, associated GitHub repositories and Jupyter notebooks, and the notebooks' reproducibility. We took this dataset, converted it into semantic triples and loaded these into a triple store to create a knowledge graph, FAIR Jupyter, that we made accessible via a web service. This enables granular data exploration and analysis through queries that can be tailored to specific use cases. Such queries may provide details about any of the variables from the original dataset, highlight relationships between them or combine some of the graph's content with materials from corresponding external resources. We provide a collection of example queries addressing a range of use cases in research and education. We also outline how sets of such queries can be used to profile specific content types, either individually or by class. We conclude by discussing how such a semantically enhanced sharing of complex datasets can both enhance their FAIRness, i.e., their findability, accessibility, interoperability, and reusability, and help identify and communicate best practices, particularly with regards to data quality, standardization, automation and reproducibility.

Sequential recommender systems have demonstrated a huge success for next-item recommendation by explicitly exploiting the temporal order of users' historical interactions. In practice, user interactions contain more useful temporal information beyond order, as shown by some pioneering studies. In this paper, we systematically investigate various temporal information for sequential recommendation and identify three types of advantageous temporal patterns beyond order, including absolute time information, relative item time intervals and relative recommendation time intervals. We are the first to explore item-oriented absolute time patterns. While existing models consider only one or two of these three patterns, we propose a novel holistic temporal pattern based neural network, named HTP, to fully leverage all these three patterns. In particular, we introduce novel components to address the subtle correlations between relative item time intervals and relative recommendation time intervals, which render a major technical challenge. Extensive experiments on three real-world benchmark datasets show that our HTP model consistently and substantially outperforms many state-of-the-art models. Our code is publically available at https://github.com/623851394/HTP/tree/main/HTP-main

This paper presents a compute-efficient approach to pre-training a Language Model-the "1.5-Pints"-in only 9 days, while outperforming state-of-the-art models as an instruction-following assistant.Based on MT-Bench (a benchmark that emulates human judgments), 1.5-Pints outperforms Apple's OpenELM and Microsoft's Phi.This is achieved by a carefully curated pre-training dataset of 57 billion tokens, using a mix of automated workflows and manual human review. The selection of the dataset prioritizes content that is considered expository and "textbook-like" to aid the model in reasoning and logical deduction, culminating in its overall ability as a strong and versatile AI model. In terms of the model architecture, we employed a modified Mistral tokenizer, alongside a Llama-2 architecture for wider compatibility. For training, we adopted the methodologies used by StableLM, TinyLlama, and Huggingface Zephyr. 1.5-Pints demonstrates that by focusing on data quality over quantity in LLM training, we can significantly reduce training time and resources required. We believe this approach will not only make pre-training more accessible but also reduce our carbon footprint. Our findings and resources from this research are open-sourced, aiming to facilitate further advancements in the field. The 1.5-Pints model is available in two versions: 2K and 16K context windows.

The paper ``Tropical Geometry of Deep Neural Networks'' by L. Zhang et al. introduces an equivalence between integer-valued neural networks (IVNN) with ReLU_{t} and tropical rational functions, which come with a map to polytopes. Here, IVNN refers to a network with integer weights but real biases, and ReLU_{t} is defined as ReLU_{t}(x)=max(x,t) for tinRcup{-infty}. For every poset with n points, there exists a corresponding order polytope, i.e., a convex polytope in the unit cube [0,1]^n whose coordinates obey the inequalities of the poset. We study neural networks whose associated polytope is an order polytope. We then explain how posets with four points induce neural networks that can be interpreted as 2times 2 convolutional filters. These poset filters can be added to any neural network, not only IVNN. Similarly to maxout, poset pooling filters update the weights of the neural network during backpropagation with more precision than average pooling, max pooling, or mixed pooling, without the need to train extra parameters. We report experiments that support our statements. We also define the structure of algebra over the operad of posets on poset neural networks and tropical polynomials. This formalism allows us to study the composition of poset neural network arquitectures and the effect on their corresponding Newton polytopes, via the introduction of the generalization of two operations on polytopes: the Minkowski sum and the convex envelope.

Since its 2009 genesis block, the Bitcoin network has processed >1.08 billion (B) transactions representing >8.72B BTC, offering rich potential for machine learning (ML); yet, its pseudonymity and obscured flow of funds inherent in its \utxo-based design, have rendered this data largely inaccessible for ML research. Addressing this gap, we present an ML-compatible graph modeling the Bitcoin's economic topology by reconstructing the flow of funds. This temporal, heterogeneous graph encompasses complete transaction history up to block \cutoffHeight, consisting of >2.4B nodes and >39.72B edges. Additionally, we provide custom sampling methods yielding node and edge feature vectors of sampled communities, tools to load and analyze the Bitcoin graph data within specialized graph databases, and ready-to-use database snapshots. This comprehensive dataset and toolkit empower the ML community to tackle Bitcoin's intricate ecosystem at scale, driving progress in applications such as anomaly detection, address classification, market analysis, and large-scale graph ML benchmarking. Dataset and code available at https://github.com/B1AAB/EBA{github.com/b1aab/eba}

We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale and proficiency, moving from early results in undergraduate topology and restructuring of existing library content to a full standalone formalization of a graduate textbook. The formalization comprises 130K lines of code and 5900 Lean declarations and was conducted within one week by a total of 30K Claude 4.5 Opus agents collaborating in parallel on a shared code base via version control, simultaneously setting a record in multi-agent software engineering with usable results. The inference cost matches or undercuts what we estimate as the salaries required for a team of human experts, and we expect there is still the potential for large efficiencies to be made without the need for better models. We make our code, the resulting Lean code base and a side-by-side blueprint website available open-source.

Long-tailed data distributions pose challenges for a variety of domains like e-commerce, finance, biomedical science, and cyber security, where the performance of machine learning models is often dominated by head categories while tail categories are inadequately learned. This work aims to provide a systematic view of long-tailed learning with regard to three pivotal angles: (A1) the characterization of data long-tailedness, (A2) the data complexity of various domains, and (A3) the heterogeneity of emerging tasks. We develop HeroLT, a comprehensive long-tailed learning benchmark integrating 18 state-of-the-art algorithms, 10 evaluation metrics, and 17 real-world datasets across 6 tasks and 4 data modalities. HeroLT with novel angles and extensive experiments (315 in total) enables effective and fair evaluation of newly proposed methods compared with existing baselines on varying dataset types. Finally, we conclude by highlighting the significant applications of long-tailed learning and identifying several promising future directions. For accessibility and reproducibility, we open-source our benchmark HeroLT and corresponding results at https://github.com/SSSKJ/HeroLT.

Recent advances in foundation models have shown great promise in domains such as natural language processing and computer vision, and similar efforts are now emerging in the Earth Observation community. These models aim to generalize across tasks with limited supervision, reducing the need for training separate models for each task. However, current strategies, which largely focus on scaling model size and dataset volume, require prohibitive computational and data resources, limiting accessibility to only a few large institutions. Moreover, this paradigm of ever-larger models stands in stark contrast with the principles of sustainable and environmentally responsible AI, as it leads to immense carbon footprints and resource inefficiency. In this work, we present a novel and efficient alternative: an Ensemble-of-Specialists framework for building Remote Sensing Foundation Models (RSFMs). Our method decomposes the training process into lightweight, task-specific ConvNeXtV2 specialists that can be frozen and reused. This modular approach offers strong advantages in efficiency, interpretability, and extensibility. Moreover, it naturally supports federated training, pruning, and continuous specialist integration, making it particularly well-suited for collaborative and resource-constrained settings. Our framework sets a new direction for building scalable and efficient RSFMs. All codes and pretrained models are available at https://github.com/pierreadorni/EoS-FM.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX_0, EFX^3 and EF1^3 - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1^3 allocation. With -alpha/0/alpha utilities, this algorithm returns an EFX^3 and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With -alpha/0/beta utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

The Right to Explanation and the Right to be Forgotten are two important principles outlined to regulate algorithmic decision making and data usage in real-world applications. While the right to explanation allows individuals to request an actionable explanation for an algorithmic decision, the right to be forgotten grants them the right to ask for their data to be deleted from all the databases and models of an organization. Intuitively, enforcing the right to be forgotten may trigger model updates which in turn invalidate previously provided explanations, thus violating the right to explanation. In this work, we investigate the technical implications arising due to the interference between the two aforementioned regulatory principles, and propose the first algorithmic framework to resolve the tension between them. To this end, we formulate a novel optimization problem to generate explanations that are robust to model updates due to the removal of training data instances by data deletion requests. We then derive an efficient approximation algorithm to handle the combinatorial complexity of this optimization problem. We theoretically demonstrate that our method generates explanations that are provably robust to worst-case data deletion requests with bounded costs in case of linear models and certain classes of non-linear models. Extensive experimentation with real-world datasets demonstrates the efficacy of the proposed framework.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

This report presents Wan, a comprehensive and open suite of video foundation models designed to push the boundaries of video generation. Built upon the mainstream diffusion transformer paradigm, Wan achieves significant advancements in generative capabilities through a series of innovations, including our novel VAE, scalable pre-training strategies, large-scale data curation, and automated evaluation metrics. These contributions collectively enhance the model's performance and versatility. Specifically, Wan is characterized by four key features: Leading Performance: The 14B model of Wan, trained on a vast dataset comprising billions of images and videos, demonstrates the scaling laws of video generation with respect to both data and model size. It consistently outperforms the existing open-source models as well as state-of-the-art commercial solutions across multiple internal and external benchmarks, demonstrating a clear and significant performance superiority. Comprehensiveness: Wan offers two capable models, i.e., 1.3B and 14B parameters, for efficiency and effectiveness respectively. It also covers multiple downstream applications, including image-to-video, instruction-guided video editing, and personal video generation, encompassing up to eight tasks. Consumer-Grade Efficiency: The 1.3B model demonstrates exceptional resource efficiency, requiring only 8.19 GB VRAM, making it compatible with a wide range of consumer-grade GPUs. Openness: We open-source the entire series of Wan, including source code and all models, with the goal of fostering the growth of the video generation community. This openness seeks to significantly expand the creative possibilities of video production in the industry and provide academia with high-quality video foundation models. All the code and models are available at https://github.com/Wan-Video/Wan2.1.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Foundation models are redefining how AI systems are built. Practitioners now follow a standard procedure to build their machine learning solutions: from a pre-trained foundation model, they fine-tune the weights on the target task of interest. So, the Internet is swarmed by a handful of foundation models fine-tuned on many diverse tasks: these individual fine-tunings exist in isolation without benefiting from each other. In our opinion, this is a missed opportunity, as these specialized models contain rich and diverse features. In this paper, we thus propose model ratatouille, a new strategy to recycle the multiple fine-tunings of the same foundation model on diverse auxiliary tasks. Specifically, we repurpose these auxiliary weights as initializations for multiple parallel fine-tunings on the target task; then, we average all fine-tuned weights to obtain the final model. This recycling strategy aims at maximizing the diversity in weights by leveraging the diversity in auxiliary tasks. Empirically, it improves the state of the art on the reference DomainBed benchmark for out-of-distribution generalization. Looking forward, this work contributes to the emerging paradigm of updatable machine learning where, akin to open-source software development, the community collaborates to reliably update machine learning models.

To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary (Z_2), modular ternary (Z_3) and integer ternary (Z_T = {-1,0,1}) -- and implements both fixed-dimension and meta-dimensional search operators. Using efficient bit-level encoding of coefficient vectors and OpenMP parallelism, the tools enable large-scale exploration on commodity hardware. The study covers 680 schemes ranging from (2 times 2 times 2) to (16 times 16 times 16), with 276 schemes now in Z_T coefficients and 117 in integer coefficients. With this framework, the multiplicative complexity (rank) is improved for 79 matrix multiplication schemes. Notably, a new 4 times 4 times 10 scheme requiring only 115 multiplications is discovered, achieving ωapprox 2.80478 and beating Strassen's exponent for this specific size. Additionally, 93 schemes are rediscovered in ternary coefficients that were previously known only over rationals or integers, and 68 schemes in integer coefficients that previously required fractions. All tools and discovered schemes are made publicly available to enable reproducible research.

Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability is still lacking. In this work, we introduce a comprehensive benchmarking framework designed to systematically evaluate a range of quantum optimization techniques against well-established NP-hard combinatorial problems. Our framework focuses on key problem classes, including the Multi-Dimensional Knapsack Problem (MDKP), Maximum Independent Set (MIS), Quadratic Assignment Problem (QAP), and Market Share Problem (MSP). Our study evaluates gate-based quantum approaches, including the Variational Quantum Eigensolver (VQE) and its CVaR-enhanced variant, alongside advanced quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and its extensions. To address resource constraints, we incorporate qubit compression techniques like Pauli Correlation Encoding (PCE) and Quantum Random Access Optimization (QRAO). Experimental results, obtained from simulated quantum environments and classical solvers, provide key insights into feasibility, optimality gaps, and scalability. Our findings highlight both the promise and current limitations of quantum optimization, offering a structured pathway for future research and practical applications in quantum-enhanced decision-making.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the AWS S3 bucket access policy code. We also curate a dataset based on the FVEL\textnormal{ER} dataset for future training tasks.

Parameter-Efficient Fine-Tuning (PEFT) methods have gained significant popularity for adapting pre-trained Large Language Models (LLMs) to downstream tasks, primarily due to their potential to significantly reduce memory and computational overheads. However, a common limitation in most PEFT approaches is their application of a uniform architectural design across all layers. This uniformity involves identical trainable modules and ignores the varying importance of each layer, leading to sub-optimal fine-tuning results. To overcome the above limitation and obtain better performance, we develop a novel approach, Importance-aware Sparse Tuning (IST), to fully utilize the inherent sparsity and select the most important subset of full layers with effective layer-wise importance scoring. The proposed IST is a versatile and plug-and-play technique compatible with various PEFT methods that operate on a per-layer basis. By leveraging the estimated importance scores, IST dynamically updates these selected layers in PEFT modules, leading to reduced memory demands. We further provide theoretical proof of convergence and empirical evidence of superior performance to demonstrate the advantages of IST over uniform updating strategies. Extensive experiments on a range of LLMs, PEFTs, and downstream tasks substantiate the effectiveness of our proposed method, showcasing IST's capacity to enhance existing layer-based PEFT methods. Our code is available at https://github.com/Kaiseem/IST.

We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask spreads, discrete price movements, and serial return correlations. Our framework augments the binomial tree with path-dependent transition probabilities estimated via Random Forest classifiers trained on high-frequency market data. This approach preserves no-arbitrage conditions while embedding real-world trading dynamics into the pricing model. Using 46,655 minute-level observations of SPY from January to June 2025, we achieve an AUC of 88.25% in forecasting one-step price movements. Order flow imbalance is identified as the most influential predictor, contributing 43.2% to feature importance. After resolving time-scaling inconsistencies in tree construction, our model yields option prices that deviate by 13.79% from Black-Scholes benchmarks, highlighting the impact of microstructure on fair value estimation. While computational limitations restrict the model to short-term derivatives, our results offer a robust, data-driven alternative to classical pricing methods grounded in empirical market behavior.

Foundation models for medical imaging are typically pretrained on increasingly large datasets, following a "scale-at-all-costs" paradigm. However, this strategy faces two critical challenges: large-scale medical datasets often contain substantial redundancy and severe class imbalance that bias representation learning toward over-represented patterns, and indiscriminate training regardless of heterogeneity in data quality incurs considerable computational inefficiency. Here we demonstrate that active, principled data curation during pretraining can serve as a viable, cost-effective alternative to brute-force dataset enlargement. We introduce CheXficient, a chest X-ray (CXR) foundation model that selectively prioritizes informative training samples. CheXficient is pretrained on only 22.7% of 1,235,004 paired CXR images and reports while consuming under 27.3% of the total compute budget, yet achieving comparable or superior performance to its full-data counterpart and other large-scale pretrained models. We assess CheXficient across 20 individual benchmarks spanning 5 task types, including non-adapted off-the-shelf evaluations (zero-shot findings classification and crossmodal retrieval) and adapted downstream tasks (disease prediction, semantic segmentation, and radiology report generation). Further analyses show that CheXficient systematically prioritizes under-represented training samples, improving generalizability on long-tailed or rare conditions. Overall, our work offers practical insights into the data and computation demands for efficient pretraining and downstream adaptation of medical vision-language foundation models.

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of T inputs and produces, after receiving each input, an accurate output on the obtained inputs. In contrast, a batch algorithm receives the data as one batch and produces a single output. We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are widely studied and used in the batch model, we show that the worst case error of every continual release algorithm is tilde Omega(T^{1/3}) times larger than that of the best batch algorithm. Previous work shows only a polylogarithimic (in T) gap between the worst case error achievable in these two models; further, for many problems, including the summation of binary attributes, the polylogarithmic gap is tight (Dwork et al., 2010; Chan et al., 2010). Our results show that problems closely related to summation -- specifically, those that require selecting the largest of a set of sums -- are fundamentally harder in the continual release model than in the batch model. Our lower bounds assume only that privacy holds for streams fixed in advance (the "nonadaptive" setting). However, we provide matching upper bounds that hold in a model where privacy is required even for adaptively selected streams. This model may be of independent interest.

Traditional fixed test sets fall short in evaluating open-ended capabilities of foundation models. To address this, we propose ONEBench(OpeN-Ended Benchmarking), a new testing paradigm that consolidates individual evaluation datasets into a unified, ever-expanding sample pool. ONEBench allows users to generate custom, open-ended evaluation benchmarks from this pool, corresponding to specific capabilities of interest. By aggregating samples across test sets, ONEBench enables the assessment of diverse capabilities beyond those covered by the original test sets, while mitigating overfitting and dataset bias. Most importantly, it frames model evaluation as a collective process of selecting and aggregating sample-level tests. The shift from task-specific benchmarks to ONEBench introduces two challenges: (1)heterogeneity and (2)incompleteness. Heterogeneity refers to the aggregation over diverse metrics, while incompleteness describes comparing models evaluated on different data subsets. To address these challenges, we explore algorithms to aggregate sparse measurements into reliable model scores. Our aggregation algorithm ensures identifiability(asymptotically recovering ground-truth scores) and rapid convergence, enabling accurate model ranking with less data. On homogenous datasets, we show our aggregation algorithm provides rankings that highly correlate with those produced by average scores. We also demonstrate robustness to ~95% of measurements missing, reducing evaluation cost by up to 20x with little-to-no change in model rankings. We introduce ONEBench-LLM for language models and ONEBench-LMM for vision-language models, unifying evaluations across these domains. Overall, we present a technique for open-ended evaluation, which can aggregate over incomplete, heterogeneous sample-level measurements to continually grow a benchmark alongside the rapidly developing foundation models.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

We describe an incentive system for distributed deep learning of foundational models where peers are rewarded for contributions. The incentive system, Gauntlet, has been deployed on the bittensor blockchain and used to train a 1.2B LLM with completely permissionless contributions of pseudo-gradients: no control over the users that can register or their hardware. Gauntlet can be applied to any synchronous distributed training scheme that relies on aggregating updates or pseudo-gradients. We rely on a two-stage mechanism for fast filtering of peer uptime, reliability, and synchronization, combined with the core component that estimates the loss before and after individual pseudo-gradient contributions. We utilized an OpenSkill rating system to track competitiveness of pseudo-gradient scores across time. Finally, we introduce a novel mechanism to ensure peers on the network perform unique computations. Our live 1.2B run, which has paid out real-valued tokens to participants based on the value of their contributions, yielded a competitive (on a per-iteration basis) 1.2B model that demonstrates the utility of our incentive system.

As high-quality public text approaches exhaustion, a phenomenon known as the Data Wall, pre-training is shifting from more tokens to better tokens. However, existing methods either rely on heuristic static filters that ignore training dynamics, or use dynamic yet optimizer-agnostic criteria based on raw gradients. We propose OPUS (Optimizer-induced Projected Utility Selection), a dynamic data selection framework that defines utility in the optimizer-induced update space. OPUS scores candidates by projecting their effective updates, shaped by modern optimizers, onto a target direction derived from a stable, in-distribution proxy. To ensure scalability, we employ Ghost technique with CountSketch for computational efficiency, and Boltzmann sampling for data diversity, incurring only 4.7\% additional compute overhead. OPUS achieves remarkable results across diverse corpora, quality tiers, optimizers, and model scales. In pre-training of GPT-2 Large/XL on FineWeb and FineWeb-Edu with 30B tokens, OPUS outperforms industrial-level baselines and even full 200B-token training. Moreover, when combined with industrial-level static filters, OPUS further improves pre-training efficiency, even with lower-quality data. Furthermore, in continued pre-training of Qwen3-8B-Base on SciencePedia, OPUS achieves superior performance using only 0.5B tokens compared to full training with 3B tokens, demonstrating significant data efficiency gains in specialized domains.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

The quality of training data impacts the performance of pre-trained large language models (LMs). Given a fixed budget of tokens, we study how to best select data that leads to good downstream model performance across tasks. We develop a new framework based on a simple hypothesis: just as humans acquire interdependent skills in a deliberate order, language models also follow a natural order when learning a set of skills from their training data. If such an order exists, it can be utilized for improved understanding of LMs and for data-efficient training. Using this intuition, our framework formalizes the notion of a skill and of an ordered set of skills in terms of the associated data. First, using both synthetic and real data, we demonstrate that these ordered skill sets exist, and that their existence enables more advanced skills to be learned with less data when we train on their prerequisite skills. Second, using our proposed framework, we introduce an online data sampling algorithm, Skill-It, over mixtures of skills for both continual pre-training and fine-tuning regimes, where the objective is to efficiently learn multiple skills in the former and an individual skill in the latter. On the LEGO synthetic in the continual pre-training setting, Skill-It obtains 36.5 points higher accuracy than random sampling. On the Natural Instructions dataset in the fine-tuning setting, Skill-It reduces the validation loss on the target skill by 13.6% versus training on data associated with the target skill itself. We apply our skills framework on the recent RedPajama dataset to continually pre-train a 3B-parameter LM, achieving higher accuracy on the LM Evaluation Harness with 1B tokens than the baseline approach of sampling uniformly over data sources with 3B tokens.

Synthesizing SQL queries from natural language is a long-standing open problem and has been attracting considerable interest recently. Toward solving the problem, the de facto approach is to employ a sequence-to-sequence-style model. Such an approach will necessarily require the SQL queries to be serialized. Since the same SQL query may have multiple equivalent serializations, training a sequence-to-sequence-style model is sensitive to the choice from one of them. This phenomenon is documented as the "order-matters" problem. Existing state-of-the-art approaches rely on reinforcement learning to reward the decoder when it generates any of the equivalent serializations. However, we observe that the improvement from reinforcement learning is limited. In this paper, we propose a novel approach, i.e., SQLNet, to fundamentally solve this problem by avoiding the sequence-to-sequence structure when the order does not matter. In particular, we employ a sketch-based approach where the sketch contains a dependency graph so that one prediction can be done by taking into consideration only the previous predictions that it depends on. In addition, we propose a sequence-to-set model as well as the column attention mechanism to synthesize the query based on the sketch. By combining all these novel techniques, we show that SQLNet can outperform the prior art by 9% to 13% on the WikiSQL task.

Given a finite poset mathcal P, the hypercube-height, denoted by h^*(mathcal P), is defined to be the largest h such that, for any natural number n, the subsets of [n] of size less than h do not contain an induced copy of mathcal P. The hypercube-width, denoted by w^*(mathcal P), is the smallest w such that the subsets of [w] of size at most h^*(mathcal P) contain an induced copy of mathcal P. In other words, h^*(mathcal P) asks how `low' can a poset be embedded, and w^*(mathcal P) asks for the first hypercube in which such an `optimal' embedding occurs. These notions were introduced by Bastide, Groenland, Ivan and Johnston in connection to upper bounds for the poset saturation numbers. While it is not hard to see that h^*(mathcal P)leq |mathcal P|-1 (and this bound can be tight), the hypercube-width has proved to be much more elusive. It was shown by the authors mentioned above that w^*(mathcal P)leq|mathcal P|^2/4, but they conjectured that in fact w^*(mathcal P)leq |mathcal P| for any finite poset mathcal P. In this paper we prove this conjecture. The proof uses Hall's theorem for bipartite graphs as a precision tool for modifing an existing copy of our poset.