Fusing Models with Complementary Expertise
Authors: Hongyi Wang
Felipe Maia Polo
Yuekai Sun
Souvik Kundu
Eric Xing
Mikhail Yurochkin
Venue: ICLR 2024 poster (2024)
Keywords: Fusion of Experts
Mixture of Experts
Expert Models
Primary area: generative models

Abstract: Training AI models that generalize across tasks and domains has long been among the open problems driving AI research. The emergence of Foundation Models made it easier to obtain expert models for a given task, but the heterogeneity of data that may be encountered at test time often means that any single expert is insufficient. We consider the Fusion of Experts (FoE) problem of fusing outputs of expert models with complementary knowledge of the data distribution and formulate it as an instance of supervised learning. Our method is applicable to both discriminative and generative tasks and leads to significant performance improvements in image and text classification, text summarization, multiple-choice QA, and automatic evaluation of generated text. We also extend our method to the "frugal" setting where it is desired to reduce the number of expert model evaluations at test time. Our implementation is publicly available at https://github.com/hwang595/FoE-ICLR2024.

Published as a conference paper at ICLR 2024
FUSING MODELS WITH COMPLEMENTARY EXPERTISE
Hongyi Wang, Felipe Maia Polo, Yuekai Sun,
Souvik Kundu, Eric P. Xin Mikhail Yurochkin
Carnegie Mellon University University of Michigan Intel Labs
MBZUAI Petuum, Inc.
MITTIBM Watson AI Lab
ABSTRACT
Training Al models that generalize across tasks and domains has long been among the open problems driving Al research. The emergence of Foundation Models made it easier to obtain expert models for a given task, but the heterogeneity of data that may be encountered at test time often means that any single expert is insufficient. We consider the Fusion of Experts (FoE) problem of fusing outputs of expert models with complementary knowledge of the data distribution and formulate it to both discriminative and generative tasks and leads to significant performance improvements in image and text classification, text summarization, multiple-choice QA, and automatic evaluation of generated text. We also extend method the "frugal" setting where it is desired to reduce the number of expert model evaluations at test time. Our implementation is publicly available at ht https: //github. wwt httmm//aaaggg/5///////e/e ICI2/2220E
instance of supervised learning. Our method is applicable
INTRODUCTION
Traditional training of ML/AI models, i.e., empirical risk minimization, allows obtaining experts specialized for a particular task and domain. However, in practice, the distribution of the test data often differs leading significant performance degradation (Koh et al., 2020; Santurkar et al., 2020). The emergence of Foundation Models (Bommasani et al., 2021) allows obtaining ex- pert models with simple fine-tuning on a handful of data, but such expert models still face generalization issues (Kumar et al., 2022: Jang al., 2023; Cheng al., 2023). In the case of Large Language Models (LLMs), although most advanced commercial models can perform well on a range of tasks, they are closed-source, expensive to use, and can be outperformed by smaller specialized models (Hsieh et al., 2023; Gunasekar et al., 2023; Jang et al., 2023; Fu et al., 2023). In other words, training expert models have become extremely effective, while generalization with single model remains challenging. In this paper, we aim to develop methods for combining the strengths of models with complementary expertise to push their collective generalization capabilities.
Va +
FoE
a +
b
Figure 1: Three experts with complemen- tary expertise (geometry, natural science, and history) process input question Pythagorean theorem. They each output re- sponses that are processed by a Fusion of Ex- pents (FoE) model to arrive at final output. Note that only one expert capable of produc- high-quality output, thus ensembling the ing a h experts likely to perform poorly.
the
Combining experts is a long-standing and successful practice in ML: classical approaches like en- sembling (Dietterich, 2000; Ganaie et al., 2022) or Mixture of Experts (MoE) (Jacobs et al., 1991; Jordan & Jacobs, 1994; Masoudnia Ebrahimpour, 2014) often lead to performance improvements. These techniques typically consider experts trained and tested on the same data distribution, although improvements in terms of cut-of-distributie
(OOD) generalization have also been observed (Lak- shminarayanan et al., 2017: Shen et al., 2021). In contrast, this paper, we revisit the practice of combining experts in new setting where we are given pre- pre-trained experts with complementary expertise, and our emphasis is on generalization test data distributions where none of the experts perform well individually. See Figure for an illustration.
More specifically, we consider problem where the data distribution is comprised of K domains, and have access to K expert models, one for each of the domains. We do not make any assumptions

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about how experts were trained to make it compatible with modern practices of fine-tuning Foundation Models to obtain high-quality experts. At test time, the data sampled from the mixture of the K domains, i.e., it contains data from every domain, and thus any individual expert will be sub-optimal. Our goal is to train a model using expert outputs that produces final predictions by choosing one of the experts or by combining their outputs, for a given input data point, We refer to such models as the Fusion of Experts (FoE) models. In our experiments, we consider tasks such as image/text classification, text generation, and automatic evaluation of generated summaries (Mani, 2001). Finally, recognizing that obtaining the outputs of every expert can be expensive, we consider the "frugal" setting (Chen et al., 2020) and propose extension of our method to reduce the number of expert evaluations. Our contributions are summarized below:
generations either
1. We formulate the Fusion of Experts (FoE) problem of fusing outputs of models with complementary expertise and cast it as a supervised learning problem. Our approach is applicable to both discriminative and generative use cases.
We further extend the problem to present Frugal Fusion of Experts (FrugalFoE). In specific, we extend our formulation by casting it as graph shortest path problem that allows us to efficiently perform expert fusion while only evaluating subset of experts test time.
3. We demonstrate the efficacy of our method through extensive experimental evaluations on image classification with standard deep learning methods, text classification, summarization, and ques- tion answering using Large Language Models (LLMs), and automatic evaluation of generated summaries. Our proposed fusion method can greatly improve the performance of individual experts, while also reducing the number of expert evaluations at test time.
2 RELATED WORK
Ensemble learning. Ensemble learning combines several individual models (e.g., either model outputs model weights directly) to obtain better performance (Breiman, 1996a;b; Ganaie et al., 2022), which has also been justified by theoretical analysis (Hansen & Salamon, 1990; Krogh & Vedelsby, 1994). Classical ensemble methods include bagging (bootstrap aggregating). boosting, and stacking (model blending) (Breiman, 1996a; Freund et al.. 1996; Friedman, 2001; Wolpert, 1992). Negative correlation learning, which encourages ensemble models to learn diverse aspects from the training data, has also been widely used for deep ensemble methods (Liu & Yao, 1999; Shi et al., 2018: Zhang et al., 2019a; Buschjäger et al., 2020). Especially deep neural networks, the ensemble effect can be introduced implicitly by various methods, e.g., Dropout (Srivastava et al., 2014). Most works in this group implicitly assume that models in the ensemble have similar expertise, thus it is beneficial to aggregate their predictions. To combine models with complementary expertise, averaging their outputs might be detrimental due to most of them being not suitable for an input.
Mixture of experts (MoE). The hasic idea of MoE is learned weighted ensemble among "expert models" where the expert(s) choice is made via a "gating mechanism", i.e., that controls the expert selection for a certain inference query/instance or the weight coefficients to combine various ex- perts (Jacobs al., 1991; Jordan & Jacobs, 1994; Masoudnia & Ebrahimpour, 2014). The idea of MoE has recently been extended to LLMS where multiple MLP experts are integrated after each multi-head self-attention in the Transformer encoder/decoder blocks (Fedus et al., 2022; Chowdhery et al., 2022). The use of MoE in L.MMs has been demonstrated to effectively scale the model sizes up further without costing proportional increase in the computation complexity, as the computation in MoE is effectively sparse. The majority of works in this group are designed for the joint training of "experts" and the gating/aggregation module. In our problem setting, the experts are pre-trained on their respective domains and serve as a starting point for the Fusion of Experts.
Fedeeaaee/colllaborttie Learning. Fedeeaaed/collabbratiee learning allows various clients/agents to jointly learn using their own (mostly private) local data (Kairouz et al., 2021; Wang et al., 2021). During the federated learning, participating clients conduct in-situ learning and computing before their locally learned models are communicated to a central server for model aggregation or fusion (McMahan et al., 2017). Common federated model fusion/aggreeaation methods include various averaging schemes, ensemble-based schemes, and MoE type of gating mechanisms (MeMahan et al., 2017; Wang et al., 2020b; Li & Wang, 2019; Lin et al., 2020). Our work can be seen as a special case of federated learning where clients train their own models locally and share it with the central server for training the FoE model to aggregate them.
Combining pre-trained models. One common way practitioner can interact with pre-trained
model is via an API. Such models typically vary in performance and cost. FrugalMI. (Chen et al.,
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2020) aims to maximize the usage of the cheapest API on "easy" inputs. while only querying the more expensive ones when needed. This work has also been extended to LLMs (Chen al., 2023b). In our setting, the expert models have similar costs and complementary expertise, i.e. no expert is better than any other across all of the data distributions. Finally, (Ravaut al., 2022: Jiang et al., 2023) train auxiliary LLMs to combine generations of general (non-expert) LLMs, however, do not consider the "frugal selection of experts".
3 FUSING MODELS WITH COMPLEMENTARY EXPERTISE
The real data distributions often diverse and challenging to represent with single dataset and/or mimicked by a single AI model (Santurkar et al., 2020; Koh et al., 2020). For example, in image recognition, different geographic regions has different patterns such as colors of traditional attires (Atwood et al., 2020). In text summarization, models are typically fine-tuned for specific domains such as news articles from a particular publisher, e.g., CNN (Lewis et al., 2019), or WikiHow articles (Cohen et al., 2021). To model such distributions, we consider mixture model with K components:
K D Σ ag DK. Σ a4 =1 akk > AAK.
(3.1)
where each D2 represents a subdomain of such as images from a specific geographic location. Our goal is to train an Al system that can perform well on D leveraging the recent advances in Foundation Models that allow us obtain powerful models (experts) for any given Dy even when training data from D₁ is scarce (e.g., via few-shot learning) (Brown et al., 2020). Such experts alone typically struggle to perform well on D due to the performance drop any domain apart from the one they were fine-tuned on (Jang et al., 2023). In this work, we explore strategies for fusing different expert outputs to improve performance on D. Thus, the input to our problem is a set of models {Jk: : X' + y and some amount of validation data {x E X, k == = K. where X' and Y are input and output spaces correspondingly. We consider supervised and generative scenarios, i.e., y can be numerical, categorical, or representative natural language.
V) from every domain v E
3.1 FUSION OF CLASSIFICATION EXPERTS
Let consider a supervised learning scenario with C classes, i.e. J/ is the probability simplex A C-1, Our goal is to fuse the expert outputs, i.e., to learn mapping from [z) k=11 to associated label y. We review common measures to combine expert predictions, then present our fusing approach.
The traditional approach to combine expert predictions is to average their outputs, i.e., ensembling:
K E fx()). Another popular choice is to use the most confident model (Pearce al., 2021; Chen et al., 2023a), i.e., predict with the model that outputs the largest probability for a class: f2-(x), k* arg max, max. [fu(z)].. Model confidence is often used in selective classification (Geifman & EI- Yaniv, 2017) to decide when to abstain from making prediction. However, we found that both ensembling and model confidence are not well-suited for combining experts with complementary expertise expert confidence on OOD, i.e., on data that they did not see during training, can be poor or misleading (Koh et al., 2020).
In this work, we propose Fusion of Experts (FoE), a simple learning problem for training a fuser using validation data from the K domains that found to perform very well in practice. Let (of E Xx E 2 be validation data from every domain ls = =1,.... K. We construct features for every input by concatenating expert outputs, i.e., f(z) [fi())...... ................................ fx (x)] and train the fuser Fo parameterized by 0 via empirical risk minimization:
min Σ E ((FLF((E)).))))
(3.2)
where é is a suitable loss function such as cross-entropy. The procedure is domain agnostic, and the fuser can be small fully-connected neural network, that ingests the outputs of all experts to produce a class prediction.
3.2 FUSION OF GENERATIVE EXPERTS
Next, we discuss FoE for generative experts in the context of LLMss. The key difference that the output space is lot more complicated, e.g., natural text in LLM applications. This makes the strategies discussed above non-trivial to apply.
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Ensembling LLMs can be done by averaging the next token probabilities during generation, however, this requires that all LLMs share the tokenizer and vocabulary, which is rarely true for open-source models and essentially constraints one to fine-tuning the same model for different domains to obtain experts. Confidence-baat based expert selection is fairly straightforward to with LLMs by comparing the log-likelihoods (or perplexities) of LLMs generating corresponding outputs (Ren et al., 2023).
Directly applying the fusing strategy from supervised learning 3.2 would essentially mean training a new L.M,, i.e., a model that inputs concatenated texts generated by expert models and generates text matching the reference outputs. Jiang et al. (2023) explored such "generative fusion" in the context of single domain and regular (non-expert) L.Mss. However, training new generative L.M fuser that would be good on all K domains contradicts our problem motivation, i.e., that it is challenging to train a model simultancously suitable for all domains. Instead, we opt for a simpler fusing approach where we learn which expert to use for a given input.
First, we make a modification to how an input represented using the expert models. Instead of concatenating their generated text outputs, we concatenate the embeddings of the input and generated tokens from the last layer of the corresponding transformer models (the predominant architecture of modern LLMs). Let ft (x)) denote the average of fE's is last-layer token embeddings of the input text I and the output text f& (æ). Such embeddings were previously used by Ren et al. (2023) for OOD detection with LLMs, thus suggesting that they contain information about data distributions need to identify the correct expert.
Our representation of an input using experts is the concatenation of these averaged embeddings: f(x) = [f) (f.........()))) (x)). We train the FoE model via empirical risk minimization predict the index of the correct expert:
min ((F(OO(())))) 6
(3.3)
where é is the cross entropy loss for a K K-way classification problem. As before, Fe can be simple fully-connected neural network. In this formulation, the fuser Fg ingests a vector of concatenated embeddings f(x) and outputs the index of an expert corresponding to the input æ. The expert is then used to produce the final generation.
3.3
WHEN FUSING EXPERTS IS GOOD IDEA
Using only expert outputs may seem restrictive, but it is actually not too harmful in the applications consider. To keep things simple, consider the task of choosing one of the experts in 3.3. As we shall see, as long as (the expertise of) the experts are complementary, we expect their outputs to be sufficiently informative.
Consider the expert fusion problem multi-way hypothesis testing problem. Define (x. the ground truth best expert for input X:
(z) arg [ [((f(()),)) |
X= x]]
(3.4)
and let (xx()) be an approximation to Fz that only uses expert outputs as inputs. Fano's inequality provides a lower bound on the accuracy of F f:
P(F((()) + FL(X)) H(F.(X)) - I(f(X), FX()) F(()) - log
(3.5)
log(K K 1)
where H(F.(X) is the (Shannon) entropy of (X) and T(S(X), F. (x)) is the mutual information between f(X) and (X)... From this lower bound, we see that the larger the mutual informa- tion between F. (X) and f(X), the higher the accuracy we can expect from F o f. Intuitively, [(f(X),
is large whenever it is possible recover (X) from expert outputs f(X). and this is exactly the case when the experts are complementary.
For example, consider a classification task: the experts themselves are classifiers f& X C-11 and the label is one-hot encoded. As long as there is label shift (Lipton al., 2018) among the domains, we expect [Xx) = E [Yya] to vary across domains. Thus it is possible to distinguish between inputs from different domains from f(X) (so Fx())) is large), and we expect good expert selection performance.
4 FRUGAL FUSION OF EXPERTS (FRUGAL.FOE)
Producing a prediction or conditional generation output, from an input x via FoE, can be summarized as follows: we first query K experts, extracting vector of concatenated outputs (xx) and then use
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fuser F6 that produces final output based on fz). This leads to high performance when applied to test data but with the limitation that querying all experts can be costly. We now introduce a sequential algorithm called FrugalFoE to select a small yet sufficient set of experts. For the rest of this section, we assume that querying an expert fP incurs a non-negative cost ct. which might include energy consumption if experts are run locally or API costs when a third party provides experts.
4.1 INTRODUCING FRUGALFOE
We start with some definitions and then present our approach in general form that covers both applications to classification and generative tasks. Let (X, Z) represent a random pair of inputs and outputs; at test time, the input X, e.g., an image of a cat or a long news article, is fixed at æ while the output Z is unknown. In this setup. Z can be either label Y. in the classification case, domain membership variable, in the generative case. Let F be the set of all experts (fi,... , .x} in the classification case and the set of all embedders obtained from experts (ff..... ..k in the generative case. To ease the exposition of this section, we (i) refer to elements of F as "experts" in both classification and generative cases and (ii) drop the superscript se" in the generative case. Furthermore, define fs(x) & [fr(z]] fLES as the concatenation of the outputs of all experts in S. Finally, the conditional expected loss of predicting with a set of experts S given the event (X) = fg(r)), i.e., after querying all experts in S and observing their outputs, is defined as
S) é E ((((Fo((s())) 2) [x(() = [5(
+ A
Σ Ck. RifEES
(4.1)
where Fg represents a given fuser parameterized by and À > 0 is a constant that controls the trade-off between querying costs and errors made by the fuser. Realize that the cost sum is taken are evaluating. Note that the used fuser
over & for f& S, i.e., it depends Fg depends on S through the inputs fs(x). This implies that we need a fuser for each S E 2F. We assume that fusers for all S are available and discuss this aspect further in Section 4.2. Now we are ready to introduce the idea behind FrugalFoE.
set S of experts
Suppose that, for a fixed input x and up to a certain instant, we have queried the experts S. The expected loss of stopping at this point and applying a fuser on top of (a( is given by L(x,8,5) The question is whether to query an extra expert or not: can we find an extra expert J & & such that L(x, S. $ < L(x, S S,5 That is, given all the information collected up to that point, can we do better by querying more experts? If yes, we should find the extra expert ʃ that minimizes (x,SU {f), S) and query it. If not, we should stop and apply F& on the top of S to get a final prediction. In practice, however, we cannot evaluate the conditional expected loss L(x, S, S, for any sets S and S, because the conditional distribution of E( [F( (X)), Y) given (fs(X) = fs())) is usually unknown. In spite of that, can estimate it on the fly using sennarest-neighhoe non- non-maramttric estimator for conditional expectations (Hastie et al., 2009) using validation data:
L(x,
Σ
((Fo(ss(zm)) 2m) +
Σ Ck. IISES
(4.2)
M
The neighborhood set (I, 5) are the M nearest neighbors (and corresponding targets) of the input point æ among the validation set, where the distance between points is the Euclidean distance in the space of the queried experts' outputs, i.e., ds(r;, x') = (x) f=(('))l2 Thus, we assume access to the experts' outputs for all data points in a validation set, i.e., for each combination data point/expert, have different output.
4.2 IMPLEMENTING FRUGALFoE
Starting expert. In our problem setting we interact with input x only through the expert outputs. Thus, we should select an expert to call first, which will be the same for every input. We can make this selection by simply considering the loss of l-expert fusers on the validation data {af 2 J (= = y in classification and 2 = 1: in generation):
arg JEF Ee(ro(((()))
(4.3)
1,K
That is. we choose the expert that has the best average performance in the validation set. For interpretability reasons, we use 0-1 loss in our implementation of FrugalFoF.
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Subsequent experts. Let S be the set of experts queried so far for x. Before deciding the next expert, we update the current estimate of the quality of S. We use 5, from (4.2) as the quality estimate. Next, we find the expert f that we expect to provide the maximum improvement:
1 = arg mig 2le
(4.4)
If ( S, > 0 we terminate the search and return Fo(Jg(z)) Otherwise, we evaluate expert f on the input update S = S (U(F" and continue the search. In our experiments, we consider the cost C of all experts to equal 0.01. Then À can be interpreted as the minimal error rate reduction we want to achieve when deciding whether to query an additional expert.
Obtaining fusers for subsets of experts. So far we have assumed that we have access to fusers Fo(fs()) for all S E 2F. These fusers must be trained before FrugalFoE deployment using training data and objective functions in equations 3.2 and 3.3. In general, this is only feasible for a small if restrict FrugalFoE to always terminate after small number of expert
number of experts, calls (out of potentially bigger set of experts). It is, however, possible to bypass this limitation by using KNN classifiers as the fuser models as those do not require training and can be evaluated on the fly at test time. Specifically, let I' E NNr 8) be point from the validation dataset that is a neighbor of a test input z based on the expert outputs in S. We can evaluate the loss on this point required for FrugalFoE follows:
e ((Fo Fm) e(KNN( zm),
(4.5)
where kNN(2 is the majority output corresponding nearest neighbors of Fym in the validation data excluding itself. The neighbors for each validation point can be precomputed using the outputs of all experts F before deployment. Evidently, this procedure bypasses the need to train 2 fusers.
4.3 FRUGALFOE AS A GRAPH SHORTEST- S-TTH PROBLEM SOLVER
FrugalFoE is an algorithm that can be motivated as shortest-path problem solver with connections to the A" algorithm (Russell, 2010). We first need to frame the sequential expert selection problem as graph search problem to see that. Consider weighted directed graph g = (V, E) with 2 + 1 vertices: 2 vertices corresponding to all subsets (including the empty set) of the K experts, and an additional target vertex. We label each vertex (except the target vertex) with (the set of indices of) the subset of the experts associated with the vertex. For example, the vertex {1, is associated with the subset (/1, Each vertex associated with a subset of experts S is connected to vertices associated with the subsets of size |S| + 1, including S. The length of cach edge between two vertices associated with subsets of the experts the cost of querying the additional expert, scaled by X, in the current vertex. For example, if K = 3, the vertex {1} is connected to the vertices {1, 2] and (1, 3). and the lengths of the edges are Ac2 and Ac3. Finally, all 2 vertices associated with subsets of the experts are connected to the terminal vertex. For given input I and set of fusers, the length of the edge connecting a vertex associated with a set of experts S to the terminal vertex is M E (#mm. ((Fo (2m)), 2m) if we have gathered outputs from all experts in S (4.2).
From here, we can draw connections to the A" algorithm. In A", for any prospective vertex n to be visited on the graph, the estimated distance traversing through n from the initial to the terminal vertex can be dissected into the sum of the known distance from the initial vertex to n. denoted as g(n), and an estimate of the distance from n to the terminal vertex, denoted as (n)) Among all prospective vertices, we opt for n² that yields the smallest sum g(n²) ) +h(nn) ). In FrugalFoE, if we are currently at a vertex representing the set of experts Š, the next step is to query some extra expert J or opt for the terminal vertex, which we denote by T. If we decide to query fr, using the logic explained in equation 4.4, then ((Sff) = > & C% and f() = M Eeerst)))M E( (f )), 2..) If we decide on the terminal vertex (i.c., to conclude the search), (S, = L(x, S, and h(,,T) = O. The connection between FrugalFoF and the A algorithm is clear once we define and h; however, there is no perfect correspondence between the two algorithms since in FrugalFoE the functions g and h depend on the current set of vertices S opposed to the classical A version where these functions only depend on the candidate vertex. This difference is mainly due to the fact that we can not "undo" querying an expert, so it is more reasonable to try to utilize all expert outputs available at any given decision point.
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5 EXPERIMENTS
We evaluated the efficacy of the FoE method using a wide range of experiments, including image classification, summarization, text generation evaluation, sentiment analysis, and massive multitask language understanding (MMLUU (Hendrycks et al., 2021). Additionally, we investigated how to enhance FoE's efficiency, aiming achieve the desired accuracy while consulting the fewest number of experts, i.e., FrugalFoF. FoE: manages to achieve close (and matches on some tasks) performance compared to the "oracle model" (i.e., always selecting the most suitable expert for given task) and consistently surpasses individual experts and other popular baseline methods (including FrugalMI. (Chen et al., 2020), ensemble) by notable margin. Interestingly, FoE inherently tends to be frugal in summarization and sentiment analysis tasks. Specifically, relying information from just one expert often yields results as effective as consulting all experts. For tasks where FoE not naturally frugal, our FrugalFoE algorithm proves effective. For instance, in the CIFAR experiment, FrugalFoF queries only 37.5% of the experts match the accuracy achieved by querying all experts.
5.1 THE CIFAR- 100 CUPSS- CLASSIFICATION TASK
We start with an image classification experiment on CIFAR-100. While this is relatively simple task and on a small scale, it effectively demonstrates the capabilities of FoE.
We partition CIFAR- 100 into 20 sections where each section contains all images from 30 sub- classes (Krizhevsky et al., 2009). Out of these 30 sub-classes, 20 come exclusively from one sub-class of cach super-class (for instance, beaver from aquatic mammals, bottles from food containers, etc), while the remaining 10 are picked at random from all the other sub-classes. Thus, these sections have overlapping images, meaning they are not mutually exclusive. This partitioning strategy (inspired partly by Santurkar et al. (2020)) ensures that each expert excels in classifying one sub-class within each super-class, however, they have some shared knowledge (more details in Appendix A.2).
We train 20 experts, each of them using ResNet-18 on their own data partition to predict super- classes (He et al., 2016). We use 40k images from the CIFAR- 100 training set for partitioning and expert training and hold 10k images from the training set out as a validation set to train our fusing strategy by solving equation 3.2. The final test accuracy measured using the CIFAR test set.
Our results are shown in Table 1. In the used
Table 1: CIFAR- 100 super-class classification.
confidence-bart based fusing baseline, the maximum softmax score as an indicator of a model's confidence and then chose the model with the highest confidence for predic- tions, where models were trained with mix- up. method that effectively calibrates the model's is confidence (Guo al., 2017: Zhang et al., 2018). Additionally, we show the ac- curacy of an oracle classifier, which operates under the assumption that each test sample is always evaluated using the ideal expert- that is, the expert trained on the data containing the subclass of the the test sample. Our results demonstrate that using FoE markedly improves accuracy over individual experts. FoE also outperforms the confidence-bart based fusion approach and basic ensemble method, both in prediction accuracy and expert selection. Notably, FoE's performance comes close to matching the accuracy of the oracle expert.
Method
Final Acc. (%)
Exper Selection Acc. (%)
FeE
$2.13
75.27
Expers Average
50.04 11 1M
Confidence hased Fesion
74.07
59,69
Ensemble
Orccle Expert
$7.63
100
FrugalFoE for image classification. FoE performs well on the CIFAR task, however, for each test sample, it needs to query all 20 experts. which is computationally expensive. We seek to make it frugal using our FrugalF
80
75
70
Final Accurcc
algorithm described in Section 4.2 using the kNN fusing
65
approach 4.5 with = 97,9, 9, 11} (FoE's performance does not seem to be sensitive different values). We
60
55
Rand. Exparts
FrugalFaE k-7
vary the selection of M and À to control the number
50
FrugalML
FrugaiFaE km9
FrugalFoE k-11
of experts we end up with querying. The FrugalMoF results are shown in Figure where one can observe that FrugalFoF can use 37.5% of the experts to reach the the CIFAR task. When querying the same number of experts, FrugalFoFE outperforms FrugalMI., which also limited to up to two experts. In Figure 5 we present results with neural network as fuser where we limit the maximum number of expert calls to 5 to make the problem feasible.
45
0.0
2.5 5.0 7.5 10.0g2.555.017.5p0
Avg. Experts Queried
accuracy of using the entire 20 experts
Figure 2: Frugal CIFAR- 100 w/ various
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5.2 THE SENTIMENT ANALYSIS TASK
Table Sentiment analysis task experiments.
We consider language model applications, starting with the sentiment analysis task. We use fine-tuned sentiment clas- sification models from Hug- ging Face (more details in Ap- pendix A.4) as experts and the corresponding datasets, Twitter Sentiment Analysis, Twitter Fi- nancial News. Poem Sentiment, Data Reviews Sentiment Anal- ysis, Auditor Sentiment (Naji, 2012; Sheng & Uthus, 2020), Though sentiment analysis is essentially classification task, train the fuser using the generative model strategy 3.3. To test we combined the test sets from all tasks. Results for per task and average accuracies are Table 2 (upper part). FoE achieves 99.1% accuracy in expert selection. FoE almost reaches the best sentiment classification accuracy each downstream task, Le., the oracle expert performance.
Method
TFN
Poom
Auditer
Reviews
Avg.
FoE
95.20%
TFN Expert
87.52%
0.0%
58.54%
0,40%
26.85%
Expert
6,69%
15.24%
59.76%
46.95%
Audinor Expert
51.98%
45.71%
81.71%
49,6558
53.50%
Reviews Sens. Expert
71.12%
62.86%
32.90%
95.20%
79.44%
FoE w/ TPN Expert features
86.93%
85.71%
82.32%
95.209
91.81%
FoE w/ Poem Expert features only
87.23%
$2.86%
81.10%
95,20%
91.75%
Our other finding is that the expert outputs, i.e., the embeddings of language models are highly informative such that only querying single expert is sufficient for the FoE to predict the expert- to-use surprisingly well. In Table (lower part) we present results when using a single expert, i.e., extreme frugal case, noting that performance is almost equal to using all experts. Results using other stand-alone experts are in Table 13.
5.3 THE SUMMARIZATION TASK
In this section, we present experiments generative tasks, starting with the summarization task. We use fine-tuned Pegasus models on six downstream summarization tasks as experts (Zhang et al., 2020). We use the combined validation datasets from all six summarization tasks to train the generative fuser 3.3 for expert prediction. For testing, we combined the test sets from all tasks and used ROUGE-2 (Lin & Hovy, 2003) scores to assess the performance. Results for per task and average accuracies are in Table 3 (upper part). Expert selection accuracy of FoE is 99. %% with the six experts. One can see that FoE almost reaches the best ROUGE-2 score on each downstream task, ie., FoE almost reaches the performance of the oracle expert.
Table 3: Summarization task experiments, ROUGE-2 score (1) the evaluation metric.
Method
CNN DM
XSUM
Multi News
DallSum
Big Patent
AESLC
Avg.
FoE:
20.2225
23.8062
18.3499
36,9398
27.0756
20,676
23.7171
Expest
20.2472
3,5595
5,2049
140173
12:7726
2.4299
11,3757
XSUM Expert
7,4224
23,8901
4.0622
8.0220
11,0968
2.9332
11,9509
Muli-News Expert
10.3799
4,8769
18,5120
8,5539
BillSam Expect
8.7146
3,2458
4.6663
38.5739
6.2896
1.9568
8.1622
Big Expert
3.4595
4.1817
10.4013
27,0760
0.100
AESLIC Expert
5,9838
3,6185
1.6123
4.1015
3.0258
20 6842
4,6352
Fol: w/ CNN DM Expert features only
20.1599
23,7911
18.1450
37,8557
27,0765
20.5473
23.7180
Fol: w/ XSUM Expect features only
20.1402
23.8484
18.0188
36.3483
27.0709
20.5520
23.3963
FoF w/ Mutti-Nws Expert festures only
19 300000
23.31156
17.7478
18.1870
27. 060666
20.3217
21,9752
Similar to our sentiment analysis experiment, querying single expert is almost as good as using all experts (see Table 3 lower part and Table 14 for the remaining experts).
5.4 THE MMLU TASK
In all previous experiments, we were fusing experts properly fine-tuned for their respective domains. Here we consider a weaker notion of experts, i.c., general LLMs that happen to perform better than others on a particular domain. Specifically, we consider the MMLU (Hendrycks et al., 2021) multiple-choice QA task which consists of 57 categories (elementary mathematics, US history, etc.). As experts, we use 15 open- LLMs with sizes of 7 billion parameters from the Open LLM Leaderboard (Beeching et al., 2023). We consider an LLM with the highest accuracy on a category to be an expert for this category. FoE is trained as generative fuser 3.3 (details are in Appendix A.3). The test set is the combination of test sets from all 57 categories.
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The embedding dimension of expert LLMs is fairly high (4096), while there is only a total of 1700 sam- ples for training the fuser, thus we use single expert outputs for FOE in this experiment. Results are pre- sented in Table We see that the results with the weak experts are worse as we no longer can match the oracle performance, however, FOE still outper- forms the strongest of the considered LLMs. Next, unlike our previous experiments, we notice discrep- ancy in performance when using outputs of different weak experts, especially in terms of expert selection accuracy. Overall, we conclude that weak experts not effective, although still can benefit from FoE. We also tested the generalization capability of FoE to unseen domains on the MMLU task, the results can be found in Appendix B.
Table 4: MMLU with weak experts.
Method
Expe. Selec. Acc.
Overall
FoB Experi features only)
74.8%
FoB (w/ Expert 2 fextures only)
45.4%
48.27
Fol Expert features only)
51,9%
48.54
Arg. Experts
41 41.34
7:13
The Best Expert
47,35
Oracte Expert
100%
51.36
5.5 THE TEXT GENERATION EVALUATION TASK
We investigate the potential of using complementary ex- perts to evaluate machine- generated summaries. For this experiment, we use human-annotated summary datasets namely SummEval (Fabbri et al.. 2021), News- room (Grusky et al., 2018), MAGS-CNN/XSUM (Wang et al., 2020a), and HALL-XSUM (Maynez et al., 2020). Each dataset has human ratings for specific dimensions such as coherence and consistency. To train and evaluate experts for each one of the datasets/domains, we: (i) extract some automatic metrics, e.g., BARTScore (Yuan et al., 2021), BERTScoreFree (Shen et al., 2022), UniEval (Zhong et al., 2022), from summaries; (ii) randomly select training and test points from each dataset; (iii) for each pair domain/dimension, we train a linear model (expert) that optimally combines precomputed metrics. We compare the performances of FoE and individual experts in evaluating the consistency' (or factuality) of machine-generatee summaries. In Table 5, we can see that, for individual tasks, FoE does not lead to the highest correlations; however on the aggregated test set (last column) our approach delivers the overall best results. We present additional details and comparison to individual metrics in Appendix A.
Table 5: Correlation of human labels and automated evaluation metrics.
Method
SummEral
NEWSROUM
H-XSUM
Q-CNN
Q-XSUM
Avg.
0.613
0.652
0,237
0.738
0.343
0.517
SummExaal Expert
0.685
0,51
0,209
0,716
0.357
0.489
NEWSROOM Expert
0.293
0.685
0.167
0,673
0.112
0.386
H-XSUM Expert
0,548
0.592
0.241
0.242
0.348
0.495
Q-CNN Expert
0.502
0.612
0,237
0.747
0.337
0.487
Q-XSUM Expert
0.499
0.586
0.743
0.729
0.325
0.476
We note that our FrugalFoF approach is not directly applicable in this setting due to the design of the experts. In this case, they are simple linear models that use various automatic metrics as features. The experts themselves their input features, i.c., automatic metrics based on LLMs, to improve test-time efficiency. We leave the extension of FrugalFoE to such expert design for future work.
cheap to evaluate, however, it may be desirable to reduce the number of
6 CONCLUSION
Our work demonstrates the benefits of fusing experts fine-tuned for different data subdomains. Obtaining high-quality experts has become relatively easy with the emergence of foundation models, thanks to their few-shot learning capabilities. The fusing procedure is also fairly simple: using appropriate model outputs it suffices to train a simple neural network, as supported by our experiments. We have seen that it is even beneficial to fuse general LLMs that happen to perform well on various domains, although not effective the fusion of proper expert models.
We have also proposed a frugal extension of the expert fusion for the cases where querying all experts at test time is too costly. Our solution based on kNN classifiers and the graph shortest path analogy allowed us bypass the combinatorial nature of the problem that limited prior frugal methods to consider at most 2-3 expert/API calls (Chen et al., 2020; 2023b). Interestingly. in the considered LLM applications, using only the outputs of an arbitrary single expert for all test inputs was sufficient to identify the correct expert for the input. This observation suggests that LLM embeddings contain lot of information that can potentially be utilized in other applications. This observation extends the findings of Ren et al. (2023), who demonstrated that LLM embeddings are good for OOD detection, i... distinguishing their own domain from everything else.
"Consistency/factulity measure if the facts presented in the summary consistent with those in the source text. In the Newsroom dataset, this dimension is termed as "relevance". See Table 6 for the full set of results.
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ACKNOWLEDGMENTS
We thank the anonymous reviewers for their valuable insights and recommendations, which have greatly improved our work. This research has been graciously funded by NGA HI047620100022 NSF IIS195553,, NSF CNS2008248. NIGMS G014410 NSF IIS2123952, NSF DMS2027737, NSF BCS2040381, NSF 12222 NSF IIS231 1 1990, Semiconductor Research Corporation (SRC) AIHW award 2024AH3210, and DARPA ECOLE HR001 12390063.
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CONTENTS OF THE APPENDIX
More Details on Experimental Setups
15
A.I
More details on text generation evaluation
15
A.2
More details on the CIFAR experiment..
18
A.3 More details on the MMLU experiment
18
A.4
More details on the sentiment analysis experiment
20
B Additional Experimental Results
21
B.1
Generalization to new domains with weak ................................
21
B.2
Additional Results on FrugalFoE of the CIFAR-100 task
.a..............................
22
B.3
Additional Experiment of the Sentiment Analysis Task
22
B.4
Additional Experiment of the Summarization Task.
................................
22
C Details on The Hyperparameters
23
A MORE DETAILS ON EXPERIMENTAL SETUPS
A.1 MORE DETAILS ON TEXT GENERATION EVALUATION
The first observation need to make is that, because each dataset has a different format for the human annotations, experts' outputs are not comparable, and we cannot compute the aggregate correlation of predictions and human labels for a given task (pair dataset/dimenssion) when evaluating FoE. Instead, we estimate the expected conditional correlation between predictions and human labels in the following way: using the outputs from the eleven experts and for each domain, we classify each text in the test set according to their dataset membership, and according to the empirical distribution of classes induced by the classifier, compute weighted average of the correlations achieved by experts in that specific task. Now, we can describe our experiment detailed steps.
This experiment is repeated 25 times with different random seeds. The final correlations/numbee are the averages across the 25 repetitions. For each random seed b, we do the following:
1. For all datasets, extract automatic metrics, i.e., BARTScore (Yuan et al., 2021), BERTScore. Free (Zhang et al., 2019b; Shen et al., 2022). Unieval (Zhong et al., 2022). For BARTScore, use four variations: the first one BART three, we use Pegasus (Zhang et al., 2020) pre-trained on CNN-DM, Newsroom, and XSUM as the backbone model. We work only with reference-free metrics, and therefore do not use UniEval to evaluate relevance;
(used by Yuan et (2021)), and for the last
For each dataset, randomly select training and test samples. We select 50 test points for all datasets, but the number of training points depends on how big the datasets are. The biggest training set has 370 data points;
3. For each task (pair datasee/dimenssonn), train a linear model using non-negative least squares to predict human rating from automatic metrics. In total, we have eleven experts;
4. Evaluate the performance (Pearson correlation) of experts and individual metrics on each one of the tasks using the test sets;
5. Append all training sets with the eleven experts' outputs as columns and train CatBoost classifier (Prokhorenkova al., 2018) to predict from each dataset each point has come. Because the test set balanced, we weigh the loss to guarantee that each class has the same importance. The average confusion matrix (across Monte Carlo repetitions) can be seen in Figure 3;
6. To evaluate FoE we do the following for each task (pair dataser/dimensionn) using the outputs from the eleven experts and for each domain, classify each text in the test set using the trained CatBoost classifier according to their dataset membership; according to the empirical distribution of classes induced by the classifier, we compute a weighted average of the correlations achieved by experts in that specific task. For example, if task=" summevall coherence" and the classifier outputs the class "summeval" 90% of the times and the class "newsroom" " 10% of the times, the FoE score on that task will be .9 x PSE + .1 X PNR, where ps is the SummEval's 's expert score and pnr R is the Newsroom's 's expert score in that specific task;
In Table 6, we can see the full set of results. The row "avg" computes the average of all available methods, while con" only takes into account the dimension "consistency" (factuality), and
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Classifying points according to membership (avg confusion matrix across MC repetitions)
summeval
1.32
1.76
40
35
newsrocm
3.88
35.68
4.0
3.6
2.84
30
True label
25
qegscnn
3.12
40.16
1.24
1.28
20
qegsxsum
0.04
44.12
1.84
15
10
hallxsum
1.92
1.04 newsroam
1.04 gagsenn
1.84
44.16
summeval
gagaxsum
hallkum
Predicted label
Figure 3: Average confusion matrix across Monte Carlo repetitions.
"avg_no, rrg_no__cot con" takes into account all dimensions except "consistency". We show consistency results in the main text because it is dimension present in all datasets. For the "oracle" columns, we always select the correct expert, instead of running the classifier.
16

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Table Summarization evaluation (Pearson correlation of labels and predictions). this table, "coh" stands coherence, "con" stands for consistency, stands for fluency, and "rel" stands relevance. For an explanation of these dimensions, sec Yuan (2021); Zhong et (2022).
Published as a conference paper at ICLR 2024
Taoks Methods
Gagscm
hallssam
qegsesum
unieval
Nart_condia
peg_nows
peg_xsum
summeval_com
newstoom_com cuh
0.653
0.649
0.627
0.653
0.604
0.643
0,621
0.543
0.601
0.435
0.613
0.655
0.237
neWaroom_.co
0.688
0.682
0.51
0,685
0.612
0.592
0.386
0.615
0.667
0.634
0.529
0.589
0.41
ballxsum_sc
0.243
0.237
0.209
0.167
0.237
0.241
0.243
0.191
0.202
0.203
0,202
0.216
0.182
(pgsemn com
0.747
0.738
0.716
0.673
0.747
0.747
0.729
0.627
0.728
0.737
0.724
0.598
0.642
gagatsuma.com con
00.348
0.343
0.357
0.112
0.337
0.348
0.323
0.1
0.232
0.196
0.199
0,086
0.34
summeval_tt
newsroom fla
0.61
0.999
0.325
0.61
0.553
0.597
0.579
0.51
0.565
0.392
newsroceL_CC
0.743
0.733
0.665
0.243
0.669
0.063
0.629
0.583
0.626
0.166
Avg
0.5887
0.573
0.549
0.492
0.487
0.405
0.476
0.456
0-457
0.499
0.441
0.393
0.416
avg.
avg_po_pon
0.629
0.619
0.598
0
0.508
0.496
0.494
0.474
0.442
0.393

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Published as a conference paper at ICLR 2024
A.2 MORE DETAILS ON THE CIFAR EXPERIMENT
In this section, we provide more information about the CIFAR- 100 experiment presented in the main paper. To construct features for training the fusing strategy in FoE (i.e., classifier to directly predict labels), we use the softmax scores of the last layer for each expert. The detailed partitions used in our CIFAR-100 experiments are shown in Table 7. The overlapping of sub-classes among partitions is shown in Figure 4.
Table Partition details the CIFAR-100 experiment.
Expert
Sub-class Contained
Export
[30, 73, 62, 9, 87, 25, 12, 23, 19, 66, 99, 35, 27, 50, 96, 81, 63, 10, 69, 79,
28, 22)
Export 2
[95, 70, 87,
42,
71,
77,
50,
13, 89, 25
59,
73, 88, 411
3
[55, 62, 22, 24, 43, 12, 49 34, 45, 2, 29 50,
41, 98, 79, 56,
14, 85, 76]
Expert 4
[72, 1, 28, 83, 87, 84, 6, 12, 33, 15, 75, 26
11, 29, 65, 56, 58, 85, 99, 16, 97, 47, 54, 81, 96)
Expert 5
7,0 10, 51, 94, 24, 97, 12, 33, 19, 64, 77,
44, S0, 59, 58, 81, 4, 73, 45, 40, 79, 61, 83, 46, 7, 88)
Expert
[55, 92,
96,
831
Expert 7
[72, 67. 92, 97, 86,
69. 98,
75,
64, 85, 52)
Expert 8
195, 62, 16, 83, 39, 39, 12, 33,
58, 89, 81, 17, 71, 65, 72, 48)
Expert 9
[95, 12, 28,
94, 49,
41,
69, 40, 93, 73, 18, 85, 83, 33,
Expert
64, 61.
18,
Expert
[30, 1. 62, 83, 94,
64, 59, 23. 55,
90)
Expert 12
(4,67, 28,
88, 17,
26, 29, 74, 47, 69, 49, 62, 5. 80, 14. 84, 56, 32, 96)
Export
[55, 67, 62, 22,
88, 71, 75, 99, 29, 74, 81,
45,
34, 24, 47, 82, 83)
Export
[30, 32. 28,
20,
64,
95,
15,0115555
Expert 15
[30, 67. 54, 16, 57, 86, 25, 7, 17, 33, 19, 64, 99, 35, 78, 36, 59, 48, 94, 80, 73, 40, 50, 72, 23, 14, 62)
Expert 16
[95, 32, 54, 9, 97,,7,80 87, 84, 43, 76, 23, 15, 34, 79, 2, 50, 56, 90, 41, 72, 62, 33, 91, 99, 8, 55, 16, 471
Expert
(72, 70,9,55
84, 42,
19,
50,
16]
Expert 18
(30, 61, 86, 94, 24, 43, 60, 64, 79, 44, 80. 13, 81, 69. 20, 45,
85, 36)
Expert 19
[4,91, 82, 53, 87, 14, 33, 38, 66, 26, 35, 78, 80, 52, 90, 85, 32, 83, 81, 43, 97, 92, 22, 67, 72]
Expert 20
[4. 1, 70, 61, 83, 87, 20, 14, 88, 17, 49, 31, 75, 77, 2, 93, 74, 47, 90, 85, 35, 69, 94, 36, 86, 76, 56, 84, 59, 911
5.0
20
Experts
7.5
10.0
15
12.5
15.0
10
17.5
255
5.0
7.5
10.0
12.5
15.0
17.5
Experts
Figure 4: Overlapping among sub-classed among the 20 partitions/experts.
A.3 MORE DETAILS ON THE MMLU EXPERIMENT
In this section, we provide more information about the MMLU experiment presented in the main paper. To construct the feature to learn the fusing strategy, we use the input (without the answer choices) in the MMLJU M test as the prompt and generate output with maximum sequence length of 16.
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We average across the sequence length dimension (prompt and generated tokens) of the last decoder block and use that as the feature for each expert.
The selected LLMss.
The selected LLMs in our experiments are:
COAT-A1/cGar--8--oomnnttyy
acheren37/mannatee--1
garage-bainnd/Platyyuuu--
golaxyygoopt-77--blcom
Lnsys/vlccuna-7b-v1.3
Imsys/vulcuua-70-v115--1...
Tecalpacaa/meedalpacc--b
togetharrcomppter///TT-------
Cogechercoopptter//G/--------
The complete category scores. The complete MMLU category scores for average experts, FoE, and the oracle expert are reported Table and Table
Table 8: Detailed accuracy of all the MMLU categories (Part-1). 1)..
MMLU Category
Average Experts
Oracle Export
FoE
algehrn
anatomy
44.58
65.67
60.45
astronomy
44.02
62.91
58.28
business ethics
42.96
51.52
45.45
clinical knowledge
college biology
46.06
58.04
54.55
college chemistry
34.75
45.45
36.36
college computer science
36.77
45.45
40.40
college mathematics
33.40
college medicine
41.43
53.49
$0.58
college physics
26.47
44.55
30.69
computer security
$2.59
69.70
67.68
conceptual physies
39.09
44.87
36.75
econometrics
30.80
40.71
36.28
electrical engineering
42.96
58.33
53.47
elementary mathematics
fornal logic
11.25
16.0
15.2
global facts
34.07
44.44
39.39
high school biology
48.95
$7.93
55.66
high chemistry
high school computer
42.36
54.55
56.57
high school european history
54.11
68.90
68.29
high school goography
55.23
65.99
65.48
high school government and politics
62.05
77.08
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Published as a conference paper at ICLR 2024
Table 9: Detailed accuracy of all the MMLUU categories (Part-2).
MMLU Categury
Average Experts
Oracle Expert
FoE
high mucrocconemics
high school mathematics
26.02
30.48
26.77
high school microcconomics
42.03
49.79
51.90
high school physies
31.56
36.0
high school psychology
59.22
70.40
67.65
high school statistics
37.12
47.44
42,79
high school us history
54.98
70.94
67.49
high school world history
57.37
74.58
human aging
49.31
61.71
56.76
human sexuality
50.36
63.08
57.69
international law
55.39
71.67
69.17
jurisprudence
logical fallacies
47.65
59.26
59.26
machine learning
32.31
44.14
40.54
management
59.15
73.53
71.57
marketing
medical genetics
52.05
69.70
68.69
miscellaneous
$6.50
69.69
68.29
moral disputes
0.29
0.58
0.58
moral secnarios
30.65
outrition
48.0 02
58.69
57.38
philosophy
48.7 11.71
60.97
60.97
prehistory
professional accounting
34.45
40.21
39.50
professional law
34.22
43.12
43.12
professional medicine
44.85
59.78
59.41
professional psychology
49.92
public relations
50.28
65.14
60.55
security studies
50.52
66.80
62.70
sociology
57.47
70.5
64.5
foreign policy
74.75
virology
38.51
49.70
48.48
world religions
26.59
33.53
33.53
MMLU scores on all individual LLMSs experimented in our experiments. of individual experts used in our experiments are reported in Table 10.
The MMLU scores
A.4 MORE DETAILS ON THE SENTIMENT ANALYSIS EXPERIMENT
We select the models with their associated datasets available on Hugging Face for the sentiment analysis experiments. To train the fusing strategy, we use the input embedding (averaged across the context length dimension) as the feature. Similar the summarization experiment, the label indicates the source downstream task of the input text sequence/article.
The selected models.
Kaludi Mallud//Rviiees-eetiiie
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Table 10: MMLUU scores of our experimented individual experts.
MMLU CatuCrry
Overall MMLU Score
unload
Charlie911/vieunt 7b-v1.5 5-1ra --lera-mctaco metaco
45.8491
Fteddiche/fishh/eePaP... INCITE Chat 3D Instruction Tuning with GPT 4
25. 33.8348
GOAT AI/GOAT 7B Community
46.3568
The wtw.ravelligggggnneeee..eee satieeerr/booo111------- 1B1-RFFF
25.3128
rcheren97// waw.rrnnnnmnnattee1111
45.9349
gezage bAIad/F Latypus2 7D
47.3507
yolaxy/gogpt. 7b bloom
jul.fawergg/tlaaaa 2-t.aaaaa-----oot---ooooo-
44. 44.6764
Imays/v1 cuna-7b-v1.3
44.6121
45. 55.8062
medalpaaci//mdaapaacs--2
corboolww//oossieesseetttteeeeee -bmmini
46. 1692
togechaerrcomuuttee//-----------
42.8531
41,9020
The selected sentiment analysis dataset. For the Twitter Financial News Sentiment and Auditor Sentiment datasets, there is no split between validation and test sets. We thus split 60% of the data as the validation set and 40% of the data as the test set.
poem_sentiment
Financeiin//auddoorrsetttttiee
Details on the semantic label alignment. The goal of the semantic label alignment make sure all experimented models are aligned on the predicted labels. Our objective is to make the "O" for "negative" (or equivalent) and "I" for "positive" (or equivalent) for the adjusted and aligned labels. See Table 11.
Table 11: Label alignment in the sentiment prediction experiments
Export
Original Labels
Aligned Labels
Twitter Financial News Sentiment
O: Bearish, 1: Bullish, 2: Neutral
0: Bearish (neg.). 1: Bullish (pos.)
Poem Seatiment
0: Negative, Positive, 2: No Impact, 3: Mixed
Negative, 1: Positive
Reviows Scntiment Analysis
Negative, Positive
Nogative, Positive
Auditor Sentiment
Nogative, I: Neutral, Nogative
Negative, I: Positive
B ADDITIONAL EXPERIMENTAL RESULTS
B. GENERALIZATION TO NEW DOMAINS WITH WEAK EXPERTS
One natural question regarding the proposed FoE method what will happen when encountering previously unseen domains. We note that for FoE to generalize, it needs to have access to experts that capable of performing well (some) samples from the new domain.
To evaluate generalization of FoE new domains, we modify our MMLU experiment with weak experts. This setting is the most suitable to test generalization as the considered (weak) experts are essentially generalist models capable of handling MMLU categories beyond their strongest areas of expertise. We modified our MMLU experiment by explicitly removing subset of MMLU categories when training the fuser. Specifically, we removed five categories (i.e., high school european hi story, bust ness ethi cs, clinical knowl edge, cadical genetics i and hi
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Published as a conference paper at ICLR 2024
school history) out of 57 MMLU categories. Consequently, during the test phase, data modisioiiiicaa
from these categories represent unseen tasks categories. This modification allows to assess FoE's generalization capabilities to new data or tasks. In Table 12 we compare the performance of FoE on the aforementioned 5 MMLU categories when they included and excluded when training fuser. We see that excluding these categories results in only minor performance decrease, thus demonstrating that FoE is able to generalize to new domains. FoE noticeably improves upon the average expert performance and sometimes even approaches the Oracle expert accuracy.
Table 12: Generalization performance of FoE in MMLU experiment where five MMLU categories excluded from FoE training. thus becoming unseen data during test time.
MMLU Category
Include in FoE training
Exclude from FOE training
Experts
Oracle Expert
high school european history
68.29
54.11
business ethics
45.45
47.47
42.96
51.52
clinical knowledge
59.47
55.30
48.84
57.58
medical genetics
68.69
64.65
$2.05
69.70
high school us history
B.2 ADDITIONAL RESULTS ON FRUGALFOE OF THE CIFAR-100 TASK
The results of FrugalFoB the CIFAR-100 super-class classification task (using neural networks as the fuser model) are shown Figure 5.
Final Accuracy (%)
75
70
65
60
Random Experts
55
FrugalML
FrugalFoE
50
Avg. Experts Queried
Figure 5: FrugalFoE on CIFAR-100 with neural network as the fuser model.
B.3 ADDITIONAL EXPERIMENT OF THE SENTIMENT ANALYSIS TASK
The complete results on FrugalFoo of our sentiment analysis task reported in Table 13.
Table 13: Single expert sentiment analysis results.
Method
TFN
Poem
Auditor
Reviews Sent.
Avg.
FoE
87.54%
85.71% %
81.71%
95.20%
91.88%
TFN Features
86.93%
85.71 %
82.32%
95.20%
91.81 %
Poem Features
87.23%
82. 86%
81.10%
95.20%
91.75%
Auditor Features
86.32%
82.86%
82.32%
95.20%
91.62%
Reviews Sent. Features
87.23%
85.71%
81.10%
95.20%
91.88% %
B.4
ADDITIONAL EXPERIMENT OF THE SUMMARIZATION TASK
The complete results FrugalFoF of our summarization task is reported in Table 14.
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Table 14: FrugalFoF for the summarization task, ROUGF-2 score (f) as the evaluation metric.
Method
CNN DM
XSUM
Multi-News
BillSum
Big-Patent
AESLC
Avg.
FoE
20.2225
23.8662
18.3499
36.9398
27.0756
20.6736
23.7171
CNN feature only
20.1599
23.7911
18.1450
37.8557
27.0765
20.5473
23.7180
XSUM feature only
20.1402
23.8484
18.0158
36.3483
27.0709
20.5520
23.5963
Multi-News feature only
19.8900
23.3156
17.7478
18.1870
27.0660
20.3217
21.9752
BillSum feature only
19,5018
23.0579
17.5037
31.6007
27.0413
20.3720
22.7815
Big- eeg-Patent feature only
19.3697
22,6215
17.0606
37,0621
27.0731
20.1715
22.9850
AESL.C feature only
20.0286
23.6388
17.8641
37.8359
27.0661
20.3707
23.5954
C DETAILS ON THE HYPERPARAMETERS
Fuser training hyperparameters. For training the fusers in FoE we use the AdamW optimizer with initial learning rate 0.001 and weight decay at 10-1 We use batch size (64, 128) across various tasks in our experiments. We train the fuser until convergence in all our experiments, which usually takes 10- 50 epochs. We also use the cosine annealing learning rate scheduler for all fuser training.
Fuser model hyperparameters. For using neural networks fusers, we simply use a three-layer MLP the neural network architecture with ReLU as the activation function. We use Dropout layer with a dropout rate of 0.5 before the very last fully connected layer in the MLP. The hidden dimensions in our experiments range from 2048 to 8192.
23


Reviews:
[{"review_id": "rapCh4IHHm", "reviewer": "Reviewer_2UmK", "summary": "This paper proposes a method to train a set of experts by training the expert one at a time to be fused. Each expert is designed to complement each other during the training procedure by solving the residual gains upon introducing the new expert. Authors evaluated the method on various text domains -- classification, summarization, QA, and generation quality evaluations.\n\n---------\n\nPost rebuttal: With the discussion in the thread, the evaluation has been updated (see other comment for the details).", "questions": "Please look at the weakness section.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The proposed method provides an interesting direction that can train multiple models sequentially to train on the residuals of the previous mixture of experts.\n* Compared to pure residual approaches, because the transformation function is taken on top of each model’s outputs, we can expect this may be more general than the pure residual learning setting.", "weaknesses": "* The proposed algorithm requires multiple experts to be used together, unlike Sparse MoE, which means that the inference cost is multiple times that of each expert. Therefore, the correct baseline for the proposed algorithm is to compare it to an equal number of parameters with the sum of all individual experts. The authors should make this comparison in their paper.\n* Similar to the first point, authors provide experimental results on a variety of datasets, however, they did not include many common baselines for each dataset. For example, Figure 2 has a very crude baseline (random experts) or FrugalML/FrugalFoE. I suggest authors to consider common baselines. Few suggestions are Sparse MoE or just a single model with the similar # of parameters.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9msdE37qot", "reviewer": "Reviewer_75JM", "summary": "This paper introduces an innovative approach for combining various models to optimize performance across different tasks. Recognizing that no single model excels in all tasks and considering the complementary strengths of various pre-trained models, the authors propose a lightweight MLP fuser network trained to either fuse outputs (in the discriminative case) or select the most suitable model (in the generative case) from a pool of $N$ models. To manage the computational expense of querying all $N$ models, they introduce a cost-effective strategy that selects and queries a much smaller subset, $M \\ll N$. Their approach, named FrugalFoE, demonstrates impressive results in fusing outputs or selecting expert models, showcasing superior performance in tasks like image classification, summarization, MMLU, and text evaluation.", "questions": "- Page 8, Table 2: Could you clarify the distinction between \"TFN Expert Only\" and \"TFN Expert,\" and between \"Poem Expert\" and \"Poem Expert Only\"?\n- Page 8, Table 2: What are the results for the \"confidence-based fusion\" and \"ensemble\" baselines? The same question applies to Tables 3 and 4. The confidence-based fusion seems less intuitive in the generative case, how about simply selecting the maximum confidence at each decoding step?\n- Page 9, Table 4: Could you explain more details of FoE (Expert 1), FoE (Expert 2), and FoE (Expert 3)? Why does adding more experts appear to degrade performance?\n- Page 4: The statement \"As long as there is a label shift among the domains, we expect $E[f(X_k)] = E[Y_k]$\" needs clarification. Why is this expected?\n- Page 6: The phrase \"Then $\\lambda$ can be interpreted as the final error rate reduction we want to achieve\" – could you expound on the reasoning behind this?\n- Page 1: The statement \"our emphasis is on generalization to test data distributions where none of the experts perform well individually\". Shouldn't it be \"a few\" instead of \"none\" based on the problem formulation?\n- Page 6: The condition \"If ... <0 we terminate the search\" should be\">0\"?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper tackles a novel and significant issue: optimally leveraging different models for diverse tasks. While foundational models generally perform well across various tasks, they have differing strengths. Thus, an approach to effectively combine these models represents a significant advancement.\n- The methodology, FrugalFoE, is both technically sound and innovative. It offers a clear problem formulation and further minimizes the need to query all the expert models without sacrificing accuracy.\n- The experiments are extensive and cover a range of applications, including image classification, summarization, MMLU, and text evaluation. This demonstrates the method’s versatility and effectiveness.\n- The paper effectively situates its work within the broader context of ensemble learning, mixture of experts, and federated learning, thoughtfully introducing these methodologies and their limitations.", "weaknesses": "- A primary limitation is the assumption that data for training the fuser are readily available. The proposed approach requires a labeled dataset to train the fuser network. In the discriminative case, we feed the input example to different individual models, take model outputs as the inputs to the fuser network, and train the fuser to predict the label of the input example. Similarly, in the generative case,  we feed the fuser network with individual model outputs and train the fuser to predict the best model index, which is obtained by feeding the labeled data to individual models and selecting the model that achieves the best performance. This prerequisite may not be realistic in practical scenarios, where there is no or only a few labeled data. If a large labeled dataset is available, it might be more efficient to fine-tune a foundational model or employ few-shot learning. A pivotal aspect of this research should be the generalization capabilities of the trained fuser across different tasks (e.g,. train the fuser on some tasks and test the fuser on unseen tasks), which would significantly enhance the paper's contribution.\n- The paper lacks an in-depth analysis of the fuser network. Although it is described as a lightweight MLP network, there's no exploration of how different architectures (e.g., simpler networks like linear models or more complex ones like transformers) might impact performance. Additionally, details on the training configurations, such as learning rate, epochs, dataset, and stopping criteria, are missing. The influence of the $K$ parameter in the $K$-NN component of the fuser network is also unclear. What is the rationale for choosing $K=9$?\n- The experiment sections lack in-depth descriptions (see questions). The paper would benefit from reallocating less critical sections (like the connection between FrugalFoE and the A* algorithm) to the Appendix and expanding on the experimental details.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LSPRnPu81q", "reviewer": "Reviewer_HyG2", "summary": "This paper proposes a practical approach to fuse outputs of a set of models that are experts for complementary tasks. Two approaches are proposed:\n* FoE-classification, where a fuser is trained on top of the concatenation of outputs.\n* FoE-generation, where the fuser learns the optimal choice of expert via cross-entropy.\n\nAdditionally, FrugalFoE is proposed, as a strategy to incrementally increase the queries until a cost (loss) criteria is matched. This approach reduces the number of experts being ran.\n\nThe experimental section is solid and shows the validity of the approach in various settings, ranging from classification, sentiment analysis, summarization, QA and text generation. Models like ResNet-18 and a wide plethora of LLMs (~7B params) are used, making this evaluation relevant in the state-of-the-art.", "questions": "* To train using the loss in Eq 3.3, one needs to know a priori the labels, ie. which is the correct model for that input. How reasonable is that assumption? Do we also know \"exactly\" which model should be selected?\n\n* I have some doubts about Equations 4.3 and 4.4 that I would like the authors to clarify. As far as I understand, to obtain the optimal (argmin), we must execute all the experts individually (in Eq. 4.3) and all the subsets in $\\mathcal{F}\\backslash\\tilde{\\mathcal{S}}$ for Eq. 4.4. This sounds quite intensive, and definitely more intensive than just running $\\mathcal{S}$ experts once. I know there is something I am missing here, I kindly ask the authors to bring some clarity in this sense. \n\n* Why is the cost term in Equation 4.1 summed over $f_k\\in \\mathcal{S}$? I would have expected this sum to be over $f_k\\in \\tilde{\\mathcal{S}}$, otherwise the term becomes constant wrt. the queried experts, right?\n\n* How can we use $c_k$ in practice? Can we use it to model aspects like energy consumption (for running an expert), flops, etc.? \n\n* Can the authors comment on Figure 2? Why is FrugalML performing so poorly? Even much worse than randomly picking the experts? \n  * Additionally, it would be interesting to add std bars for the Random Experts (selecting different random subsets of them, specially at lower values of the x axis).\n\n* In Section 5.2, the authors claim `Though sentiment analysis is essentially a classification task, we train the fuser using the generative model strategy 3.3`. I believe this is a typo and should be \"using the classification model strategy\".\n\n* I enjoyed the discussion in Section 3.3.\n\n* Conversely, I found Section 4.3 (graph) somehow disconnected and not adding to the work. Unless graphs are used in practice in the code (did not check).\n\n* Minor notation consistency comment. The set $\\mathcal{S}$ is not defined when it first appears. Furthermore, one can find both  $k\\in\\mathcal{S}$ and $f_k\\in\\mathcal{S}$ in the manuscript, which complicates readability.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The approach is relevant given the availability of pre-trained models nowadays. Methods that smartly fuse models can have impact, since one does not need to re-train, and can incorporate new knowledge to previously trained models.\n\n* The experimental section is very complete, and explores several domains of interest. I specially call out the experiments with LLMs.\n\n* The mathematical derivations are sound.\n\n* The paper is written with clear language, and very few typos.", "weaknesses": "* I found the explanation of FrugalFoE harder to follow than the rest. See questions below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "etPvlJ7HI0", "reviewer": "Reviewer_w4J8", "summary": "Acquiring models that generalize across multiple tasks and domains has long been a challenge for the machine learning community. This paper presents the idea of ***Fusion of Experts (FoE)***, aiming to combine the strengths of multiple models with complementary expertise to push their collective generalization capabilities. The main contribution of the paper is to formulate the FoE problem as an instance of supervised learning, which is applicable to both discriminative and generative use cases. In addition, an extended ***FrugalFoE*** has been proposed to allow efficient expert fusion while only evaluating a subset of experts at test time.\nExtensive experimental evaluations on a wide range of tasks demonstrate that the proposed fusion method significantly improves the performance of individual experts.", "questions": "- Please take a look at **Weaknesses**.\n- Are \"Fusion of Experts\" and \"Mixture of Experts\" two different concepts, and what is the essential difference between them?\n- How to ensure that the knowledge of different experts is complementary?\n- How well does the proposed method perform with test data from outside the $K$ domains?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The motivation is sound, and the paper is well written.\n- The proposed method casts the FoE problem of fusing outputs of models with complementary expertise as a supervised learning problem. It can be applied to both discriminative and generative use cases.\n- The extended Frugal Fusion of Experts (FrugalFoE) allows to efficiently perform expert fusion by only evaluating a subset of experts at test time. \n- The proposed fusion method greatly improves the performance of individual experts on a wide range of tasks, while also reducing the number of expert evaluations at test time.", "weaknesses": "The primary concern for me is that the proposed fusion method relies on a validation set containing data samples from all $K$ domains, and potentially, the distribution of the validation data is very similar to that of the test data. I can certainly understand that traditional approaches of combining expert predictions may be ineffective, and they mostly use heuristic schemes such as averaging models' outputs or using the most confident model. However, they do not assume that there is additional validation data to access. If there is available validation data, can we train a parameterized fuser for traditional methods? Therefore, this is not fair in a sense, or can I understand that this is a setup for a new fusion task?\n\nOther concerns are as follows.\n- In the experimental section, the authors observed that \"using a single expert was almost as good as using all experts\" on different types of tasks. Could this possibly be the result of an illogical experimental setup? It looks like the knowledge between multiple experts is not complementary but redundant.\n- In Table 3, what is the difference between CNN DM Expert (higher part) and CNN DM Expert only (lower part)? Why is there such a wide performance gap between the two?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)