Michal Moshkovitz

Yishay Mansour, Michal Moshkovitz, Cynthia Rudin

Interpretability is an essential building block for trustworthiness in reinforcement learning systems. However, interpretability might come at the cost of deteriorated performance, leading many researchers to build complex models. Our goal is to analyze the cost of interpretability. We show that in certain cases, one can achieve policy interpretability while maintaining its optimality. We focus on a classical problem from reinforcement learning: mazes with $k$ obstacles in $\mathbb{R}^d$. We prove the existence of a small decision tree with a linear function at each inner node and depth $O(\log k + 2^d)$ that represents an optimal policy. Note that for the interesting case of a constant $d$, we have $O(\log k)$ depth. Thus, in this setting, there is no accuracy-interpretability tradeoff. To prove this result, we use a new "compressing" technique that might be useful in additional settings.

Chhavi Yadav, Michal Moshkovitz, Kamalika Chaudhuri

Responsible use of machine learning requires models to be audited for undesirable properties. While a body of work has proposed using explanations for auditing, how to do so and why has remained relatively ill-understood. This work formalizes the role of explanations in auditing and investigates if and how model explanations can help audits. Specifically, we propose explanation-based algorithms for auditing linear classifiers and decision trees for feature sensitivity. Our results illustrate that Counterfactual explanations are extremely helpful for auditing. While Anchors and decision paths may not be as beneficial in the worst-case, in the average-case they do aid a lot.

Ofek Glick, Vladimir Tchuiev, Marah Ghoummaid et al.

While Large Language Models (LLMs) are increasingly used for synthesizing textual PLC programming languages like Structured Text (ST) code, other IEC 61131-3 standard graphical languages like Sequential Function Charts (SFCs) remain underexplored. Generating SFCs is challenging due to graphical nature and ST actions embedded within, which are not directly compatible with standard generation techniques, often leading to non-executable code that is incompatible with industrial tool-chains In this work, we introduce LLM4SFC, the first framework to receive natural-language descriptions of industrial workflows and provide executable SFCs. LLM4SFC is based on three components: (i) A reduced structured representation that captures essential topology and in-line ST and reduced textual verbosity; (ii) Fine-tuning and few-shot retrieval-augmented generation (RAG) for alignment with SFC programming conventions; and (iii) A structured generation approach that prunes illegal tokens in real-time to ensure compliance with the textual format of SFCs. We evaluate LLM4SFC on a dataset of real-world SFCs from automated manufacturing projects, using both open-source and proprietary LLMs. The results show that LLM4SFC reliably generates syntactically valid SFC programs effectively bridging graphical and textual PLC languages, achieving a generation generation success of 75% - 94%, paving the way for automated industrial programming.

Michal Moshkovitz, Yao-Yuan Yang, Kamalika Chaudhuri

Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning behind it remained elusive. In this paper, we rigorously investigate this connection. Specifically, we focus on interpretation using decision trees and robustness to $l_{\infty}$-perturbation. Previous works defined the notion of $r$-separation as a sufficient condition for robustness. We prove upper and lower bounds on the tree size in case the data is $r$-separated. We then show that a tighter bound on the size is possible when the data is linearly separated. We provide the first algorithm with provable guarantees both on robustness, interpretability, and accuracy in the context of decision trees. Experiments confirm that our algorithm yields classifiers that are both interpretable and robust and have high accuracy. The code for the experiments is available at https://github.com/yangarbiter/interpretable-robust-trees .

Nave Frost, Michal Moshkovitz, Cyrus Rashtchian

Despite the popularity of explainable AI, there is limited work on effective methods for unsupervised learning. We study algorithms for $k$-means clustering, focusing on a trade-off between explainability and accuracy. Following prior work, we use a small decision tree to partition a dataset into $k$ clusters. This enables us to explain each cluster assignment by a short sequence of single-feature thresholds. While larger trees produce more accurate clusterings, they also require more complex explanations. To allow flexibility, we develop a new explainable $k$-means clustering algorithm, ExKMC, that takes an additional parameter $k' \geq k$ and outputs a decision tree with $k'$ leaves. We use a new surrogate cost to efficiently expand the tree and to label the leaves with one of $k$ clusters. We prove that as $k'$ increases, the surrogate cost is non-increasing, and hence, we trade explainability for accuracy. Empirically, we validate that ExKMC produces a low cost clustering, outperforming both standard decision tree methods and other algorithms for explainable clustering. Implementation of ExKMC available at https://github.com/navefr/ExKMC.

Omer Ben-Porat, Yishay Mansour, Michal Moshkovitz et al.

Principal-agent problems arise when one party acts on behalf of another, leading to conflicts of interest. The economic literature has extensively studied principal-agent problems, and recent work has extended this to more complex scenarios such as Markov Decision Processes (MDPs). In this paper, we further explore this line of research by investigating how reward shaping under budget constraints can improve the principal's utility. We study a two-player Stackelberg game where the principal and the agent have different reward functions, and the agent chooses an MDP policy for both players. The principal offers an additional reward to the agent, and the agent picks their policy selfishly to maximize their reward, which is the sum of the original and the offered reward. Our results establish the NP-hardness of the problem and offer polynomial approximation algorithms for two classes of instances: Stochastic trees and deterministic decision processes with a finite horizon.

Liran Nochumsohn, Michal Moshkovitz, Orly Avner et al.

Time series forecasting is critical in numerous real-world applications, requiring accurate predictions of future values based on observed patterns. While traditional forecasting techniques work well in in-domain scenarios with ample data, they struggle when data is scarce or not available at all, motivating the emergence of zero-shot and few-shot learning settings. Recent advancements often leverage large-scale foundation models for such tasks, but these methods require extensive data and compute resources, and their performance may be hindered by ineffective learning from the available training set. This raises a fundamental question: What factors influence effective learning from data in time series forecasting? Toward addressing this, we propose using Fourier analysis to investigate how models learn from synthetic and real-world time series data. Our findings reveal that forecasters commonly suffer from poor learning from data with multiple frequencies and poor generalization to unseen frequencies, which impedes their predictive performance. To alleviate these issues, we present a novel synthetic data generation framework, designed to enhance real data or replace it completely by creating task-specific frequency information, requiring only the sampling rate of the target data. Our approach, Freq-Synth, improves the robustness of both foundation as well as nonfoundation forecast models in zero-shot and few-shot settings, facilitating more reliable time series forecasting under limited data scenarios.

Shahaf Bassan, Michal Moshkovitz, Guy Katz

Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to hypothesize that obtaining meaningful explanations for GAMs could be performed efficiently and would not be computationally infeasible. In this work, we challenge this hypothesis by analyzing the *computational complexity* of generating different explanations for various forms of GAMs across multiple contexts. Our analysis reveals a surprisingly diverse landscape of both positive and negative complexity outcomes. Particularly, under standard complexity assumptions such as P!=NP, we establish several key findings: (1) in stark contrast to many other common ML models, the complexity of generating explanations for GAMs is heavily influenced by the structure of the input space; (2) the complexity of explaining GAMs varies significantly with the types of component models used - but interestingly, these differences only emerge under specific input domain settings; (3) significant complexity distinctions appear for obtaining explanations in regression tasks versus classification tasks in GAMs; and (4) expressing complex models like neural networks additively (e.g., as neural additive models) can make them easier to explain, though interestingly, this benefit appears only for certain explanation methods and input domains. Collectively, these results shed light on the feasibility of computing diverse explanations for GAMs, offering a rigorous theoretical picture of the conditions under which such computations are possible or provably hard.

Marah Ghoummaid, Vladimir Tchuiev, Ofek Glick et al.

AI-based code generation is increasingly prevalent, with GitHub Copilot estimated to generate 46% of the code on GitHub. Accurately evaluating how well generated code aligns with developer intent remains a critical challenge. Traditional evaluation methods, such as unit tests, are often unscalable and costly. Syntactic similarity metrics (e.g., BLEU, ROUGE) fail to capture code functionality, and metrics like CodeBERTScore require reference code, which is not always available. To address the gap in reference-free evaluation, with few alternatives such as ICE-Score, this paper introduces MATCH, a novel reference-free metric. MATCH uses Contrastive Learning to generate meaningful embeddings for code and natural language task descriptions, enabling similarity scoring that reflects how well generated code implements the task. We show that MATCH achieves stronger correlations with functional correctness and human preference than existing metrics across multiple programming languages.

Noa Cohen, Omkar Joglekar, Dotan Di Castro et al.

Training neural networks requires significant computational resources and energy. Methods like mixed-precision and quantization-aware training reduce bit usage, yet they still depend heavily on computationally expensive gradient-based optimization. In this work, we propose a paradigm shift: eliminate gradients altogether. One might hope that, in a finite quantized space, finding optimal weights with out gradients would be easier but we theoretically prove that this problem is NP-hard even in simple settings where the continuous case is efficiently solvable. To address this, we introduce a novel heuristic optimization framework that avoids full weight updates and significantly improves efficiency. Empirically, our method achieves performance comparable to that of full-precision gradient-based training on standard datasets and architectures, while using up to 3x less energy and requiring up to 5x fewer parameter updates.

Zhili Feng, Michal Moshkovitz, Dotan Di Castro et al.

Concept explanation is a popular approach for examining how human-interpretable concepts impact the predictions of a model. However, most existing methods for concept explanations are tailored to specific models. To address this issue, this paper focuses on model-agnostic measures. Specifically, we propose an approach to concept explanations that satisfy three natural axioms: linearity, recursivity, and similarity. We then establish connections with previous concept explanation methods, offering insight into their varying semantic meanings. Experimentally, we demonstrate the utility of the new method by applying it in different scenarios: for model selection, optimizer selection, and model improvement using a kind of prompt editing for zero-shot vision language models.

Lee Cohen, Yishay Mansour, Michal Moshkovitz

Given a policy of a Markov Decision Process, we define a SafeZone as a subset of states, such that most of the policy's trajectories are confined to this subset. The quality of a SafeZone is parameterized by the number of states and the escape probability, i.e., the probability that a random trajectory will leave the subset. SafeZones are especially interesting when they have a small number of states and low escape probability. We study the complexity of finding optimal SafeZones, and show that in general, the problem is computationally hard. Our main result is a bi-criteria approximation learning algorithm with a factor of almost $2$ approximation for both the escape probability and SafeZone size, using a polynomial size sample complexity.

Sanjoy Dasgupta, Nave Frost, Michal Moshkovitz

We study the faithfulness of an explanation system to the underlying prediction model. We show that this can be captured by two properties, consistency and sufficiency, and introduce quantitative measures of the extent to which these hold. Interestingly, these measures depend on the test-time data distribution. For a variety of existing explanation systems, such as anchors, we analytically study these quantities. We also provide estimators and sample complexity bounds for empirically determining the faithfulness of black-box explanation systems. Finally, we experimentally validate the new properties and estimators.

Robi Bhattacharjee, Jacob Imola, Michal Moshkovitz et al.

We consider online $k$-means clustering where each new point is assigned to the nearest cluster center, after which the algorithm may update its centers. The loss incurred is the sum of squared distances from new points to their assigned cluster centers. The goal over a data stream $X$ is to achieve loss that is a constant factor of $L(X, OPT_k)$, the best possible loss using $k$ fixed points in hindsight. We propose a data parameter, $Λ(X)$, such that for any algorithm maintaining $O(k\text{poly}(\log n))$ centers at time $n$, there exists a data stream $X$ for which a loss of $Ω(Λ(X))$ is inevitable. We then give a randomized algorithm that achieves clustering loss $O(Λ(X) + L(X, OPT_k))$. Our algorithm uses $O(k\text{poly}(\log n))$ memory and maintains $O(k\text{poly}(\log n))$ cluster centers. Our algorithm also enjoys a running time of $O(k\text{poly}(\log n))$ and is the first algorithm to achieve polynomial space and time complexity in this setting. It also is the first to have provable guarantees without making any assumptions on the input data.

Max Hopkins, Daniel Kane, Shachar Lovett et al.

The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial parameter called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions.

Tom Hess, Michal Moshkovitz, Sivan Sabato

We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as a center only immediately after it is observed, before observing the next point. In addition, a selected center cannot be substituted later. We give the first algorithm for this setting that obtains a constant approximation factor on the optimal risk under a random arrival order, an exponential improvement over previous work. This is also the first constant approximation guarantee that holds without any structural assumptions on the input data. Moreover, the number of selected centers is only quasi-linear in k. Our algorithm and analysis are based on a careful risk estimation that avoids outliers, a new concept of a linear bin division, and a multiscale approach to center selection.

Robi Bhattacharjee, Michal Moshkovitz

We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take the current point as a center before observing the next point. Decisions are irrevocable. The goal is to minimize both the number of centers and the $k$-means cost. Previous works in this setting assume that the input's order is random, or that the input's aspect ratio is bounded. It is known that if the order is arbitrary and there is no assumption on the input, then any algorithm must take all points as centers. Moreover, assuming a bounded aspect ratio is too restrictive -- it does not include natural input generated from mixture models. We introduce a new complexity measure that quantifies the difficulty of clustering a dataset arriving in arbitrary order. We design a new random algorithm and prove that if applied on data with complexity $d$, the algorithm takes $O(d\log(n) k\log(k))$ centers and is an $O(k^3)$-approximation. We also prove that if the data is sampled from a ``natural" distribution, such as a mixture of $k$ Gaussians, then the new complexity measure is equal to $O(k^2\log(n))$. This implies that for data generated from those distributions, our new algorithm takes only $\text{poly}(k\log(n))$ centers and is a $\text{poly}(k)$-approximation. In terms of negative results, we prove that the number of centers needed to achieve an $α$-approximation is at least $Ω\left(\frac{d}{k\log(nα)}\right)$.

Sanjoy Dasgupta, Nave Frost, Michal Moshkovitz et al.

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the $k$-means and $k$-medians objectives: Must there exist a tree-induced clustering whose cost is comparable to that of the best unconstrained clustering, and if so, how can it be found? In terms of negative results, we show, first, that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and second, that any tree-induced clustering must in general incur an $Ω(\log k)$ approximation factor compared to the optimal clustering. On the positive side, we design an efficient algorithm that produces explainable clusters using a tree with $k$ leaves. For two means/medians, we show that a single threshold cut suffices to achieve a constant factor approximation, and we give nearly-matching lower bounds. For general $k \geq 2$, our algorithm is an $O(k)$ approximation to the optimal $k$-medians and an $O(k^2)$ approximation to the optimal $k$-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.

Alon Gonen, Shachar Lovett, Michal Moshkovitz

Combinatorial dimensions play an important role in the theory of machine learning. For example, VC dimension characterizes PAC learning, SQ dimension characterizes weak learning with statistical queries, and Littlestone dimension characterizes online learning. In this paper we aim to develop combinatorial dimensions that characterize bounded memory learning. We propose a candidate solution for the case of realizable strong learning under a known distribution, based on the SQ dimension of neighboring distributions. We prove both upper and lower bounds for our candidate solution, that match in some regime of parameters. In this parameter regime there is an equivalence between bounded memory and SQ learning. We conjecture that our characterization holds in a much wider regime of parameters.

Michal Moshkovitz

Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of points, n, is known in advance or not. Their exact effects are unknown. In this paper we focus on the online setting where the decisions are irreversible: after a point arrives, the algorithm needs to decide whether to take the point as a center or not, and this decision is final. How many centers are needed and sufficient to achieve constant approximation in this setting? We show upper and lower bounds for all the different cases. These bounds are exactly the same up to a constant, thus achieving optimal bounds. For example, for k-means cost with constant k>1 and random order, Theta(log n) centers are enough to achieve a constant approximation, while the mere a priori knowledge of n reduces the number of centers to a constant. These bounds hold for any distance function that obeys a triangle-type inequality.

Tal Kachman, Michal Moshkovitz, Michal Rosen-Zvi

Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of thinned networks with extensive weight sharing. Recent studies that dropout can be viewed as an approximate variational inference in Gaussian processes, and used as a practical tool to obtain uncertainty estimates of the network. We propose a novel statistical mechanics based framework to dropout and use this framework to propose a new generic algorithm that focuses on estimates of the variance of the loss as measured by the ensemble of thinned networks. Our approach can be applied to a wide range of deep neural network architectures and machine learning tasks. In classification, this algorithm allows the generation of a don't-know answer to be generated, which can increase the reliability of the classifier. Empirically we demonstrate state-of-the-art AUC results on publicly available benchmarks.

Michal Moshkovitz, Naftali Tishby

Designing bounded-memory algorithms is becoming increasingly important nowadays. Previous works studying bounded-memory algorithms focused on proving impossibility results, while the design of bounded-memory algorithms was left relatively unexplored. To remedy this situation, in this work we design a general bounded-memory learning algorithm, when the underlying distribution is known. The core idea of the algorithm is not to save the exact example received, but only a few important bits that give sufficient information. This algorithm applies to any hypothesis class that has an "anti-mixing" property. This paper complements previous works on unlearnability with bounded memory and provides a step towards a full characterization of bounded-memory learning.

Michal Moshkovitz, Naftali Tishby

We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time tradeoffs that we call mixing complexity. This notion was devised in order to measure the (in)ability to learn using a bounded-memory algorithm. In this paper we describe how we use mixing complexity to obtain new results on what can and cannot be learned using neural networks.

Roy Fox, Michal Moshkovitz, Naftali Tishby

It is well known that options can make planning more efficient, among their many benefits. Thus far, algorithms for autonomously discovering a set of useful options were heuristic. Naturally, a principled way of finding a set of useful options may be more promising and insightful. In this paper we suggest a mathematical characterization of good sets of options using tools from information theory. This characterization enables us to find conditions for a set of options to be optimal and an algorithm that outputs a useful set of options and illustrate the proposed algorithm in simulation.