A HEAD - OF -T IME P-T UNING
Anonymous authors
Paper under double-blind review
A BSTRACT
This paper proposes a new parameter-efficient method for fine-tuning, AoT PTuning.
This method adds input-dependent biases before evaluating the Transformer layer, reducing the required evaluation time when compared to P-Tuning.
Same as P-Tuning, AoT P-Tuning allows multi-task inference with a single backbone model for evaluating different tasks in a single batch.
We experimented with the proposed method on the GLUE and SuperGLUE benchmarking datasets using RoBERTa-Base, RoBERTa-Large, and DeBERTa-XL backbone models.
Our observations show that AoT P-tuning performed on par with or better than P-Tuning v2 while being up to 1 .
3 × times faster during inference.
Based on these experiments, AoT P-Tuning performed on par with or better than P-Tuning v2.
See
Section 5.2 for more details.
I NTRODUCTION
P-Tuning (Liu et al.
, 2021b;a; Lester et al., 2021) is a promising way to fine-tune large Language
Models (LMs) (Devlin et al., 2019; Lan et al., 2020; Liu et al., 2019; Radford et al., 2019).
While it currently underperforms compared to other methods for parameter-efficient fine-tuning (Hu et al., 2022; Houlsby et al., 2019) on a wide range of tasks (Ding et al., 2022), it has a practical, valuable property that allows it to evaluate different trained prompts parallel in a multi-task manner (i.e., a single backbone LM could be used for different tasks during inference, which can simplify model serving in real-world applications) (Lester et al., 2021).
This property is why researchers aim to further develop P-Tuning methods.
Although it is possible to perform multi-task evaluation with P-Tuning, it introduces significant computational overhead due to the concatenation of prefixes to sequences and the evaluation of the attention mechanism (Vaswani et al., 2017) on longer sequences.
We propose a simple mechanism for parameter-efficient fine-tuning of Language Models, namely
Ahead-of-Time (AoT) P-Tuning , for which we add input-dependent bias before each Transformer layer.
Same as P-Tuning, it is possible to use AoT P-Tuning in multi-task inference setups when a single backbone LM is used for several downstream tasks.
The contributions of this paper can be summarized as follows:
We described the intuition behind AoT P-Tuning, which illustrates the connection of the proposed method with P-Tuning.
We proposed two reparameterizations of AoT P-Tuning weights: first based on a factorized matrix trained from scratch, and second based on a LM’s embeddings matrix passed through a trainable Fully Connected network.
We experimented with the proposed method on GLUE and SuperGLUE Benchmarking Datasets (Wang et al., 2018; 2019) with the RoBERTa (Liu et al., 2019) and DeBERTa (He et al., 2020) models and observed that AoT P-Tuning performed on par with or better than P-Tuning v2 (Liu et al., 2021a) while being up to 1 .
3 × times faster during evaluation.
R ECENT W ORKS
Currently, a wide range of different methods could be referenced with P-Tuning.
Liu et al.
(2021b) proposed to add soft prompts to the embeddings of GPT-2’s input sequence (Radford et al., 2019) to train it on classification tasks.
Lester et al.
(2021) proposed a scheme similar to the one used in Liu et al.
(2021b)
, but trained a T5 model (Raffel et al., 2020) with P-Tuning to show how the performance of the method changes with the increased scale of the backbone model.
Recently, Qin & Eisner (2021); Li & Liang (2021); Liu et al.
(2021a) proposed to add prefixes not only to input embeddings but also at each layer of the Transformer model.
In addition, Liu et al.
(2021a) suggested training a linear classification head on top of the backbone model instead of utilizing a LM head to obtain classification results.
Due to this range of similar methods, we will follow the naming used by Liu et al.
(2021a)
and refer to Prompt-Tuning (adding soft prompts to the input embeddings) as P-Tuning v1 and to Prefix-Tuning (adding soft prefixes at each layer of Transformer backbone) as P-Tuning v2.
B ACKGROUND 3. E VALUATION OF T RANSFORMER
Having an input sequence x = { x 1 , . . .
, x n } , where x i is token index, the embeddings of input texts are evaluated as H
=
{ E x 1 , . . . ,
E x n } , where E ∈ R | V |× d is the embeddings matrix, | V | is the vocabulary size, d is the size of the hidden state of the model, and E x i is an embedding of the token x i .
Hidden states H i are then passed to the ( i + 1) -th layer of the Transformer to evaluate H i + with a total l number of layers.
To do so, H i are first mapped through three matrices W Q , W K ,
W V ∈ R d × d to get Q , K and V , which are then used to evaluate the attention layer’s results as:
[Equation]
After A is evaluated, it is passed through the remaining layers 1 , including residual connections and
FC layers to get H
i +1 .
Here and later, we omit the layer index i for attention result A for visibility.
3. P-T UNING V
Having a pre-trained Transformer LM with parameters Θ , instead of fine-tuning all parameters of this model on a downstream task, it is possible to define soft prompts P ∈ R
p ×
d (Liu et al., 2021b), where p is the length of prompt.
P is then concatenated to input sequence embeddings as:
[Equation]
Then, only P and Classification Head are fine-tuned on a downstream task, while Θ remains frozen 2 .
Such parametrization of fine-tuning makes it possible to perform multi-task inference.
3. P-T UNING V
Instead of concatenation of a single prompt P to the H 0 , Liu et al.
(2021a) proposed to concatenate soft prefixes at each layer of the Transformer model.
To apply P-Tuning v2, soft prefixes P K , P V ∈ R p × d are defined for each layer and concatenated to the K and V matrices before evaluating the attention K ′ =
concat ( P K , K ) , V ′ =
concat ( P V , V ) .
Then, Attention is evaluated as follows:
[Equation]
) where i -th component of A ′ could be then written as:
[Equation]
Note that a ∈ R p + n are attention weights for the i -th token
(we omit the i -th index for simplicity) and thus (cid:80) p + n j =1 a j = 1 .
As for P-Tuning v1, only parameters of soft prefixes P K , P V and Classification Head are optimized on a downstream task while freezing the parameters of a backbone model.
3. O N THE O VERHEAD OF P-T UNING
While the Transformer model has O ( n 2 ) time complexity and GPU memory consumption for sequence length n .
For P-Tuning v1, this complexity transforms into O (( n + p ) 2 ) since the length of input sequence is increased by the length of the prompt p , while for P-Tuning v2 the complexity is equal to O ( n ( n + p )) .
Liu et al.
(2021a) showed that for some tasks, the prompt length p could reach values of 100 , increasing time and memory footprint during evaluation.
A HEAD - OF -T IME P-T UNING 4. P ROPOSED M ECHANISM
With AoT P-Tuning, we propose to augment each Transformer layer with a simple procedure.
We define trainable matrices P ∈ R | V |× d for each layer.
Then, before the evaluation of the i -th layer, we modify the hidden states as follows:
[Equation]
where P x j ∈ R d is a lockup of x j -th prompt embedding from P .
Such a scheme allows us to save a significant amount of time during evaluation since AoT P-Tuning does not imply an increase in sequence length.
While P in naive implementation will require lot of memory to store parameters, in the following Section 4.3, we describe reparametrizations which make training more tractable.
Note that AoT P-Tuning, same as plain P-Tuning, could be evaluated in parallel with several tasks in a batch due to the fact that performing look-up from P can be easily parallelized.
As for P-Tuning v1 and P-Tuning v2, we only optimize parameters of P and Classification Head during fine-tuning.
4. I NTUITION B EHIND A O T P-T UNING AND C ONNECTION TO THE P-T UNING
One may note that the proposed method is more similar to Adapters Tuning (Houlsby et al., 2019) than P-Tuning.
Although, Adapters do not imply performing multi-task inference, thus we refer to the proposed method as a variant of P-Tuning, rather than a special case of Adapters.
Furthermore, considering Ding et al.
; He et al.
(2022), most methods for parameter-efficient fine-tuning could be seen with a unified view, and thus Adapters could be seen as a variant of P-Tuning and vice versa.
Having H ′ , after passing through W Q , W K , and W V we obtain Q ′ , K ′ , and V ′ .
Note that
V ′ =
[Equation]
+ { P x 1 , . .
, P x
[Equation]
W [Equation] The result of evaluating Attention with AoT P-Tuning could be seen as:
[Equation]
From such a perspective, there is a clear connection between AoT P-Tuning (Equation 6) and P-Tuning v2 (Equation 4) with the following changes:
For AoT P-Tuning, attention weights a j , j ∈ 1 , l are used for both terms in Equation 6. 2.
For AoT P-Tuning, attention is evaluated on modified Q ′ .
In addition, there is a difference in the form of dependency of K ′ and V ′ on prefix weight.
For AoT P-Tuning, we add prefixes to K and V , while for P-Tuning v2, prefixes are concatenated to these matrices.
For AoT P-Tuning, the first term of Equation 6 implies evaluation of Attention with a prompt which is dependent on the input text, while for P-Tuning v2, the prompt P V is constant.
Considering Equation 6, AoT could be seen as a form of the P-Tuning method, for which we embed prefixes before evaluating the attention layer 3 .
See Appendix Table 3 for the side-by-side comparison of AoT P-Tuning and P-Tuning v2.
4. O N THE P ARAMETER E FFICIENCY OF A O T P-T UNING
It is notable that, in most cases, one cannot afford to optimize the weight P ∈ R | V |× d for each layer.
If we consider training RoBERTa-Large with such a scheme (which has | V | = 50265 , d = 1024 and l = 24 ), then storing all biases P will exceed 1 .
2 B parameters, while the model itself has roughly 350 M parameters.
To overcome this limitation, we propose two reparametrizations of P so that it can use fewer parameters during training.
The first is based on the Kronecker product (namely, Kronecker AoT P-Tuning ).
More specifically, we reparametrize P as
[Equation]
where W L ∈ R a × r ,
W M ∈ R b × r , W R ∈ R r 2 × d , a and b are selected in such a way so a ∗ b
= | V | , r is a rank of factorization which is a hyperparameter to tune, and ⊗ denotes the Kronecker product.
With this reparametrization, training AoT P-Tuning becomes tractable.
E.g., for RoBERTa-Large, with a = 256 , b = 200 , and r = 20 , P will contain roughly 10 M parameters, which is less than 3% of the total number of parameters in the model 4 .
The second approach to work with P , which we used in our experiments, is based on passing the embeddings matrix E through a learnable Fully Connected network (namely, FC AoT P-Tuning ).
Thus, we reparametrize P as
[Equation]
where W 1 ∈ R d × r , b 1 ∈ R r , W 2 ∈ R r × d , b 2 ∈ R d , f is a non-linearity, and r is a rank of mapping, which is also hyperparameter to tune as for Kronecker AoT P-Tuning.
With FC AoT P-Tuning, we utilize knowledge stored in the pre-trained embeddings matrix E , which should hypothetically perform better than training P from scratch as Kronecker AoT P-Tuning.
Note that for both Kronecker and FC AoT P-Tuning, we can evaluate only specific rows { P x i , . .
, P x n } for input sequence { x 1 , . .
, x n } , making training more efficient.
For both reparametrizations, P could be fused once training is complete, and thus the rank of factorization r does not affect inference speed.
During the evaluation, there is no need to store the full P in GPU memory.
Instead, it could be stored in RAM, and only rows of these matrices should be placed in GPU memory to be added to the hidden states before each layer.
From a certain perspective, choosing between AoT P-Tuning and P-Tuning is a trade-off between evaluation speed and RAM consumption during inference.
If RAM is limited, then usual P-Tuning could be used at the cost of slower inference.
In other cases, AoT P-Tuning could be used if there is enough volume of RAM and inference speed is crucial.
Although, in most cases, P matrices for different tasks could be easily stored in the RAM.
For RoBERTa-Large, a single task parameter will roughly require 2 .
4 Gb if stored in half-precision.
However, as we observed later in our experiments, for FC AoT P-Tuning, performing fusing is not crucial, and the re-evaluation of { P x i , . .
, P x n } for each sequence ran at 98 .
5% the speed of fused
P (See Section 5.3 for more details).
[Table]
E XPERIMENTS 5. E XPERIMENTAL D ETAILS
We compared AoT P-Tuning (Kronecker and FC reparametrizations of P ) with other fine-tuning methods capable of performing multi-task inference: P-Tuning v1, P-Tuning v2 on GLUE and
SuperGLUE (Wang et al., 2018; 2019)
Benchmarking Datasets 5 .
We also evaluated plain fine-tuning for reference though it is impossible to perform multi-task inference with it.
For each fine-tuning approach, we experimented with RoBERTa-Base, RoBERTa-Large, and DeBERTa-XL backbone models.
For each task, we performed a grid hyperparameter search (see Appendix Table 5 for hyperparameter ranges).
For RoBERTa models, we evaluated each hyperparameter set with 5 different seed values and reported median and std values of scores for each task.
For DeBERTa-XL, we used to assess each hyperparameter assignment only with a single seed due to longer training time.
See Appendix
Table 4 for a list of metrics used for each task.
[Table]
We used Adam (Kingma & Ba, 2015) optimizer with a constant learning rate for each task.
We stopped training once the validation metric stopped increasing ("patience" parameter in Appendix
Table 6).
For Kronecker AoT P-Tuning with RoBERTa models we parametrized matrix P =
( W L ⊗ W M ) W R with a = 256 , and b = 200 , while for DeBERTa we used a = b = 360 .
W L and W M were initialized randomly, while W R was initialized as a zero matrix.
For FC AoT P-Tuning, we initialized Wrandomly, while W 2 , b 1 , and b 2 were initialized with zeros.
For Kronecker AoT P-Tuning, we applied dropout (Srivastava et al., 2014) to the P x with a fixed probability equal to 0 .
In contrast, for FC AoT P-Tuning, we applied dropout to E before multiplying it with W 1 .
Each experiment was run on a single NVidia A100 GPU with a total compute time of roughlydays.
5. R ESULTS
See Tables 1, 2 for the results of trained models.
We observed that FC AoT P-Tuning performed better than Kronecker AoT P-Tuning.
We hypothesize that this result is mostly caused by the fact that FC reparametrization utilized a pre-trained embedding matrix rather than learning biases from scratch.
[Figure]
[Figure]
For RoBERTa-Base, FC AoT P-Tuning performed on par with P-Tuning v2 and produced the same
Macro score.
For RoBERTa-Large, FC AoT P-Tuning outperformed P-Tuning v2 for GLUE tasks and showed a Macro score equal to plain Fine-Tuning.
AoT P-Tuning with DeBERTa-XL performed on par with P-Tuning v2 ( 89 . 2 vs 89 .
3 macro score respectively).
We also observed that both AoT P-Tuning reparametrizations mainly showed a lower variance of metrics across different seeds.
Note that P-Tuning v1 performed unstably and showed higher results with RoBERTa-Base (although still underperforming other methods by a large margin).
See Figure 3 for macro scores of P-Tuning v2 and AoT P-Tuning with different prefix lengths p and prefix ranks r 6 .
We observed that P-Tuning v2 performed worse for RoBERTa-Base with shorter prompt lengths and became comparable to or better than AoT P-Tuning when p > 50 .
For GLUE tasks with RoBERTa-Large, FC AoT P-Tuning performed better for all prefixes p , while droppoing performance for large rank r .
For DeBERTa-XL both P-Tuning v2 and FC AoT P-Tuning performed on par.
We also provide per-task results with different prefix scales (see Appendix Figures 5, 7).
It is notable that P-Tuning v2, in most cases, suffers from small prefix size p for Base and Large models and achieves results comparable with AoT P-Tuning with larger p (which corresponds to the result with Figure 3).
At the same time, FC AoT P-Tuning mostly showed stale performance across different ranks r , only performing unstable for MultiRC task with large rank r .
We also analyzed trained P matrices for FC AoT P-Tuning with the DeBERTa-XL model.
See Appendix Section A for more details.
With per-task Expected Validation Performance (EVP) (Dodge et al., 2019), we observed that AoT
P-Tuning mainly highly depends on the number of hyperparameter assignments (see Appendix
Figures 6, 8).
Although, in most cases, it is enough to use less than 100 hyperparameter assignments for AoT P-Tuning to outperform P-Tuning v2, which is not crucial in most cases.
5. I NFERENCE S PEED O VERHEAD
With Figure 4, we also investigated the computational overhead of AoT P-Tuning compared to other baselines.
To estimate inference speed overhead, we evaluated each model 100 times on a sequence with length n = 128 and batch size 256 .
We evaluated AoT P-Tuning in two setups.
The first setup implies fusing P for the inference, thus saving computational time at the cost of a higher memory footprint.
Since P is fused, it no longer depends on factorization rank r for both FC and Kronecker AoT P-Tuning.
For the second setup, we did not fuse P , but rather evaluated { P x i , . .
, P x n } for each sequence.
This approach emulates setup with limited memory during inference when fusing P is not feasible.
The growth of p P-Tuning v1 quickly reaches 2 × speed overhead since its complexity depends on p quadratically.
While P-Tuning v2 involves linear dependency on p (see Section 3.4 for details), it also reaches up to 1 .
3 × inference speed overhead for large prefix lengths p .
Fused AoT P-Tuning adds negligible computational overhead (less than 1% ) compared to plain
Fine-Tuning.
Compared to P-Tuning v2, Fused AoT P-Tuning performed up to 1 .
3 × times faster, depending on the prefix size used for P-Tuning v2.
When P is not fused, FC AoT P-Tuning is performing 1 .
13 − 1 .
25 × times faster than P-Tuning v with large prefixes p , which indicates that for this reparametrization, performing weight fusing is not crucial in most cases and huge inference speed-up could be achieved without it.
Although not performing fusing of P could reduce memory footprint during the inference, in such a setup, there is no ability to perform multi-task inference, which is available for both P-Tuning v1/v2 and Fused AoT
P-Tuning.
Kronecker’s reparametrization performed worse.
For small factorization rates (e.g., r ∈ [5 , 10] ), it performed comparable to FC AoT P-Tuning.
Although, for larger r values, it performed up to 1 .
12 × times slower than P-Tuning v2.
Thus, it is important to fuse P with such a reparametrization when a large rank r is used.
Also note that with model growth, the contribution of re-evaluation of P for both Kronecker and FC reparametrizations of AoT P-Tuning becomes lower.
E.g., RoBERTa-Base re-evaluation of P with
FC AoT P-Tuning in the worst case (with r = 512 ) adds 1 .
× overhead of inference time compared to a model trained with plain Fine-Tuning, while for DeBERTa-XL we observed 1 .
× overhead.
The same holds for small ranks ( r = 64 ), where for DeBERTa-XL, we observed 1 .
02 × overhead in inference time compared to the plain model.
C ONCLUSION AND F UTURE W ORK
In this paper, we proposed a new method for parameter-efficient fine-tuning of pre-trained models:
AoT P-Tuning.
We also offered two reparametrizations of learnable weights for this method.
We observed that AoT P-Tuning performed on par or better than P-Tuning v2 based on GLUE and
SuperGLUE Benchmarking Datasets macro scores.
At the same time, AoT P-Tuning performed up to 1 .
3 × times faster than P-Tuning v2, adding a negligible inference time footprint compared to plain Fine-Tuning.
When FC AoT P-Tuning is used, we observed that one could not fuse weights P not to introduce memory footprint since it performs up to 1 .
25 × times faster than P-Tuning v2.
We experimented only with two reparametrizations based on the Kronecker product and FC network.
It is possible to further explore other possible reparametrizations for weight P , which could further increase the performance of the proposed method.
Also, while we proposed a simple method, there are a lot of possible architectural changes which could also boost the performance of AoT P-Tuning and reduce the number of necessary hyperparameter assignments.
R EPRODUCIBILITY
We organized experiments so that one could quickly reproduce all results reported in this paper.
tools/run_sweeps.py runs wandb sweeps used in our hyperparameter search and outputs with wandb agent commands to run these sweeps.
Once the hyperparameter search is finished, tools/glue_results.py and tools/superglue_results.py scripts are used to parse results from these sweeps and output plots reported by us.
One can find the data processing pipeline for all datasets used in this paper in zarya/data_ processing.py script.
It could be helpful for tasks such as WSC, where several ways to tokenize input sequences could primarily affect resulting performance.
We also provided requirements.txt (with fixed dependencies versions) and Dockerfile with our source files so one could quickly reproduce our training setup, and no issues should appear with versions of libraries used for our experiments.
A A NALYSIS OF T RAINED W EIGHTS P
We also investigated trained P matrices for WSC, COPA, CB, and RTE tasks with the DeBERTa-XL model.
Since FC AoT P-Tuning performed better than Kronecker factorization, we selected this reparametrization method to report the results.
More specifically, we sorted rows of P matrices for each layer measured by L 2 norm and reported tokens appropriate for these rows.
See Tables 7, 8, 10, 9 for results.
For the WSC task, there is a clear interpretation of trained rows for P since rows with a large Lnorm represent tokens responsible for pronouns and names, which is crucial for solving WSC.
For the COPA task, we observed that the model tends to assign large norms for verb tokens.
For RTE and
CB tasks, P also assigns large norms for name tokens which often occur in the training data, while
CB also primarily modifies adverbs for later layers.
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For implied attention results
A ′
i , differences in evaluation are shown in color.
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[Figure] [Figure]
[Figure]
We also provide results of plain fine-tuning for reference.
See Section 5.2 for more details.
[Figure]
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encrypt
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Reviewed
[Table]
Chance, Sw, chance, Nine, Shares, Chance, Scientists, Tw, Besides, Prof, chances,
Sn, sw, TW, EFF, J, IJ, Besides, chance, Between, icist, GU, SW, pan, Ja, Psy, tw, Between, xon, Bj, Conj, Shares, Moh, UTH, Prediction, science, intend, Science, iov, Nine, jp, dds, NJ, Jr, y, Nin, etsy,
Ibid, ymm, Reporting
[Table]
Shant, Georg, Expect, Led, Assistant, Amph, Registered, Ear, McA, THEIR, Prev,
Emb, -„ Called, Gw, Alc, Until, Rhod, Introduced, that, Lat, Unt, Ul,
Sv, Gh, to, of, Fernand, „ elta, jac, unch, Ov, Sebast, apologised,
JOHN, !"
, Ll, hid, Somewhere, Been, Recently, and, Somebody, Fram, Coh, ’).,
Sty, Elsewhere, Unt ’s, ’re, A, ’ve, the, a, her, ’, be, A, a, have, DOES, LIKE, ?", "?, ’d, )?
, ?, s, ABOUT, ", Like,
Pant, didnt, ’m, ’?
, E, The, doesnt, Was, re, :, ie,
Surely, ’ll, Corinth, At, Across, your, their, ?„
THEY, ...?, or,
Fra, HOW, )/
I, ’?
, he, "?, ?’
, )?, ’t, ”., .?
, ?"., ’:, He, !?
He, I, and, ?’", ?!"
, he, .
, she, +., )!, ’., .’
", we, CLOSE, ‘., "!, .], .
, ’/, ’re, .’" .
, ’s, ’t, ?, ’, :, I, -, ’, „ of, he, B, B, in, I, and, ’m, -, s, ", ’d, by, for, ;, b, on, you, !, ", He, to, /, ’ve, y, ’re, ed, with, .
, ’ll, a, back, the, b, she,
He, E, C ’t, not, NOT, the, not, Not, never, Not, ’s, ’re, NOT, ’ve, you, of, [SEP], t, nt, Never, The, in, NEVER, he, to, the, [CLS], hardly, never, neither, I, „ ’m, cannot, no, The, annot, it, Their, me, didnt, He, and, doesnt, Ear, a, .
, Never, none, if, on, nobody