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Generating bitmap graphics from text has gained considerable attention, yet for scientific figures, vector graphics are often preferred. Given that vector graphics are typically encoded using low-level graphics primitives, generating them directly is difficult. To address this, we propose the use of TikZ, a well-known abstract graphics language that can be compiled to vector graphics, as an intermediate representation of scientific figures. TikZ offers human-oriented, high-level commands, thereby facilitating conditional language modeling with any large language model. To this end, we introduce DaTikZ, the first large-scale TikZ dataset consisting of 120k TikZ drawings aligned with captions. We fine-tune LLaMA on DaTikZ, as well as our new model CLiMA, which augments LLaMA with multimodal CLIP embeddings. In both human and automatic evaluation, CLiMA and LLaMA outperform commercial GPT-4 and Claude 2 in terms of similarity to human-created figures, with CLiMA additionally improving text-image alignment. Our detailed analysis shows that all models generalize well and are not susceptible to memorization. GPT-4 and Claude 2, however, tend to generate more simplistic figures compared to both humans and our models. We make our framework, AutomaTikZ, along with model weights and datasets, publicly available.

Attribution scores reflect how important the feature values in an input entity are for the output of a machine learning model. One of the most popular attribution scores is the SHAP score, which is an instantiation of the general Shapley value used in coalition game theory. The definition of this score relies on a probability distribution on the entity population. Since the exact distribution is generally unknown, it needs to be assigned subjectively or be estimated from data, which may lead to misleading feature scores. In this paper, we propose a principled framework for reasoning on SHAP scores under unknown entity population distributions. In our framework, we consider an uncertainty region that contains the potential distributions, and the SHAP score of a feature becomes a function defined over this region. We study the basic problems of finding maxima and minima of this function, which allows us to determine tight ranges for the SHAP scores of all features. In particular, we pinpoint the complexity of these problems, and other related ones, showing them to be NP-complete. Finally, we present experiments on a real-world dataset, showing that our framework may contribute to a more robust feature scoring.

Recently, a data-driven Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm tailored to channels with intersymbol interference has been introduced. This so-called BCJRNet algorithm utilizes neural networks to calculate channel likelihoods. BCJRNet has demonstrated resilience against inaccurate channel tap estimations when applied to a time-invariant channel with ideal exponential decay profiles. However, its generalization capabilities for practically-relevant time-varying channels, where the receiver can only access incorrect channel parameters, remain largely unexplored. The primary contribution of this paper is to expand upon the results from existing literature to encompass a variety of imperfect channel knowledge cases that appear in real-world transmissions. Our findings demonstrate that BCJRNet significantly outperforms the conventional BCJR algorithm for stationary transmission scenarios when learning from noisy channel data and with imperfect channel decay profiles. However, this advantage is shown to diminish when the operating channel is also rapidly time-varying. Our results also show the importance of memory assumptions for conventional BCJR and BCJRNet. An underestimation of the memory largely degrades the performance of both BCJR and BCJRNet, especially in a slow-decaying channel. To mimic a situation closer to a practical scenario, we also combined channel tap uncertainty with imperfect channel memory knowledge. Somewhat surprisingly, our results revealed improved performance when employing the conventional BCJR with an underestimated memory assumption. BCJRNet, on the other hand, showed a consistent performance improvement as the level of accurate memory knowledge increased.

The class of basic feasible functionals (BFF) is the analog of FP (polynomial time functions) for type-two functionals, that is, functionals that can take (first-order) functions as arguments. BFF can be defined by means of oracle Turing machines of time bounded by a second-order polynomial. On the other hand, higher-order term rewriting provides an elegant formalism for expressing higher-order computation. We address the problem of characterizing the class BFF by higher-order term rewriting. Various kinds of interpretations for first-order term rewriting have been introduced in the literature for proving termination and characterizing (first-order) complexity classes. Here we consider a recently introduced notion of cost-size interpretations for higher-order term rewriting and see definitions as ways of computing functionals. We then prove that the class of functionals represented by higher-order terms admitting a certain kind of cost-size interpretation is exactly BFF.

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another interesting feature of these networks is their connection to the attention mechanism which is part of the Transformer architectures widely applied in deep learning. In this work, we study a generic family of pattern ensembles using a statistical mechanics analysis which gives exact asymptotic thresholds for the retrieval of a typical pattern, $\alpha_1$, and lower bounds for the maximum of the load $\alpha$ for which all patterns can be retrieved, $\alpha_c$, as well as sizes of attraction basins. We discuss in detail the cases of Gaussian and spherical patterns, and show that they display rich and qualitatively different phase diagrams.

This paper addresses the problem of finding a minimum-cost $m$-state Markov chain $(S_0,\ldots,S_{m-1})$ in a large set of chains. The chains studied have a reward associated with each state. The cost of a chain is its "gain", i.e., its average reward under its stationary distribution. Specifically, for each $k=0,\ldots,m-1$ there is a known set ${\mathbb S}_k$ of type-$k$ states. A permissible Markov chain contains exactly one state of each type; the problem is to find a minimum-cost permissible chain. The original motivation was to find a cheapest binary AIFV-$m$ lossless code on a source alphabet of size $n$. Such a code is an $m$-tuple of trees, in which each tree can be viewed as a Markov Chain state. This formulation was then used to address other problems in lossless compression. The known solution techniques for finding minimum-cost Markov chains were iterative and ran in exponential time. This paper shows how to map every possible type-$k$ state into a type-$k$ hyperplane and then define a "Markov Chain Polytope" as the lower envelope of all such hyperplanes. Finding a minimum-cost Markov chain can then be shown to be equivalent to finding a "highest" point on this polytope. The local optimization procedures used in the previous iterative algorithms are shown to be separation oracles for this polytope. Since these were often polynomial time, an application of the Ellipsoid method immediately leads to polynomial time algorithms for these problems.

We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$ distance-based loss functions in the \textit{reconstruction} of SDEs from noisy data. To demonstrate the practicality of our Wasserstein distance-based loss functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that arise across a number of applications.

Various static analysis problems are reformulated as instances of the Context-Free Language Reachability (CFL-r) problem. One promising way to make solving CFL-r more practical for large-scale interprocedural graphs is to reduce CFL-r to linear algebra operations on sparse matrices, as they are efficiently executed on modern hardware. In this work, we present five optimizations for a matrix-based CFL-r algorithm that utilize the specific properties of both the underlying semiring and the widely-used linear algebra library SuiteSparse:GraphBlas. Our experimental results show that these optimizations result in orders of magnitude speedup, with the optimized matrix-based CFL-r algorithm consistently outperforming state-of-the-art CFL-r solvers across four considered static analyses.

Symmetries of input and latent vectors have provided valuable insights for disentanglement learning in VAEs.However, only a few works were proposed as an unsupervised method, and even these works require known factor information in training data. We propose a novel method, Composite Factor-Aligned Symmetry Learning (CFASL), which is integrated into VAEs for learning symmetry-based disentanglement in unsupervised learning without any knowledge of the dataset factor information.CFASL incorporates three novel features for learning symmetry-based disentanglement: 1) Injecting inductive bias to align latent vector dimensions to factor-aligned symmetries within an explicit learnable symmetry codebook 2) Learning a composite symmetry to express unknown factors change between two random samples by learning factor-aligned symmetries within the codebook 3) Inducing group equivariant encoder and decoder in training VAEs with the two conditions. In addition, we propose an extended evaluation metric for multi-factor changes in comparison to disentanglement evaluation in VAEs. In quantitative and in-depth qualitative analysis, CFASL demonstrates a significant improvement of disentanglement in single-factor change, and multi-factor change conditions compared to state-of-the-art methods.

We give a procedure for computing group-level $(\epsilon, \delta)$-DP guarantees for DP-SGD, when using Poisson sampling or fixed batch size sampling. Up to discretization errors in the implementation, the DP guarantees computed by this procedure are tight (assuming we release every intermediate iterate).