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We study the problem of realizing strategies for an LTLf goal specification while ensuring that at least an LTLf backup specification is satisfied in case of unreliability of certain input variables. We formally define the problem and characterize its worst-case complexity as 2EXPTIME-complete, like standard LTLf synthesis. Then we devise three different solution techniques: one based on direct automata manipulation, which is 2EXPTIME, one disregarding unreliable input variables by adopting a belief construction, which is 3EXPTIME, and one leveraging second-order quantified LTLf (QLTLf), which is 2EXPTIME and allows for a direct encoding into monadic second-order logic, which in turn is worst-case nonelementary. We prove their correctness and evaluate them against each other empirically. Interestingly, theoretical worst-case bounds do not translate into observed performance; the MSO technique performs best, followed by belief construction and direct automata manipulation. As a byproduct of our study, we provide a general synthesis procedure for arbitrary QLTLf specifications., Comment: 8 pages, to appear at AAAI2025

Screening questionnaires are used in medicine as a diagnostic aid. Creating them is a long and expensive process, which could potentially be improved through analysis of social media posts related to symptoms and behaviors prior to diagnosis. Here we show a preliminary investigation into the feasibility of generating screening questionnaires for a given medical condition from social media postings. The method first identifies a cohort of relevant users through their posts in dedicated patient groups and a control group of users who reported similar symptoms but did not report being diagnosed with the condition of interest. Posts made prior to diagnosis are used to generate decision rules to differentiate between the different groups, by clustering symptoms mentioned by these users and training a decision tree to differentiate between the two groups. We validate the generated rules by correlating them with scores given by medical doctors to matching hypothetical cases. We demonstrate the proposed method by creating questionnaires for three conditions (endometriosis, lupus, and gout) using the data of several hundreds of users from Reddit. These questionnaires were then validated by medical doctors. The average Pearson's correlation between the latter's scores and the decision rules were 0.58 (endometriosis), 0.40 (lupus) and 0.27 (gout). Our results suggest that the process of questionnaire generation can be, at least partly, automated. These questionnaires are advantageous in that they are based on real-world experience but are currently lacking in their ability to capture the context, duration, and timing of symptoms.

We introduce LTLf+ and PPLTL+, two logics to express properties of infinite traces, that are based on the linear-time temporal logics LTLf and PPLTL on finite traces. LTLf+/PPLTL+ use levels of Manna and Pnueli's LTL safety-progress hierarchy, and thus have the same expressive power as LTL. However, they also retain a crucial characteristic of the reactive synthesis problem for the base logics: the game arena for strategy extraction can be derived from deterministic finite automata (DFA). Consequently, these logics circumvent the notorious difficulties associated with determinizing infinite trace automata, typical of LTL reactive synthesis. We present DFA-based synthesis techniques for LTLf+/PPLTL+, and show that synthesis is 2EXPTIME-complete for LTLf+ (matching LTLf) and EXPTIME-complete for PPLTL+ (matching PPLTL). Notably, while PPLTL+ retains the full expressive power of LTL, reactive synthesis is EXPTIME-complete instead of 2EXPTIME-complete. The techniques are also adapted to optimally solve satisfiability, validity, and model-checking, to get EXPSPACE-complete for LTLf+ (extending a recent result for the guarantee level using LTLf), and PSPACE-complete for PPLTL+.

We study the implicit bias of the general family of steepest descent algorithms, which includes gradient descent, sign descent and coordinate descent, in deep homogeneous neural networks. We prove that an algorithm-dependent geometric margin starts increasing once the networks reach perfect training accuracy and characterize the late-stage bias of the algorithms. In particular, we define a generalized notion of stationarity for optimization problems and show that the algorithms progressively reduce a (generalized) Bregman divergence, which quantifies proximity to such stationary points of a margin-maximization problem. We then experimentally zoom into the trajectories of neural networks optimized with various steepest descent algorithms, highlighting connections to the implicit bias of Adam.

We study the overfitting behavior of fully connected deep Neural Networks (NNs) with binary weights fitted to perfectly classify a noisy training set. We consider interpolation using both the smallest NN (having the minimal number of weights) and a random interpolating NN. For both learning rules, we prove overfitting is tempered. Our analysis rests on a new bound on the size of a threshold circuit consistent with a partial function. To the best of our knowledge, ours are the first theoretical results on benign or tempered overfitting that: (1) apply to deep NNs, and (2) do not require a very high or very low input dimension., Comment: 60 pages, 4 figures

The phenomenon of benign overfitting, where a trained neural network perfectly fits noisy training data but still achieves near-optimal test performance, has been extensively studied in recent years for linear models and fully-connected/convolutional networks. In this work, we study benign overfitting in a single-head softmax attention model, which is the fundamental building block of Transformers. We prove that under appropriate conditions, the model exhibits benign overfitting in a classification setting already after two steps of gradient descent. Moreover, we show conditions where a minimum-norm/maximum-margin interpolator exhibits benign overfitting. We study how the overfitting behavior depends on the signal-to-noise ratio (SNR) of the data distribution, namely, the ratio between norms of signal and noise tokens, and prove that a sufficiently large SNR is both necessary and sufficient for benign overfitting.

We study what provable privacy attacks can be shown on trained, 2-layer ReLU neural networks. We explore two types of attacks; data reconstruction attacks, and membership inference attacks. We prove that theoretical results on the implicit bias of 2-layer neural networks can be used to provably reconstruct a set of which at least a constant fraction are training points in a univariate setting, and can also be used to identify with high probability whether a given point was used in the training set in a high dimensional setting. To the best of our knowledge, our work is the first to show provable vulnerabilities in this setting.

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the forward pass of the transformer can produce predictions for that unlabeled test example. A line of recent work has shown that when linear transformers are pre-trained on random instances for linear regression tasks, these trained transformers make predictions using an algorithm similar to that of ordinary least squares. In this work, we investigate the behavior of linear transformers trained on random linear classification tasks. Via an analysis of the implicit regularization of gradient descent, we characterize how many pre-training tasks and in-context examples are needed for the trained transformer to generalize well at test-time. We further show that in some settings, these trained transformers can exhibit "benign overfitting in-context": when in-context examples are corrupted by label flipping noise, the transformer memorizes all of its in-context examples (including those with noisy labels) yet still generalizes near-optimally for clean test examples., Comment: 36 pages; added experiments

Multi-Robot Task Planning (MR-TP) is the search for a discrete-action plan a team of robots should take to complete a task. The complexity of such problems scales exponentially with the number of robots and task complexity, making them challenging for online solution. To accelerate MR-TP over a system's lifetime, this work looks at combining two recent advances: (i) Decomposable State Space Hypergraph (DaSH), a novel hypergraph-based framework to efficiently model and solve MR-TP problems; and \mbox{(ii) learning-by-abstraction,} a technique that enables automatic extraction of generalizable planning strategies from individual planning experiences for later reuse. Specifically, we wish to extend this strategy-learning technique, originally designed for single-robot planning, to benefit multi-robot planning using hypergraph-based MR-TP.

We consider the overfitting behavior of minimum norm interpolating solutions of Gaussian kernel ridge regression (i.e. kernel ridgeless regression), when the bandwidth or input dimension varies with the sample size. For fixed dimensions, we show that even with varying or tuned bandwidth, the ridgeless solution is never consistent and, at least with large enough noise, always worse than the null predictor. For increasing dimension, we give a generic characterization of the overfitting behavior for any scaling of the dimension with sample size. We use this to provide the first example of benign overfitting using the Gaussian kernel with sub-polynomial scaling dimension. All our results are under the Gaussian universality ansatz and the (non-rigorous) risk predictions in terms of the kernel eigenstructure.

Adiabatic passage in systems of interacting bosons is substantially affected by interactions and inter-particle entanglement. We consider STIRAP-like schemes in Bose-Hubbard chains that exhibit low-dimensional chaos (a 3 site chain), and high-dimensional chaos (more than 3 sites). The dynamics that is generated by a transfer protocol exhibits striking classical and quantum chaos fingerprints that are manifest in the mean-field classical treatment, in the truncated-Wigner semiclassical treatment, and in the full many-body quantum simulations., Comment: 13 pages, 14 figures

There has recently been a growing effort to understand in a comprehensive manner the physics and intricate dynamics of many-body and many-state (multimode) interacting bosonic systems. For instance, in photonics, nonlinear multimode fibers are nowadays intensely investigated due to their promise for ultra-high-bandwidth and high-power capabilities. Similar prospects are pursued in connection with magnon Bose-Einstein condensates, and ultra-cold atoms in periodic lattices for room-temperature quantum devices and quantum computation respectively. While it is practically impossible to monitor the phase space of such complex systems (classically or quantum mechanically), thermodynamics, has succeeded to predict their thermal state: the Rayleigh-Jeans (RJ) distribution for classical fields and the Bose-Einstein (BE) distribution for quantum systems. These distributions are monotonic and promote either the ground state or the most excited mode. Here, we demonstrate the possibility to advance the participation of other modes in the thermal state of bosonic oligomers. The resulting non-monotonic modal occupancies are described by a microcanonical treatment while they deviate drastically from the RJ/BE predictions of canonical and grand-canonical ensembles. Our results provide a paradigm of ensemble equivalence violation and can be used for designing the shape of thermal states., Comment: 17 pages, 11 figures

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in optimization across various experiments, from small-scale ``grokking'' to large-scale tasks like image classification with ConvNets, image generation with UNets, speech recognition with LSTMs, and language modeling with Transformers. We also demonstrate that weight decay enhances this bias beyond its role as a norm regularizer, even in practical systems. Moreover, we show that these spectral dynamics distinguish memorizing networks from generalizing ones, offering a novel perspective on this longstanding conundrum. Additionally, we leverage spectral dynamics to explore the emergence of well-performing sparse subnetworks (lottery tickets) and the structure of the loss surface through linear mode connectivity. Our findings suggest that spectral dynamics provide a coherent framework to better understand the behavior of neural networks across diverse settings.

We present an on-the-fly synthesis framework for Linear Temporal Logic over finite traces (LTLf) based on top-down deterministic automata construction. Existing approaches rely on constructing a complete Deterministic Finite Automaton (DFA) corresponding to the LTLf specification, a process with doubly exponential complexity relative to the formula size in the worst case. In this case, the synthesis procedure cannot be conducted until the entire DFA is constructed. This inefficiency is the main bottleneck of existing approaches. To address this challenge, we first present a method for converting LTLf into Transition-based DFA (TDFA) by directly leveraging LTLf semantics, incorporating intermediate results as direct components of the final automaton to enable parallelized synthesis and automata construction. We then explore the relationship between LTLf synthesis and TDFA games and subsequently develop an algorithm for performing LTLf synthesis using on-the-fly TDFA game solving. This algorithm traverses the state space in a global forward manner combined with a local backward method, along with the detection of strongly connected components. Moreover, we introduce two optimization techniques -- model-guided synthesis and state entailment -- to enhance the practical efficiency of our approach. Experimental results demonstrate that our on-the-fly approach achieves the best performance on the tested benchmarks and effectively complements existing tools and approaches., Comment: 32 pages, 3 figures, 3 tables

Current methods for reconstructing training data from trained classifiers are restricted to very small models, limited training set sizes, and low-resolution images. Such restrictions hinder their applicability to real-world scenarios. In this paper, we present a novel approach enabling data reconstruction in realistic settings for models trained on high-resolution images. Our method adapts the reconstruction scheme of arXiv:2206.07758 to real-world scenarios -- specifically, targeting models trained via transfer learning over image embeddings of large pre-trained models like DINO-ViT and CLIP. Our work employs data reconstruction in the embedding space rather than in the image space, showcasing its applicability beyond visual data. Moreover, we introduce a novel clustering-based method to identify good reconstructions from thousands of candidates. This significantly improves on previous works that relied on knowledge of the training set to identify good reconstructed images. Our findings shed light on a potential privacy risk for data leakage from models trained using transfer learning.

Inspired by recent progress in dynamic programming approaches for weighted model counting, we investigate a dynamic-programming approach in the context of boolean realizability and synthesis, which takes a conjunctive-normal-form boolean formula over input and output variables, and aims at synthesizing witness functions for the output variables in terms of the inputs. We show how graded project-join trees, obtained via tree decomposition, can be used to compute a BDD representing the realizability set for the input formulas in a bottom-up order. We then show how the intermediate BDDs generated during realizability checking phase can be applied to synthesizing the witness functions in a top-down manner. An experimental evaluation of a solver -- DPSynth -- based on these ideas demonstrates that our approach for Boolean realizabilty and synthesis has superior time and space performance over a heuristics-based approach using same symbolic representations. We discuss the advantage on scalability of the new approach, and also investigate our findings on the performance of the DP framework., Comment: 32 pages including appendices and bibliography, 5 figures, paper is to be published in CAV 2024, but this version is inclusive of the Appendix

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation., Comment: The paper is accepted by IJCAI 2024

Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase-space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states supported by quasi-chaotic regions turns out to be insufficient to capture the richness of the Hilbert space. Berry's conjecture and the eigenstate thermalization hypothesis are not applicable and quantum effects such as tunneling, scarring, and localization, do not obey the standard paradigms. We demonstrate these statements for a prototype Bose-Hubbard model. We highlight the hybridization of chaotic and regular regions from opposing perspectives of ergodicity and localization., Comment: 11 pages, 13 figures

As robots become more prevalent, the complexity of robot-robot, robot-human, and robot-environment interactions increases. In these interactions, a robot needs to consider not only the effects of its own actions, but also the effects of other agents' actions and the possible interactions between agents. Previous works have considered reactive synthesis, where the human/environment is modeled as a deterministic, adversarial agent; as well as probabilistic synthesis, where the human/environment is modeled via a Markov chain. While they provide strong theoretical frameworks, there are still many aspects of human-robot interaction that cannot be fully expressed and many assumptions that must be made in each model. In this work, we propose stochastic games as a general model for human-robot interaction, which subsumes the expressivity of all previous representations. In addition, it allows us to make fewer modeling assumptions and leads to more natural and powerful models of interaction. We introduce the semantics of this abstraction and show how existing tools can be utilized to synthesize strategies to achieve complex tasks with guarantees. Further, we discuss the current computational limitations and improve the scalability by two orders of magnitude by a new way of constructing models for PRISM-games., Comment: Accepted: ICRA 2024