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This work focuses on the gradient flow dynamics of a neural network model that uses correlation loss to approximate a multi-index function on high-dimensional standard Gaussian data. Specifically, the multi-index function we consider is a sum of neurons $f^*(x) \!=\! \sum_{j=1}^k \! \sigma^*(v_j^T x)$ where $v_1, \dots, v_k$ are unit vectors, and $\sigma^*$ lacks the first and second Hermite polynomials in its Hermite expansion. It is known that, for the single-index case ($k\!=\!1$), overcoming the search phase requires polynomial time complexity. We first generalize this result to multi-index functions characterized by vectors in arbitrary directions. After the search phase, it is not clear whether the network neurons converge to the index vectors, or get stuck at a sub-optimal solution. When the index vectors are orthogonal, we give a complete characterization of the fixed points and prove that neurons converge to the nearest index vectors. Therefore, using $n \! \asymp \! k \log k$ neurons ensures finding the full set of index vectors with gradient flow with high probability over random initialization. When $ v_i^T v_j \!=\! \beta \! \geq \! 0$ for all $i \neq j$, we prove the existence of a sharp threshold $\beta_c \!=\! c/(c+k)$ at which the fixed point that computes the average of the index vectors transitions from a saddle point to a minimum. Numerical simulations show that using a correlation loss and a mild overparameterization suffices to learn all of the index vectors when they are nearly orthogonal, however, the correlation loss fails when the dot product between the index vectors exceeds a certain threshold.

Video understanding requires the extraction of rich spatio-temporal representations, which transformer models achieve through self-attention. Unfortunately, self-attention poses a computational burden. In NLP, Mamba has surfaced as an efficient alternative for transformers. However, Mamba's successes do not trivially extend to vision tasks, including those in video analysis. In this paper, we theoretically analyze the differences between self-attention and Mamba. We identify two limitations in Mamba's token processing: historical decay and element contradiction. We propose VideoMambaPro (VMP) that solves the identified limitations by adding masked backward computation and elemental residual connections to a VideoMamba backbone. Differently sized VideoMambaPro models surpass VideoMamba by 1.6-2.8% and 1.1-1.9% top-1 on Kinetics-400 and Something-Something V2, respectively. Even without extensive pre-training, our models present an increasingly attractive and efficient alternative to current transformer models. Moreover, our two solutions are orthogonal to recent advances in Vision Mamba models, and are likely to provide further improvements in future models.

This paper addresses the problem of visual target tracking in scenarios where a pursuer may experience intermittent loss of visibility of the target. The design of a Switched Visual Tracker (SVT) is presented which aims to meet the competing requirements of maintaining both proximity and visibility. SVT alternates between a visual tracking mode for following the target, and a recovery mode for regaining visual contact when the target falls out of sight. We establish the stability of SVT by extending the average dwell time theorem from switched systems theory, which may be of independent interest. Our implementation of SVT on an Agilicious drone [1] illustrates its effectiveness on tracking various target trajectories: it reduces the average tracking error by up to 45% and significantly improves visibility duration compared to a baseline algorithm. The results show that our approach effectively handles intermittent vision loss, offering enhanced robustness and adaptability for real-world autonomous missions. Additionally, we demonstrate how the stability analysis provides valuable guidance for selecting parameters, such as tracking speed and recovery distance, to optimize the SVT's performance.

Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution proof (or a more expressive proof), which is commonly used for verification purposes. Empirically, modern SAT solvers produce relatively short proofs, however, there are no inherent guarantees that these proofs cannot be significantly reduced. This paper proposes a novel branch-and-bound algorithm for finding the shortest resolution proofs; to this end, we introduce a layer list representation of proofs that groups clauses by their level of indirection. As we show, this representation breaks all permutational symmetries, thereby improving upon the state-of-the-art symmetry-breaking and informing the design of a novel workflow for proof minimization. In addition to that, we design pruning procedures that reason on proof length lower bound, clause subsumption, and dominance. Our experiments suggest that the proofs from state-of-the-art solvers could be shortened by 30-60% on the instances from SAT Competition 2002 and by 25-50% on small synthetic formulas. When treated as an algorithm for finding the shortest proof, our approach solves twice as many instances as the previous work based on SAT solving and reduces the time to optimality by orders of magnitude for the instances solved by both approaches.

Recently, there has been a significant upsurge of interest in leveraging large language models (LLMs) to assist scientific discovery. However, most LLMs only focus on general science, while they lack domain-specific knowledge, such as chemical molecules and amino acid sequences. To bridge these gaps, we introduce SciDFM, a mixture-of-experts LLM, which is trained from scratch and is able to conduct college-level scientific reasoning and understand molecules and amino acid sequences. We collect a large-scale training corpus containing numerous scientific papers and books from different disciplines as well as data from domain-specific databases. We further fine-tune the pre-trained model on lots of instruction data to improve performances on downstream benchmarks. From experiment results, we show that SciDFM achieves strong performance on general scientific benchmarks such as SciEval and SciQ, and it reaches a SOTA performance on domain-specific benchmarks among models of similar size. We further analyze the expert layers and show that the results of expert selection vary with data from different disciplines. To benefit the broader research community, we open-source SciDFM at //huggingface.co/OpenDFM/SciDFM-MoE-A5.6B-v1.0.

In the field of emotion analysis, much NLP research focuses on identifying a limited number of discrete emotion categories, often applied across languages. These basic sets, however, are rarely designed with textual data in mind, and culture, language, and dialect can influence how particular emotions are interpreted. In this work, we broaden our scope to a practically unbounded set of \textit{affective states}, which includes any terms that humans use to describe their experiences of feeling. We collect and publish MASIVE, a dataset of Reddit posts in English and Spanish containing over 1,000 unique affective states each. We then define the new problem of \textit{affective state identification} for language generation models framed as a masked span prediction task. On this task, we find that smaller finetuned multilingual models outperform much larger LLMs, even on region-specific Spanish affective states. Additionally, we show that pretraining on MASIVE improves model performance on existing emotion benchmarks. Finally, through machine translation experiments, we find that native speaker-written data is vital to good performance on this task.

Traditional compilers, designed for optimizing low-level code, fall short when dealing with modern, computation-heavy applications like image processing, machine learning, or numerical simulations. Optimizations should understand the primitive operations of the specific application domain and thus happen on that level. Domain-specific languages (DSLs) fulfill these requirements. However, DSL compilers reinvent the wheel over and over again as standard optimizations, code generators, and general infrastructure & boilerplate code must be reimplemented for each DSL compiler. This paper presents MimIR, an extensible, higher-order intermediate representation. At its core, MimIR is a pure type system and, hence, a form of a typed lambda calculus. Developers can declare the signatures of new (domain-specific) operations, called "axioms". An axiom can be the declaration of a function, a type operator, or any other entity with a possibly polymorphic, polytypic, and/or dependent type. This way, developers can extend MimIR at any low or high level and bundle them in a plugin. Plugins extend the compiler and take care of optimizing and lowering the plugins' axioms. We show the expressiveness and effectiveness of MimIR in three case studies: Low-level plugins that operate at the same level of abstraction as LLVM, a regular-expression matching plugin, and plugins for linear algebra and automatic differentiation. We show that in all three studies, MimIR produces code that has state-of-the-art performance.

Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of machine learning models is essential to the development of trustworthy machine-learning-based systems. A burgeoning body of research seeks to define the goals and methods of explainability in machine learning. In this paper, we seek to review and categorize research on counterfactual explanations, a specific class of explanation that provides a link between what could have happened had input to a model been changed in a particular way. Modern approaches to counterfactual explainability in machine learning draw connections to the established legal doctrine in many countries, making them appealing to fielded systems in high-impact areas such as finance and healthcare. Thus, we design a rubric with desirable properties of counterfactual explanation algorithms and comprehensively evaluate all currently-proposed algorithms against that rubric. Our rubric provides easy comparison and comprehension of the advantages and disadvantages of different approaches and serves as an introduction to major research themes in this field. We also identify gaps and discuss promising research directions in the space of counterfactual explainability.