arXiv subjects

Christopher Ye

Publications and source records attributed to Christopher Ye.

17 recordsLinked to original sources

arXiv2026

Almost Optimal Multiple Source Shortest Paths and Reachability

Given a graph, computing distances and reachabilities from a small set of vertices to the whole graph is an important primitive both in theory and in practice. In undirected unweighted graphs, while computing single-source shortest path (SSSP) requires $O(n^2)$ time in dense graphs, all-pairs shortest paths (APSP) can be computed in $\hat{O}(n^\omega) = O(n^{2.372})$ time [Seidel '95] providing significant savings over running $n$ SSSP instances separately. However, if one needs to compute multiple-source shortest paths (MSSP) from a set of $n^\sigma$ vertices, the previously best known running time was $\hat{O}(\min\{n^\omega, n^{2 + \sigma}\})$: either compute APSP or run SSSP from each source. On the other hand, MSSP is only as hard as computing Boolean matrix product (BMM) between an $n^\sigma \times n$ matrix and $n \times n$ matrix, leaving a significant gap. Our first main result is an almost optimal algorithm for MSSP on undirected unweighted graphs running in $\hat{O}(n^{\omega(\sigma, 1, 1)})$ time, which gives a smooth interpolation between the SSSP and APSP algorithms. The main technical tool behind our result is a novel graph decomposition, which may be of independent interest. Next, we study the multiple-source reachability problem, where we need to determine whether a given set of $n^\sigma$ vertices can reach each of the vertices in a given directed graph. Multiple-source reachability can also be solved in $\hat{O}(\min\{n^\omega, n^{2 + \sigma}\})$ time, with the same lower bound from rectangular BMM. We give an optimal algorithm that runs in $\hat{O}(n^{\omega(\sigma, 1, 1)})$ time, again matching the running time for BMM. Our algorithm for multiple-source reachability can be generalized to MSSP on DAGs. As an application, we provide an $O(n^{2.084})$ time algorithm for computing an $\widetilde{O}(n)$-size shortcut set that reduces diameter to $O(n^{1/3})$.

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arXiv2026

Furthest Pair Requires Quadratic Time in Superconstant Dimension under SETH

Several fundamental problems in computational geometry admit algorithms with running time $f(d) \cdot n^{2-\Theta(1/d)}$ for $n$ points in $d$ dimensions, making them among the most prominent examples of barely subquadratic computation. Notable members of this class include Furthest Pair, Bichromatic Closest Pair, (Bichromatic) Maximum Innter Product, and Hopcroft's Problem. Chen [Theory Comput. 2020] proved that, assuming the Strong Exponential Time Hypothesis (SETH), these problems require $n^{2-o(1)}$ time when the dimension satisfies $d=2^{\Theta(\log^* n)}$. We extend this lower bound to all efficiently constructible dimensions $d=\omega(1)$. Thus, assuming SETH, the dependence of the best known algorithms on the dimension is essentially unavoidable. The proof utilizes techniques in OpenAI's recent disproof of the Erdos unit distance conjecture. The proof was initially discovered by ChatGPT 5.5 Pro. The authors have validated and substantially edited the proof to improve the presentation.

cs.CG↗

arXiv2026

On the Computational Hardness of Transformers

The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input consists of $N$ tokens, each a vector of dimension $m$. The attention mechanism involves multiplying three $N \times m$ matrices, applying softmax to an intermediate product. Several recent works have advanced our understanding of the complexity of attention. Known algorithms for transformers compute each attention head independently. This raises a fundamental question that has recurred throughout TCS under the guise of ``direct sum'' problems: can multiple instances of the same problem be solved more efficiently than solving each instance separately? Many answers to this question, both positive and negative, have arisen in fields spanning communication complexity and algorithm design. Thus, we ask whether transformers can be computed more efficiently than $LH$ independent evaluations of attention. In this paper, we resolve this question in the negative, and give the first non-trivial computational lower bounds for multi-head multi-layer transformers. In the small embedding regime ($m = N^{o(1)}$), computing $LH$ attention heads separately takes $LHN^{2 + o(1)}$ time. We establish that this is essentially optimal under SETH. In the large embedding regime ($m = N$), one can compute $LH$ attention heads separately using $LHN^{\omega + o(1)}$ arithmetic operations (plus exponents), where $\omega$ is the matrix multiplication exponent. We establish that this is optimal, by showing that $LHN^{\omega - o(1)}$ arithmetic operations are necessary when $\omega > 2$. Our lower bound in the large embedding regime relies on a novel application of the Baur-Strassen theorem, a powerful algorithmic tool underpinning the famous backpropagation algorithm.

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arXiv2025

Approximate Replicability in Learning

Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the cost of replicability can be prohibitive: there is no replicable algorithm, for instance, for tasks as simple as threshold learning (Bun et al. STOC '23). Given such strong impossibility results we ask: under what approximate notions of replicability is learning possible? In this work, we propose three natural relaxations of replicability in the context of PAC learning: (1) Pointwise: the learner must be consistent on any fixed input, but not across all inputs simultaneously, (2) Approximate: the learner must output hypotheses that classify most of the distribution consistently, (3) Semi: the algorithm is fully replicable, but may additionally use shared unlabeled samples. In all three cases, for constant replicability we obtain close to sample-optimal agnostic PAC learners: 1) and 2) are achievable using $O(d/\alpha^2 + 1/\alpha^{4})$ samples, while 3) requires $\Theta(d^2/\alpha^2)$ labeled samples.

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arXiv2025

Distribution Testing in the Presence of Arbitrarily Dominant Noise with Verification Queries

We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a statistical task on distribution $\boldsymbol{p}$ given sample access to a mixture $\boldsymbol{r} = \lambda \boldsymbol{p} + (1-\lambda)\boldsymbol{q}$ and the ability to query whether a sample was generated by $\boldsymbol{p}$ or by $\boldsymbol{q}$. In general, if $m_0$ samples from $\boldsymbol{p}$ suffice for a task, then $O(m_0/\lambda)$ samples and queries always suffice in our model. Are there tasks for which the number of queries can be significantly reduced? We study the canonical problems in distribution testing, and obtain matching upper and lower bounds that reveal smooth trade-offs between sample and query complexity. For all $m \leq n$, we obtain (i) a uniformity and identity tester using $O(m + \frac{\sqrt{n}}{\varepsilon^2 \lambda})$ samples and $O(\frac{n}{m \varepsilon^4 \lambda^2})$ queries, and (ii) a closeness tester using $O(m + \frac{n^{2/3}}{\varepsilon^{4/3} \lambda} + \frac{1}{\varepsilon^4 \lambda^3})$ samples and $O(\frac{n^2}{m^2 \varepsilon^4 \lambda^3})$ queries. Moreover, we show that these query complexities are tight for all testers using $m \ll n$ samples. Next, we show that for testing closeness using $m = \widetilde{O}(\frac{n}{\varepsilon^2\lambda})$ samples we can achieve query complexity $\widetilde{O}(\frac{1}{\varepsilon^2\lambda})$ which is nearly optimal even for the basic task of bias estimation with unbounded samples. Our uniformity testers work in the more challenging setting where the contaminated samples are generated by an adaptive adversary (at the cost of a $\log n$ factor). Finally, we show that our lower bounds can be circumvented if the algorithm is provided with the PDF of the mixture.

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arXiv2025

From Generative to Episodic: Sample-Efficient Replicable Reinforcement Learning

The epidemic failure of replicability across empirical science and machine learning has recently motivated the formal study of replicable learning algorithms [Impagliazzo et al. (2022)]. In batch settings where data comes from a fixed i.i.d. source (e.g., hypothesis testing, supervised learning), the design of data-efficient replicable algorithms is now more or less understood. In contrast, there remain significant gaps in our knowledge for control settings like reinforcement learning where an agent must interact directly with a shifting environment. Karbasi et. al show that with access to a generative model of an environment with $S$ states and $A$ actions (the RL 'batch setting'), replicably learning a near-optimal policy costs only $\tilde{O}(S^2A^2)$ samples. On the other hand, the best upper bound without a generative model jumps to $\tilde{O}(S^7 A^7)$ [Eaton et al. (2024)] due to the substantial difficulty of environment exploration. This gap raises a key question in the broader theory of replicability: Is replicable exploration inherently more expensive than batch learning? Is sample-efficient replicable RL even possible? In this work, we (nearly) resolve this problem (for low-horizon tabular MDPs): exploration is not a significant barrier to replicable learning! Our main result is a replicable RL algorithm on $\tilde{O}(S^2A)$ samples, bridging the gap between the generative and episodic settings. We complement this with a matching $\tilde{\Omega}(S^2A)$ lower bound in the generative setting (under the common parallel sampling assumption) and an unconditional lower bound in the episodic setting of $\tilde{\Omega}(S^2)$ showcasing the near-optimality of our algorithm with respect to the state space $S$.

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arXiv2025

Replicable Distribution Testing

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing -- answering an open question from prior work -- and closeness testing.

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arXiv2025

Subquadratic Algorithms and Hardness for Attention with Any Temperature

Despite the popularity of the Transformer architecture, the standard algorithm for computing Attention suffers from quadratic time complexity in context length $n$. Alman and Song [NeurIPS 2023] showed that when the head dimension $d = \Theta(\log n)$, subquadratic Attention is possible if and only if the inputs have small entries bounded by $B = o(\sqrt{\log n})$ in absolute values, under the Strong Exponential Time Hypothesis ($\mathsf{SETH}$). Equivalently, subquadratic Attention is possible if and only if the softmax is applied with high temperature for $d=\Theta(\log n)$. Running times of these algorithms depend exponentially on $B$ and thus they do not lead to even a polynomial-time algorithm outside the specific range of $B$. This naturally leads to the question: when can Attention be computed efficiently without strong assumptions on temperature? Are there fast attention algorithms that scale polylogarithmically with entry size $B$? In this work, we resolve this question and characterize when fast Attention for arbitrary temperatures is possible. First, for all constant $d = O(1)$, we give the first subquadratic $\tilde{O}(n^{2 - 1/d} \cdot \mathrm{polylog}(B))$ time algorithm for Attention with large $B$. Our result holds even for matrices with large head dimension if they have low rank. In this regime, we also give a similar running time for Attention gradient computation, and therefore for the full LLM training process. Furthermore, we show that any substantial improvement on our algorithm is unlikely. In particular, we show that even when $d = 2^{\Theta(\log^* n)}$, Attention requires $n^{2 - o(1)}$ time under $\mathsf{SETH}$. Finally, in the regime where $d = \mathrm{poly}(n)$, we show that the standard algorithm is optimal under popular fine-grained complexity assumptions.

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arXiv2024

Faster Weighted and Unweighted Tree Edit Distance and APSP Equivalence

The tree edit distance (TED) between two rooted ordered trees with $n$ nodes labeled from an alphabet $\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of valid operations consisting of insertions, deletions and relabeling of nodes. The tree edit distance is a well-known generalization of string edit distance and has been studied since the 1970s. Years of steady improvements have led to an $O(n^3)$ algorithm [DMRW 2010]. Fine-grained complexity casts light onto the hardness of TED showing that a truly subcubic time algorithm for TED implies a truly subcubic time algorithm for All-Pairs Shortest Paths (APSP) [BGMW 2020]. Therefore, under the popular APSP hypothesis, a truly subcubic time algorithm for TED cannot exist. However, unlike many problems in fine-grained complexity for which conditional hardness based on APSP also comes with equivalence to APSP, whether TED can be reduced to APSP has remained unknown. In this paper, we resolve this. Not only we show that TED is fine-grained equivalent to APSP, our reduction is tight enough, so that combined with the fastest APSP algorithm to-date [Williams 2018] it gives the first ever subcubic time algorithm for TED running in $n^3/2^{\Omega(\sqrt{\log{n}})}$ time. We also consider the unweighted tree edit distance problem in which the cost of each edit is one. For unweighted TED, a truly subcubic algorithm is known due to Mao [Mao 2022], later improved slightly by D\"{u}rr [D\"{u}rr 2023] to run in $O(n^{2.9148})$. Their algorithm uses bounded monotone min-plus product as a crucial subroutine, and the best running time for this product is $\tilde{O}(n^{\frac{3+\omega}{2}})\leq O(n^{2.6857})$ (where $\omega$ is the exponent of fast matrix multiplication). In this work, we close this gap and give an algorithm for unweighted TED that runs in $\tilde{O}(n^{\frac{3+\omega}{2}})$ time.

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arXiv2024

Replicable Uniformity Testing

Uniformity testing is arguably one of the most fundamental distribution testing problems. Given sample access to an unknown distribution $\mathbf{p}$ on $[n]$, one must decide if $\mathbf{p}$ is uniform or $\varepsilon$-far from uniform (in total variation distance). A long line of work established that uniformity testing has sample complexity $\Theta(\sqrt{n}\varepsilon^{-2})$. However, when the input distribution is neither uniform nor far from uniform, known algorithms may have highly non-replicable behavior. Consequently, if these algorithms are applied in scientific studies, they may lead to contradictory results that erode public trust in science. In this work, we revisit uniformity testing under the framework of algorithmic replicability [STOC '22], requiring the algorithm to be replicable under arbitrary distributions. While replicability typically incurs a $\rho^{-2}$ factor overhead in sample complexity, we obtain a replicable uniformity tester using only $\tilde{O}(\sqrt{n} \varepsilon^{-2} \rho^{-1})$ samples. To our knowledge, this is the first replicable learning algorithm with (nearly) linear dependence on $\rho$. Lastly, we consider a class of ``symmetric" algorithms [FOCS '00] whose outputs are invariant under relabeling of the domain $[n]$, which includes all existing uniformity testers (including ours). For this natural class of algorithms, we prove a nearly matching sample complexity lower bound for replicable uniformity testing.

stat.ML↗

arXiv2024

The Computational Complexity of Factored Graphs

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct representation. An efficient algorithm (with respect to the compressed input size) could then lead to more efficient computations than algorithms taking the explicit, uncompressed object as input. This leads to a natural question: when does knowing the input instance has a more succinct representation make computation easier? We initiate the study of the computational complexity of problems on factored graphs: graphs that are given as a formula of products and unions on smaller graphs. For any graph problem, we define a parameterized version that takes factored graphs as input, parameterized by the number of (smaller) ordinary graphs used to construct the factored graph. In this setting, we characterize the parameterized complexity of several natural graph problems, exhibiting a variety of complexities. We show that a decision version of lexicographically first maximal independent set is $\mathbf{XP}$-complete, and therefore unconditionally not fixed-parameter tractable ($\mathbf{FPT}$). On the other hand, we show that clique counting is $\mathbf{FPT}$. Finally, we show that reachability is $\mathbf{XNL}$-complete. Moreover, $\mathbf{XNL}$ is contained in $\mathbf{FPT}$ if and only if $\mathbf{NL}$ is contained in some fixed polynomial time.

cs.CC↗

arXiv2024

Fine-Grained Optimality of Partially Dynamic Shortest Paths and More

Single Source Shortest Paths ($\textrm{SSSP}$) is among the most well-studied problems in computer science. In the incremental (resp. decremental) setting, the goal is to maintain distances from a fixed source in a graph undergoing edge insertions (resp. deletions). A long line of research culminated in a near-optimal deterministic $(1 + \varepsilon)$-approximate data structure with $m^{1 + o(1)}$ total update time over all $m$ updates by Bernstein, Probst Gutenberg and Saranurak [FOCS 2021]. However, there has been remarkably little progress on the exact $\textrm{SSSP}$ problem beyond Even and Shiloach's algorithm [J. ACM 1981] for unweighted graphs. For weighted graphs, there are no exact algorithms beyond recomputing $\textrm{SSSP}$ from scratch in $\widetilde{O}(m^2)$ total update time, even for the simpler Single-Source Single-Target Shortest Path problem ($\textrm{stSP}$). Despite this lack of progress, known (conditional) lower bounds only rule out algorithms with amortized update time better than $m^{1/2 - o(1)}$ in dense graphs. In this paper, we give a tight (conditional) lower bound: any partially dynamic exact $\textrm{stSP}$ algorithm requires $m^{2 - o(1)}$ total update time for any sparsity $m$. We thus resolve the complexity of partially dynamic shortest paths, and separate the hardness of exact and approximate shortest paths, giving evidence as to why no non-trivial exact algorithms have been obtained while fast approximation algorithms are known. Moreover, we give tight bounds on the complexity of combinatorial algorithms for several path problems that have been studied in the static setting since early sixties: Node-weighted shortest paths (studied alongside edge-weighted shortest paths), bottleneck paths (early work dates back to 1960), and earliest arrivals (early work dates back to 1958).

cs.DS↗

arXiv2024

Replicability in High Dimensional Statistics

The replicability crisis is a major issue across nearly all areas of empirical science, calling for the formal study of replicability in statistics. Motivated in this context, [Impagliazzo, Lei, Pitassi, and Sorrell STOC 2022] introduced the notion of replicable learning algorithms, and gave basic procedures for $1$-dimensional tasks including statistical queries. In this work, we study the computational and statistical cost of replicability for several fundamental high dimensional statistical tasks, including multi-hypothesis testing and mean estimation. Our main contribution establishes a computational and statistical equivalence between optimal replicable algorithms and high dimensional isoperimetric tilings. As a consequence, we obtain matching sample complexity upper and lower bounds for replicable mean estimation of distributions with bounded covariance, resolving an open problem of [Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sivakumar, and Sorrell, STOC2023] and for the $N$-Coin Problem, resolving a problem of [Karbasi, Velegkas, Yang, and Zhou, NeurIPS2023] up to log factors. While our equivalence is computational, allowing us to shave log factors in sample complexity from the best known efficient algorithms, efficient isoperimetric tilings are not known. To circumvent this, we introduce several relaxed paradigms that do allow for sample and computationally efficient algorithms, including allowing pre-processing, adaptivity, and approximate replicability. In these cases we give efficient algorithms matching or beating the best known sample complexity for mean estimation and the coin problem, including a generic procedure that reduces the standard quadratic overhead of replicability to linear in expectation.

stat.ML↗

arXiv2024

The I/O Complexity of Attention, or How Optimal is Flash Attention?

Self-attention is at the heart of the popular Transformer architecture, yet suffers from quadratic time and memory complexity. The breakthrough FlashAttention algorithm revealed I/O complexity as the true bottleneck in scaling Transformers. Given two levels of memory hierarchy, a fast cache (e.g. GPU on-chip SRAM) and a slow memory (e.g. GPU high-bandwidth memory), the I/O complexity measures the number of accesses to memory. FlashAttention computes attention using $\frac{N^2d^2}{M}$ I/O operations where $N$ is the dimension of the attention matrix, $d$ the head-dimension and $M$ the cache size. However, is this I/O complexity optimal? The known lower bound only rules out an I/O complexity of $o(Nd)$ when $M=\Theta(Nd)$, since the output that needs to be written to slow memory is $\Omega(Nd)$. This leads to the main question of our work: Is FlashAttention I/O optimal for all values of $M$? We resolve the above question in its full generality by showing an I/O complexity lower bound that matches the upper bound provided by FlashAttention for any values of $M \geq d^2$ within any constant factors. Further, we give a better algorithm with lower I/O complexity for $M < d^2$, and show that it is optimal as well. Moreover, our lower bounds do not rely on using combinatorial matrix multiplication for computing the attention matrix. We show even if one uses fast matrix multiplication, the above I/O complexity bounds cannot be improved. We do so by introducing a new communication complexity protocol for matrix compression, and connecting communication complexity to I/O complexity. To the best of our knowledge, this is the first work to establish a connection between communication complexity and I/O complexity, and we believe this connection could be of independent interest and will find many more applications in proving I/O complexity lower bounds in the future.

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arXiv2023

Faster Approximate All Pairs Shortest Paths

The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is popularly known as the APSP conjecture and has played a prominent role in developing the field of fine-grained complexity. The seminal result of Seidel uses fast matrix multiplication (FMM) to compute APSP on unweighted undirected graphs exactly in $\tilde{O}(n^{\omega})$ time, where $\omega=2.372$. Even for unweighted undirected graphs, it is not possible to obtain a $(2-\epsilon)$-approximation of APSP in $o(n^\omega)$ time. In this paper, we provide a multitude of new results for multiplicative and additive approximations of APSP in undirected graphs for both unweighted and weighted cases. We provide new algorithms for multiplicative 2-approximation of unweighted graphs: a deterministic one that runs in $\tilde{O}(n^{2.072})$ time and a randomized one that runs in $\tilde{O}(n^{2.032})$ on expectation improving upon the best known bound of $\tilde{O}(n^{2.25})$ by Roditty (STOC, 2023). For $2$-approximating paths of length $\geq k$, $k \geq 4$, we provide the first improvement after Dor, Halperin, Zwick (2000) for dense graphs even just using combinatorial methods, and then improve it further using FMM. We next consider additive approximations, and provide improved bounds for all additive $\beta$-approximations, $\beta \geq 4$. For weighted graphs, we show that by allowing small additive errors along with an $(1+\epsilon)$-multiplicative approximation, it is possible to improve upon Zwick's $\tilde{O}(n^\omega)$ algorithm. Our results point out the crucial role that FMM can play even on approximating APSP on unweighted undirected graphs, and reveal new bottlenecks towards achieving a quadratic running time to approximate APSP.

cs.DS↗

arXiv2023

On the Complexity of Algorithms with Predictions for Dynamic Graph Problems

{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate the study of complexity of dynamic data structures with predictions, including dynamic graph algorithms. Unlike in online algorithms, the main goal in dynamic data structures is to maintain the solution {\em efficiently} with every update. Motivated by work in online algorithms, we investigate three natural models of predictions: (1) $\varepsilon$-accurate predictions where each predicted request matches the true request with probability at least $\varepsilon$, (2) list-accurate predictions where a true request comes from a list of possible requests, and (3) bounded delay predictions where the true requests are some (unknown) permutations of the predicted requests. For $\varepsilon$-accurate predictions, we show that lower bounds from the non-prediction setting of a problem carry over, up to a $1-\varepsilon$ factor. Then we give general reductions among the prediction models for a problem, showing that lower bounds for bounded delay imply lower bounds for list-accurate predictions, which imply lower bounds for $\varepsilon$-accurate predictions. Further, we identify two broad problem classes based on lower bounds due to the Online Matrix Vector (OMv) conjecture. Specifically, we show that dynamic problems that are {\em locally correctable} have strong conditional lower bounds for list-accurate predictions that are equivalent to the non-prediction setting, unless list-accurate predictions are perfect. Moreover, dynamic problems that are {\em locally reducible} have a smooth transition in the running time. We categorize problems accordingly and give upper bounds that show that our lower bounds are almost tight, including problems in dynamic graphs.

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arXiv2021

Predicting the Stereoselectivity of Chemical Transformations by Machine Learning

Stereoselective reactions (both chemical and enzymatic reactions) have been essential for origin of life, evolution, human biology and medicine. Since late 1960s, there have been numerous successes in the exciting new frontier of asymmetric catalysis. However, most industrial and academic asymmetric catalysis nowadays do follow the trial-and-error model, since the energetic difference for success or failure in asymmetric catalysis is incredibly small. Our current understanding about stereoselective reactions is mostly qualitative that stereoselectivity arises from differences in steric effects and electronic effects in multiple competing mechanistic pathways. Quantitatively understanding and modulating the stereoselectivity of for a given chemical reaction still remains extremely difficult. As a proof of principle, we herein present a novel machine learning technique, which combines a LASSO model and two Random Forest model via two Gaussian Mixture models, for quantitatively predicting stereoselectivity of chemical reactions. Compared to the recent ground-breaking approach [1], our approach is able to capture interactions between features and exploit complex data distributions, which are important for predicting stereoselectivity. Experimental results on a recently published dataset demonstrate that our approach significantly outperform [1]. The insight obtained from our results provide a solid foundation for further exploration of other synthetically valuable yet mechanistically intriguing stereoselective reactions.

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