Do Llamas Work in English? On the Latent Language of Multilingual Transformers

We ask whether multilingual language models trained on unbalanced, English-dominated corpora use English as an internal pivot language -- a question of key importance for understanding how language models function and the origins of linguistic bias. Focusing on the Llama-2 family of transformer models, our study uses carefully constructed non-English prompts with a unique correct single-token continuation. From layer to layer, transformers gradually map an input embedding of the final prompt token to an output embedding from which next-token probabilities are computed. Tracking intermediate embeddings through their high-dimensional space reveals three distinct phases, whereby intermediate embeddings (1) start far away from output token embeddings; (2) already allow for decoding a semantically correct next token in the middle layers, but give higher probability to its version in English than in the input language; (3) finally move into an input-language-specific region of the embedding space. We cast these results into a conceptual model where the three phases operate in "input space", "concept space", and "output space", respectively. Crucially, our evidence suggests that the abstract "concept space" lies closer to English than to other languages, which may have important consequences regarding the biases held by multilingual language models.

Sketch-Guided Constrained Decoding for Boosting Blackbox Large Language Models without Logit Access

Constrained decoding, a technique for enforcing constraints on language model outputs, offers a way to control text generation without retraining or architectural modifications. Its application is, however, typically restricted to models that give users access to next-token distributions (usually via softmax logits), which poses a limitation with blackbox large language models (LLMs). This paper introduces sketch-guided constrained decoding (SGCD), a novel approach to constrained decoding for blackbox LLMs, which operates without access to the logits of the blackbox LLM. SGCD utilizes a locally hosted auxiliary model to refine the output of an unconstrained blackbox LLM, effectively treating this initial output as a "sketch" for further elaboration. This approach is complementary to traditional logit-based techniques and enables the application of constrained decoding in settings where full model transparency is unavailable. We demonstrate the efficacy of SGCD through experiments in closed information extraction and constituency parsing, showing how it enhances the utility and flexibility of blackbox LLMs for complex NLP tasks.

The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data

In drug discovery, mapping interactions between genes within cellular systems is a crucial early step. This helps formulate hypotheses regarding molecular mechanisms that could potentially be targeted by future medicines. The CausalBench Challenge was an initiative to invite the machine learning community to advance the state of the art in constructing gene-gene interaction networks. These networks, derived from large-scale, real-world datasets of single cells under various perturbations, are crucial for understanding the causal mechanisms underlying disease biology. Using the framework provided by the CausalBench benchmark, participants were tasked with enhancing the capacity of the state of the art methods to leverage large-scale genetic perturbation data. This report provides an analysis and summary of the methods submitted during the challenge to give a partial image of the state of the art at the time of the challenge. The winning solutions significantly improved performance compared to previous baselines, establishing a new state of the art for this critical task in biology and medicine.

Learning DAGs from Data with Few Root Causes

We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.

Causal Fourier Analysis on Directed Acyclic Graphs and Posets

We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a suitable notion of shift and convolution operators that we define. DAGs are the common model to capture causal relationships between data and our framework is causal in that shift, convolution, and Fourier transform are computed only from predecessors in the DAG. The Fourier transform requires the transitive closure of the DAG for which several forms are possible depending on the interpretation of the edge weights. Examples include level of influence, distance, or pollution distribution. Our framework is different from prior GSP: it is specific to DAGs and leverages, and extends, the classical theory of Moebius inversion from combinatorics. For a prototypical application we consider DAGs modeling dynamic networks in which edges change over time. Specifically, we model the spread of an infection on such a DAG obtained from real-world contact tracing data and learn the infection signal from samples assuming sparsity in the Fourier domain.

Instance-wise algorithm configuration with graph neural networks

We present our submission for the configuration task of the Machine Learning for Combinatorial Optimization (ML4CO) NeurIPS 2021 competition. The configuration task is to predict a good configuration of the open-source solver SCIP to solve a mixed integer linear program (MILP) efficiently. We pose this task as a supervised learning problem: First, we compile a large dataset of the solver performance for various configurations and all provided MILP instances. Second, we use this data to train a graph neural network that learns to predict a good configuration for a specific instance. The submission was tested on the three problem benchmarks of the competition and improved solver performance over the default by 12% and 35% and 8% across the hidden test instances. We ranked 3rd out of 15 on the global leaderboard and won the student leaderboard. We make our code publicly available at \url{https://github.com/RomeoV/ml4co-competition} .

Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases

Many applications of machine learning on discrete domains, such as learning preference functions in recommender systems or auctions, can be reduced to estimating a set function that is sparse in the Fourier domain. In this work, we present a new family of algorithms for learning Fourier-sparse set functions. They require at most $nk - k \log_2 k + k$ queries (set function evaluations), under mild conditions on the Fourier coefficients, where $n$ is the size of the ground set and $k$ the number of non-zero Fourier coefficients. In contrast to other work that focused on the orthogonal Walsh-Hadamard transform, our novel algorithms operate with recently introduced non-orthogonal Fourier transforms that offer different notions of Fourier-sparsity. These naturally arise when modeling, e.g., sets of items forming substitutes and complements. We demonstrate effectiveness on several real-world applications.

Discrete Signal Processing with Set Functions

Set functions are functions (or signals) indexed by the power set (set of all subsets) of a finite set $N$. They are ubiquitous in many application domains. For example, they are equivalent to node- or edge-weighted hypergraphs and to cooperative games in game theory. Further, the subclass of submodular functions occurs in many optimization and machine learning problems. In this paper, we derive discrete-set signal processing (SP), a shift-invariant linear signal processing framework for set functions. Discrete-set SP provides suitable definitions of shift, shift-invariant systems, convolution, Fourier transform, frequency response, and other SP concepts. Different variants are possible due to different possible shifts. Discrete-set SP is inherently different from graph SP as it distinguishes the neighbors of an index $A\subseteq N$, i.e., those with one elements more or less by providing $n = |N|$ shifts. Finally, we show three prototypical applications and experiments with discrete-set SP including compression in submodular function optimization, sampling for preference elicitation in auctions, and novel power set neural networks.

Powerset Convolutional Neural Networks

We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.